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řešení ",[1047,1048,1049],"strong",{},"všech 8 zkouškových zadání"," (každé 4 úlohy, dohromady 32 úloh) z předmětu ",[1052,1053,1058],"a",{"className":1054,"dataFsResolvedFilePath":1056,"href":1057},[1055],"wikilink","courses\u002Fimek.md","\u002Fwiki\u002Fimek","Matematická ekonomie",". Pro každou úlohu: zadání, klíčová myšlenka, postup, dílčí výpočty, výsledek a odkaz na příslušnou topic stránku. Stránka slouží jako ",[1047,1061,1062],{},"závěrečný materiál ke studiu"," — předpokládá, že už máš prostudované jednotlivé téma a chceš si je upevnit přímo na zkouškových úlohách.",[1065,1066,1068],"h2",{"id":1067},"struktura-zadání","Struktura zadání",[1030,1070,1071],{},"Každé zadání má 4 úlohy s pevnou strukturou bodování:",[1073,1074,1075,1091],"table",{},[1076,1077,1078],"thead",{},[1079,1080,1081,1085,1088],"tr",{},[1082,1083,1084],"th",{},"Úloha",[1082,1086,1087],{},"Body",[1082,1089,1090],{},"Charakter",[1092,1093,1094,1109,1123,1137],"tbody",{},[1079,1095,1096,1100,1103],{},[1097,1098,1099],"td",{},"Q1",[1097,1101,1102],{},"10 b",[1097,1104,1105,1108],{},[1047,1106,1107],{},"Kvalitativní rozhodování"," — která z 5 funkcí může být TR, AC, nabídka, úspory, …",[1079,1110,1111,1114,1117],{},[1097,1112,1113],{},"Q2",[1097,1115,1116],{},"20 b",[1097,1118,1119,1122],{},[1047,1120,1121],{},"Definice + interpretace"," mezní veličiny (MPK, MRTS, MRCS, EPA)",[1079,1124,1125,1128,1131],{},[1097,1126,1127],{},"Q3",[1097,1129,1130],{},"30 b",[1097,1132,1133,1136],{},[1047,1134,1135],{},"Optimalizace"," — max užitečnosti, min výdajů, max produkce, max zisku, rovnováha trhu",[1079,1138,1139,1142,1145],{},[1097,1140,1141],{},"Q4",[1097,1143,1144],{},"40 b",[1097,1146,1147,1150],{},[1047,1148,1149],{},"Komplexní úloha"," — model C-I, IS-LM, cenová diskriminace, vícefaktorová poptávka, MR\u002FMC firmy",[1023,1152,1156,1164],{"className":1153,"dataCallout":1155},[1026,1154],"callout-warning","warning",[1030,1157,1159,1163],{"className":1158},[1033],[1035,1160],{"className":1161,"ariaHidden":1041},[1038,1162,1040],"i-lucide:triangle-alert","Pozor na aproximace",[1030,1165,1166,1167,1170,1171,1174,1175,1178,1179,1182],{},"Úlohy s diferenciálem (ΔY, Δr, ΔMC při změně parametru) používají ",[1047,1168,1169],{},"lineární aproximaci",". Ta je přesná jen pro ",[1047,1172,1173],{},"malé změny",". Pokud se parametr změní o 50 % nebo víc (např. ",[1176,1177,1052],"em",{}," z 0,2 na 0,4), aproximace se může lišit od přesné hodnoty o 10–30 %. V řešení vždy spočítáme ",[1047,1180,1181],{},"obě hodnoty"," a porovnáme.",[1023,1184,1187,1195,1202,1242],{"className":1185,"dataCallout":582},[1026,1186],"callout-info",[1030,1188,1190,1194],{"className":1189},[1033],[1035,1191],{"className":1192,"ariaHidden":1041},[1038,1193,1040],"i-lucide:info","Pozorování o opakování",[1030,1196,1197,1198,1201],{},"Z analýzy 8 zadání vyplývá, že některé úlohy se ",[1047,1199,1200],{},"opakují"," (často beze změny):",[1203,1204,1205,1212,1218,1224,1230,1236],"ul",{},[1206,1207,1208,1211],"li",{},[1047,1209,1210],{},"Z1\u002FQ4 ≈ Z6\u002FQ4"," (model C-I; (a)–(d) totožné, liší se jen perturbace v (e))",[1206,1213,1214,1217],{},[1047,1215,1216],{},"Z3\u002FQ3 = Z5\u002FQ3"," (produkce Q = −0,2L³ + 12L²)",[1206,1219,1220,1223],{},[1047,1221,1222],{},"Z3\u002FQ4 = Z4\u002FQ4"," (IS-LM s identickými parametry)",[1206,1225,1226,1229],{},[1047,1227,1228],{},"Z3\u002FQ1 = Z5\u002FQ1"," (5 funkcí AC)",[1206,1231,1232,1235],{},[1047,1233,1234],{},"Z2\u002FQ3 = Z8\u002FQ3"," (min výdajů, U = Q₁^¼·Q₂^½, U*=10)",[1206,1237,1238,1241],{},[1047,1239,1240],{},"Z7\u002FQ4 = Z8\u002FQ4"," (kašmírové ponožky, vícefaktorová poptávka)",[1030,1243,1244],{},"Týž matematický postup tedy zvládne víc úloh.",[1246,1247],"hr",{},[1019,1249,1251],{"id":1250},"zadání-1","Zadání 1",[1065,1253,1255,1256,1258],{"id":1254},"z1q1-10-b-které-funkce-mohou-být-trq","Z1\u002FQ1 ",[1035,1257,1102],{}," — Které funkce mohou být TR(Q)?",[1030,1260,1261,1264],{},[1047,1262,1263],{},"Zadání:"," Rozhodněte, které z funkcí mohou být funkcí celkového příjmu TR = TR(Q):\n(a) TR = 200Q − 10Q²; (b) TR = Q(50 − Q²); (c) TR = 20Q + Q²; (d) TR = 1000 − 2Q²; (e) TR = 10Q − Q².",[1030,1266,1267,1270,1271,1274],{},[1047,1268,1269],{},"Klíč k úloze:"," Funkce TR musí splnit ",[1047,1272,1273],{},"dvě podmínky",":",[1276,1277,1278,1284],"ol",{},[1206,1279,1280,1283],{},[1047,1281,1282],{},"TR(0) = 0"," — při nulovém prodeji nulový příjem (TR = P·Q).",[1206,1285,1286,1289],{},[1047,1287,1288],{},"P = TR\u002FQ je klesající"," v Q (zákon klesající poptávky — TR pochází z poptávky).",[1030,1291,1292],{},"Ekvivalentně: pokud TR = aQ² + bQ (kvadratická), pak parabola musí mít a \u003C 0 a procházet počátkem.",[1030,1294,1295,1296,1302],{},"Viz ",[1052,1297,1301],{"className":1298,"dataFsResolvedFilePath":1299,"href":1300},[1055],"topics\u002Fprijem-naklady-zisk.md","\u002Fwiki\u002Fprijem-naklady-zisk","Příjem, náklady, zisk"," (vzorec 3.1).",[1304,1305,1307],"h3",{"id":1306},"rozbor","Rozbor",[1073,1309,1310,1328],{},[1076,1311,1312],{},[1079,1313,1314,1316,1319,1322,1325],{},[1082,1315],{},[1082,1317,1318],{},"Funkce",[1082,1320,1321],{},"TR(0)",[1082,1323,1324],{},"P = TR\u002FQ",[1082,1326,1327],{},"Verdikt",[1092,1329,1330,1349,1366,1388,1410],{},[1079,1331,1332,1335,1338,1341,1344],{},[1097,1333,1334],{},"(a)",[1097,1336,1337],{},"200Q − 10Q²",[1097,1339,1340],{},"= 0 ✓",[1097,1342,1343],{},"200 − 10Q (klesá) ✓",[1097,1345,1346],{},[1047,1347,1348],{},"ANO",[1079,1350,1351,1354,1357,1359,1362],{},[1097,1352,1353],{},"(b)",[1097,1355,1356],{},"Q(50 − Q²) = 50Q − Q³",[1097,1358,1340],{},[1097,1360,1361],{},"50 − Q² (klesá pro Q > 0) ✓",[1097,1363,1364],{},[1047,1365,1348],{},[1079,1367,1368,1371,1374,1376,1383],{},[1097,1369,1370],{},"(c)",[1097,1372,1373],{},"20Q + Q²",[1097,1375,1340],{},[1097,1377,1378,1379,1382],{},"20 + Q (",[1047,1380,1381],{},"roste!",") ✗",[1097,1384,1385],{},[1047,1386,1387],{},"NE",[1079,1389,1390,1393,1396,1403,1406],{},[1097,1391,1392],{},"(d)",[1097,1394,1395],{},"1000 − 2Q²",[1097,1397,1398,1399,1402],{},"= ",[1047,1400,1401],{},"1000"," ✗",[1097,1404,1405],{},"—",[1097,1407,1408],{},[1047,1409,1387],{},[1079,1411,1412,1415,1418,1420,1423],{},[1097,1413,1414],{},"(e)",[1097,1416,1417],{},"10Q − Q²",[1097,1419,1340],{},[1097,1421,1422],{},"10 − Q (klesá) ✓",[1097,1424,1425],{},[1047,1426,1348],{},[1030,1428,1429,1432],{},[1047,1430,1431],{},"Zdůvodnění (c):"," P = 20 + Q je rostoucí poptávka, což porušuje zákon klesající poptávky.",[1030,1434,1435,1438],{},[1047,1436,1437],{},"Zdůvodnění (d):"," Při Q = 0 je TR = 1000 ≠ 0 — když nic neprodáme, nemůžeme mít kladný příjem.",[1023,1440,1444,1452],{"className":1441,"dataCallout":1443},[1026,1442],"callout-tip","tip",[1030,1445,1447,1451],{"className":1446},[1033],[1035,1448],{"className":1449,"ariaHidden":1041},[1038,1450,1040],"i-lucide:lightbulb","Rychlý filtr",[1030,1453,1454,1455,1458],{},"Stačí ověřit ",[1047,1456,1457],{},"kvadratický tvar TR = aQ² + bQ"," (žádný absolutní člen, a \u003C 0, b > 0). Funkce, které nemají tuto strukturu nebo mají kladný absolutní člen, vypadnou.",[1246,1460],{},[1065,1462,1464,1465,1467],{"id":1463},"z1q2-20-b-mezní-produkt-kapitálu-mpk","Z1\u002FQ2 ",[1035,1466,1116],{}," — Mezní produkt kapitálu MPK",[1030,1469,1470,1472],{},[1047,1471,1263],{}," Definujte MPK(L,K) a interpretujte MPK(10,100) = 5. Může nabývat záporných hodnot? Pokud ano, interpretujte MPK(20,80) = −5.",[1304,1474,1476],{"id":1475},"definice","Definice",[1035,1478,1481],{"className":1479},[1480],"katex",[1482,1483,1486],"math",{"xmlns":1484,"display":1485},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1487,1488,1489,1527],"semantics",{},[1490,1491,1492,1496,1505,1509],"mrow",{},[1493,1494,1495],"mi",{},"M",[1497,1498,1499,1502],"msub",{},[1493,1500,1501],{},"P",[1493,1503,1504],{},"K",[1506,1507,1508],"mo",{},"=",[1510,1511,1512,1521],"mfrac",{},[1490,1513,1514,1518],{},[1493,1515,1517],{"mathvariant":1516},"normal","∂",[1493,1519,1520],{},"Q",[1490,1522,1523,1525],{},[1493,1524,1517],{"mathvariant":1516},[1493,1526,1504],{},[1528,1529,1531],"annotation",{"encoding":1530},"application\u002Fx-tex","MP_K = \\frac{\\partial Q}{\\partial K}",[1030,1533,1534,1535,1568,1569,1575],{},"Parciální derivace produkční funkce ",[1035,1536,1538],{"className":1537},[1480],[1482,1539,1540],{"xmlns":1484},[1487,1541,1542,1565],{},[1490,1543,1544,1546,1548,1550,1554,1557,1560,1562],{},[1493,1545,1520],{},[1506,1547,1508],{},[1493,1549,1520],{},[1506,1551,1553],{"stretchy":1552},"false","(",[1493,1555,1556],{},"L",[1506,1558,1559],{"separator":1041},",",[1493,1561,1504],{},[1506,1563,1564],{"stretchy":1552},")",[1528,1566,1567],{"encoding":1530},"Q = Q(L,K)"," podle kapitálu (při fixní práci). Viz ",[1052,1570,1574],{"className":1571,"dataFsResolvedFilePath":1572,"href":1573},[1055],"topics\u002Fprodukce.md","\u002Fwiki\u002Fprodukce","Produkce — produkční funkce, Cobb-Douglas, MRTS"," (vzorec 5.2).",[1304,1577,1579],{"id":1578},"interpretace-mpk10100-5","Interpretace MPK(10,100) = 5",[1030,1581,1582,1583,1586,1587,1590,1591,1594],{},"Při zaměstnání ",[1047,1584,1585],{},"L = 10 pracovníků"," a ",[1047,1588,1589],{},"K = 100 jednotek kapitálu"," se produkce přibližně ",[1047,1592,1593],{},"zvýší o 5 jednotek",", jestliže se kapitál zvýší o 1 jednotku (z 100 na 101) — práce zůstává konstantní.",[1030,1596,1597],{},"Slovně: „další stroj (či jednotka kapitálu) přidá v daném bodě cca 5 jednotek produkce.\"",[1304,1599,1601],{"id":1600},"záporné-hodnoty","Záporné hodnoty?",[1030,1603,1604,1606,1607,1610],{},[1047,1605,1348],{},", matematicky možné. Ekonomicky vzácné, ale objevuje se v případech ",[1047,1608,1609],{},"přebytku kapitálu"," vůči práci — zákon klesajících výnosů přejde do záporu.",[1304,1612,1614],{"id":1613},"interpretace-mpk2080-5","Interpretace MPK(20,80) = −5",[1030,1616,1617,1618,1621,1622,1625,1626,1629],{},"Při L=20 a K=80 by ",[1047,1619,1620],{},"další jednotka kapitálu snížila produkci o ~5 jednotek",". Ekonomicky: kapitálu je ",[1176,1623,1624],{},"tolik",", že další jednotka je kontraproduktivní (např. další stroj, na který nemáme operátora; přeplnění výrobní haly; obsluha rostoucí kapitálové základny zatěžuje stávající práci). Indikuje ",[1047,1627,1628],{},"překročení optimálního poměru K\u002FL"," — firmě by se vyplatilo kapitál spíše snížit nebo přidat pracovníky.",[1023,1631,1633,1640],{"className":1632,"dataCallout":582},[1026,1186],[1030,1634,1636,1639],{"className":1635},[1033],[1035,1637],{"className":1638,"ariaHidden":1041},[1038,1193,1040],"Klíčový kontrast",[1030,1641,1642],{},"MPK = +5 → kapitál v optimální zóně, přidávání pomáhá.\nMPK = −5 → kapitál v zóně přesycení, přidávání škodí. Takový bod je za maximem produkce v daném směru.",[1246,1644],{},[1065,1646,1648,1649,1651],{"id":1647},"z1q3-30-b-maximalizace-užitečnosti","Z1\u002FQ3 ",[1035,1650,1130],{}," — Maximalizace užitečnosti",[1030,1653,1654,1656,1657,1732,1733,1732,1756,1779,1780,1800,1801,1827],{},[1047,1655,1263],{}," ",[1035,1658,1660],{"className":1659},[1480],[1482,1661,1662],{"xmlns":1484},[1487,1663,1664,1729],{},[1490,1665,1666,1669,1671,1673,1675,1683,1685,1692,1694,1696,1712,1715],{},[1493,1667,1668],{},"U",[1506,1670,1508],{},[1493,1672,1668],{},[1506,1674,1553],{"stretchy":1552},[1497,1676,1677,1679],{},[1493,1678,1520],{},[1680,1681,1682],"mn",{},"1",[1506,1684,1559],{"separator":1041},[1497,1686,1687,1689],{},[1493,1688,1520],{},[1680,1690,1691],{},"2",[1506,1693,1564],{"stretchy":1552},[1506,1695,1508],{},[1697,1698,1699,1701,1703],"msubsup",{},[1493,1700,1520],{},[1680,1702,1682],{},[1490,1704,1705,1707,1710],{},[1680,1706,1682],{},[1493,1708,1709],{"mathvariant":1516},"\u002F",[1680,1711,1691],{},[1506,1713,1714],{},"⋅",[1697,1716,1717,1719,1721],{},[1493,1718,1520],{},[1680,1720,1691],{},[1490,1722,1723,1725,1727],{},[1680,1724,1682],{},[1493,1726,1709],{"mathvariant":1516},[1680,1728,1691],{},[1528,1730,1731],{"encoding":1530},"U = U(Q_1, Q_2) = Q_1^{1\u002F2} \\cdot Q_2^{1\u002F2}",", ",[1035,1734,1736],{"className":1735},[1480],[1482,1737,1738],{"xmlns":1484},[1487,1739,1740,1753],{},[1490,1741,1742,1748,1750],{},[1497,1743,1744,1746],{},[1493,1745,1501],{},[1680,1747,1682],{},[1506,1749,1508],{},[1680,1751,1752],{},"5",[1528,1754,1755],{"encoding":1530},"P_1 = 5",[1035,1757,1759],{"className":1758},[1480],[1482,1760,1761],{"xmlns":1484},[1487,1762,1763,1776],{},[1490,1764,1765,1771,1773],{},[1497,1766,1767,1769],{},[1493,1768,1501],{},[1680,1770,1691],{},[1506,1772,1508],{},[1680,1774,1775],{},"10",[1528,1777,1778],{"encoding":1530},"P_2 = 10",", důchod ",[1035,1781,1783],{"className":1782},[1480],[1482,1784,1785],{"xmlns":1484},[1487,1786,1787,1797],{},[1490,1788,1789,1792,1794],{},[1493,1790,1791],{},"Y",[1506,1793,1508],{},[1680,1795,1796],{},"500",[1528,1798,1799],{"encoding":1530},"Y = 500",". Určete ",[1035,1802,1804],{"className":1803},[1480],[1482,1805,1806],{"xmlns":1484},[1487,1807,1808,1824],{},[1490,1809,1810,1816,1818],{},[1497,1811,1812,1814],{},[1493,1813,1520],{},[1680,1815,1682],{},[1506,1817,1559],{"separator":1041},[1497,1819,1820,1822],{},[1493,1821,1520],{},[1680,1823,1691],{},[1528,1825,1826],{"encoding":1530},"Q_1, Q_2"," maximalizující užitečnost.",[1030,1829,1830,1833,1834,1837,1838,1844],{},[1047,1831,1832],{},"Klíč:"," Lagrangeova metoda → podmínka ",[1047,1835,1836],{},"MRCS = P₁\u002FP₂"," + rozpočtové omezení. Viz ",[1052,1839,1843],{"className":1840,"dataFsResolvedFilePath":1841,"href":1842},[1055],"topics\u002Foptimalizace-spotrebitele.md","\u002Fwiki\u002Foptimalizace-spotrebitele","Optimalizace spotřebitele"," (vzorec 6.13–6.14).",[1304,1846,1848],{"id":1847},"krok-1-mrcs","Krok 1: MRCS",[1035,1850,1852],{"className":1851},[1480],[1482,1853,1854],{"xmlns":1484,"display":1485},[1487,1855,1856,1963],{},[1490,1857,1858,1860,1866,1868,1878,1895,1909,1911,1915,1917,1923,1925,1933,1947],{},[1493,1859,1495],{},[1497,1861,1862,1864],{},[1493,1863,1668],{},[1680,1865,1682],{},[1506,1867,1508],{},[1869,1870,1872],"mstyle",{"scriptlevel":1871,"displaystyle":1552},"0",[1510,1873,1874,1876],{},[1680,1875,1682],{},[1680,1877,1691],{},[1697,1879,1880,1882,1884],{},[1493,1881,1520],{},[1680,1883,1682],{},[1490,1885,1886,1889,1891,1893],{},[1506,1887,1888],{},"−",[1680,1890,1682],{},[1493,1892,1709],{"mathvariant":1516},[1680,1894,1691],{},[1697,1896,1897,1899,1901],{},[1493,1898,1520],{},[1680,1900,1691],{},[1490,1902,1903,1905,1907],{},[1680,1904,1682],{},[1493,1906,1709],{"mathvariant":1516},[1680,1908,1691],{},[1506,1910,1559],{"separator":1041},[1912,1913],"mspace",{"width":1914},"2em",[1493,1916,1495],{},[1497,1918,1919,1921],{},[1493,1920,1668],{},[1680,1922,1691],{},[1506,1924,1508],{},[1869,1926,1927],{"scriptlevel":1871,"displaystyle":1552},[1510,1928,1929,1931],{},[1680,1930,1682],{},[1680,1932,1691],{},[1697,1934,1935,1937,1939],{},[1493,1936,1520],{},[1680,1938,1682],{},[1490,1940,1941,1943,1945],{},[1680,1942,1682],{},[1493,1944,1709],{"mathvariant":1516},[1680,1946,1691],{},[1697,1948,1949,1951,1953],{},[1493,1950,1520],{},[1680,1952,1691],{},[1490,1954,1955,1957,1959,1961],{},[1506,1956,1888],{},[1680,1958,1682],{},[1493,1960,1709],{"mathvariant":1516},[1680,1962,1691],{},[1528,1964,1965],{"encoding":1530},"MU_1 = \\tfrac{1}{2} Q_1^{-1\u002F2} Q_2^{1\u002F2}, \\qquad MU_2 = \\tfrac{1}{2} Q_1^{1\u002F2} Q_2^{-1\u002F2}",[1035,1967,1969],{"className":1968},[1480],[1482,1970,1971],{"xmlns":1484,"display":1485},[1487,1972,1973,2044],{},[1490,1974,1975],{},[1976,1977,1979],"menclose",{"notation":1978},"box",[1869,1980,1981],{"scriptlevel":1871,"displaystyle":1552},[1869,1982,1983],{"scriptlevel":1871,"displaystyle":1552},[1869,1984,1985],{"scriptlevel":1871,"displaystyle":1041},[1490,1986,1987,1991,1993,1996,1999,2002,2004,2026,2028,2042],{},[1988,1989,1990],"mtext",{},"  ",[1493,1992,1495],{},[1493,1994,1995],{},"R",[1493,1997,1998],{},"C",[1493,2000,2001],{},"S",[1506,2003,1508],{},[1510,2005,2006,2016],{},[1490,2007,2008,2010],{},[1493,2009,1495],{},[1497,2011,2012,2014],{},[1493,2013,1668],{},[1680,2015,1682],{},[1490,2017,2018,2020],{},[1493,2019,1495],{},[1497,2021,2022,2024],{},[1493,2023,1668],{},[1680,2025,1691],{},[1506,2027,1508],{},[1510,2029,2030,2036],{},[1497,2031,2032,2034],{},[1493,2033,1520],{},[1680,2035,1691],{},[1497,2037,2038,2040],{},[1493,2039,1520],{},[1680,2041,1682],{},[1988,2043,1990],{},[1528,2045,2046],{"encoding":1530},"\\boxed{\\; MRCS = \\frac{MU_1}{MU_2} = \\frac{Q_2}{Q_1} \\;}",[1304,2048,2050],{"id":2049},"krok-2-podmínka-optimality","Krok 2: Podmínka optimality",[1035,2052,2054],{"className":2053},[1480],[1482,2055,2056],{"xmlns":1484,"display":1485},[1487,2057,2058,2136],{},[1490,2059,2060,2074,2076,2090,2092,2098,2100,2106,2109,2112,2114,2120,2122,2130],{},[1510,2061,2062,2068],{},[1497,2063,2064,2066],{},[1493,2065,1520],{},[1680,2067,1691],{},[1497,2069,2070,2072],{},[1493,2071,1520],{},[1680,2073,1682],{},[1506,2075,1508],{},[1510,2077,2078,2084],{},[1497,2079,2080,2082],{},[1493,2081,1501],{},[1680,2083,1682],{},[1497,2085,2086,2088],{},[1493,2087,1501],{},[1680,2089,1691],{},[1506,2091,1508],{},[1510,2093,2094,2096],{},[1680,2095,1752],{},[1680,2097,1775],{},[1506,2099,1508],{},[1510,2101,2102,2104],{},[1680,2103,1682],{},[1680,2105,1691],{},[1912,2107],{"width":2108},"1em",[1506,2110,2111],{},"⟹",[1912,2113],{"width":2108},[1497,2115,2116,2118],{},[1493,2117,1520],{},[1680,2119,1691],{},[1506,2121,1508],{},[1869,2123,2124],{"scriptlevel":1871,"displaystyle":1552},[1510,2125,2126,2128],{},[1680,2127,1682],{},[1680,2129,1691],{},[1497,2131,2132,2134],{},[1493,2133,1520],{},[1680,2135,1682],{},[1528,2137,2138],{"encoding":1530},"\\frac{Q_2}{Q_1} = \\frac{P_1}{P_2} = \\frac{5}{10} = \\frac{1}{2} \\quad\\Longrightarrow\\quad Q_2 = \\tfrac{1}{2} Q_1",[1304,2140,2142],{"id":2141},"krok-3-rozpočtové-omezení","Krok 3: Rozpočtové omezení",[1035,2144,2146],{"className":2145},[1480],[1482,2147,2148],{"xmlns":1484,"display":1485},[1487,2149,2150,2251],{},[1490,2151,2152,2154,2160,2163,2165,2171,2173,2175,2177,2209,2211,2213,2219,2221,2223,2225,2237,2239,2241,2247,2249],{},[1680,2153,1752],{},[1497,2155,2156,2158],{},[1493,2157,1520],{},[1680,2159,1682],{},[1506,2161,2162],{},"+",[1680,2164,1775],{},[1497,2166,2167,2169],{},[1493,2168,1520],{},[1680,2170,1691],{},[1506,2172,1508],{},[1680,2174,1796],{},[1988,2176,1990],{},[2178,2179,2180,2184],"mover",{},[1506,2181,2183],{"stretchy":1041,"minsize":2182},"3.0em","⇒",[2185,2186,2189],"mpadded",{"width":2187,"lspace":2188},"+0.6em","0.3em",[1490,2190,2191,2197,2199,2205,2207],{},[1497,2192,2193,2195],{},[1493,2194,1520],{},[1680,2196,1691],{},[1506,2198,1508],{},[1497,2200,2201,2203],{},[1493,2202,1520],{},[1680,2204,1682],{},[1493,2206,1709],{"mathvariant":1516},[1680,2208,1691],{},[1988,2210,1990],{},[1680,2212,1752],{},[1497,2214,2215,2217],{},[1493,2216,1520],{},[1680,2218,1682],{},[1506,2220,2162],{},[1680,2222,1775],{},[1506,2224,1714],{},[1869,2226,2227],{"scriptlevel":1871,"displaystyle":1552},[1510,2228,2229,2235],{},[1497,2230,2231,2233],{},[1493,2232,1520],{},[1680,2234,1682],{},[1680,2236,1691],{},[1506,2238,1508],{},[1680,2240,1775],{},[1497,2242,2243,2245],{},[1493,2244,1520],{},[1680,2246,1682],{},[1506,2248,1508],{},[1680,2250,1796],{},[1528,2252,2253],{"encoding":1530},"5 Q_1 + 10 Q_2 = 500 \\;\\xRightarrow{Q_2 = Q_1\u002F2}\\; 5Q_1 + 10 \\cdot \\tfrac{Q_1}{2} = 10 Q_1 = 500",[1304,2255,2257],{"id":2256},"výsledek","Výsledek",[1035,2259,2261],{"className":2260},[1480],[1482,2262,2263],{"xmlns":1484,"display":1485},[1487,2264,2265,2349],{},[1490,2266,2267],{},[1976,2268,2269],{"notation":1978},[1869,2270,2271],{"scriptlevel":1871,"displaystyle":1552},[1869,2272,2273],{"scriptlevel":1871,"displaystyle":1552},[1869,2274,2275],{"scriptlevel":1871,"displaystyle":1041},[1490,2276,2277,2279,2288,2290,2293,2295,2297,2305,2307,2310,2312,2314,2321,2323,2334,2336,2341,2344,2347],{},[1988,2278,1990],{},[1697,2280,2281,2283,2285],{},[1493,2282,1520],{},[1680,2284,1682],{},[1506,2286,2287],{},"∗",[1506,2289,1508],{},[1680,2291,2292],{},"50",[1506,2294,1559],{"separator":1041},[1912,2296],{"width":2108},[1697,2298,2299,2301,2303],{},[1493,2300,1520],{},[1680,2302,1691],{},[1506,2304,2287],{},[1506,2306,1508],{},[1680,2308,2309],{},"25",[1506,2311,1559],{"separator":1041},[1912,2313],{"width":2108},[2315,2316,2317,2319],"msup",{},[1493,2318,1668],{},[1506,2320,2287],{},[1506,2322,1508],{},[2324,2325,2326],"msqrt",{},[1490,2327,2328,2330,2332],{},[1680,2329,2292],{},[1506,2331,1714],{},[1680,2333,2309],{},[1506,2335,1508],{},[2324,2337,2338],{},[1680,2339,2340],{},"1250",[1506,2342,2343],{},"≈",[1680,2345,2346],{},"35,36",[1988,2348,1990],{},[1528,2350,2351],{"encoding":1530},"\\boxed{\\; Q_1^* = 50, \\quad Q_2^* = 25, \\quad U^* = \\sqrt{50 \\cdot 25} = \\sqrt{1250} \\approx 35{,}36 \\;}",[1023,2353,2355,2362],{"className":2354,"dataCallout":1443},[1026,1442],[1030,2356,2358,2361],{"className":2357},[1033],[1035,2359],{"className":2360,"ariaHidden":1041},[1038,1450,1040],"Cobb-Douglas zkratka",[1030,2363,2364,2365,2398,2399,2425,2426,2510,2511,1732,2555,2599],{},"Pro ",[1035,2366,2368],{"className":2367},[1480],[1482,2369,2370],{"xmlns":1484},[1487,2371,2372,2395],{},[1490,2373,2374,2376,2378,2386],{},[1493,2375,1668],{},[1506,2377,1508],{},[1697,2379,2380,2382,2384],{},[1493,2381,1520],{},[1680,2383,1682],{},[1493,2385,1052],{},[1697,2387,2388,2390,2392],{},[1493,2389,1520],{},[1680,2391,1691],{},[1493,2393,2394],{},"b",[1528,2396,2397],{"encoding":1530},"U = Q_1^a Q_2^b"," s ryzí Cobb-Douglas (zde ",[1035,2400,2402],{"className":2401},[1480],[1482,2403,2404],{"xmlns":1484},[1487,2405,2406,2422],{},[1490,2407,2408,2410,2412,2414,2416,2418,2420],{},[1493,2409,1052],{},[1506,2411,1508],{},[1493,2413,2394],{},[1506,2415,1508],{},[1680,2417,1682],{},[1493,2419,1709],{"mathvariant":1516},[1680,2421,1691],{},[1528,2423,2424],{"encoding":1530},"a = b = 1\u002F2",", symetrický případ) platí:\n",[1035,2427,2429],{"className":2428},[1480],[1482,2430,2431],{"xmlns":1484},[1487,2432,2433,2507],{},[1490,2434,2435,2443,2445,2457,2459,2469,2471,2473,2481,2483,2495,2497],{},[1697,2436,2437,2439,2441],{},[1493,2438,1520],{},[1680,2440,1682],{},[1506,2442,2287],{},[1506,2444,1508],{},[1510,2446,2447,2449],{},[1493,2448,1052],{},[1490,2450,2451,2453,2455],{},[1493,2452,1052],{},[1506,2454,2162],{},[1493,2456,2394],{},[1506,2458,1714],{},[1510,2460,2461,2463],{},[1493,2462,1791],{},[1497,2464,2465,2467],{},[1493,2466,1501],{},[1680,2468,1682],{},[1506,2470,1559],{"separator":1041},[1912,2472],{"width":1914},[1697,2474,2475,2477,2479],{},[1493,2476,1520],{},[1680,2478,1691],{},[1506,2480,2287],{},[1506,2482,1508],{},[1510,2484,2485,2487],{},[1493,2486,2394],{},[1490,2488,2489,2491,2493],{},[1493,2490,1052],{},[1506,2492,2162],{},[1493,2494,2394],{},[1506,2496,1714],{},[1510,2498,2499,2501],{},[1493,2500,1791],{},[1497,2502,2503,2505],{},[1493,2504,1501],{},[1680,2506,1691],{},[1528,2508,2509],{"encoding":1530},"Q_1^* = \\frac{a}{a+b} \\cdot \\frac{Y}{P_1}, \\qquad Q_2^* = \\frac{b}{a+b} \\cdot \\frac{Y}{P_2}","\nPro náš případ: ",[1035,2512,2514],{"className":2513},[1480],[1482,2515,2516],{"xmlns":1484},[1487,2517,2518,2552],{},[1490,2519,2520,2528,2530,2538,2540,2548,2550],{},[1697,2521,2522,2524,2526],{},[1493,2523,1520],{},[1680,2525,1682],{},[1506,2527,2287],{},[1506,2529,1508],{},[1869,2531,2532],{"scriptlevel":1871,"displaystyle":1552},[1510,2533,2534,2536],{},[1680,2535,1682],{},[1680,2537,1691],{},[1506,2539,1714],{},[1869,2541,2542],{"scriptlevel":1871,"displaystyle":1552},[1510,2543,2544,2546],{},[1680,2545,1796],{},[1680,2547,1752],{},[1506,2549,1508],{},[1680,2551,2292],{},[1528,2553,2554],{"encoding":1530},"Q_1^* = \\tfrac{1}{2} \\cdot \\tfrac{500}{5} = 50",[1035,2556,2558],{"className":2557},[1480],[1482,2559,2560],{"xmlns":1484},[1487,2561,2562,2596],{},[1490,2563,2564,2572,2574,2582,2584,2592,2594],{},[1697,2565,2566,2568,2570],{},[1493,2567,1520],{},[1680,2569,1691],{},[1506,2571,2287],{},[1506,2573,1508],{},[1869,2575,2576],{"scriptlevel":1871,"displaystyle":1552},[1510,2577,2578,2580],{},[1680,2579,1682],{},[1680,2581,1691],{},[1506,2583,1714],{},[1869,2585,2586],{"scriptlevel":1871,"displaystyle":1552},[1510,2587,2588,2590],{},[1680,2589,1796],{},[1680,2591,1775],{},[1506,2593,1508],{},[1680,2595,2309],{},[1528,2597,2598],{"encoding":1530},"Q_2^* = \\tfrac{1}{2} \\cdot \\tfrac{500}{10} = 25",". Stejný výsledek bez Lagrange.",[1246,2601],{},[1065,2603,2605,2606,2608],{"id":2604},"z1q4-40-b-model-c-i","Z1\u002FQ4 ",[1035,2607,1144],{}," — Model C-I",[1030,2610,2611,2613],{},[1047,2612,1263],{}," Y = C + I, C = aY + b. Najděte (a) redukovaný tvar pro Y; (b) multiplikátory + znaménka; (c) Y^E pro a = 0,2; b = 100; I = 1000; (d) ΔY ≈ při ΔI = 100; (e) ΔY ≈ při da = 0,2; db = 3; dI = 10.",[1030,2615,2616,2618,2619,2625,2626,2632],{},[1047,2617,1832],{}," Viz ",[1052,2620,2624],{"className":2621,"dataFsResolvedFilePath":2622,"href":2623},[1055],"topics\u002Fnarodni-duchod.md","\u002Fwiki\u002Fnarodni-duchod","Národní důchod"," (vzorce 7.6–7.7) a ",[1052,2627,2631],{"className":2628,"dataFsResolvedFilePath":2629,"href":2630},[1055],"outputs\u002Fimek-vzorce-prehled.md","\u002Fwiki\u002Fimek-vzorce-prehled#13. Makroekonomie — národní důchod","sekce 13 přehledu vzorců",".",[1304,2634,2636],{"id":2635},"a-redukovaný-tvar","(a) Redukovaný tvar",[1035,2638,2640],{"className":2639},[1480],[1482,2641,2642],{"xmlns":1484,"display":1485},[1487,2643,2644,2732],{},[1490,2645,2646,2648,2650,2652,2654,2656,2658,2660,2663,2665,2667,2669,2671,2673,2675,2677,2679,2681,2683,2685,2687,2689,2691,2693,2695],{},[1493,2647,1791],{},[1506,2649,1508],{},[1493,2651,1052],{},[1493,2653,1791],{},[1506,2655,2162],{},[1493,2657,2394],{},[1506,2659,2162],{},[1493,2661,2662],{},"I",[1988,2664,1990],{},[1506,2666,2111],{},[1988,2668,1990],{},[1493,2670,1791],{},[1506,2672,1553],{"stretchy":1552},[1680,2674,1682],{},[1506,2676,1888],{},[1493,2678,1052],{},[1506,2680,1564],{"stretchy":1552},[1506,2682,1508],{},[1493,2684,2394],{},[1506,2686,2162],{},[1493,2688,2662],{},[1988,2690,1990],{},[1506,2692,2111],{},[1988,2694,1990],{},[1976,2696,2697],{"notation":1978},[1869,2698,2699],{"scriptlevel":1871,"displaystyle":1552},[1869,2700,2701],{"scriptlevel":1871,"displaystyle":1552},[1869,2702,2703],{"scriptlevel":1871,"displaystyle":1041},[1490,2704,2705,2712,2714],{},[2315,2706,2707,2709],{},[1493,2708,1791],{},[1493,2710,2711],{},"E",[1506,2713,1508],{},[1510,2715,2716,2724],{},[1490,2717,2718,2720,2722],{},[1493,2719,2394],{},[1506,2721,2162],{},[1493,2723,2662],{},[1490,2725,2726,2728,2730],{},[1680,2727,1682],{},[1506,2729,1888],{},[1493,2731,1052],{},[1528,2733,2734],{"encoding":1530},"Y = aY + b + I \\;\\Longrightarrow\\; Y(1-a) = b + I \\;\\Longrightarrow\\; \\boxed{Y^E = \\frac{b + I}{1 - a}}",[1304,2736,2738],{"id":2737},"b-multiplikátory","(b) Multiplikátory",[1035,2740,2742],{"className":2741},[1480],[1482,2743,2744],{"xmlns":1484,"display":1485},[1487,2745,2746,2879],{},[1490,2747,2748,2766,2768,2794,2797,2799,2801,2803,2821,2823,2835,2837,2839,2841,2843,2861,2863,2875,2877],{},[1510,2749,2750,2760],{},[1490,2751,2752,2754],{},[1493,2753,1517],{"mathvariant":1516},[2315,2755,2756,2758],{},[1493,2757,1791],{},[1493,2759,2711],{},[1490,2761,2762,2764],{},[1493,2763,1517],{"mathvariant":1516},[1493,2765,1052],{},[1506,2767,1508],{},[1510,2769,2770,2778],{},[1490,2771,2772,2774,2776],{},[1493,2773,2394],{},[1506,2775,2162],{},[1493,2777,2662],{},[1490,2779,2780,2782,2784,2786,2788],{},[1506,2781,1553],{"stretchy":1552},[1680,2783,1682],{},[1506,2785,1888],{},[1493,2787,1052],{},[2315,2789,2790,2792],{},[1506,2791,1564],{"stretchy":1552},[1680,2793,1691],{},[1506,2795,2796],{},">",[1680,2798,1871],{},[1506,2800,1559],{"separator":1041},[1912,2802],{"width":1914},[1510,2804,2805,2815],{},[1490,2806,2807,2809],{},[1493,2808,1517],{"mathvariant":1516},[2315,2810,2811,2813],{},[1493,2812,1791],{},[1493,2814,2711],{},[1490,2816,2817,2819],{},[1493,2818,1517],{"mathvariant":1516},[1493,2820,2394],{},[1506,2822,1508],{},[1510,2824,2825,2827],{},[1680,2826,1682],{},[1490,2828,2829,2831,2833],{},[1680,2830,1682],{},[1506,2832,1888],{},[1493,2834,1052],{},[1506,2836,2796],{},[1680,2838,1871],{},[1506,2840,1559],{"separator":1041},[1912,2842],{"width":1914},[1510,2844,2845,2855],{},[1490,2846,2847,2849],{},[1493,2848,1517],{"mathvariant":1516},[2315,2850,2851,2853],{},[1493,2852,1791],{},[1493,2854,2711],{},[1490,2856,2857,2859],{},[1493,2858,1517],{"mathvariant":1516},[1493,2860,2662],{},[1506,2862,1508],{},[1510,2864,2865,2867],{},[1680,2866,1682],{},[1490,2868,2869,2871,2873],{},[1680,2870,1682],{},[1506,2872,1888],{},[1493,2874,1052],{},[1506,2876,2796],{},[1680,2878,1871],{},[1528,2880,2881],{"encoding":1530},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I}{(1-a)^2} > 0, \\qquad \\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1-a} > 0, \\qquad \\frac{\\partial Y^E}{\\partial I} = \\frac{1}{1-a} > 0",[1030,2883,2884,2885,2888],{},"Při běžných předpokladech 0 \u003C a \u003C 1, b > 0, I > 0 jsou ",[1047,2886,2887],{},"všechny multiplikátory kladné"," — růst libovolného z parametrů zvyšuje rovnovážný důchod.",[1304,2890,2892],{"id":2891},"c-rovnovážný-důchod","(c) Rovnovážný důchod",[1035,2894,2896],{"className":2895},[1480],[1482,2897,2898],{"xmlns":1484,"display":1485},[1487,2899,2900,2953],{},[1490,2901,2902,2908,2910,2930,2932,2940,2942],{},[2315,2903,2904,2906],{},[1493,2905,1791],{},[1493,2907,2711],{},[1506,2909,1508],{},[1510,2911,2912,2921],{},[1490,2913,2914,2917,2919],{},[1680,2915,2916],{},"100",[1506,2918,2162],{},[1680,2920,1401],{},[1490,2922,2923,2925,2927],{},[1680,2924,1682],{},[1506,2926,1888],{},[1680,2928,2929],{},"0,2",[1506,2931,1508],{},[1510,2933,2934,2937],{},[1680,2935,2936],{},"1100",[1680,2938,2939],{},"0,8",[1506,2941,1508],{},[1976,2943,2944],{"notation":1978},[1869,2945,2946],{"scriptlevel":1871,"displaystyle":1552},[1869,2947,2948],{"scriptlevel":1871,"displaystyle":1552},[1869,2949,2950],{"scriptlevel":1871,"displaystyle":1041},[1680,2951,2952],{},"1375",[1528,2954,2955],{"encoding":1530},"Y^E = \\frac{100 + 1000}{1 - 0{,}2} = \\frac{1100}{0{,}8} = \\boxed{1375}",[1304,2957,2959],{"id":2958},"d-δi-100","(d) ΔI = 100",[1030,2961,2962],{},[1047,2963,2964],{},"Aproximace (diferenciál):",[1035,2966,2968],{"className":2967},[1480],[1482,2969,2970],{"xmlns":1484,"display":1485},[1487,2971,2972,3022],{},[1490,2973,2974,2977,2979,2981,2999,3001,3003,3005,3007,3013,3015,3017,3019],{},[1493,2975,2976],{"mathvariant":1516},"Δ",[1493,2978,1791],{},[1506,2980,2343],{},[1510,2982,2983,2993],{},[1490,2984,2985,2987],{},[1493,2986,1517],{"mathvariant":1516},[2315,2988,2989,2991],{},[1493,2990,1791],{},[1493,2992,2711],{},[1490,2994,2995,2997],{},[1493,2996,1517],{"mathvariant":1516},[1493,2998,2662],{},[1506,3000,1714],{},[1493,3002,2976],{"mathvariant":1516},[1493,3004,2662],{},[1506,3006,1508],{},[1510,3008,3009,3011],{},[1680,3010,1682],{},[1680,3012,2939],{},[1506,3014,1714],{},[1680,3016,2916],{},[1506,3018,1508],{},[1680,3020,3021],{},"125",[1528,3023,3024],{"encoding":1530},"\\Delta Y \\approx \\frac{\\partial Y^E}{\\partial I} \\cdot \\Delta I = \\frac{1}{0{,}8} \\cdot 100 = 125",[1030,3026,3027],{},[1047,3028,3029],{},"Přesně:",[1035,3031,3033],{"className":3032},[1480],[1482,3034,3035],{"xmlns":1484,"display":1485},[1487,3036,3037,3099],{},[1490,3038,3039,3058,3060,3072,3074,3077,3079,3081,3083,3085,3087,3089,3091,3093,3095,3097],{},[1697,3040,3041,3043,3056],{},[1493,3042,1791],{},[1490,3044,3045,3048],{},[1988,3046,3047],{},"nov",[2178,3049,3050,3053],{"accent":1041},[1988,3051,3052],{},"y",[1506,3054,3055],{},"ˊ",[1493,3057,2711],{},[1506,3059,1508],{},[1510,3061,3062,3070],{},[1490,3063,3064,3066,3068],{},[1680,3065,2916],{},[1506,3067,2162],{},[1680,3069,2936],{},[1680,3071,2939],{},[1506,3073,1508],{},[1680,3075,3076],{},"1500",[1988,3078,1990],{},[1506,3080,2111],{},[1988,3082,1990],{},[1493,3084,2976],{"mathvariant":1516},[1493,3086,1791],{},[1506,3088,1508],{},[1680,3090,3076],{},[1506,3092,1888],{},[1680,3094,2952],{},[1506,3096,1508],{},[1680,3098,3021],{},[1528,3100,3101],{"encoding":1530},"Y^E_{\\text{nový}} = \\frac{100 + 1100}{0{,}8} = 1500 \\;\\Longrightarrow\\; \\Delta Y = 1500 - 1375 = 125",[1023,3103,3105,3112],{"className":3104,"dataCallout":582},[1026,1186],[1030,3106,3108,3111],{"className":3107},[1033],[1035,3109],{"className":3110,"ariaHidden":1041},[1038,1193,1040],"Proč jsou hodnoty stejné?",[1030,3113,3114,3115,3118,3119,3122,3123,3125],{},"Y^E je ",[1047,3116,3117],{},"lineární v I"," (multiplikátor 1\u002F(1−a) nezávisí na I). Pro lineární funkce jsou diferenciál a přesná změna identické. Stejně to bude pro změny ",[1047,3120,3121],{},"jen"," v I nebo ",[1047,3124,3121],{}," v b.",[1304,3127,3129],{"id":3128},"e-současné-změny-da-02-db-3-di-10","(e) Současné změny da = 0,2; db = 3; dI = 10",[1030,3131,3132],{},[1047,3133,3134],{},"Aproximace:",[1035,3136,3138],{"className":3137},[1480],[1482,3139,3140],{"xmlns":1484,"display":1485},[1487,3141,3142,3226],{},[1490,3143,3144,3146,3148,3150,3172,3174,3176,3178,3197,3199,3202,3204,3222,3224],{},[1493,3145,2976],{"mathvariant":1516},[1493,3147,1791],{},[1506,3149,2343],{},[3151,3152,3153,3165],"munder",{},[3151,3154,3155,3162],{},[1510,3156,3157,3159],{},[1680,3158,2936],{},[1680,3160,3161],{},"0,64",[1506,3163,3164],{"stretchy":1041},"⏟",[1490,3166,3167,3169],{},[1506,3168,1508],{},[1680,3170,3171],{},"1718,75",[1506,3173,1714],{},[1680,3175,2929],{},[1506,3177,2162],{},[3151,3179,3180,3190],{},[3151,3181,3182,3188],{},[1510,3183,3184,3186],{},[1680,3185,1682],{},[1680,3187,2939],{},[1506,3189,3164],{"stretchy":1041},[1490,3191,3192,3194],{},[1506,3193,1508],{},[1680,3195,3196],{},"1,25",[1506,3198,1714],{},[1680,3200,3201],{},"3",[1506,3203,2162],{},[3151,3205,3206,3216],{},[3151,3207,3208,3214],{},[1510,3209,3210,3212],{},[1680,3211,1682],{},[1680,3213,2939],{},[1506,3215,3164],{"stretchy":1041},[1490,3217,3218,3220],{},[1506,3219,1508],{},[1680,3221,3196],{},[1506,3223,1714],{},[1680,3225,1775],{},[1528,3227,3228],{"encoding":1530},"\\Delta Y \\approx \\underbrace{\\frac{1100}{0{,}64}}_{=1718{,}75} \\cdot 0{,}2 + \\underbrace{\\frac{1}{0{,}8}}_{=1{,}25} \\cdot 3 + \\underbrace{\\frac{1}{0{,}8}}_{=1{,}25} \\cdot 10",[1035,3230,3232],{"className":3231},[1480],[1482,3233,3234],{"xmlns":1484,"display":1485},[1487,3235,3236,3266],{},[1490,3237,3238,3240,3243,3245,3248,3250,3253,3255],{},[1506,3239,1508],{},[1680,3241,3242],{},"343,75",[1506,3244,2162],{},[1680,3246,3247],{},"3,75",[1506,3249,2162],{},[1680,3251,3252],{},"12,5",[1506,3254,1508],{},[1976,3256,3257],{"notation":1978},[1869,3258,3259],{"scriptlevel":1871,"displaystyle":1552},[1869,3260,3261],{"scriptlevel":1871,"displaystyle":1552},[1869,3262,3263],{"scriptlevel":1871,"displaystyle":1041},[1680,3264,3265],{},"360",[1528,3267,3268],{"encoding":1530},"= 343{,}75 + 3{,}75 + 12{,}5 = \\boxed{360}",[1030,3270,3271,3274],{},[1047,3272,3273],{},"Přesně"," (a → 0,4; b → 103; I → 1010):",[1035,3276,3278],{"className":3277},[1480],[1482,3279,3280],{"xmlns":1484,"display":1485},[1487,3281,3282,3353],{},[1490,3283,3284,3300,3302,3323,3325,3333,3335,3338,3340,3342,3344,3346,3348,3350],{},[1697,3285,3286,3288,3298],{},[1493,3287,1791],{},[1490,3289,3290,3292],{},[1988,3291,3047],{},[2178,3293,3294,3296],{"accent":1041},[1988,3295,3052],{},[1506,3297,3055],{},[1493,3299,2711],{},[1506,3301,1508],{},[1510,3303,3304,3314],{},[1490,3305,3306,3309,3311],{},[1680,3307,3308],{},"103",[1506,3310,2162],{},[1680,3312,3313],{},"1010",[1490,3315,3316,3318,3320],{},[1680,3317,1682],{},[1506,3319,1888],{},[1680,3321,3322],{},"0,4",[1506,3324,1508],{},[1510,3326,3327,3330],{},[1680,3328,3329],{},"1113",[1680,3331,3332],{},"0,6",[1506,3334,1508],{},[1680,3336,3337],{},"1855",[1988,3339,1990],{},[1506,3341,2111],{},[1988,3343,1990],{},[1493,3345,2976],{"mathvariant":1516},[1493,3347,1791],{},[1506,3349,1508],{},[1680,3351,3352],{},"480",[1528,3354,3355],{"encoding":1530},"Y^E_{\\text{nový}} = \\frac{103 + 1010}{1 - 0{,}4} = \\frac{1113}{0{,}6} = 1855 \\;\\Longrightarrow\\; \\Delta Y = 480",[1023,3357,3359,3366,3451],{"className":3358,"dataCallout":1155},[1026,1154],[1030,3360,3362,3365],{"className":3361},[1033],[1035,3363],{"className":3364,"ariaHidden":1041},[1038,1162,1040],"Velká chyba aproximace!",[1030,3367,3368,3369,3372,3373,3394,3395,3397,3398,3401,3402,3420,3421,3423,3424,3450],{},"Aproximace 360 vs. přesných 480 — chyba ",[1047,3370,3371],{},"25 %",". Důvod: změna ",[1035,3374,3376],{"className":3375},[1480],[1482,3377,3378],{"xmlns":1484},[1487,3379,3380,3391],{},[1490,3381,3382,3385,3387,3389],{},[1493,3383,3384],{},"d",[1493,3386,1052],{},[1506,3388,1508],{},[1680,3390,2929],{},[1528,3392,3393],{"encoding":1530},"da = 0{,}2"," znamená, že ",[1176,3396,1052],{}," se ",[1047,3399,3400],{},"zdvojnásobuje"," (z 0,2 na 0,4). Lineární aproximace funguje jen pro malé perturbace; tady už máme „velkou změnu\", a ",[1035,3403,3405],{"className":3404},[1480],[1482,3406,3407],{"xmlns":1484},[1487,3408,3409,3417],{},[1490,3410,3411],{},[2315,3412,3413,3415],{},[1493,3414,1791],{},[1493,3416,2711],{},[1528,3418,3419],{"encoding":1530},"Y^E"," je vůči ",[1176,3422,1052],{}," silně nelineární (přes ",[1035,3425,3427],{"className":3426},[1480],[1482,3428,3429],{"xmlns":1484},[1487,3430,3431,3447],{},[1490,3432,3433,3435,3437,3439,3441],{},[1506,3434,1553],{"stretchy":1552},[1680,3436,1682],{},[1506,3438,1888],{},[1493,3440,1052],{},[2315,3442,3443,3445],{},[1506,3444,1564],{"stretchy":1552},[1680,3446,1691],{},[1528,3448,3449],{"encoding":1530},"(1-a)^2"," ve jmenovateli).",[1030,3452,3453,3456],{},[1047,3454,3455],{},"Poučení:"," v zadání takto velké perturbace si všimni a uveď, že aproximace je orientační. Ke zkoušce odevzdáš obě hodnoty.",[1246,3458],{},[1019,3460,3462],{"id":3461},"zadání-2","Zadání 2",[1065,3464,3466,3467,3469],{"id":3465},"z2q1-10-b-které-funkce-mohou-být-nabídka","Z2\u002FQ1 ",[1035,3468,1102],{}," — Které funkce mohou být nabídka?",[1030,3471,3472,3474],{},[1047,3473,1263],{}," Rozhodněte, které z funkcí mohou být funkcí nabídky:\n(a) P = 100 + 0,2Q²; (b) Q = 50 + 0,5P; (c) P = −80 + 2Q; (d) P = 500 − 2Q; (e) Q = 0,5P − 200.",[1030,3476,3477,3479,3480,3483,3484,2632],{},[1047,3478,1832],{}," Funkce nabídky musí být ",[1047,3481,3482],{},"rostoucí"," v ceně (zákon rostoucí nabídky). Viz ",[1052,3485,3489],{"className":3486,"dataFsResolvedFilePath":3487,"href":3488},[1055],"topics\u002Fpoptavka-nabidka.md","\u002Fwiki\u002Fpoptavka-nabidka","Poptávka, nabídka a tržní rovnováha",[1304,3491,3493],{"id":3492},"test-kladná-derivace","Test: kladná derivace",[1073,3495,3496,3509],{},[1076,3497,3498],{},[1079,3499,3500,3502,3504,3507],{},[1082,3501],{},[1082,3503,1318],{},[1082,3505,3506],{},"Derivace",[1082,3508,1327],{},[1092,3510,3511,3525,3539,3553,3568],{},[1079,3512,3513,3515,3518,3521],{},[1097,3514,1334],{},[1097,3516,3517],{},"P = 100 + 0,2Q²",[1097,3519,3520],{},"dP\u002FdQ = 0,4Q ≥ 0",[1097,3522,3523],{},[1047,3524,1348],{},[1079,3526,3527,3529,3532,3535],{},[1097,3528,1353],{},[1097,3530,3531],{},"Q = 50 + 0,5P",[1097,3533,3534],{},"dQ\u002FdP = 0,5 > 0",[1097,3536,3537],{},[1047,3538,1348],{},[1079,3540,3541,3543,3546,3549],{},[1097,3542,1370],{},[1097,3544,3545],{},"P = −80 + 2Q",[1097,3547,3548],{},"dP\u002FdQ = 2 > 0",[1097,3550,3551],{},[1047,3552,1348],{},[1079,3554,3555,3557,3560,3563],{},[1097,3556,1392],{},[1097,3558,3559],{},"P = 500 − 2Q",[1097,3561,3562],{},"dP\u002FdQ = −2 \u003C 0",[1097,3564,3565,3567],{},[1047,3566,1387],{}," (klesá!)",[1079,3569,3570,3572,3575,3577],{},[1097,3571,1414],{},[1097,3573,3574],{},"Q = 0,5P − 200",[1097,3576,3534],{},[1097,3578,3579],{},[1047,3580,1348],{},[1030,3582,3583,3585],{},[1047,3584,1437],{}," P klesá s Q — to není zákon nabídky, ale spíš poptávky.",[1030,3587,3588],{},[1047,3589,3590],{},"Poznámka k omezením:",[1203,3592,3593,3596,3599],{},[1206,3594,3595],{},"(b) má smysl pro Q ≥ 50 (alternativně P = 2Q − 100 → P ≥ 0 ⟺ Q ≥ 50).",[1206,3597,3598],{},"(c) má smysl pro Q ≥ 40 (P = −80 + 2Q ≥ 0 ⟺ Q ≥ 40).",[1206,3600,3601],{},"(e) má smysl pro P ≥ 400 (Q ≥ 0).",[1030,3603,3604],{},"Tato omezení nezruší platnost — připustí se s reálným cenovým rozpětím.",[1246,3606],{},[1065,3608,3610,3611,3613,3614],{"id":3609},"z2q2-20-b-křížová-cenová-elasticita-poptávky-epae_p_a","Z2\u002FQ2 ",[1035,3612,1116],{}," — Křížová cenová elasticita poptávky ",[1035,3615,3617],{"className":3616},[1480],[1482,3618,3619],{"xmlns":1484},[1487,3620,3621,3634],{},[1490,3622,3623],{},[1497,3624,3625,3627],{},[1493,3626,2711],{},[1497,3628,3629,3631],{},[1493,3630,1501],{},[1493,3632,3633],{},"A",[1528,3635,3636],{"encoding":1530},"E_{P_A}",[1030,3638,3639,3641,3642,3663,3664,2632],{},[1047,3640,1263],{}," Definujte ",[1035,3643,3645],{"className":3644},[1480],[1482,3646,3647],{"xmlns":1484},[1487,3648,3649,3661],{},[1490,3650,3651],{},[1497,3652,3653,3655],{},[1493,3654,2711],{},[1497,3656,3657,3659],{},[1493,3658,1501],{},[1493,3660,3633],{},[1528,3662,3636],{"encoding":1530}," a interpretujte ",[1035,3665,3667],{"className":3666},[1480],[1482,3668,3669],{"xmlns":1484},[1487,3670,3671,3688],{},[1490,3672,3673,3683,3685],{},[1497,3674,3675,3677],{},[1493,3676,2711],{},[1497,3678,3679,3681],{},[1493,3680,1501],{},[1493,3682,3633],{},[1506,3684,1508],{},[1680,3686,3687],{},"0,5",[1528,3689,3690],{"encoding":1530},"E_{P_A} = 0{,}5",[1304,3692,1476],{"id":3693},"definice-1",[1030,3695,3696,3697,1274],{},"Pro vícefaktorovou poptávku ",[1035,3698,3700],{"className":3699},[1480],[1482,3701,3702],{"xmlns":1484},[1487,3703,3704,3731],{},[1490,3705,3706,3708,3710,3713,3715,3717,3719,3725,3727,3729],{},[1493,3707,1520],{},[1506,3709,1508],{},[1493,3711,3712],{},"D",[1506,3714,1553],{"stretchy":1552},[1493,3716,1501],{},[1506,3718,1559],{"separator":1041},[1497,3720,3721,3723],{},[1493,3722,1501],{},[1493,3724,3633],{},[1506,3726,1559],{"separator":1041},[1493,3728,1791],{},[1506,3730,1564],{"stretchy":1552},[1528,3732,3733],{"encoding":1530},"Q = D(P, P_A, Y)",[1035,3735,3737],{"className":3736},[1480],[1482,3738,3739],{"xmlns":1484,"display":1485},[1487,3740,3741,3799],{},[1490,3742,3743],{},[1976,3744,3745],{"notation":1978},[1869,3746,3747],{"scriptlevel":1871,"displaystyle":1552},[1869,3748,3749],{"scriptlevel":1871,"displaystyle":1552},[1869,3750,3751],{"scriptlevel":1871,"displaystyle":1041},[1490,3752,3753,3755,3765,3767,3777,3779,3797],{},[1988,3754,1990],{},[1497,3756,3757,3759],{},[1493,3758,2711],{},[1497,3760,3761,3763],{},[1493,3762,1501],{},[1493,3764,3633],{},[1506,3766,1508],{},[1510,3768,3769,3775],{},[1497,3770,3771,3773],{},[1493,3772,1501],{},[1493,3774,3633],{},[1493,3776,1520],{},[1506,3778,1714],{},[1510,3780,3781,3787],{},[1490,3782,3783,3785],{},[1493,3784,1517],{"mathvariant":1516},[1493,3786,1520],{},[1490,3788,3789,3791],{},[1493,3790,1517],{"mathvariant":1516},[1497,3792,3793,3795],{},[1493,3794,1501],{},[1493,3796,3633],{},[1988,3798,1990],{},[1528,3800,3801],{"encoding":1530},"\\boxed{\\; E_{P_A} = \\frac{P_A}{Q} \\cdot \\frac{\\partial Q}{\\partial P_A} \\;}",[1030,3803,1295,3804,3810],{},[1052,3805,3809],{"className":3806,"dataFsResolvedFilePath":3807,"href":3808},[1055],"topics\u002Felasticita.md","\u002Fwiki\u002Felasticita","Elasticita poptávky a nabídky"," (vzorec 4.19).",[1304,3812,3814,3815],{"id":3813},"interpretace-epa05e_p_a-05","Interpretace ",[1035,3816,3818],{"className":3817},[1480],[1482,3819,3820],{"xmlns":1484},[1487,3821,3822,3838],{},[1490,3823,3824,3834,3836],{},[1497,3825,3826,3828],{},[1493,3827,2711],{},[1497,3829,3830,3832],{},[1493,3831,1501],{},[1493,3833,3633],{},[1506,3835,1508],{},[1680,3837,3687],{},[1528,3839,3690],{"encoding":1530},[1030,3841,3842,3864],{},[1047,3843,3844,3845,3863],{},"Vzroste-li cena alternativního zboží ",[1035,3846,3848],{"className":3847},[1480],[1482,3849,3850],{"xmlns":1484},[1487,3851,3852,3860],{},[1490,3853,3854],{},[1497,3855,3856,3858],{},[1493,3857,1501],{},[1493,3859,3633],{},[1528,3861,3862],{"encoding":1530},"P_A"," o 1 %, poptávané množství základního zboží Q se zvýší přibližně o 0,5 %"," (ceteris paribus).",[1030,3866,3867,1656,3870,3896,3897,3900],{},[1047,3868,3869],{},"Charakter zboží:",[1035,3871,3873],{"className":3872},[1480],[1482,3874,3875],{"xmlns":1484},[1487,3876,3877,3893],{},[1490,3878,3879,3889,3891],{},[1497,3880,3881,3883],{},[1493,3882,2711],{},[1497,3884,3885,3887],{},[1493,3886,1501],{},[1493,3888,3633],{},[1506,3890,2796],{},[1680,3892,1871],{},[1528,3894,3895],{"encoding":1530},"E_{P_A} > 0"," → zboží jsou ",[1047,3898,3899],{},"substituty"," (zdražení alternativy přesouvá poptávku na základní zboží).",[1023,3902,3904,3911],{"className":3903,"dataCallout":582},[1026,1186],[1030,3905,3907,3910],{"className":3906},[1033],[1035,3908],{"className":3909,"ariaHidden":1041},[1038,1193,1040],"Příklad",[1030,3912,3913,3914,3939,3940,2632],{},"Máslo a margarín: zdraží-li se margarín, lidé kupují víc másla → ",[1035,3915,3917],{"className":3916},[1480],[1482,3918,3919],{"xmlns":1484},[1487,3920,3921,3937],{},[1490,3922,3923,3933,3935],{},[1497,3924,3925,3927],{},[1493,3926,2711],{},[1497,3928,3929,3931],{},[1493,3930,1501],{},[1493,3932,3633],{},[1506,3934,2796],{},[1680,3936,1871],{},[1528,3938,3895],{"encoding":1530},".\nAuto a benzín (komplementy): zdraží-li se benzín, lidé kupují méně aut → ",[1035,3941,3943],{"className":3942},[1480],[1482,3944,3945],{"xmlns":1484},[1487,3946,3947,3964],{},[1490,3948,3949,3959,3962],{},[1497,3950,3951,3953],{},[1493,3952,2711],{},[1497,3954,3955,3957],{},[1493,3956,1501],{},[1493,3958,3633],{},[1506,3960,3961],{},"\u003C",[1680,3963,1871],{},[1528,3965,3966],{"encoding":1530},"E_{P_A} \u003C 0",[1246,3968],{},[1065,3970,3972,3973,3975],{"id":3971},"z2q3-30-b-minimalizace-výdajů","Z2\u002FQ3 ",[1035,3974,1130],{}," — Minimalizace výdajů",[1030,3977,3978,1656,3980,1732,4027,1732,4049,1732,4070,1800,4092,4117],{},[1047,3979,1263],{},[1035,3981,3983],{"className":3982},[1480],[1482,3984,3985],{"xmlns":1484},[1487,3986,3987,4024],{},[1490,3988,3989,3991,3993,4008,4010],{},[1493,3990,1668],{},[1506,3992,1508],{},[1697,3994,3995,3997,3999],{},[1493,3996,1520],{},[1680,3998,1682],{},[1490,4000,4001,4003,4005],{},[1680,4002,1682],{},[1493,4004,1709],{"mathvariant":1516},[1680,4006,4007],{},"4",[1506,4009,1714],{},[1697,4011,4012,4014,4016],{},[1493,4013,1520],{},[1680,4015,1691],{},[1490,4017,4018,4020,4022],{},[1680,4019,1682],{},[1493,4021,1709],{"mathvariant":1516},[1680,4023,1691],{},[1528,4025,4026],{"encoding":1530},"U = Q_1^{1\u002F4} \\cdot Q_2^{1\u002F2}",[1035,4028,4030],{"className":4029},[1480],[1482,4031,4032],{"xmlns":1484},[1487,4033,4034,4046],{},[1490,4035,4036,4042,4044],{},[2315,4037,4038,4040],{},[1493,4039,1668],{},[1506,4041,2287],{},[1506,4043,1508],{},[1680,4045,1775],{},[1528,4047,4048],{"encoding":1530},"U^* = 10",[1035,4050,4052],{"className":4051},[1480],[1482,4053,4054],{"xmlns":1484},[1487,4055,4056,4068],{},[1490,4057,4058,4064,4066],{},[1497,4059,4060,4062],{},[1493,4061,1501],{},[1680,4063,1682],{},[1506,4065,1508],{},[1680,4067,1752],{},[1528,4069,1755],{"encoding":1530},[1035,4071,4073],{"className":4072},[1480],[1482,4074,4075],{"xmlns":1484},[1487,4076,4077,4089],{},[1490,4078,4079,4085,4087],{},[1497,4080,4081,4083],{},[1493,4082,1501],{},[1680,4084,1691],{},[1506,4086,1508],{},[1680,4088,4007],{},[1528,4090,4091],{"encoding":1530},"P_2 = 4",[1035,4093,4095],{"className":4094},[1480],[1482,4096,4097],{"xmlns":1484},[1487,4098,4099,4115],{},[1490,4100,4101,4107,4109],{},[1497,4102,4103,4105],{},[1493,4104,1520],{},[1680,4106,1682],{},[1506,4108,1559],{"separator":1041},[1497,4110,4111,4113],{},[1493,4112,1520],{},[1680,4114,1691],{},[1528,4116,1826],{"encoding":1530}," minimalizující výdaje.",[1030,4119,4120,1656,4122,4125,4126,4166,4167,4209,4210,4212,4213,2632],{},[1047,4121,1832],{},[1047,4123,4124],{},"Duální úloha"," — Lagrange s vazbou ",[1035,4127,4129],{"className":4128},[1480],[1482,4130,4131],{"xmlns":1484},[1487,4132,4133,4163],{},[1490,4134,4135,4137,4139,4145,4147,4153,4155,4157],{},[1493,4136,1668],{},[1506,4138,1553],{"stretchy":1552},[1497,4140,4141,4143],{},[1493,4142,1520],{},[1680,4144,1682],{},[1506,4146,1559],{"separator":1041},[1497,4148,4149,4151],{},[1493,4150,1520],{},[1680,4152,1691],{},[1506,4154,1564],{"stretchy":1552},[1506,4156,1508],{},[2315,4158,4159,4161],{},[1493,4160,1668],{},[1506,4162,2287],{},[1528,4164,4165],{"encoding":1530},"U(Q_1,Q_2) = U^*"," a minimalizujeme ",[1035,4168,4170],{"className":4169},[1480],[1482,4171,4172],{"xmlns":1484},[1487,4173,4174,4206],{},[1490,4175,4176,4178,4180,4186,4192,4194,4200],{},[1493,4177,2711],{},[1506,4179,1508],{},[1497,4181,4182,4184],{},[1493,4183,1501],{},[1680,4185,1682],{},[1497,4187,4188,4190],{},[1493,4189,1520],{},[1680,4191,1682],{},[1506,4193,2162],{},[1497,4195,4196,4198],{},[1493,4197,1501],{},[1680,4199,1691],{},[1497,4201,4202,4204],{},[1493,4203,1520],{},[1680,4205,1691],{},[1528,4207,4208],{"encoding":1530},"E = P_1 Q_1 + P_2 Q_2",". V optimu opět ",[1047,4211,1836],{},". Viz ",[1052,4214,4217],{"className":4215,"dataFsResolvedFilePath":1841,"href":4216},[1055],"\u002Fwiki\u002Foptimalizace-spotrebitele#Duální úloha — minimalizace výdajů","sekce duální úlohy",[1304,4219,1848],{"id":4220},"krok-1-mrcs-1",[1035,4222,4224],{"className":4223},[1480],[1482,4225,4226],{"xmlns":1484,"display":1485},[1487,4227,4228,4330],{},[1490,4229,4230,4232,4238,4240,4248,4264,4278,4280,4282,4284,4290,4292,4300,4314],{},[1493,4231,1495],{},[1497,4233,4234,4236],{},[1493,4235,1668],{},[1680,4237,1682],{},[1506,4239,1508],{},[1869,4241,4242],{"scriptlevel":1871,"displaystyle":1552},[1510,4243,4244,4246],{},[1680,4245,1682],{},[1680,4247,4007],{},[1697,4249,4250,4252,4254],{},[1493,4251,1520],{},[1680,4253,1682],{},[1490,4255,4256,4258,4260,4262],{},[1506,4257,1888],{},[1680,4259,3201],{},[1493,4261,1709],{"mathvariant":1516},[1680,4263,4007],{},[1697,4265,4266,4268,4270],{},[1493,4267,1520],{},[1680,4269,1691],{},[1490,4271,4272,4274,4276],{},[1680,4273,1682],{},[1493,4275,1709],{"mathvariant":1516},[1680,4277,1691],{},[1506,4279,1559],{"separator":1041},[1912,4281],{"width":1914},[1493,4283,1495],{},[1497,4285,4286,4288],{},[1493,4287,1668],{},[1680,4289,1691],{},[1506,4291,1508],{},[1869,4293,4294],{"scriptlevel":1871,"displaystyle":1552},[1510,4295,4296,4298],{},[1680,4297,1682],{},[1680,4299,1691],{},[1697,4301,4302,4304,4306],{},[1493,4303,1520],{},[1680,4305,1682],{},[1490,4307,4308,4310,4312],{},[1680,4309,1682],{},[1493,4311,1709],{"mathvariant":1516},[1680,4313,4007],{},[1697,4315,4316,4318,4320],{},[1493,4317,1520],{},[1680,4319,1691],{},[1490,4321,4322,4324,4326,4328],{},[1506,4323,1888],{},[1680,4325,1682],{},[1493,4327,1709],{"mathvariant":1516},[1680,4329,1691],{},[1528,4331,4332],{"encoding":1530},"MU_1 = \\tfrac{1}{4} Q_1^{-3\u002F4} Q_2^{1\u002F2}, \\qquad MU_2 = \\tfrac{1}{2} Q_1^{1\u002F4} Q_2^{-1\u002F2}",[1035,4334,4336],{"className":4335},[1480],[1482,4337,4338],{"xmlns":1484,"display":1485},[1487,4339,4340,4436],{},[1490,4341,4342,4344,4346,4348,4350,4352,4374,4376,4394,4396,4408,4410,4416,4418],{},[1493,4343,1495],{},[1493,4345,1995],{},[1493,4347,1998],{},[1493,4349,2001],{},[1506,4351,1508],{},[1510,4353,4354,4364],{},[1490,4355,4356,4358],{},[1493,4357,1495],{},[1497,4359,4360,4362],{},[1493,4361,1668],{},[1680,4363,1682],{},[1490,4365,4366,4368],{},[1493,4367,1495],{},[1497,4369,4370,4372],{},[1493,4371,1668],{},[1680,4373,1691],{},[1506,4375,1508],{},[1510,4377,4378,4386],{},[1490,4379,4380,4382,4384],{},[1680,4381,1682],{},[1493,4383,1709],{"mathvariant":1516},[1680,4385,4007],{},[1490,4387,4388,4390,4392],{},[1680,4389,1682],{},[1493,4391,1709],{"mathvariant":1516},[1680,4393,1691],{},[1506,4395,1714],{},[1697,4397,4398,4400,4402],{},[1493,4399,1520],{},[1680,4401,1682],{},[1490,4403,4404,4406],{},[1506,4405,1888],{},[1680,4407,1682],{},[1506,4409,1714],{},[1497,4411,4412,4414],{},[1493,4413,1520],{},[1680,4415,1691],{},[1506,4417,1508],{},[1510,4419,4420,4426],{},[1497,4421,4422,4424],{},[1493,4423,1520],{},[1680,4425,1691],{},[1490,4427,4428,4430],{},[1680,4429,1691],{},[1497,4431,4432,4434],{},[1493,4433,1520],{},[1680,4435,1682],{},[1528,4437,4438],{"encoding":1530},"MRCS = \\frac{MU_1}{MU_2} = \\frac{1\u002F4}{1\u002F2} \\cdot Q_1^{-1} \\cdot Q_2 = \\frac{Q_2}{2 Q_1}",[1304,4440,2050],{"id":4441},"krok-2-podmínka-optimality-1",[1035,4443,4445],{"className":4444},[1480],[1482,4446,4447],{"xmlns":1484,"display":1485},[1487,4448,4449,4505],{},[1490,4450,4451,4469,4471,4477,4479,4481,4483,4489,4491,4499],{},[1510,4452,4453,4459],{},[1497,4454,4455,4457],{},[1493,4456,1520],{},[1680,4458,1691],{},[1490,4460,4461,4463],{},[1680,4462,1691],{},[1497,4464,4465,4467],{},[1493,4466,1520],{},[1680,4468,1682],{},[1506,4470,1508],{},[1510,4472,4473,4475],{},[1680,4474,1752],{},[1680,4476,4007],{},[1988,4478,1990],{},[1506,4480,2111],{},[1988,4482,1990],{},[1497,4484,4485,4487],{},[1493,4486,1520],{},[1680,4488,1691],{},[1506,4490,1508],{},[1869,4492,4493],{"scriptlevel":1871,"displaystyle":1552},[1510,4494,4495,4497],{},[1680,4496,1752],{},[1680,4498,1691],{},[1497,4500,4501,4503],{},[1493,4502,1520],{},[1680,4504,1682],{},[1528,4506,4507],{"encoding":1530},"\\frac{Q_2}{2 Q_1} = \\frac{5}{4} \\;\\Longrightarrow\\; Q_2 = \\tfrac{5}{2} Q_1",[1304,4509,4511],{"id":4510},"krok-3-vazba-užitečnosti","Krok 3: Vazba užitečnosti",[1035,4513,4515],{"className":4514},[1480],[1482,4516,4517],{"xmlns":1484,"display":1485},[1487,4518,4519,4571],{},[1490,4520,4521,4535,4537,4567,4569],{},[1697,4522,4523,4525,4527],{},[1493,4524,1520],{},[1680,4526,1682],{},[1490,4528,4529,4531,4533],{},[1680,4530,1682],{},[1493,4532,1709],{"mathvariant":1516},[1680,4534,4007],{},[1506,4536,1714],{},[2315,4538,4539,4559],{},[1490,4540,4541,4543,4551,4557],{},[1506,4542,1553],{"fence":1041},[1869,4544,4545],{"scriptlevel":1871,"displaystyle":1552},[1510,4546,4547,4549],{},[1680,4548,1752],{},[1680,4550,1691],{},[1497,4552,4553,4555],{},[1493,4554,1520],{},[1680,4556,1682],{},[1506,4558,1564],{"fence":1041},[1490,4560,4561,4563,4565],{},[1680,4562,1682],{},[1493,4564,1709],{"mathvariant":1516},[1680,4566,1691],{},[1506,4568,1508],{},[1680,4570,1775],{},[1528,4572,4573],{"encoding":1530},"Q_1^{1\u002F4} \\cdot \\left(\\tfrac{5}{2} Q_1\\right)^{1\u002F2} = 10",[1035,4575,4577],{"className":4576},[1480],[1482,4578,4579],{"xmlns":1484,"display":1485},[1487,4580,4581,4657],{},[1490,4582,4583,4597,4599,4609,4611,4625,4627,4641,4643,4653,4655],{},[1697,4584,4585,4587,4589],{},[1493,4586,1520],{},[1680,4588,1682],{},[1490,4590,4591,4593,4595],{},[1680,4592,1682],{},[1493,4594,1709],{"mathvariant":1516},[1680,4596,4007],{},[1506,4598,1714],{},[2324,4600,4601],{},[1869,4602,4603],{"scriptlevel":1871,"displaystyle":1552},[1510,4604,4605,4607],{},[1680,4606,1752],{},[1680,4608,1691],{},[1506,4610,1714],{},[1697,4612,4613,4615,4617],{},[1493,4614,1520],{},[1680,4616,1682],{},[1490,4618,4619,4621,4623],{},[1680,4620,1682],{},[1493,4622,1709],{"mathvariant":1516},[1680,4624,1691],{},[1506,4626,1508],{},[1697,4628,4629,4631,4633],{},[1493,4630,1520],{},[1680,4632,1682],{},[1490,4634,4635,4637,4639],{},[1680,4636,3201],{},[1493,4638,1709],{"mathvariant":1516},[1680,4640,4007],{},[1506,4642,1714],{},[2324,4644,4645],{},[1869,4646,4647],{"scriptlevel":1871,"displaystyle":1552},[1510,4648,4649,4651],{},[1680,4650,1752],{},[1680,4652,1691],{},[1506,4654,1508],{},[1680,4656,1775],{},[1528,4658,4659],{"encoding":1530},"Q_1^{1\u002F4} \\cdot \\sqrt{\\tfrac{5}{2}} \\cdot Q_1^{1\u002F2} = Q_1^{3\u002F4} \\cdot \\sqrt{\\tfrac{5}{2}} = 10",[1035,4661,4663],{"className":4662},[1480],[1482,4664,4665],{"xmlns":1484,"display":1485},[1487,4666,4667,4721],{},[1490,4668,4669,4683,4685,4699,4701,4703,4713,4715,4717],{},[1697,4670,4671,4673,4675],{},[1493,4672,1520],{},[1680,4674,1682],{},[1490,4676,4677,4679,4681],{},[1680,4678,3201],{},[1493,4680,1709],{"mathvariant":1516},[1680,4682,4007],{},[1506,4684,1508],{},[1510,4686,4687,4689],{},[1680,4688,1775],{},[2324,4690,4691],{},[1490,4692,4693,4695,4697],{},[1680,4694,1752],{},[1493,4696,1709],{"mathvariant":1516},[1680,4698,1691],{},[1506,4700,1508],{},[1680,4702,1775],{},[2324,4704,4705],{},[1869,4706,4707],{"scriptlevel":1871,"displaystyle":1552},[1510,4708,4709,4711],{},[1680,4710,1691],{},[1680,4712,1752],{},[1506,4714,1508],{},[1680,4716,1691],{},[2324,4718,4719],{},[1680,4720,1775],{},[1528,4722,4723],{"encoding":1530},"Q_1^{3\u002F4} = \\frac{10}{\\sqrt{5\u002F2}} = 10\\sqrt{\\tfrac{2}{5}} = 2\\sqrt{10}",[1035,4725,4727],{"className":4726},[1480],[1482,4728,4729],{"xmlns":1484,"display":1485},[1487,4730,4731,4807],{},[1490,4732,4733,4739,4741,4743,4745,4749,4761,4763,4775,4777,4789,4791,4793,4795],{},[1497,4734,4735,4737],{},[1493,4736,1520],{},[1680,4738,1682],{},[1506,4740,1508],{},[1506,4742,1553],{"stretchy":1552},[1680,4744,1691],{},[2324,4746,4747],{},[1680,4748,1775],{},[2315,4750,4751,4753],{},[1506,4752,1564],{"stretchy":1552},[1490,4754,4755,4757,4759],{},[1680,4756,4007],{},[1493,4758,1709],{"mathvariant":1516},[1680,4760,3201],{},[1506,4762,1508],{},[2315,4764,4765,4767],{},[1680,4766,1691],{},[1490,4768,4769,4771,4773],{},[1680,4770,4007],{},[1493,4772,1709],{"mathvariant":1516},[1680,4774,3201],{},[1506,4776,1714],{},[2315,4778,4779,4781],{},[1680,4780,1775],{},[1490,4782,4783,4785,4787],{},[1680,4784,1691],{},[1493,4786,1709],{"mathvariant":1516},[1680,4788,3201],{},[1506,4790,1508],{},[1680,4792,4007],{},[1506,4794,1714],{},[2315,4796,4797,4799],{},[1680,4798,1752],{},[1490,4800,4801,4803,4805],{},[1680,4802,1691],{},[1493,4804,1709],{"mathvariant":1516},[1680,4806,3201],{},[1528,4808,4809],{"encoding":1530},"Q_1 = (2\\sqrt{10})^{4\u002F3} = 2^{4\u002F3} \\cdot 10^{2\u002F3} = 4 \\cdot 5^{2\u002F3}",[1304,4811,4813],{"id":4812},"výsledek-přesně","Výsledek (přesně)",[1035,4815,4817],{"className":4816},[1480],[1482,4818,4819],{"xmlns":1484,"display":1485},[1487,4820,4821,4903],{},[1490,4822,4823],{},[1976,4824,4825],{"notation":1978},[1869,4826,4827],{"scriptlevel":1871,"displaystyle":1552},[1869,4828,4829],{"scriptlevel":1871,"displaystyle":1552},[1869,4830,4831],{"scriptlevel":1871,"displaystyle":1041},[1490,4832,4833,4835,4843,4845,4847,4849,4861,4863,4866,4868,4870,4878,4880,4882,4884,4896,4898,4901],{},[1988,4834,1990],{},[1697,4836,4837,4839,4841],{},[1493,4838,1520],{},[1680,4840,1682],{},[1506,4842,2287],{},[1506,4844,1508],{},[1680,4846,4007],{},[1506,4848,1714],{},[2315,4850,4851,4853],{},[1680,4852,1752],{},[1490,4854,4855,4857,4859],{},[1680,4856,1691],{},[1493,4858,1709],{"mathvariant":1516},[1680,4860,3201],{},[1506,4862,2343],{},[1680,4864,4865],{},"11,696",[1506,4867,1559],{"separator":1041},[1912,4869],{"width":2108},[1697,4871,4872,4874,4876],{},[1493,4873,1520],{},[1680,4875,1691],{},[1506,4877,2287],{},[1506,4879,1508],{},[1680,4881,1775],{},[1506,4883,1714],{},[2315,4885,4886,4888],{},[1680,4887,1752],{},[1490,4889,4890,4892,4894],{},[1680,4891,1691],{},[1493,4893,1709],{"mathvariant":1516},[1680,4895,3201],{},[1506,4897,2343],{},[1680,4899,4900],{},"29,240",[1988,4902,1990],{},[1528,4904,4905],{"encoding":1530},"\\boxed{\\; Q_1^* = 4 \\cdot 5^{2\u002F3} \\approx 11{,}696, \\quad Q_2^* = 10 \\cdot 5^{2\u002F3} \\approx 29{,}240 \\;}",[1035,4907,4909],{"className":4908},[1480],[1482,4910,4911],{"xmlns":1484,"display":1485},[1487,4912,4913,4987],{},[1490,4914,4915],{},[1976,4916,4917],{"notation":1978},[1869,4918,4919],{"scriptlevel":1871,"displaystyle":1552},[1869,4920,4921],{"scriptlevel":1871,"displaystyle":1552},[1869,4922,4923],{"scriptlevel":1871,"displaystyle":1041},[1490,4924,4925,4927,4933,4935,4937,4939,4947,4949,4951,4953,4961,4963,4966,4968,4980,4982,4985],{},[1988,4926,1990],{},[2315,4928,4929,4931],{},[1493,4930,2711],{},[1506,4932,2287],{},[1506,4934,1508],{},[1680,4936,1752],{},[1506,4938,1714],{},[1697,4940,4941,4943,4945],{},[1493,4942,1520],{},[1680,4944,1682],{},[1506,4946,2287],{},[1506,4948,2162],{},[1680,4950,4007],{},[1506,4952,1714],{},[1697,4954,4955,4957,4959],{},[1493,4956,1520],{},[1680,4958,1691],{},[1506,4960,2287],{},[1506,4962,1508],{},[1680,4964,4965],{},"60",[1506,4967,1714],{},[2315,4969,4970,4972],{},[1680,4971,1752],{},[1490,4973,4974,4976,4978],{},[1680,4975,1691],{},[1493,4977,1709],{"mathvariant":1516},[1680,4979,3201],{},[1506,4981,2343],{},[1680,4983,4984],{},"175,44",[1988,4986,1990],{},[1528,4988,4989],{"encoding":1530},"\\boxed{\\; E^* = 5 \\cdot Q_1^* + 4 \\cdot Q_2^* = 60 \\cdot 5^{2\u002F3} \\approx 175{,}44 \\;}",[1030,4991,4992,1656,4995,5078],{},[1047,4993,4994],{},"Ověření vazby:",[1035,4996,4998],{"className":4997},[1480],[1482,4999,5000],{"xmlns":1484},[1487,5001,5002,5075],{},[1490,5003,5004,5023,5025,5043,5045,5052,5054,5060,5062,5065,5067,5070,5072],{},[1697,5005,5006,5008,5010],{},[1493,5007,1520],{},[1680,5009,1682],{},[1490,5011,5012,5014,5017,5019,5021],{},[1506,5013,2287],{},[1988,5015,5016],{}," ",[1680,5018,1682],{},[1493,5020,1709],{"mathvariant":1516},[1680,5022,4007],{},[1506,5024,1714],{},[1697,5026,5027,5029,5031],{},[1493,5028,1520],{},[1680,5030,1691],{},[1490,5032,5033,5035,5037,5039,5041],{},[1506,5034,2287],{},[1988,5036,5016],{},[1680,5038,1682],{},[1493,5040,1709],{"mathvariant":1516},[1680,5042,1691],{},[1506,5044,1508],{},[2315,5046,5047,5049],{},[1680,5048,4865],{},[1680,5050,5051],{},"0,25",[1506,5053,1714],{},[2315,5055,5056,5058],{},[1680,5057,4900],{},[1680,5059,3687],{},[1506,5061,2343],{},[1680,5063,5064],{},"1,849",[1506,5066,1714],{},[1680,5068,5069],{},"5,408",[1506,5071,2343],{},[1680,5073,5074],{},"10,00",[1528,5076,5077],{"encoding":1530},"Q_1^{*\\,1\u002F4} \\cdot Q_2^{*\\,1\u002F2} = 11{,}696^{0{,}25} \\cdot 29{,}240^{0{,}5} \\approx 1{,}849 \\cdot 5{,}408 \\approx 10{,}00"," ✓",[1023,5080,5082,5089],{"className":5081,"dataCallout":1443},[1026,1442],[1030,5083,5085,5088],{"className":5084},[1033],[1035,5086],{"className":5087,"ariaHidden":1041},[1038,1450,1040],"Proč tahle úloha vyšla nehezky?",[1030,5090,5091,5092,1586,5110,5128,5129,5153,5154,5198],{},"Exponenty ",[1035,5093,5095],{"className":5094},[1480],[1482,5096,5097],{"xmlns":1484},[1487,5098,5099,5107],{},[1490,5100,5101,5103,5105],{},[1680,5102,1682],{},[1493,5104,1709],{"mathvariant":1516},[1680,5106,4007],{},[1528,5108,5109],{"encoding":1530},"1\u002F4",[1035,5111,5113],{"className":5112},[1480],[1482,5114,5115],{"xmlns":1484},[1487,5116,5117,5125],{},[1490,5118,5119,5121,5123],{},[1680,5120,1682],{},[1493,5122,1709],{"mathvariant":1516},[1680,5124,1691],{},[1528,5126,5127],{"encoding":1530},"1\u002F2"," nesoudí (součet 3\u002F4, ne 1) → Cobb-Douglas se neredukuje na ryzí tvar a výsledek obsahuje ",[1035,5130,5132],{"className":5131},[1480],[1482,5133,5134],{"xmlns":1484},[1487,5135,5136,5150],{},[1490,5137,5138],{},[2315,5139,5140,5142],{},[1680,5141,1752],{},[1490,5143,5144,5146,5148],{},[1680,5145,1691],{},[1493,5147,1709],{"mathvariant":1516},[1680,5149,3201],{},[1528,5151,5152],{"encoding":1530},"5^{2\u002F3}",". Pro ",[1035,5155,5157],{"className":5156},[1480],[1482,5158,5159],{"xmlns":1484},[1487,5160,5161,5195],{},[1490,5162,5163,5165,5167,5181],{},[1493,5164,1668],{},[1506,5166,1508],{},[1697,5168,5169,5171,5173],{},[1493,5170,1520],{},[1680,5172,1682],{},[1490,5174,5175,5177,5179],{},[1680,5176,1682],{},[1493,5178,1709],{"mathvariant":1516},[1680,5180,1691],{},[1697,5182,5183,5185,5187],{},[1493,5184,1520],{},[1680,5186,1691],{},[1490,5188,5189,5191,5193],{},[1680,5190,1682],{},[1493,5192,1709],{"mathvariant":1516},[1680,5194,1691],{},[1528,5196,5197],{"encoding":1530},"U = Q_1^{1\u002F2} Q_2^{1\u002F2}"," (Z1\u002FQ3) to vyšlo na celá čísla 50 a 25.",[1246,5200],{},[1065,5202,5204,5205,5207],{"id":5203},"z2q4-40-b-cenová-diskriminace","Z2\u002FQ4 ",[1035,5206,1144],{}," — Cenová diskriminace",[1030,5209,5210,1656,5212,5243,5244,5277,5278,1732,5306,5336],{},[1047,5211,1263],{},[1035,5213,5215],{"className":5214},[1480],[1482,5216,5217],{"xmlns":1484},[1487,5218,5219,5240],{},[1490,5220,5221,5227,5229,5232,5234],{},[1497,5222,5223,5225],{},[1493,5224,1501],{},[1680,5226,1682],{},[1506,5228,1508],{},[1680,5230,5231],{},"300",[1506,5233,1888],{},[1497,5235,5236,5238],{},[1493,5237,1520],{},[1680,5239,1682],{},[1528,5241,5242],{"encoding":1530},"P_1 = 300 - Q_1"," (domácí), ",[1035,5245,5247],{"className":5246},[1480],[1482,5248,5249],{"xmlns":1484},[1487,5250,5251,5274],{},[1490,5252,5253,5259,5261,5264,5266,5268],{},[1497,5254,5255,5257],{},[1493,5256,1501],{},[1680,5258,1691],{},[1506,5260,1508],{},[1680,5262,5263],{},"200",[1506,5265,1888],{},[1680,5267,3687],{},[1497,5269,5270,5272],{},[1493,5271,1520],{},[1680,5273,1691],{},[1528,5275,5276],{"encoding":1530},"P_2 = 200 - 0{,}5 Q_2"," (zahraniční), ",[1035,5279,5281],{"className":5280},[1480],[1482,5282,5283],{"xmlns":1484},[1487,5284,5285,5303],{},[1490,5286,5287,5290,5292,5294,5297,5299,5301],{},[1493,5288,5289],{},"T",[1493,5291,1998],{},[1506,5293,1508],{},[1680,5295,5296],{},"5000",[1506,5298,2162],{},[1680,5300,2916],{},[1493,5302,1520],{},[1528,5304,5305],{"encoding":1530},"TC = 5000 + 100Q",[1035,5307,5309],{"className":5308},[1480],[1482,5310,5311],{"xmlns":1484},[1487,5312,5313,5333],{},[1490,5314,5315,5317,5319,5325,5327],{},[1493,5316,1520],{},[1506,5318,1508],{},[1497,5320,5321,5323],{},[1493,5322,1520],{},[1680,5324,1682],{},[1506,5326,2162],{},[1497,5328,5329,5331],{},[1493,5330,1520],{},[1680,5332,1691],{},[1528,5334,5335],{"encoding":1530},"Q = Q_1 + Q_2",". Stanovte ceny pro max zisku (a) s diskriminací; (b) bez diskriminace; (c) porovnejte.",[1030,5338,5339,1656,5341,5344,5345,5348,5349,5352],{},[1047,5340,1832],{},[1047,5342,5343],{},"MR_i = MC pro každý segment"," při diskriminaci; ",[1047,5346,5347],{},"MR(Q) = MC"," pro tržní poptávku bez diskriminace. Viz ",[1052,5350,1301],{"className":5351,"dataFsResolvedFilePath":1299,"href":1300},[1055]," (Příklad 3.25 — totožná úloha v knize Mezník).",[1304,5354,5356],{"id":5355},"a-s-cenovou-diskriminací","(a) S cenovou diskriminací",[1030,5358,5359],{},[1047,5360,5361],{},"Mezní příjmy a mezní náklady:",[1035,5363,5365],{"className":5364},[1480],[1482,5366,5367],{"xmlns":1484,"display":1485},[1487,5368,5369,5429],{},[1490,5370,5371,5373,5379,5381,5383,5385,5387,5393,5395,5397,5399,5405,5407,5409,5411,5417,5419,5421,5423,5425,5427],{},[1493,5372,1495],{},[1497,5374,5375,5377],{},[1493,5376,1995],{},[1680,5378,1682],{},[1506,5380,1508],{},[1680,5382,5231],{},[1506,5384,1888],{},[1680,5386,1691],{},[1497,5388,5389,5391],{},[1493,5390,1520],{},[1680,5392,1682],{},[1506,5394,1559],{"separator":1041},[1912,5396],{"width":2108},[1493,5398,1495],{},[1497,5400,5401,5403],{},[1493,5402,1995],{},[1680,5404,1691],{},[1506,5406,1508],{},[1680,5408,5263],{},[1506,5410,1888],{},[1497,5412,5413,5415],{},[1493,5414,1520],{},[1680,5416,1691],{},[1506,5418,1559],{"separator":1041},[1912,5420],{"width":2108},[1493,5422,1495],{},[1493,5424,1998],{},[1506,5426,1508],{},[1680,5428,2916],{},[1528,5430,5431],{"encoding":1530},"MR_1 = 300 - 2 Q_1, \\quad MR_2 = 200 - Q_2, \\quad MC = 100",[1030,5433,5434,1656,5437,5495,1656,5498],{},[1047,5435,5436],{},"Trh 1:",[1035,5438,5440],{"className":5439},[1480],[1482,5441,5442],{"xmlns":1484},[1487,5443,5444,5492],{},[1490,5445,5446,5448,5450,5452,5458,5460,5462,5464,5466,5468,5474,5476,5478,5480,5482,5488,5490],{},[1680,5447,5231],{},[1506,5449,1888],{},[1680,5451,1691],{},[1497,5453,5454,5456],{},[1493,5455,1520],{},[1680,5457,1682],{},[1506,5459,1508],{},[1680,5461,2916],{},[1988,5463,1990],{},[1506,5465,2111],{},[1988,5467,1990],{},[1497,5469,5470,5472],{},[1493,5471,1520],{},[1680,5473,1682],{},[1506,5475,1508],{},[1680,5477,2916],{},[1506,5479,1559],{"separator":1041},[1988,5481,1990],{},[1497,5483,5484,5486],{},[1493,5485,1501],{},[1680,5487,1682],{},[1506,5489,1508],{},[1680,5491,5263],{},[1528,5493,5494],{"encoding":1530},"300 - 2 Q_1 = 100 \\;\\Longrightarrow\\; Q_1 = 100, \\; P_1 = 200",[1047,5496,5497],{},"Trh 2:",[1035,5499,5501],{"className":5500},[1480],[1482,5502,5503],{"xmlns":1484},[1487,5504,5505,5552],{},[1490,5506,5507,5509,5511,5517,5519,5521,5523,5525,5527,5533,5535,5537,5539,5541,5547,5549],{},[1680,5508,5263],{},[1506,5510,1888],{},[1497,5512,5513,5515],{},[1493,5514,1520],{},[1680,5516,1691],{},[1506,5518,1508],{},[1680,5520,2916],{},[1988,5522,1990],{},[1506,5524,2111],{},[1988,5526,1990],{},[1497,5528,5529,5531],{},[1493,5530,1520],{},[1680,5532,1691],{},[1506,5534,1508],{},[1680,5536,2916],{},[1506,5538,1559],{"separator":1041},[1988,5540,1990],{},[1497,5542,5543,5545],{},[1493,5544,1501],{},[1680,5546,1691],{},[1506,5548,1508],{},[1680,5550,5551],{},"150",[1528,5553,5554],{"encoding":1530},"200 - Q_2 = 100 \\;\\Longrightarrow\\; Q_2 = 100, \\; P_2 = 150",[1030,5556,5557],{},[1047,5558,5559],{},"Zisk:",[1035,5561,5563],{"className":5562},[1480],[1482,5564,5565],{"xmlns":1484,"display":1485},[1487,5566,5567,5637],{},[1490,5568,5569,5571,5573,5575,5577,5579,5581,5583,5585,5587,5589,5591,5593,5595,5597,5599,5601,5604,5606,5609,5611,5613,5615,5617,5619,5621,5623,5625,5627,5629,5631,5633,5635],{},[1493,5570,1520],{},[1506,5572,1508],{},[1680,5574,5263],{},[1506,5576,1559],{"separator":1041},[1988,5578,1990],{},[1493,5580,5289],{},[1493,5582,1995],{},[1506,5584,1508],{},[1680,5586,5263],{},[1506,5588,1714],{},[1680,5590,2916],{},[1506,5592,2162],{},[1680,5594,5551],{},[1506,5596,1714],{},[1680,5598,2916],{},[1506,5600,1508],{},[1680,5602,5603],{},"35",[1988,5605,5016],{},[1680,5607,5608],{},"000",[1506,5610,1559],{"separator":1041},[1988,5612,1990],{},[1493,5614,5289],{},[1493,5616,1998],{},[1506,5618,1508],{},[1680,5620,5296],{},[1506,5622,2162],{},[1680,5624,2916],{},[1506,5626,1714],{},[1680,5628,5263],{},[1506,5630,1508],{},[1680,5632,2309],{},[1988,5634,5016],{},[1680,5636,5608],{},[1528,5638,5639],{"encoding":1530},"Q = 200, \\; TR = 200 \\cdot 100 + 150 \\cdot 100 = 35\\,000, \\; TC = 5000 + 100 \\cdot 200 = 25\\,000",[1035,5641,5643],{"className":5642},[1480],[1482,5644,5645],{"xmlns":1484,"display":1485},[1487,5646,5647,5701],{},[1490,5648,5649],{},[1976,5650,5651],{"notation":1978},[1869,5652,5653],{"scriptlevel":1871,"displaystyle":1552},[1869,5654,5655],{"scriptlevel":1871,"displaystyle":1552},[1869,5656,5657],{"scriptlevel":1871,"displaystyle":1041},[1490,5658,5659,5661,5663,5675,5677,5679,5681,5683,5685,5687,5689,5691,5693,5695,5697,5699],{},[1988,5660,1990],{},[1493,5662,1501],{},[2315,5664,5665,5667],{},[1493,5666,1995],{},[1490,5668,5669,5671,5673],{},[1506,5670,1553],{"stretchy":1552},[1493,5672,1052],{},[1506,5674,1564],{"stretchy":1552},[1506,5676,1508],{},[1680,5678,5603],{},[1988,5680,5016],{},[1680,5682,5608],{},[1506,5684,1888],{},[1680,5686,2309],{},[1988,5688,5016],{},[1680,5690,5608],{},[1506,5692,1508],{},[1680,5694,1775],{},[1988,5696,5016],{},[1680,5698,5608],{},[1988,5700,1990],{},[1528,5702,5703],{"encoding":1530},"\\boxed{\\; PR^{(a)} = 35\\,000 - 25\\,000 = 10\\,000 \\;}",[1304,5705,5707],{"id":5706},"b-bez-cenové-diskriminace","(b) Bez cenové diskriminace",[1030,5709,5710,5713],{},[1047,5711,5712],{},"Tržní poptávka"," (jediná cena P pro oba segmenty). Z inverzí:",[1035,5715,5717],{"className":5716},[1480],[1482,5718,5719],{"xmlns":1484,"display":1485},[1487,5720,5721,5772],{},[1490,5722,5723,5729,5731,5733,5735,5737,5739,5741,5747,5749,5761,5763,5766,5768,5770],{},[1497,5724,5725,5727],{},[1493,5726,1520],{},[1680,5728,1682],{},[1506,5730,1508],{},[1680,5732,5231],{},[1506,5734,1888],{},[1493,5736,1501],{},[1506,5738,1559],{"separator":1041},[1912,5740],{"width":1914},[1497,5742,5743,5745],{},[1493,5744,1520],{},[1680,5746,1691],{},[1506,5748,1508],{},[1510,5750,5751,5759],{},[1490,5752,5753,5755,5757],{},[1680,5754,5263],{},[1506,5756,1888],{},[1493,5758,1501],{},[1680,5760,3687],{},[1506,5762,1508],{},[1680,5764,5765],{},"400",[1506,5767,1888],{},[1680,5769,1691],{},[1493,5771,1501],{},[1528,5773,5774],{"encoding":1530},"Q_1 = 300 - P, \\qquad Q_2 = \\frac{200 - P}{0{,}5} = 400 - 2P",[1030,5776,5777],{},"Pro P ≤ 200 (jinak Q₂ = 0):",[1035,5779,5781],{"className":5780},[1480],[1482,5782,5783],{"xmlns":1484,"display":1485},[1487,5784,5785,5838],{},[1490,5786,5787,5789,5791,5797,5799,5805,5807,5810,5812,5814,5816,5818,5820,5822,5824,5826],{},[1493,5788,1520],{},[1506,5790,1508],{},[1497,5792,5793,5795],{},[1493,5794,1520],{},[1680,5796,1682],{},[1506,5798,2162],{},[1497,5800,5801,5803],{},[1493,5802,1520],{},[1680,5804,1691],{},[1506,5806,1508],{},[1680,5808,5809],{},"700",[1506,5811,1888],{},[1680,5813,3201],{},[1493,5815,1501],{},[1988,5817,1990],{},[1506,5819,2111],{},[1988,5821,1990],{},[1493,5823,1501],{},[1506,5825,1508],{},[1510,5827,5828,5836],{},[1490,5829,5830,5832,5834],{},[1680,5831,5809],{},[1506,5833,1888],{},[1493,5835,1520],{},[1680,5837,3201],{},[1528,5839,5840],{"encoding":1530},"Q = Q_1 + Q_2 = 700 - 3P \\;\\Longrightarrow\\; P = \\frac{700 - Q}{3}",[1030,5842,5843],{},[1047,5844,5845],{},"Mezní příjem:",[1035,5847,5849],{"className":5848},[1480],[1482,5850,5851],{"xmlns":1484,"display":1485},[1487,5852,5853,5911],{},[1490,5854,5855,5857,5859,5861,5863,5865,5867,5869,5887,5889,5891,5893,5895,5897],{},[1493,5856,5289],{},[1493,5858,1995],{},[1506,5860,1508],{},[1493,5862,1501],{},[1506,5864,1714],{},[1493,5866,1520],{},[1506,5868,1508],{},[1510,5870,5871,5885],{},[1490,5872,5873,5875,5877,5879],{},[1680,5874,5809],{},[1493,5876,1520],{},[1506,5878,1888],{},[2315,5880,5881,5883],{},[1493,5882,1520],{},[1680,5884,1691],{},[1680,5886,3201],{},[1506,5888,1559],{"separator":1041},[1912,5890],{"width":2108},[1493,5892,1495],{},[1493,5894,1995],{},[1506,5896,1508],{},[1510,5898,5899,5909],{},[1490,5900,5901,5903,5905,5907],{},[1680,5902,5809],{},[1506,5904,1888],{},[1680,5906,1691],{},[1493,5908,1520],{},[1680,5910,3201],{},[1528,5912,5913],{"encoding":1530},"TR = P \\cdot Q = \\frac{700 Q - Q^2}{3}, \\quad MR = \\frac{700 - 2Q}{3}",[1030,5915,5916,1656,5919],{},[1047,5917,5918],{},"MR = MC:",[1035,5920,5922],{"className":5921},[1480],[1482,5923,5924],{"xmlns":1484},[1487,5925,5926,5976],{},[1490,5927,5928,5942,5944,5946,5948,5950,5952,5954,5956,5958,5960,5962,5964,5966,5968,5970,5972,5974],{},[1510,5929,5930,5940],{},[1490,5931,5932,5934,5936,5938],{},[1680,5933,5809],{},[1506,5935,1888],{},[1680,5937,1691],{},[1493,5939,1520],{},[1680,5941,3201],{},[1506,5943,1508],{},[1680,5945,2916],{},[1988,5947,1990],{},[1506,5949,2111],{},[1988,5951,1990],{},[1680,5953,5809],{},[1506,5955,1888],{},[1680,5957,1691],{},[1493,5959,1520],{},[1506,5961,1508],{},[1680,5963,5231],{},[1988,5965,1990],{},[1506,5967,2111],{},[1988,5969,1990],{},[1493,5971,1520],{},[1506,5973,1508],{},[1680,5975,5263],{},[1528,5977,5978],{"encoding":1530},"\\frac{700 - 2Q}{3} = 100 \\;\\Longrightarrow\\; 700 - 2Q = 300 \\;\\Longrightarrow\\; Q = 200",[1035,5980,5982],{"className":5981},[1480],[1482,5983,5984],{"xmlns":1484,"display":1485},[1487,5985,5986,6003],{},[1490,5987,5988,5990,5992,5998,6000],{},[1493,5989,1501],{},[1506,5991,1508],{},[1510,5993,5994,5996],{},[1680,5995,1796],{},[1680,5997,3201],{},[1506,5999,2343],{},[1680,6001,6002],{},"166,67",[1528,6004,6005],{"encoding":1530},"P = \\frac{500}{3} \\approx 166{,}67",[1030,6007,6008],{},[1047,6009,5559],{},[1035,6011,6013],{"className":6012},[1480],[1482,6014,6015],{"xmlns":1484,"display":1485},[1487,6016,6017,6080],{},[1490,6018,6019,6021,6023,6025,6033,6035,6037,6039,6053,6055,6058,6060,6063,6066,6068,6070,6072,6074,6076,6078],{},[1493,6020,5289],{},[1493,6022,1995],{},[1506,6024,1508],{},[1869,6026,6027],{"scriptlevel":1871,"displaystyle":1552},[1510,6028,6029,6031],{},[1680,6030,1796],{},[1680,6032,3201],{},[1506,6034,1714],{},[1680,6036,5263],{},[1506,6038,1508],{},[1869,6040,6041],{"scriptlevel":1871,"displaystyle":1552},[1510,6042,6043,6051],{},[1490,6044,6045,6047,6049],{},[1680,6046,2916],{},[1988,6048,5016],{},[1680,6050,5608],{},[1680,6052,3201],{},[1506,6054,2343],{},[1680,6056,6057],{},"33",[1988,6059,5016],{},[1680,6061,6062],{},"333,33",[1506,6064,6065],{"separator":1041},";",[1912,6067],{"width":2108},[1493,6069,5289],{},[1493,6071,1998],{},[1506,6073,1508],{},[1680,6075,2309],{},[1988,6077,5016],{},[1680,6079,5608],{},[1528,6081,6082],{"encoding":1530},"TR = \\tfrac{500}{3} \\cdot 200 = \\tfrac{100\\,000}{3} \\approx 33\\,333{,}33; \\quad TC = 25\\,000",[1035,6084,6086],{"className":6085},[1480],[1482,6087,6088],{"xmlns":1484,"display":1485},[1487,6089,6090,6145],{},[1490,6091,6092],{},[1976,6093,6094],{"notation":1978},[1869,6095,6096],{"scriptlevel":1871,"displaystyle":1552},[1869,6097,6098],{"scriptlevel":1871,"displaystyle":1552},[1869,6099,6100],{"scriptlevel":1871,"displaystyle":1041},[1490,6101,6102,6104,6106,6118,6120,6134,6136,6139,6141,6143],{},[1988,6103,1990],{},[1493,6105,1501],{},[2315,6107,6108,6110],{},[1493,6109,1995],{},[1490,6111,6112,6114,6116],{},[1506,6113,1553],{"stretchy":1552},[1493,6115,2394],{},[1506,6117,1564],{"stretchy":1552},[1506,6119,1508],{},[1869,6121,6122],{"scriptlevel":1871,"displaystyle":1552},[1510,6123,6124,6132],{},[1490,6125,6126,6128,6130],{},[1680,6127,2309],{},[1988,6129,5016],{},[1680,6131,5608],{},[1680,6133,3201],{},[1506,6135,2343],{},[1680,6137,6138],{},"8",[1988,6140,5016],{},[1680,6142,6062],{},[1988,6144,1990],{},[1528,6146,6147],{"encoding":1530},"\\boxed{\\; PR^{(b)} = \\tfrac{25\\,000}{3} \\approx 8\\,333{,}33 \\;}",[1304,6149,6151],{"id":6150},"c-porovnání","(c) Porovnání",[1035,6153,6155],{"className":6154},[1480],[1482,6156,6157],{"xmlns":1484,"display":1485},[1487,6158,6159,6234],{},[1490,6160,6161,6163,6165,6167,6169,6171,6183,6185,6187,6199,6201,6203,6205,6207,6209,6211,6213,6215,6217],{},[1493,6162,2976],{"mathvariant":1516},[1493,6164,1501],{},[1493,6166,1995],{},[1506,6168,1508],{},[1493,6170,1501],{},[2315,6172,6173,6175],{},[1493,6174,1995],{},[1490,6176,6177,6179,6181],{},[1506,6178,1553],{"stretchy":1552},[1493,6180,1052],{},[1506,6182,1564],{"stretchy":1552},[1506,6184,1888],{},[1493,6186,1501],{},[2315,6188,6189,6191],{},[1493,6190,1995],{},[1490,6192,6193,6195,6197],{},[1506,6194,1553],{"stretchy":1552},[1493,6196,2394],{},[1506,6198,1564],{"stretchy":1552},[1506,6200,1508],{},[1680,6202,1775],{},[1988,6204,5016],{},[1680,6206,5608],{},[1506,6208,1888],{},[1680,6210,6138],{},[1988,6212,5016],{},[1680,6214,6062],{},[1506,6216,1508],{},[1976,6218,6219],{"notation":1978},[1869,6220,6221],{"scriptlevel":1871,"displaystyle":1552},[1869,6222,6223],{"scriptlevel":1871,"displaystyle":1552},[1869,6224,6225],{"scriptlevel":1871,"displaystyle":1041},[1490,6226,6227,6229,6231],{},[1680,6228,1682],{},[1988,6230,5016],{},[1680,6232,6233],{},"666,67",[1528,6235,6236],{"encoding":1530},"\\Delta PR = PR^{(a)} - PR^{(b)} = 10\\,000 - 8\\,333{,}33 = \\boxed{1\\,666{,}67}",[1030,6238,6239,6242],{},[1047,6240,6241],{},"Cenová diskriminace přináší firmě o 1 666,67 vyšší zisk."," Důvod: v (a) může firma zachytit přebytek spotřebitele zvlášť na každém trhu — na elastičtějším trhu (zahraniční, sklon −0,5) dá nižší cenu, na neelastičtějším (domácí, sklon −1) vyšší. Bez diskriminace je nucena dát „kompromisní\" cenu, která je na žádném trhu optimální.",[1023,6244,6246,6253],{"className":6245,"dataCallout":582},[1026,1186],[1030,6247,6249,6252],{"className":6248},[1033],[1035,6250],{"className":6251,"ariaHidden":1041},[1038,1193,1040],"Klíčové pravidlo cenové diskriminace",[1030,6254,6255,6256,6259,6260,6287,6288,2632],{},"Při diskriminaci vyrovnává firma ",[1047,6257,6258],{},"MR"," napříč trhy (každý trh dostane své ",[1035,6261,6263],{"className":6262},[1480],[1482,6264,6265],{"xmlns":1484},[1487,6266,6267,6284],{},[1490,6268,6269,6271,6278,6280,6282],{},[1493,6270,1495],{},[1497,6272,6273,6275],{},[1493,6274,1995],{},[1493,6276,6277],{},"i",[1506,6279,1508],{},[1493,6281,1495],{},[1493,6283,1998],{},[1528,6285,6286],{"encoding":1530},"MR_i = MC","). Firma vyrovnává mezní zisk plynoucí z každého trhu, ne ceny. Cena bývá ",[1047,6289,6290],{},"vyšší tam, kde je poptávka méně elastická",[1246,6292],{},[1019,6294,6296],{"id":6295},"zadání-3","Zadání 3",[1065,6298,6300,6301,6303],{"id":6299},"z3q1-10-b-které-funkce-mohou-být-acq","Z3\u002FQ1 ",[1035,6302,1102],{}," — Které funkce mohou být AC(Q)?",[1030,6305,6306,6308],{},[1047,6307,1263],{}," (a) AC = 100\u002FQ + 0,1Q; (b) AC = 50\u002FQ − 0,1; (c) AC = −1000\u002FQ + Q; (d) AC = −1000\u002FQ − 2Q; (e) AC = 200\u002FQ + 0,5 + 0,001Q.",[1030,6310,6311,6313,6314,6317,6318,2632],{},[1047,6312,1832],{}," Průměrné náklady musí splnit ",[1047,6315,6316],{},"AC > 0 pro všechna Q > 0"," (jinak by TC = AC·Q bylo záporné, což nemá smysl). Viz ",[1052,6319,6322],{"className":6320,"dataFsResolvedFilePath":1299,"href":6321},[1055],"\u002Fwiki\u002Fprijem-naklady-zisk#Náklady firmy","sekce Náklady firmy",[1304,6324,1307],{"id":6325},"rozbor-1",[1073,6327,6328,6341],{},[1076,6329,6330],{},[1079,6331,6332,6334,6336,6339],{},[1082,6333],{},[1082,6335,1318],{},[1082,6337,6338],{},"Test",[1082,6340,1327],{},[1092,6342,6343,6357,6392,6406,6420],{},[1079,6344,6345,6347,6350,6353],{},[1097,6346,1334],{},[1097,6348,6349],{},"100\u002FQ + 0,1Q",[1097,6351,6352],{},"TC = 100 + 0,1Q² > 0; FC = 100; vždy >0 ✓",[1097,6354,6355],{},[1047,6356,1348],{},[1079,6358,6359,6361,6364,6388],{},[1097,6360,1353],{},[1097,6362,6363],{},"50\u002FQ − 0,1",[1097,6365,6366,6367,6387],{},"pro ",[1035,6368,6370],{"className":6369},[1480],[1482,6371,6372],{"xmlns":1484},[1487,6373,6374,6384],{},[1490,6375,6376,6378,6381],{},[1493,6377,1520],{},[1506,6379,6380],{},"→",[1493,6382,6383],{"mathvariant":1516},"∞",[1528,6385,6386],{"encoding":1530},"Q \\to \\infty",": AC → −0,1 \u003C 0 ✗",[1097,6389,6390],{},[1047,6391,1387],{},[1079,6393,6394,6396,6399,6402],{},[1097,6395,1370],{},[1097,6397,6398],{},"−1000\u002FQ + Q",[1097,6400,6401],{},"pro Q = 1: AC = −999 \u003C 0 ✗",[1097,6403,6404],{},[1047,6405,1387],{},[1079,6407,6408,6410,6413,6416],{},[1097,6409,1392],{},[1097,6411,6412],{},"−1000\u002FQ − 2Q",[1097,6414,6415],{},"vždy záporné ✗",[1097,6417,6418],{},[1047,6419,1387],{},[1079,6421,6422,6424,6427,6430],{},[1097,6423,1414],{},[1097,6425,6426],{},"200\u002FQ + 0,5 + 0,001Q",[1097,6428,6429],{},"TC = 200 + 0,5Q + 0,001Q² > 0; FC = 200 ✓",[1097,6431,6432],{},[1047,6433,1348],{},[1030,6435,6436,6439],{},[1047,6437,6438],{},"Numerické ověření (b):"," AC(1000) = 50\u002F1000 − 0,1 = 0,05 − 0,1 = −0,05 \u003C 0. Skutečně nesplňuje.",[1023,6441,6443,6450],{"className":6442,"dataCallout":1443},[1026,1442],[1030,6444,6446,6449],{"className":6445},[1033],[1035,6447],{"className":6448,"ariaHidden":1041},[1038,1450,1040],"Filtr",[1030,6451,6452,6453,6456],{},"Standardní AC vychází z TC = FC + aQ + bQ² + cQ³ → AC = FC\u002FQ + a + bQ + cQ². Členy s ",[1047,6454,6455],{},"kladnou"," mocninou Q i konstanta musí být nezáporné (jinak AC pro velká Q půjde do mínusu). Záporné koeficienty u −1000\u002FQ jsou červený praporek.",[1246,6458],{},[1065,6460,6462,6463,6465],{"id":6461},"z3q2-20-b-mrcslk-vlastně-mrcsqq","Z3\u002FQ2 ",[1035,6464,1116],{}," — MRCS(L,K) — vlastně MRCS(Q₁,Q₂)",[1030,6467,6468,6470],{},[1047,6469,1263],{}," Definujte mezní míru komoditní substituce MRCS a interpretujte MRCS(100,200) = 5.",[1023,6472,6474,6481],{"className":6473,"dataCallout":1155},[1026,1154],[1030,6475,6477,6480],{"className":6476},[1033],[1035,6478],{"className":6479,"ariaHidden":1041},[1038,1162,1040],"Pozor na pojmenování",[1030,6482,6483,6484,6502,6503,6506,6507,6510],{},"Symbol ",[1035,6485,6487],{"className":6486},[1480],[1482,6488,6489],{"xmlns":1484},[1487,6490,6491,6499],{},[1490,6492,6493,6495,6497],{},[1493,6494,1556],{},[1506,6496,1559],{"separator":1041},[1493,6498,1504],{},[1528,6500,6501],{"encoding":1530},"L, K"," je v zadání nezvyklý pro MRCS — typicky se MRCS používá pro ",[1047,6504,6505],{},"užitečnost"," (Q₁, Q₂), zatímco MRTS pro ",[1047,6508,6509],{},"produkci"," (L, K). Pravděpodobně jde o překlep v zadání; obsahově se ptá na MRCS(Q₁, Q₂).",[1304,6512,1476],{"id":6513},"definice-2",[1035,6515,6517],{"className":6516},[1480],[1482,6518,6519],{"xmlns":1484,"display":1485},[1487,6520,6521,6605],{},[1490,6522,6523],{},[1976,6524,6525],{"notation":1978},[1869,6526,6527],{"scriptlevel":1871,"displaystyle":1552},[1869,6528,6529],{"scriptlevel":1871,"displaystyle":1552},[1869,6530,6531],{"scriptlevel":1871,"displaystyle":1041},[1490,6532,6533,6535,6537,6539,6541,6543,6545,6567,6569,6603],{},[1988,6534,1990],{},[1493,6536,1495],{},[1493,6538,1995],{},[1493,6540,1998],{},[1493,6542,2001],{},[1506,6544,1508],{},[1510,6546,6547,6557],{},[1490,6548,6549,6551],{},[1493,6550,1495],{},[1497,6552,6553,6555],{},[1493,6554,1668],{},[1680,6556,1682],{},[1490,6558,6559,6561],{},[1493,6560,1495],{},[1497,6562,6563,6565],{},[1493,6564,1668],{},[1680,6566,1691],{},[1506,6568,1508],{},[1510,6570,6571,6587],{},[1490,6572,6573,6575,6577,6579,6581],{},[1493,6574,1517],{"mathvariant":1516},[1493,6576,1668],{},[1493,6578,1709],{"mathvariant":1516},[1493,6580,1517],{"mathvariant":1516},[1497,6582,6583,6585],{},[1493,6584,1520],{},[1680,6586,1682],{},[1490,6588,6589,6591,6593,6595,6597],{},[1493,6590,1517],{"mathvariant":1516},[1493,6592,1668],{},[1493,6594,1709],{"mathvariant":1516},[1493,6596,1517],{"mathvariant":1516},[1497,6598,6599,6601],{},[1493,6600,1520],{},[1680,6602,1691],{},[1988,6604,1990],{},[1528,6606,6607],{"encoding":1530},"\\boxed{\\; MRCS = \\frac{MU_1}{MU_2} = \\frac{\\partial U \u002F \\partial Q_1}{\\partial U \u002F \\partial Q_2} \\;}",[1030,6609,1295,6610,6616],{},[1052,6611,6615],{"className":6612,"dataFsResolvedFilePath":6613,"href":6614},[1055],"topics\u002Fuzitecnost.md","\u002Fwiki\u002Fuzitecnost","Užitečnost"," (vzorec 6.9).",[1304,6618,6620],{"id":6619},"interpretace-mrcs100200-5","Interpretace MRCS(100,200) = 5",[1030,6622,6623,6624,6662,6663,6704],{},"Na svazku ",[1035,6625,6627],{"className":6626},[1480],[1482,6628,6629],{"xmlns":1484},[1487,6630,6631,6659],{},[1490,6632,6633,6635,6641,6643,6645,6647,6653,6655,6657],{},[1506,6634,1553],{"stretchy":1552},[1497,6636,6637,6639],{},[1493,6638,1520],{},[1680,6640,1682],{},[1506,6642,1508],{},[1680,6644,2916],{},[1506,6646,1559],{"separator":1041},[1497,6648,6649,6651],{},[1493,6650,1520],{},[1680,6652,1691],{},[1506,6654,1508],{},[1680,6656,5263],{},[1506,6658,1564],{"stretchy":1552},[1528,6660,6661],{"encoding":1530},"(Q_1 = 100, Q_2 = 200)"," je spotřebitel ochoten ",[1047,6664,6665,6666,6684,6685,6703],{},"obětovat 5 jednotek ",[1035,6667,6669],{"className":6668},[1480],[1482,6670,6671],{"xmlns":1484},[1487,6672,6673,6681],{},[1490,6674,6675],{},[1497,6676,6677,6679],{},[1493,6678,1520],{},[1680,6680,1691],{},[1528,6682,6683],{"encoding":1530},"Q_2"," za získání 1 jednotky ",[1035,6686,6688],{"className":6687},[1480],[1482,6689,6690],{"xmlns":1484},[1487,6691,6692,6700],{},[1490,6693,6694],{},[1497,6695,6696,6698],{},[1493,6697,1520],{},[1680,6699,1682],{},[1528,6701,6702],{"encoding":1530},"Q_1"," navíc",", aby zachoval stejnou užitečnost (zůstal na téže indiferenční křivce).",[1030,6706,6707,6708,6711,6712,2632],{},"Geometricky: ",[1047,6709,6710],{},"sklon indiferenční křivky"," v daném bodě je ",[1035,6713,6715],{"className":6714},[1480],[1482,6716,6717],{"xmlns":1484},[1487,6718,6719,6737],{},[1490,6720,6721,6723,6725,6727,6729,6731,6733,6735],{},[1506,6722,1888],{},[1493,6724,1495],{},[1493,6726,1995],{},[1493,6728,1998],{},[1493,6730,2001],{},[1506,6732,1508],{},[1506,6734,1888],{},[1680,6736,1752],{},[1528,6738,6739],{"encoding":1530},"-MRCS = -5",[1023,6741,6743,6750],{"className":6742,"dataCallout":582},[1026,1186],[1030,6744,6746,6749],{"className":6745},[1033],[1035,6747],{"className":6748,"ariaHidden":1041},[1038,1193,1040],"Intuice",[1030,6751,6752,6753,6756],{},"MRCS odpovídá na otázku „kolik ",[1047,6754,6755],{},"vzdám"," druhého zboží za jednu jednotku prvního?\"\nVysoké MRCS = první zboží subjektivně vzácné, ochotně se zbavuju druhého za něj.\nNízké MRCS = první zboží mám už dost, druhého se zbavím nerad.",[1246,6758],{},[1065,6760,6762,6763,6765],{"id":6761},"z3q3-30-b-maximalizace-produkce-a-produktivity","Z3\u002FQ3 ",[1035,6764,1130],{}," — Maximalizace produkce a produktivity",[1030,6767,6768,1656,6770,6807,6808,6828],{},[1047,6769,1263],{},[1035,6771,6773],{"className":6772},[1480],[1482,6774,6775],{"xmlns":1484},[1487,6776,6777,6804],{},[1490,6778,6779,6781,6783,6785,6787,6793,6795,6798],{},[1493,6780,1520],{},[1506,6782,1508],{},[1506,6784,1888],{},[1680,6786,2929],{},[2315,6788,6789,6791],{},[1493,6790,1556],{},[1680,6792,3201],{},[1506,6794,2162],{},[1680,6796,6797],{},"12",[2315,6799,6800,6802],{},[1493,6801,1556],{},[1680,6803,1691],{},[1528,6805,6806],{"encoding":1530},"Q = -0{,}2 L^3 + 12 L^2",". (a) Max produktivity práce + odpovídající produkce na pracovníka. (b) Ověření principu max ",[1035,6809,6811],{"className":6810},[1480],[1482,6812,6813],{"xmlns":1484},[1487,6814,6815,6825],{},[1490,6816,6817,6819],{},[1493,6818,3633],{},[1497,6820,6821,6823],{},[1493,6822,1501],{},[1493,6824,1556],{},[1528,6826,6827],{"encoding":1530},"AP_L",". (c) Max produkce + maximum.",[1030,6830,6831,2618,6833,6837],{},[1047,6832,1832],{},[1052,6834,6836],{"className":6835,"dataFsResolvedFilePath":1572,"href":1573},[1055],"Produkce"," (sekce „Princip maximalizace průměrného produktu práce\", úloha 5.5 v knize).",[1304,6839,6841,6842,1564],{"id":6840},"a-max-produktivity-práce-aplap_l","(a) Max produktivity práce (",[1035,6843,6845],{"className":6844},[1480],[1482,6846,6847],{"xmlns":1484},[1487,6848,6849,6859],{},[1490,6850,6851,6853],{},[1493,6852,3633],{},[1497,6854,6855,6857],{},[1493,6856,1501],{},[1493,6858,1556],{},[1528,6860,6827],{"encoding":1530},[1035,6862,6864],{"className":6863},[1480],[1482,6865,6866],{"xmlns":1484,"display":1485},[1487,6867,6868,6904],{},[1490,6869,6870,6872,6878,6880,6886,6888,6890,6892,6898,6900,6902],{},[1493,6871,3633],{},[1497,6873,6874,6876],{},[1493,6875,1501],{},[1493,6877,1556],{},[1506,6879,1508],{},[1510,6881,6882,6884],{},[1493,6883,1520],{},[1493,6885,1556],{},[1506,6887,1508],{},[1506,6889,1888],{},[1680,6891,2929],{},[2315,6893,6894,6896],{},[1493,6895,1556],{},[1680,6897,1691],{},[1506,6899,2162],{},[1680,6901,6797],{},[1493,6903,1556],{},[1528,6905,6906],{"encoding":1530},"AP_L = \\frac{Q}{L} = -0{,}2 L^2 + 12 L",[1035,6908,6910],{"className":6909},[1480],[1482,6911,6912],{"xmlns":1484,"display":1485},[1487,6913,6914,6957],{},[1490,6915,6916,6918,6928,6930,6932,6934,6936,6938,6940,6942,6944,6946,6948,6950,6952,6954],{},[1493,6917,3633],{},[1697,6919,6920,6922,6924],{},[1493,6921,1501],{},[1493,6923,1556],{},[1506,6925,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},"0em","′",[1506,6929,1508],{},[1506,6931,1888],{},[1680,6933,3322],{},[1493,6935,1556],{},[1506,6937,2162],{},[1680,6939,6797],{},[1506,6941,1508],{},[1680,6943,1871],{},[1988,6945,1990],{},[1506,6947,2111],{},[1988,6949,1990],{},[1493,6951,1556],{},[1506,6953,1508],{},[1680,6955,6956],{},"30",[1528,6958,6959],{"encoding":1530},"AP_L' = -0{,}4 L + 12 = 0 \\;\\Longrightarrow\\; L = 30",[1030,6961,6962,6998],{},[1035,6963,6965],{"className":6964},[1480],[1482,6966,6967],{"xmlns":1484},[1487,6968,6969,6995],{},[1490,6970,6971,6973,6985,6987,6989,6991,6993],{},[1493,6972,3633],{},[1697,6974,6975,6977,6979],{},[1493,6976,1501],{},[1493,6978,1556],{},[1490,6980,6981,6983],{},[1506,6982,6927],{"mathvariant":1516},[1506,6984,6927],{"mathvariant":1516},[1506,6986,1508],{},[1506,6988,1888],{},[1680,6990,3322],{},[1506,6992,3961],{},[1680,6994,1871],{},[1528,6996,6997],{"encoding":1530},"AP_L'' = -0{,}4 \u003C 0"," → maximum.",[1035,7000,7002],{"className":7001},[1480],[1482,7003,7004],{"xmlns":1484,"display":1485},[1487,7005,7006,7056],{},[1490,7007,7008,7010,7016,7018,7020,7022,7024,7026,7028,7030,7033,7035,7037,7039,7041,7043,7045,7048,7050,7052,7054],{},[1493,7009,3633],{},[1497,7011,7012,7014],{},[1493,7013,1501],{},[1493,7015,1556],{},[1506,7017,1553],{"stretchy":1552},[1680,7019,6956],{},[1506,7021,1564],{"stretchy":1552},[1506,7023,1508],{},[1506,7025,1888],{},[1680,7027,2929],{},[1506,7029,1714],{},[1680,7031,7032],{},"900",[1506,7034,2162],{},[1680,7036,6797],{},[1506,7038,1714],{},[1680,7040,6956],{},[1506,7042,1508],{},[1506,7044,1888],{},[1680,7046,7047],{},"180",[1506,7049,2162],{},[1680,7051,3265],{},[1506,7053,1508],{},[1680,7055,7047],{},[1528,7057,7058],{"encoding":1530},"AP_L(30) = -0{,}2 \\cdot 900 + 12 \\cdot 30 = -180 + 360 = 180",[1035,7060,7062],{"className":7061},[1480],[1482,7063,7064],{"xmlns":1484,"display":1485},[1487,7065,7066,7147],{},[1490,7067,7068],{},[1976,7069,7070],{"notation":1978},[1869,7071,7072],{"scriptlevel":1871,"displaystyle":1552},[1869,7073,7074],{"scriptlevel":1871,"displaystyle":1552},[1869,7075,7076],{"scriptlevel":1871,"displaystyle":1041},[1490,7077,7078,7080,7082,7084,7086,7109,7111,7113,7115,7121,7123,7125,7127,7129,7131,7145],{},[1988,7079,1990],{},[1493,7081,1556],{},[1506,7083,1508],{},[1680,7085,6956],{},[1490,7087,7088,7091,7098,7101],{},[1988,7089,7090],{}," pracovn",[2178,7092,7093,7096],{"accent":1041},[1988,7094,7095],{},"ı",[1506,7097,3055],{},[1988,7099,7100],{},"k",[2178,7102,7103,7106],{"accent":1041},[1988,7104,7105],{},"u",[1506,7107,7108],{},"˚",[1506,7110,1559],{"separator":1041},[1988,7112,1990],{},[1493,7114,3633],{},[1497,7116,7117,7119],{},[1493,7118,1501],{},[1493,7120,1556],{},[1506,7122,1553],{"stretchy":1552},[1680,7124,6956],{},[1506,7126,1564],{"stretchy":1552},[1506,7128,1508],{},[1680,7130,7047],{},[1490,7132,7133,7136,7142],{},[1988,7134,7135],{}," jednotek\u002Fpracovn",[2178,7137,7138,7140],{"accent":1041},[1988,7139,7095],{},[1506,7141,3055],{},[1988,7143,7144],{},"ka",[1988,7146,1990],{},[1528,7148,7149],{"encoding":1530},"\\boxed{\\; L = 30 \\text{ pracovníků}, \\; AP_L(30) = 180 \\text{ jednotek\u002Fpracovníka} \\;}",[1304,7151,7153],{"id":7152},"b-ověření-principu-mp_l-ap_l-v-max-ap_l","(b) Ověření principu MP_L = AP_L v max AP_L",[1035,7155,7157],{"className":7156},[1480],[1482,7158,7159],{"xmlns":1484,"display":1485},[1487,7160,7161,7204],{},[1490,7162,7163,7165,7171,7173,7179,7181,7183,7185,7187,7189,7191,7197,7199,7202],{},[1493,7164,1495],{},[1497,7166,7167,7169],{},[1493,7168,1501],{},[1493,7170,1556],{},[1506,7172,1508],{},[2315,7174,7175,7177],{},[1493,7176,1520],{},[1506,7178,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,7180,1553],{"stretchy":1552},[1493,7182,1556],{},[1506,7184,1564],{"stretchy":1552},[1506,7186,1508],{},[1506,7188,1888],{},[1680,7190,3332],{},[2315,7192,7193,7195],{},[1493,7194,1556],{},[1680,7196,1691],{},[1506,7198,2162],{},[1680,7200,7201],{},"24",[1493,7203,1556],{},[1528,7205,7206],{"encoding":1530},"MP_L = Q'(L) = -0{,}6 L^2 + 24 L",[1035,7208,7210],{"className":7209},[1480],[1482,7211,7212],{"xmlns":1484,"display":1485},[1487,7213,7214,7285],{},[1490,7215,7216,7218,7224,7226,7228,7230,7232,7234,7236,7238,7240,7242,7244,7246,7248,7250,7252,7255,7257,7260,7262,7264,7266,7268,7274,7276,7278,7280,7282],{},[1493,7217,1495],{},[1497,7219,7220,7222],{},[1493,7221,1501],{},[1493,7223,1556],{},[1506,7225,1553],{"stretchy":1552},[1680,7227,6956],{},[1506,7229,1564],{"stretchy":1552},[1506,7231,1508],{},[1506,7233,1888],{},[1680,7235,3332],{},[1506,7237,1714],{},[1680,7239,7032],{},[1506,7241,2162],{},[1680,7243,7201],{},[1506,7245,1714],{},[1680,7247,6956],{},[1506,7249,1508],{},[1506,7251,1888],{},[1680,7253,7254],{},"540",[1506,7256,2162],{},[1680,7258,7259],{},"720",[1506,7261,1508],{},[1680,7263,7047],{},[1506,7265,1508],{},[1493,7267,3633],{},[1497,7269,7270,7272],{},[1493,7271,1501],{},[1493,7273,1556],{},[1506,7275,1553],{"stretchy":1552},[1680,7277,6956],{},[1506,7279,1564],{"stretchy":1552},[1988,7281,1990],{},[1493,7283,7284],{"mathvariant":1516},"✓",[1528,7286,7287],{"encoding":1530},"MP_L(30) = -0{,}6 \\cdot 900 + 24 \\cdot 30 = -540 + 720 = 180 = AP_L(30) \\;\\checkmark",[1030,7289,7290,7293],{},[1047,7291,7292],{},"Princip platí:"," v bodě maxima průměrného produktu práce se mezní produkt rovná průměrnému.",[1304,7295,7297],{"id":7296},"c-max-produkce","(c) Max produkce",[1035,7299,7301],{"className":7300},[1480],[1482,7302,7303],{"xmlns":1484,"display":1485},[1487,7304,7305,7381],{},[1490,7306,7307,7313,7315,7317,7319,7321,7323,7325,7331,7333,7335,7337,7339,7341,7343,7345,7347,7349,7351,7353,7355,7357,7359,7361,7363,7365,7367,7369,7371,7374,7376,7378],{},[2315,7308,7309,7311],{},[1493,7310,1520],{},[1506,7312,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,7314,1553],{"stretchy":1552},[1493,7316,1556],{},[1506,7318,1564],{"stretchy":1552},[1506,7320,1508],{},[1506,7322,1888],{},[1680,7324,3332],{},[2315,7326,7327,7329],{},[1493,7328,1556],{},[1680,7330,1691],{},[1506,7332,2162],{},[1680,7334,7201],{},[1493,7336,1556],{},[1506,7338,1508],{},[1493,7340,1556],{},[1506,7342,1553],{"stretchy":1552},[1506,7344,1888],{},[1680,7346,3332],{},[1493,7348,1556],{},[1506,7350,2162],{},[1680,7352,7201],{},[1506,7354,1564],{"stretchy":1552},[1506,7356,1508],{},[1680,7358,1871],{},[1988,7360,1990],{},[1506,7362,2111],{},[1988,7364,1990],{},[1493,7366,1556],{},[1506,7368,1508],{},[1680,7370,1871],{},[1988,7372,7373],{}," nebo ",[1493,7375,1556],{},[1506,7377,1508],{},[1680,7379,7380],{},"40",[1528,7382,7383],{"encoding":1530},"Q'(L) = -0{,}6 L^2 + 24 L = L(-0{,}6 L + 24) = 0 \\;\\Longrightarrow\\; L = 0 \\text{ nebo } L = 40",[1030,7385,7386,6998],{},[1035,7387,7389],{"className":7388},[1480],[1482,7390,7391],{"xmlns":1484},[1487,7392,7393,7436],{},[1490,7394,7395,7405,7407,7409,7411,7413,7415,7418,7420,7422,7424,7426,7428,7430,7432,7434],{},[2315,7396,7397,7399],{},[1493,7398,1520],{},[1490,7400,7401,7403],{},[1506,7402,6927],{"mathvariant":1516},[1506,7404,6927],{"mathvariant":1516},[1506,7406,1553],{"stretchy":1552},[1680,7408,7380],{},[1506,7410,1564],{"stretchy":1552},[1506,7412,1508],{},[1506,7414,1888],{},[1680,7416,7417],{},"1,2",[1506,7419,1714],{},[1680,7421,7380],{},[1506,7423,2162],{},[1680,7425,7201],{},[1506,7427,1508],{},[1506,7429,1888],{},[1680,7431,7201],{},[1506,7433,3961],{},[1680,7435,1871],{},[1528,7437,7438],{"encoding":1530},"Q''(40) = -1{,}2 \\cdot 40 + 24 = -24 \u003C 0",[1035,7440,7442],{"className":7441},[1480],[1482,7443,7444],{"xmlns":1484,"display":1485},[1487,7445,7446,7513],{},[1490,7447,7448,7450,7452,7454,7456,7458,7460,7462,7464,7467,7469,7471,7473,7475,7477,7479,7481,7484,7486,7488,7490,7492,7495,7497,7500,7502,7504,7506,7509,7511],{},[1493,7449,1520],{},[1506,7451,1553],{"stretchy":1552},[1680,7453,7380],{},[1506,7455,1564],{"stretchy":1552},[1506,7457,1508],{},[1506,7459,1888],{},[1680,7461,2929],{},[1506,7463,1714],{},[1680,7465,7466],{},"64",[1988,7468,5016],{},[1680,7470,5608],{},[1506,7472,2162],{},[1680,7474,6797],{},[1506,7476,1714],{},[1680,7478,1682],{},[1988,7480,5016],{},[1680,7482,7483],{},"600",[1506,7485,1508],{},[1506,7487,1888],{},[1680,7489,6797],{},[1988,7491,5016],{},[1680,7493,7494],{},"800",[1506,7496,2162],{},[1680,7498,7499],{},"19",[1988,7501,5016],{},[1680,7503,5263],{},[1506,7505,1508],{},[1680,7507,7508],{},"6",[1988,7510,5016],{},[1680,7512,5765],{},[1528,7514,7515],{"encoding":1530},"Q(40) = -0{,}2 \\cdot 64\\,000 + 12 \\cdot 1\\,600 = -12\\,800 + 19\\,200 = 6\\,400",[1035,7517,7519],{"className":7518},[1480],[1482,7520,7521],{"xmlns":1484,"display":1485},[1487,7522,7523,7588],{},[1490,7524,7525],{},[1976,7526,7527],{"notation":1978},[1869,7528,7529],{"scriptlevel":1871,"displaystyle":1552},[1869,7530,7531],{"scriptlevel":1871,"displaystyle":1552},[1869,7532,7533],{"scriptlevel":1871,"displaystyle":1041},[1490,7534,7535,7537,7539,7541,7543,7561,7563,7565,7575,7577,7579,7581,7583,7586],{},[1988,7536,1990],{},[1493,7538,1556],{},[1506,7540,1508],{},[1680,7542,7380],{},[1490,7544,7545,7547,7553,7555],{},[1988,7546,7090],{},[2178,7548,7549,7551],{"accent":1041},[1988,7550,7095],{},[1506,7552,3055],{},[1988,7554,7100],{},[2178,7556,7557,7559],{"accent":1041},[1988,7558,7105],{},[1506,7560,7108],{},[1506,7562,1559],{"separator":1041},[1988,7564,1990],{},[1497,7566,7567,7569,7572],{},[1493,7568,1520],{},[1493,7570,7571],{},"max",[1506,7573,7574],{},"⁡",[1506,7576,1508],{},[1680,7578,7508],{},[1988,7580,5016],{},[1680,7582,5765],{},[1988,7584,7585],{}," jednotek",[1988,7587,1990],{},[1528,7589,7590],{"encoding":1530},"\\boxed{\\; L = 40 \\text{ pracovníků}, \\; Q_{\\max} = 6\\,400 \\text{ jednotek} \\;}",[1023,7592,7594,7601],{"className":7593,"dataCallout":582},[1026,1186],[1030,7595,7597,7600],{"className":7596},[1033],[1035,7598],{"className":7599,"ariaHidden":1041},[1038,1193,1040],"Pozor — dvě různá maxima",[1030,7602,7603,7606,7607,7625,7626,7606,7629,7647,7648,1586,7665,7682,7683,7686,7687,7704],{},[1047,7604,7605],{},"Max produktivity"," (",[1035,7608,7610],{"className":7609},[1480],[1482,7611,7612],{"xmlns":1484},[1487,7613,7614,7622],{},[1490,7615,7616,7618,7620],{},[1493,7617,1556],{},[1506,7619,1508],{},[1680,7621,6956],{},[1528,7623,7624],{"encoding":1530},"L = 30",") ≠ ",[1047,7627,7628],{},"max produkce",[1035,7630,7632],{"className":7631},[1480],[1482,7633,7634],{"xmlns":1484},[1487,7635,7636,7644],{},[1490,7637,7638,7640,7642],{},[1493,7639,1556],{},[1506,7641,1508],{},[1680,7643,7380],{},[1528,7645,7646],{"encoding":1530},"L = 40","). Mezi ",[1035,7649,7651],{"className":7650},[1480],[1482,7652,7653],{"xmlns":1484},[1487,7654,7655,7663],{},[1490,7656,7657,7659,7661],{},[1493,7658,1556],{},[1506,7660,1508],{},[1680,7662,6956],{},[1528,7664,7624],{"encoding":1530},[1035,7666,7668],{"className":7667},[1480],[1482,7669,7670],{"xmlns":1484},[1487,7671,7672,7680],{},[1490,7673,7674,7676,7678],{},[1493,7675,1556],{},[1506,7677,1508],{},[1680,7679,7380],{},[1528,7681,7646],{"encoding":1530}," produkce stále ",[1047,7684,7685],{},"roste"," (přidávat pracovníky se vyplatí), ale klesá průměrný produkt na pracovníka (MP_L \u003C AP_L). Po ",[1035,7688,7690],{"className":7689},[1480],[1482,7691,7692],{"xmlns":1484},[1487,7693,7694,7702],{},[1490,7695,7696,7698,7700],{},[1493,7697,1556],{},[1506,7699,1508],{},[1680,7701,7380],{},[1528,7703,7646],{"encoding":1530}," je produkce na vrcholu a další pracovníci by ji už snižovali (MP_L \u003C 0).",[1246,7706],{},[1065,7708,7710,7711,7713],{"id":7709},"z3q4-40-b-is-lm-analýza","Z3\u002FQ4 ",[1035,7712,1144],{}," — IS-LM analýza",[1030,7715,7716,7718,7719,7746],{},[1047,7717,1263],{}," Y = mr + n (IS), Y = pr + q (LM); m = −50, n = 2000, p = 200, q = 1000.\n(a) Redukovaný tvar pro r. (b) Multiplikátory. (c) Vypočtěte ",[1035,7720,7722],{"className":7721},[1480],[1482,7723,7724],{"xmlns":1484},[1487,7725,7726,7743],{},[1490,7727,7728,7734,7736],{},[2315,7729,7730,7732],{},[1493,7731,1791],{},[1493,7733,2711],{},[1506,7735,1559],{"separator":1041},[2315,7737,7738,7741],{},[1493,7739,7740],{},"r",[1493,7742,2711],{},[1528,7744,7745],{"encoding":1530},"Y^E, r^E",". (d) Δr ≈ při dp = −20, dm = +10; porovnejte s přesným.",[1030,7748,7749,2618,7751,2632],{},[1047,7750,1832],{},[1052,7752,7756],{"className":7753,"dataFsResolvedFilePath":7754,"href":7755},[1055],"topics\u002Fis-lm.md","\u002Fwiki\u002Fis-lm","IS-LM analýza",[1304,7758,2636],{"id":7759},"a-redukovaný-tvar-1",[1030,7761,7762,7763,1274],{},"Z ",[1035,7764,7766],{"className":7765},[1480],[1482,7767,7768],{"xmlns":1484},[1487,7769,7770,7793],{},[1490,7771,7772,7775,7777,7779,7782,7784,7786,7788,7790],{},[1493,7773,7774],{},"m",[1493,7776,7740],{},[1506,7778,2162],{},[1493,7780,7781],{},"n",[1506,7783,1508],{},[1493,7785,1030],{},[1493,7787,7740],{},[1506,7789,2162],{},[1493,7791,7792],{},"q",[1528,7794,7795],{"encoding":1530},"mr + n = pr + q",[1035,7797,7799],{"className":7798},[1480],[1482,7800,7801],{"xmlns":1484,"display":1485},[1487,7802,7803,7845],{},[1490,7804,7805],{},[1976,7806,7807],{"notation":1978},[1869,7808,7809],{"scriptlevel":1871,"displaystyle":1552},[1869,7810,7811],{"scriptlevel":1871,"displaystyle":1552},[1869,7812,7813],{"scriptlevel":1871,"displaystyle":1041},[1490,7814,7815,7817,7823,7825,7843],{},[1988,7816,1990],{},[2315,7818,7819,7821],{},[1493,7820,7740],{},[1493,7822,2711],{},[1506,7824,1508],{},[1510,7826,7827,7835],{},[1490,7828,7829,7831,7833],{},[1493,7830,7792],{},[1506,7832,1888],{},[1493,7834,7781],{},[1490,7836,7837,7839,7841],{},[1493,7838,7774],{},[1506,7840,1888],{},[1493,7842,1030],{},[1988,7844,1990],{},[1528,7846,7847],{"encoding":1530},"\\boxed{\\; r^E = \\frac{q - n}{m - p} \\;}",[1030,7849,7850,7851,7909],{},"(Obecně: ",[1035,7852,7854],{"className":7853},[1480],[1482,7855,7856],{"xmlns":1484},[1487,7857,7858,7906],{},[1490,7859,7860,7866,7868,7870,7872,7878,7880,7882,7884],{},[2315,7861,7862,7864],{},[1493,7863,1791],{},[1493,7865,2711],{},[1506,7867,1508],{},[1493,7869,7774],{},[1506,7871,1714],{},[2315,7873,7874,7876],{},[1493,7875,7740],{},[1493,7877,2711],{},[1506,7879,2162],{},[1493,7881,7781],{},[1506,7883,1508],{},[1510,7885,7886,7898],{},[1490,7887,7888,7890,7892,7894,7896],{},[1493,7889,7774],{},[1493,7891,7792],{},[1506,7893,1888],{},[1493,7895,7781],{},[1493,7897,1030],{},[1490,7899,7900,7902,7904],{},[1493,7901,7774],{},[1506,7903,1888],{},[1493,7905,1030],{},[1528,7907,7908],{"encoding":1530},"Y^E = m \\cdot r^E + n = \\frac{mq - np}{m - p}",".)",[1304,7911,7913],{"id":7912},"b-multiplikátory-pro-r","(b) Multiplikátory pro r",[1035,7915,7917],{"className":7916},[1480],[1482,7918,7919],{"xmlns":1484,"display":1485},[1487,7920,7921,8079],{},[1490,7922,7923,7937,7939,7941,7967,7969,7971,7985,7987,7989,8001,8003,8005,8019,8021,8047,8049,8051,8065,8067],{},[1510,7924,7925,7931],{},[1490,7926,7927,7929],{},[1493,7928,1517],{"mathvariant":1516},[1493,7930,7740],{},[1490,7932,7933,7935],{},[1493,7934,1517],{"mathvariant":1516},[1493,7936,7774],{},[1506,7938,1508],{},[1506,7940,1888],{},[1510,7942,7943,7951],{},[1490,7944,7945,7947,7949],{},[1493,7946,7792],{},[1506,7948,1888],{},[1493,7950,7781],{},[1490,7952,7953,7955,7957,7959,7961],{},[1506,7954,1553],{"stretchy":1552},[1493,7956,7774],{},[1506,7958,1888],{},[1493,7960,1030],{},[2315,7962,7963,7965],{},[1506,7964,1564],{"stretchy":1552},[1680,7966,1691],{},[1506,7968,1559],{"separator":1041},[1912,7970],{"width":1914},[1510,7972,7973,7979],{},[1490,7974,7975,7977],{},[1493,7976,1517],{"mathvariant":1516},[1493,7978,7740],{},[1490,7980,7981,7983],{},[1493,7982,1517],{"mathvariant":1516},[1493,7984,7781],{},[1506,7986,1508],{},[1506,7988,1888],{},[1510,7990,7991,7993],{},[1680,7992,1682],{},[1490,7994,7995,7997,7999],{},[1493,7996,7774],{},[1506,7998,1888],{},[1493,8000,1030],{},[1506,8002,1559],{"separator":1041},[1912,8004],{"width":1914},[1510,8006,8007,8013],{},[1490,8008,8009,8011],{},[1493,8010,1517],{"mathvariant":1516},[1493,8012,7740],{},[1490,8014,8015,8017],{},[1493,8016,1517],{"mathvariant":1516},[1493,8018,1030],{},[1506,8020,1508],{},[1510,8022,8023,8031],{},[1490,8024,8025,8027,8029],{},[1493,8026,7792],{},[1506,8028,1888],{},[1493,8030,7781],{},[1490,8032,8033,8035,8037,8039,8041],{},[1506,8034,1553],{"stretchy":1552},[1493,8036,7774],{},[1506,8038,1888],{},[1493,8040,1030],{},[2315,8042,8043,8045],{},[1506,8044,1564],{"stretchy":1552},[1680,8046,1691],{},[1506,8048,1559],{"separator":1041},[1912,8050],{"width":1914},[1510,8052,8053,8059],{},[1490,8054,8055,8057],{},[1493,8056,1517],{"mathvariant":1516},[1493,8058,7740],{},[1490,8060,8061,8063],{},[1493,8062,1517],{"mathvariant":1516},[1493,8064,7792],{},[1506,8066,1508],{},[1510,8068,8069,8071],{},[1680,8070,1682],{},[1490,8072,8073,8075,8077],{},[1493,8074,7774],{},[1506,8076,1888],{},[1493,8078,1030],{},[1528,8080,8081],{"encoding":1530},"\\frac{\\partial r}{\\partial m} = -\\frac{q - n}{(m-p)^2}, \\qquad \\frac{\\partial r}{\\partial n} = -\\frac{1}{m-p}, \\qquad \\frac{\\partial r}{\\partial p} = \\frac{q - n}{(m-p)^2}, \\qquad \\frac{\\partial r}{\\partial q} = \\frac{1}{m-p}",[1304,8083,8085],{"id":8084},"c-rovnovážné-hodnoty","(c) Rovnovážné hodnoty",[1035,8087,8089],{"className":8088},[1480],[1482,8090,8091],{"xmlns":1484,"display":1485},[1487,8092,8093,8153],{},[1490,8094,8095,8101,8103,8124,8126,8141,8143],{},[2315,8096,8097,8099],{},[1493,8098,7740],{},[1493,8100,2711],{},[1506,8102,1508],{},[1510,8104,8105,8114],{},[1490,8106,8107,8109,8111],{},[1680,8108,1401],{},[1506,8110,1888],{},[1680,8112,8113],{},"2000",[1490,8115,8116,8118,8120,8122],{},[1506,8117,1888],{},[1680,8119,2292],{},[1506,8121,1888],{},[1680,8123,5263],{},[1506,8125,1508],{},[1510,8127,8128,8134],{},[1490,8129,8130,8132],{},[1506,8131,1888],{},[1680,8133,1401],{},[1490,8135,8136,8138],{},[1506,8137,1888],{},[1680,8139,8140],{},"250",[1506,8142,1508],{},[1976,8144,8145],{"notation":1978},[1869,8146,8147],{"scriptlevel":1871,"displaystyle":1552},[1869,8148,8149],{"scriptlevel":1871,"displaystyle":1552},[1869,8150,8151],{"scriptlevel":1871,"displaystyle":1041},[1680,8152,4007],{},[1528,8154,8155],{"encoding":1530},"r^E = \\frac{1000 - 2000}{-50 - 200} = \\frac{-1000}{-250} = \\boxed{4}",[1035,8157,8159],{"className":8158},[1480],[1482,8160,8161],{"xmlns":1484,"display":1485},[1487,8162,8163,8208],{},[1490,8164,8165,8171,8173,8175,8177,8179,8181,8183,8185,8187,8189,8191,8193,8195,8197],{},[2315,8166,8167,8169],{},[1493,8168,1791],{},[1493,8170,2711],{},[1506,8172,1508],{},[1506,8174,1888],{},[1680,8176,2292],{},[1506,8178,1714],{},[1680,8180,4007],{},[1506,8182,2162],{},[1680,8184,8113],{},[1506,8186,1508],{},[1506,8188,1888],{},[1680,8190,5263],{},[1506,8192,2162],{},[1680,8194,8113],{},[1506,8196,1508],{},[1976,8198,8199],{"notation":1978},[1869,8200,8201],{"scriptlevel":1871,"displaystyle":1552},[1869,8202,8203],{"scriptlevel":1871,"displaystyle":1552},[1869,8204,8205],{"scriptlevel":1871,"displaystyle":1041},[1680,8206,8207],{},"1800",[1528,8209,8210],{"encoding":1530},"Y^E = -50 \\cdot 4 + 2000 = -200 + 2000 = \\boxed{1800}",[1030,8212,8213,1656,8216,5078],{},[1047,8214,8215],{},"Kontrola přes LM:",[1035,8217,8219],{"className":8218},[1480],[1482,8220,8221],{"xmlns":1484},[1487,8222,8223,8239],{},[1490,8224,8225,8227,8229,8231,8233,8235,8237],{},[1680,8226,5263],{},[1506,8228,1714],{},[1680,8230,4007],{},[1506,8232,2162],{},[1680,8234,1401],{},[1506,8236,1508],{},[1680,8238,8207],{},[1528,8240,8241],{"encoding":1530},"200 \\cdot 4 + 1000 = 1800",[1304,8243,8245],{"id":8244},"d-změna-při-dp-20-dm-10","(d) Změna při dp = −20, dm = +10",[1030,8247,8248,1656,8251],{},[1047,8249,8250],{},"Multiplikátory v hladině (c):",[1035,8252,8254],{"className":8253},[1480],[1482,8255,8256],{"xmlns":1484},[1487,8257,8258,8297],{},[1490,8259,8260,8262,8264,8266,8268,8274,8276,8278,8280,8282,8288,8290,8293,8295],{},[1506,8261,1553],{"stretchy":1552},[1493,8263,7774],{},[1506,8265,1888],{},[1493,8267,1030],{},[2315,8269,8270,8272],{},[1506,8271,1564],{"stretchy":1552},[1680,8273,1691],{},[1506,8275,1508],{},[1506,8277,1553],{"stretchy":1552},[1506,8279,1888],{},[1680,8281,8140],{},[2315,8283,8284,8286],{},[1506,8285,1564],{"stretchy":1552},[1680,8287,1691],{},[1506,8289,1508],{},[1680,8291,8292],{},"62",[1988,8294,5016],{},[1680,8296,1796],{},[1528,8298,8299],{"encoding":1530},"(m - p)^2 = (-250)^2 = 62\\,500",[1035,8301,8303],{"className":8302},[1480],[1482,8304,8305],{"xmlns":1484,"display":1485},[1487,8306,8307,8390],{},[1490,8308,8309,8323,8325,8327,8343,8345,8348,8350,8352,8366,8368,8384,8386,8388],{},[1510,8310,8311,8317],{},[1490,8312,8313,8315],{},[1493,8314,1517],{"mathvariant":1516},[1493,8316,7740],{},[1490,8318,8319,8321],{},[1493,8320,1517],{"mathvariant":1516},[1493,8322,7774],{},[1506,8324,1508],{},[1506,8326,1888],{},[1510,8328,8329,8335],{},[1490,8330,8331,8333],{},[1506,8332,1888],{},[1680,8334,1401],{},[1490,8336,8337,8339,8341],{},[1680,8338,8292],{},[1988,8340,5016],{},[1680,8342,1796],{},[1506,8344,1508],{},[1680,8346,8347],{},"0,016",[1506,8349,1559],{"separator":1041},[1912,8351],{"width":1914},[1510,8353,8354,8360],{},[1490,8355,8356,8358],{},[1493,8357,1517],{"mathvariant":1516},[1493,8359,7740],{},[1490,8361,8362,8364],{},[1493,8363,1517],{"mathvariant":1516},[1493,8365,1030],{},[1506,8367,1508],{},[1510,8369,8370,8376],{},[1490,8371,8372,8374],{},[1506,8373,1888],{},[1680,8375,1401],{},[1490,8377,8378,8380,8382],{},[1680,8379,8292],{},[1988,8381,5016],{},[1680,8383,1796],{},[1506,8385,1508],{},[1506,8387,1888],{},[1680,8389,8347],{},[1528,8391,8392],{"encoding":1530},"\\frac{\\partial r}{\\partial m} = -\\frac{-1000}{62\\,500} = 0{,}016, \\qquad \\frac{\\partial r}{\\partial p} = \\frac{-1000}{62\\,500} = -0{,}016",[1030,8394,8395],{},[1047,8396,3134],{},[1035,8398,8400],{"className":8399},[1480],[1482,8401,8402],{"xmlns":1484,"display":1485},[1487,8403,8404,8462],{},[1490,8405,8406,8408,8410,8412,8414,8416,8418,8420,8422,8424,8426,8428,8430,8432,8434,8437,8439,8441,8444,8446,8449,8451],{},[1493,8407,2976],{"mathvariant":1516},[1493,8409,7740],{},[1506,8411,2343],{},[1680,8413,8347],{},[1506,8415,1714],{},[1680,8417,1775],{},[1506,8419,2162],{},[1506,8421,1553],{"stretchy":1552},[1506,8423,1888],{},[1680,8425,8347],{},[1506,8427,1564],{"stretchy":1552},[1506,8429,1714],{},[1506,8431,1553],{"stretchy":1552},[1506,8433,1888],{},[1680,8435,8436],{},"20",[1506,8438,1564],{"stretchy":1552},[1506,8440,1508],{},[1680,8442,8443],{},"0,16",[1506,8445,2162],{},[1680,8447,8448],{},"0,32",[1506,8450,1508],{},[1976,8452,8453],{"notation":1978},[1869,8454,8455],{"scriptlevel":1871,"displaystyle":1552},[1869,8456,8457],{"scriptlevel":1871,"displaystyle":1552},[1869,8458,8459],{"scriptlevel":1871,"displaystyle":1041},[1680,8460,8461],{},"0,48",[1528,8463,8464],{"encoding":1530},"\\Delta r \\approx 0{,}016 \\cdot 10 + (-0{,}016) \\cdot (-20) = 0{,}16 + 0{,}32 = \\boxed{0{,}48}",[1030,8466,8467,8469],{},[1047,8468,3273],{}," (m₁ = −40, p₁ = 180):",[1035,8471,8473],{"className":8472},[1480],[1482,8474,8475],{"xmlns":1484,"display":1485},[1487,8476,8477,8548],{},[1490,8478,8479,8495,8497,8517,8519,8534,8536,8543,8545],{},[1697,8480,8481,8483,8493],{},[1493,8482,7740],{},[1490,8484,8485,8487],{},[1988,8486,3047],{},[2178,8488,8489,8491],{"accent":1041},[1988,8490,3052],{},[1506,8492,3055],{},[1493,8494,2711],{},[1506,8496,1508],{},[1510,8498,8499,8507],{},[1490,8500,8501,8503,8505],{},[1680,8502,1401],{},[1506,8504,1888],{},[1680,8506,8113],{},[1490,8508,8509,8511,8513,8515],{},[1506,8510,1888],{},[1680,8512,7380],{},[1506,8514,1888],{},[1680,8516,7047],{},[1506,8518,1508],{},[1510,8520,8521,8527],{},[1490,8522,8523,8525],{},[1506,8524,1888],{},[1680,8526,1401],{},[1490,8528,8529,8531],{},[1506,8530,1888],{},[1680,8532,8533],{},"220",[1506,8535,1508],{},[1510,8537,8538,8540],{},[1680,8539,2292],{},[1680,8541,8542],{},"11",[1506,8544,2343],{},[1680,8546,8547],{},"4,5455",[1528,8549,8550],{"encoding":1530},"r^E_{\\text{nový}} = \\frac{1000 - 2000}{-40 - 180} = \\frac{-1000}{-220} = \\frac{50}{11} \\approx 4{,}5455",[1035,8552,8554],{"className":8553},[1480],[1482,8555,8556],{"xmlns":1484,"display":1485},[1487,8557,8558,8600],{},[1490,8559,8560,8562,8587,8589,8591,8593,8595,8597],{},[1493,8561,2976],{"mathvariant":1516},[1497,8563,8564,8566],{},[1493,8565,7740],{},[1490,8567,8568,8570,8577,8580],{},[1988,8569,1030],{},[2178,8571,8572,8574],{"accent":1041},[1988,8573,7740],{},[1506,8575,8576],{},"ˇ",[1988,8578,8579],{},"esn",[2178,8581,8582,8585],{"accent":1041},[1988,8583,8584],{},"e",[1506,8586,3055],{},[1506,8588,1508],{},[1680,8590,8547],{},[1506,8592,1888],{},[1680,8594,4007],{},[1506,8596,1508],{},[1680,8598,8599],{},"0,5455",[1528,8601,8602],{"encoding":1530},"\\Delta r_{\\text{přesné}} = 4{,}5455 - 4 = 0{,}5455",[1030,8604,8605,8608,8609,8636,8637,8663],{},[1047,8606,8607],{},"Porovnání:"," aproximace 0,48 vs. přesných 0,5455 → chyba ~12 %. Důvod: změny dp = −20 a dm = +10 jsou poměrně malé proti ",[1035,8610,8612],{"className":8611},[1480],[1482,8613,8614],{"xmlns":1484},[1487,8615,8616,8633],{},[1490,8617,8618,8621,8623,8625,8627,8629,8631],{},[1493,8619,8620],{"mathvariant":1516},"∣",[1493,8622,7774],{},[1506,8624,1888],{},[1493,8626,1030],{},[1493,8628,8620],{"mathvariant":1516},[1506,8630,1508],{},[1680,8632,8140],{},[1528,8634,8635],{"encoding":1530},"|m - p| = 250"," (cca 4–8 %), ale druhá derivace přes ",[1035,8638,8640],{"className":8639},[1480],[1482,8641,8642],{"xmlns":1484},[1487,8643,8644,8660],{},[1490,8645,8646,8648,8650,8652,8654],{},[1506,8647,1553],{"stretchy":1552},[1493,8649,7774],{},[1506,8651,1888],{},[1493,8653,1030],{},[2315,8655,8656,8658],{},[1506,8657,1564],{"stretchy":1552},[1680,8659,1691],{},[1528,8661,8662],{"encoding":1530},"(m-p)^2"," stále působí. Pro čistě informativní odhad směru a řádu změny je aproximace dobrá.",[1246,8665],{},[1019,8667,8669],{"id":8668},"zadání-4","Zadání 4",[1065,8671,8673,8674,8676],{"id":8672},"z4q1-10-b-páry-funkcí-poptávky-ve-dvoukomoditním-trhu","Z4\u002FQ1 ",[1035,8675,1102],{}," — Páry funkcí poptávky ve dvoukomoditním trhu",[1030,8678,8679,8681],{},[1047,8680,1263],{}," Pro 5 dvojic funkcí (Q₁, Q₂) rozhodněte, zda jde o poptávku, a v kladném případě určete typ vztahu (substituty\u002Fkomplementy).",[1030,8683,8684,8686,8687,8742],{},[1047,8685,1832],{}," Pro ",[1035,8688,8690],{"className":8689},[1480],[1482,8691,8692],{"xmlns":1484},[1487,8693,8694,8739],{},[1490,8695,8696,8702,8704,8710,8712,8718,8724,8726,8733],{},[1497,8697,8698,8700],{},[1493,8699,1520],{},[1493,8701,6277],{},[1506,8703,1508],{},[1497,8705,8706,8708],{},[1493,8707,1052],{},[1493,8709,6277],{},[1506,8711,2162],{},[1497,8713,8714,8716],{},[1493,8715,2394],{},[1493,8717,6277],{},[1497,8719,8720,8722],{},[1493,8721,1501],{},[1680,8723,1682],{},[1506,8725,2162],{},[1497,8727,8728,8731],{},[1493,8729,8730],{},"c",[1493,8732,6277],{},[1497,8734,8735,8737],{},[1493,8736,1501],{},[1680,8738,1691],{},[1528,8740,8741],{"encoding":1530},"Q_i = a_i + b_i P_1 + c_i P_2"," musí platit:",[1203,8744,8745,8751,8757,8763],{},[1206,8746,8747,8750],{},[1047,8748,8749],{},"a₁, a₂ > 0"," (kladné množství při nulových cenách);",[1206,8752,8753,8756],{},[1047,8754,8755],{},"b₁, c₂ \u003C 0"," (vlastní cenové koeficienty — zákon klesající poptávky);",[1206,8758,8759,8762],{},[1047,8760,8761],{},"substituty:"," c₁ > 0, b₂ > 0;",[1206,8764,8765,8768],{},[1047,8766,8767],{},"komplementy:"," c₁ \u003C 0, b₂ \u003C 0.",[1030,8770,1295,8771,8776],{},[1052,8772,8775],{"className":8773,"dataFsResolvedFilePath":3487,"href":8774},[1055],"\u002Fwiki\u002Fpoptavka-nabidka#Vícekomoditní (dvoukomoditní) trh","Dvoukomoditní trh"," (vzorec 2.6).",[1304,8778,1307],{"id":8779},"rozbor-2",[1073,8781,8782,8801],{},[1076,8783,8784],{},[1079,8785,8786,8788,8790,8793,8796,8799],{},[1082,8787],{},[1082,8789,1318],{},[1082,8791,8792],{},"a₁,a₂",[1082,8794,8795],{},"b₁,c₂ (vlastní)",[1082,8797,8798],{},"c₁,b₂ (zkřížené)",[1082,8800,1327],{},[1092,8802,8803,8826,8848,8872,8892],{},[1079,8804,8805,8807,8810,8813,8816,8821],{},[1097,8806,1334],{},[1097,8808,8809],{},"Q₁ = 10 − 2P₁ + P₂; Q₂ = 5 + 2P₁ − 2P₂",[1097,8811,8812],{},"10, 5 ✓",[1097,8814,8815],{},"−2, −2 ✓",[1097,8817,8818,8819],{},"+1, +2 → ",[1047,8820,3899],{},[1097,8822,8823],{},[1047,8824,8825],{},"ANO – substituty",[1079,8827,8828,8830,8833,8836,8842,8844],{},[1097,8829,1353],{},[1097,8831,8832],{},"Q₁ = 3 − P₁ − P₂; Q₂ = 4 + P₁ + P₂",[1097,8834,8835],{},"3, 4 ✓",[1097,8837,8838,8839,1402],{},"−1, ",[1047,8840,8841],{},"+1",[1097,8843,1405],{},[1097,8845,8846],{},[1047,8847,1387],{},[1079,8849,8850,8852,8855,8858,8861,8867],{},[1097,8851,1370],{},[1097,8853,8854],{},"Q₁ = 6 − P₁ − P₂; Q₂ = 7 − P₁ − P₂",[1097,8856,8857],{},"6, 7 ✓",[1097,8859,8860],{},"−1, −1 ✓",[1097,8862,8863,8864],{},"−1, −1 → ",[1047,8865,8866],{},"komplementy",[1097,8868,8869],{},[1047,8870,8871],{},"ANO – komplementy",[1079,8873,8874,8876,8879,8884,8886,8888],{},[1097,8875,1392],{},[1097,8877,8878],{},"Q₁ = −8 − P₁ + P₂; Q₂ = 2 + P₁ − P₂",[1097,8880,8881,1402],{},[1047,8882,8883],{},"−8",[1097,8885,1405],{},[1097,8887,1405],{},[1097,8889,8890],{},[1047,8891,1387],{},[1079,8893,8894,8896,8899,8902,8907,8909],{},[1097,8895,1414],{},[1097,8897,8898],{},"Q₁ = 3 + P₁ + 4P₂; Q₂ = 3 + 5P₁ + P₂",[1097,8900,8901],{},"3, 3 ✓",[1097,8903,8904,1402],{},[1047,8905,8906],{},"+1, +1",[1097,8908,1405],{},[1097,8910,8911],{},[1047,8912,1387],{},[1030,8914,8915,1656,8918,8958],{},[1047,8916,8917],{},"Zdůvodnění (b):",[1035,8919,8921],{"className":8920},[1480],[1482,8922,8923],{"xmlns":1484},[1487,8924,8925,8955],{},[1490,8926,8927,8929,8935,8937,8939,8945,8947,8949,8951,8953],{},[1493,8928,1517],{"mathvariant":1516},[1497,8930,8931,8933],{},[1493,8932,1520],{},[1680,8934,1691],{},[1493,8936,1709],{"mathvariant":1516},[1493,8938,1517],{"mathvariant":1516},[1497,8940,8941,8943],{},[1493,8942,1501],{},[1680,8944,1691],{},[1506,8946,1508],{},[1506,8948,2162],{},[1680,8950,1682],{},[1506,8952,2796],{},[1680,8954,1871],{},[1528,8956,8957],{"encoding":1530},"\\partial Q_2 \u002F \\partial P_2 = +1 > 0"," — Q₂ roste s vlastní cenou, porušuje zákon klesající poptávky.",[1030,8960,8961,8963,8964,8994,8995,9023],{},[1047,8962,1437],{}," Při ",[1035,8965,8967],{"className":8966},[1480],[1482,8968,8969],{"xmlns":1484},[1487,8970,8971,8991],{},[1490,8972,8973,8979,8981,8987,8989],{},[1497,8974,8975,8977],{},[1493,8976,1501],{},[1680,8978,1682],{},[1506,8980,1508],{},[1497,8982,8983,8985],{},[1493,8984,1501],{},[1680,8986,1691],{},[1506,8988,1508],{},[1680,8990,1871],{},[1528,8992,8993],{"encoding":1530},"P_1 = P_2 = 0"," je ",[1035,8996,8998],{"className":8997},[1480],[1482,8999,9000],{"xmlns":1484},[1487,9001,9002,9020],{},[1490,9003,9004,9010,9012,9014,9016,9018],{},[1497,9005,9006,9008],{},[1493,9007,1520],{},[1680,9009,1682],{},[1506,9011,1508],{},[1506,9013,1888],{},[1680,9015,6138],{},[1506,9017,3961],{},[1680,9019,1871],{},[1528,9021,9022],{"encoding":1530},"Q_1 = -8 \u003C 0"," — záporné množství.",[1030,9025,9026,9029],{},[1047,9027,9028],{},"Zdůvodnění (e):"," Obě vlastní cenové derivace jsou kladné (Q₁ roste s P₁, Q₂ s P₂) — obě porušují zákon klesající poptávky.",[1246,9031],{},[1065,9033,9035,9036,9038],{"id":9034},"z4q2-20-b-mrcs-interpretace","Z4\u002FQ2 ",[1035,9037,1116],{}," — MRCS interpretace",[1030,9040,9041,9044,9045,9085,9086,9103,9104,9121],{},[1047,9042,9043],{},"Zadání identické s Z3\u002FQ2"," — viz výše. Definice ",[1035,9046,9048],{"className":9047},[1480],[1482,9049,9050],{"xmlns":1484},[1487,9051,9052,9082],{},[1490,9053,9054,9056,9058,9060,9062,9064,9066,9072,9074,9076],{},[1493,9055,1495],{},[1493,9057,1995],{},[1493,9059,1998],{},[1493,9061,2001],{},[1506,9063,1508],{},[1493,9065,1495],{},[1497,9067,9068,9070],{},[1493,9069,1668],{},[1680,9071,1682],{},[1493,9073,1709],{"mathvariant":1516},[1493,9075,1495],{},[1497,9077,9078,9080],{},[1493,9079,1668],{},[1680,9081,1691],{},[1528,9083,9084],{"encoding":1530},"MRCS = MU_1\u002FMU_2",", interpretace MRCS(100,200) = 5: spotřebitel ochotně obětuje 5 jednotek ",[1035,9087,9089],{"className":9088},[1480],[1482,9090,9091],{"xmlns":1484},[1487,9092,9093,9101],{},[1490,9094,9095],{},[1497,9096,9097,9099],{},[1493,9098,1520],{},[1680,9100,1691],{},[1528,9102,6683],{"encoding":1530}," za 1 jednotku ",[1035,9105,9107],{"className":9106},[1480],[1482,9108,9109],{"xmlns":1484},[1487,9110,9111,9119],{},[1490,9112,9113],{},[1497,9114,9115,9117],{},[1493,9116,1520],{},[1680,9118,1682],{},[1528,9120,6702],{"encoding":1530}," navíc při zachované užitečnosti.",[1246,9123],{},[1065,9125,9127,9128,9130],{"id":9126},"z4q3-30-b-firma-s-dvěma-zbožími-v-dokonalé-konkurenci","Z4\u002FQ3 ",[1035,9129,1130],{}," — Firma s dvěma zbožími v dokonalé konkurenci",[1030,9132,9133,1656,9135,9189,9190,9220,9221,9283,9284,9323],{},[1047,9134,1263],{},[1035,9136,9138],{"className":9137},[1480],[1482,9139,9140],{"xmlns":1484},[1487,9141,9142,9186],{},[1490,9143,9144,9146,9148,9150,9152,9160,9162,9168,9174,9176,9178],{},[1493,9145,5289],{},[1493,9147,1998],{},[1506,9149,1508],{},[1680,9151,1691],{},[1697,9153,9154,9156,9158],{},[1493,9155,1520],{},[1680,9157,1682],{},[1680,9159,1691],{},[1506,9161,2162],{},[1497,9163,9164,9166],{},[1493,9165,1520],{},[1680,9167,1682],{},[1497,9169,9170,9172],{},[1493,9171,1520],{},[1680,9173,1691],{},[1506,9175,2162],{},[1680,9177,1691],{},[1697,9179,9180,9182,9184],{},[1493,9181,1520],{},[1680,9183,1691],{},[1680,9185,1691],{},[1528,9187,9188],{"encoding":1530},"TC = 2 Q_1^2 + Q_1 Q_2 + 2 Q_2^2","; ceny ",[1035,9191,9193],{"className":9192},[1480],[1482,9194,9195],{"xmlns":1484},[1487,9196,9197,9217],{},[1490,9198,9199,9207,9209],{},[1697,9200,9201,9203,9205],{},[1493,9202,1501],{},[1680,9204,1682],{},[1506,9206,2287],{},[1506,9208,1559],{"separator":1041},[1697,9210,9211,9213,9215],{},[1493,9212,1501],{},[1680,9214,1691],{},[1506,9216,2287],{},[1528,9218,9219],{"encoding":1530},"P_1^*, P_2^*"," pevně dány. (a) Funkce ",[1035,9222,9224],{"className":9223},[1480],[1482,9225,9226],{"xmlns":1484},[1487,9227,9228,9280],{},[1490,9229,9230,9236,9238,9244,9246,9252,9254,9256,9262,9264,9270,9272,9278],{},[1497,9231,9232,9234],{},[1493,9233,1520],{},[1680,9235,1682],{},[1506,9237,1553],{"stretchy":1552},[1497,9239,9240,9242],{},[1493,9241,1501],{},[1680,9243,1682],{},[1506,9245,1559],{"separator":1041},[1497,9247,9248,9250],{},[1493,9249,1501],{},[1680,9251,1691],{},[1506,9253,1564],{"stretchy":1552},[1506,9255,1559],{"separator":1041},[1497,9257,9258,9260],{},[1493,9259,1520],{},[1680,9261,1691],{},[1506,9263,1553],{"stretchy":1552},[1497,9265,9266,9268],{},[1493,9267,1501],{},[1680,9269,1682],{},[1506,9271,1559],{"separator":1041},[1497,9273,9274,9276],{},[1493,9275,1501],{},[1680,9277,1691],{},[1506,9279,1564],{"stretchy":1552},[1528,9281,9282],{"encoding":1530},"Q_1(P_1, P_2), Q_2(P_1, P_2)"," pro max zisk. (b) Pro ",[1035,9285,9287],{"className":9286},[1480],[1482,9288,9289],{"xmlns":1484},[1487,9290,9291,9320],{},[1490,9292,9293,9301,9303,9305,9307,9315,9317],{},[1697,9294,9295,9297,9299],{},[1493,9296,1501],{},[1680,9298,1682],{},[1506,9300,2287],{},[1506,9302,1508],{},[1680,9304,6797],{},[1506,9306,1559],{"separator":1041},[1697,9308,9309,9311,9313],{},[1493,9310,1501],{},[1680,9312,1691],{},[1506,9314,2287],{},[1506,9316,1508],{},[1680,9318,9319],{},"18",[1528,9321,9322],{"encoding":1530},"P_1^* = 12, P_2^* = 18"," vypočtěte zisk.",[1030,9325,9326,9328,9329,9373,9374,9402,9403,1732,9435,4212,9467,1586,9473,2632],{},[1047,9327,1832],{}," V dokonalé konkurenci ",[1035,9330,9332],{"className":9331},[1480],[1482,9333,9334],{"xmlns":1484},[1487,9335,9336,9370],{},[1490,9337,9338,9340,9342,9344,9350,9356,9358,9364],{},[1493,9339,5289],{},[1493,9341,1995],{},[1506,9343,1508],{},[1497,9345,9346,9348],{},[1493,9347,1501],{},[1680,9349,1682],{},[1497,9351,9352,9354],{},[1493,9353,1520],{},[1680,9355,1682],{},[1506,9357,2162],{},[1497,9359,9360,9362],{},[1493,9361,1501],{},[1680,9363,1691],{},[1497,9365,9366,9368],{},[1493,9367,1520],{},[1680,9369,1691],{},[1528,9371,9372],{"encoding":1530},"TR = P_1 Q_1 + P_2 Q_2",". Maximalizace zisku ",[1035,9375,9377],{"className":9376},[1480],[1482,9378,9379],{"xmlns":1484},[1487,9380,9381,9399],{},[1490,9382,9383,9385,9387,9389,9391,9393,9395,9397],{},[1493,9384,1501],{},[1493,9386,1995],{},[1506,9388,1508],{},[1493,9390,5289],{},[1493,9392,1995],{},[1506,9394,1888],{},[1493,9396,5289],{},[1493,9398,1998],{},[1528,9400,9401],{"encoding":1530},"PR = TR - TC"," přes obě množství: nutné podmínky ",[1035,9404,9406],{"className":9405},[1480],[1482,9407,9408],{"xmlns":1484},[1487,9409,9410,9432],{},[1490,9411,9412,9414,9416,9418,9420,9422,9428,9430],{},[1493,9413,1517],{"mathvariant":1516},[1493,9415,1501],{},[1493,9417,1995],{},[1493,9419,1709],{"mathvariant":1516},[1493,9421,1517],{"mathvariant":1516},[1497,9423,9424,9426],{},[1493,9425,1520],{},[1680,9427,1682],{},[1506,9429,1508],{},[1680,9431,1871],{},[1528,9433,9434],{"encoding":1530},"\\partial PR \u002F \\partial Q_1 = 0",[1035,9436,9438],{"className":9437},[1480],[1482,9439,9440],{"xmlns":1484},[1487,9441,9442,9464],{},[1490,9443,9444,9446,9448,9450,9452,9454,9460,9462],{},[1493,9445,1517],{"mathvariant":1516},[1493,9447,1501],{},[1493,9449,1995],{},[1493,9451,1709],{"mathvariant":1516},[1493,9453,1517],{"mathvariant":1516},[1497,9455,9456,9458],{},[1493,9457,1520],{},[1680,9459,1691],{},[1506,9461,1508],{},[1680,9463,1871],{},[1528,9465,9466],{"encoding":1530},"\\partial PR \u002F \\partial Q_2 = 0",[1052,9468,9472],{"className":9469,"dataFsResolvedFilePath":9470,"href":9471},[1055],"topics\u002Ffunkce-vice-promennych.md","\u002Fwiki\u002Ffunkce-vice-promennych","Funkce více proměnných",[1052,9474,820],{"className":9475,"dataFsResolvedFilePath":1299,"href":1300},[1055],[1304,9477,9479],{"id":9478},"a-optimální-množství","(a) Optimální množství",[1035,9481,9483],{"className":9482},[1480],[1482,9484,9485],{"xmlns":1484,"display":1485},[1487,9486,9487,9563],{},[1490,9488,9489,9491,9493,9495,9501,9507,9509,9515,9521,9523,9525,9527,9535,9537,9543,9549,9551,9553,9561],{},[1493,9490,1501],{},[1493,9492,1995],{},[1506,9494,1508],{},[1497,9496,9497,9499],{},[1493,9498,1501],{},[1680,9500,1682],{},[1497,9502,9503,9505],{},[1493,9504,1520],{},[1680,9506,1682],{},[1506,9508,2162],{},[1497,9510,9511,9513],{},[1493,9512,1501],{},[1680,9514,1691],{},[1497,9516,9517,9519],{},[1493,9518,1520],{},[1680,9520,1691],{},[1506,9522,1888],{},[1506,9524,1553],{"stretchy":1552},[1680,9526,1691],{},[1697,9528,9529,9531,9533],{},[1493,9530,1520],{},[1680,9532,1682],{},[1680,9534,1691],{},[1506,9536,2162],{},[1497,9538,9539,9541],{},[1493,9540,1520],{},[1680,9542,1682],{},[1497,9544,9545,9547],{},[1493,9546,1520],{},[1680,9548,1691],{},[1506,9550,2162],{},[1680,9552,1691],{},[1697,9554,9555,9557,9559],{},[1493,9556,1520],{},[1680,9558,1691],{},[1680,9560,1691],{},[1506,9562,1564],{"stretchy":1552},[1528,9564,9565],{"encoding":1530},"PR = P_1 Q_1 + P_2 Q_2 - (2 Q_1^2 + Q_1 Q_2 + 2 Q_2^2)",[1030,9567,9568],{},[1047,9569,9570],{},"Nutné podmínky:",[1035,9572,9574],{"className":9573},[1480],[1482,9575,9576],{"xmlns":1484,"display":1485},[1487,9577,9578,9660],{},[1490,9579,9580,9600,9602,9608,9610,9612,9618,9620,9626,9628,9630,9632,9634,9636,9638,9644,9646,9652,9654],{},[1510,9581,9582,9590],{},[1490,9583,9584,9586,9588],{},[1493,9585,1517],{"mathvariant":1516},[1493,9587,1501],{},[1493,9589,1995],{},[1490,9591,9592,9594],{},[1493,9593,1517],{"mathvariant":1516},[1497,9595,9596,9598],{},[1493,9597,1520],{},[1680,9599,1682],{},[1506,9601,1508],{},[1497,9603,9604,9606],{},[1493,9605,1501],{},[1680,9607,1682],{},[1506,9609,1888],{},[1680,9611,4007],{},[1497,9613,9614,9616],{},[1493,9615,1520],{},[1680,9617,1682],{},[1506,9619,1888],{},[1497,9621,9622,9624],{},[1493,9623,1520],{},[1680,9625,1691],{},[1506,9627,1508],{},[1680,9629,1871],{},[1988,9631,1990],{},[1506,9633,2111],{},[1988,9635,1990],{},[1680,9637,4007],{},[1497,9639,9640,9642],{},[1493,9641,1520],{},[1680,9643,1682],{},[1506,9645,2162],{},[1497,9647,9648,9650],{},[1493,9649,1520],{},[1680,9651,1691],{},[1506,9653,1508],{},[1497,9655,9656,9658],{},[1493,9657,1501],{},[1680,9659,1682],{},[1528,9661,9662],{"encoding":1530},"\\frac{\\partial PR}{\\partial Q_1} = P_1 - 4 Q_1 - Q_2 = 0 \\;\\Longrightarrow\\; 4 Q_1 + Q_2 = P_1",[1035,9664,9666],{"className":9665},[1480],[1482,9667,9668],{"xmlns":1484,"display":1485},[1487,9669,9670,9752],{},[1490,9671,9672,9692,9694,9700,9702,9708,9710,9712,9718,9720,9722,9724,9726,9728,9734,9736,9738,9744,9746],{},[1510,9673,9674,9682],{},[1490,9675,9676,9678,9680],{},[1493,9677,1517],{"mathvariant":1516},[1493,9679,1501],{},[1493,9681,1995],{},[1490,9683,9684,9686],{},[1493,9685,1517],{"mathvariant":1516},[1497,9687,9688,9690],{},[1493,9689,1520],{},[1680,9691,1691],{},[1506,9693,1508],{},[1497,9695,9696,9698],{},[1493,9697,1501],{},[1680,9699,1691],{},[1506,9701,1888],{},[1497,9703,9704,9706],{},[1493,9705,1520],{},[1680,9707,1682],{},[1506,9709,1888],{},[1680,9711,4007],{},[1497,9713,9714,9716],{},[1493,9715,1520],{},[1680,9717,1691],{},[1506,9719,1508],{},[1680,9721,1871],{},[1988,9723,1990],{},[1506,9725,2111],{},[1988,9727,1990],{},[1497,9729,9730,9732],{},[1493,9731,1520],{},[1680,9733,1682],{},[1506,9735,2162],{},[1680,9737,4007],{},[1497,9739,9740,9742],{},[1493,9741,1520],{},[1680,9743,1691],{},[1506,9745,1508],{},[1497,9747,9748,9750],{},[1493,9749,1501],{},[1680,9751,1691],{},[1528,9753,9754],{"encoding":1530},"\\frac{\\partial PR}{\\partial Q_2} = P_2 - Q_1 - 4 Q_2 = 0 \\;\\Longrightarrow\\; Q_1 + 4 Q_2 = P_2",[1030,9756,9757,1656,9760],{},[1047,9758,9759],{},"Determinant soustavy:",[1035,9761,9763],{"className":9762},[1480],[1482,9764,9765],{"xmlns":1484},[1487,9766,9767,9788],{},[1490,9768,9769,9771,9773,9775,9777,9779,9781,9783,9785],{},[1680,9770,4007],{},[1506,9772,1714],{},[1680,9774,4007],{},[1506,9776,1888],{},[1680,9778,1682],{},[1506,9780,1714],{},[1680,9782,1682],{},[1506,9784,1508],{},[1680,9786,9787],{},"15",[1528,9789,9790],{"encoding":1530},"4 \\cdot 4 - 1 \\cdot 1 = 15",[1035,9792,9794],{"className":9793},[1480],[1482,9795,9796],{"xmlns":1484,"display":1485},[1487,9797,9798,9878],{},[1490,9799,9800],{},[1976,9801,9802],{"notation":1978},[1869,9803,9804],{"scriptlevel":1871,"displaystyle":1552},[1869,9805,9806],{"scriptlevel":1871,"displaystyle":1552},[1869,9807,9808],{"scriptlevel":1871,"displaystyle":1041},[1490,9809,9810,9812,9818,9820,9842,9844,9846,9852,9854,9876],{},[1988,9811,1990],{},[1497,9813,9814,9816],{},[1493,9815,1520],{},[1680,9817,1682],{},[1506,9819,1508],{},[1510,9821,9822,9840],{},[1490,9823,9824,9826,9832,9834],{},[1680,9825,4007],{},[1497,9827,9828,9830],{},[1493,9829,1501],{},[1680,9831,1682],{},[1506,9833,1888],{},[1497,9835,9836,9838],{},[1493,9837,1501],{},[1680,9839,1691],{},[1680,9841,9787],{},[1506,9843,1559],{"separator":1041},[1912,9845],{"width":1914},[1497,9847,9848,9850],{},[1493,9849,1520],{},[1680,9851,1691],{},[1506,9853,1508],{},[1510,9855,9856,9874],{},[1490,9857,9858,9860,9866,9868],{},[1680,9859,4007],{},[1497,9861,9862,9864],{},[1493,9863,1501],{},[1680,9865,1691],{},[1506,9867,1888],{},[1497,9869,9870,9872],{},[1493,9871,1501],{},[1680,9873,1682],{},[1680,9875,9787],{},[1988,9877,1990],{},[1528,9879,9880],{"encoding":1530},"\\boxed{\\; Q_1 = \\frac{4 P_1 - P_2}{15}, \\qquad Q_2 = \\frac{4 P_2 - P_1}{15} \\;}",[1030,9882,9883,9886],{},[1047,9884,9885],{},"Postačující podmínky"," (Hessián):",[1035,9888,9890],{"className":9889},[1480],[1482,9891,9892],{"xmlns":1484,"display":1485},[1487,9893,9894,9983],{},[1490,9895,9896,9903,9905,9907,9909,9911,9913,9915,9917,9924,9926,9928,9930,9932,9934,9940,9942,9944,9946,9948,9950,9953,9955,9957,9959,9962,9964,9966,9968,9970,9972,9974,9976,9978,9980],{},[1497,9897,9898,9901],{},[1493,9899,9900],{},"H",[1680,9902,8542],{},[1506,9904,1508],{},[1506,9906,1888],{},[1680,9908,4007],{},[1506,9910,3961],{},[1680,9912,1871],{},[1506,9914,1559],{"separator":1041},[1912,9916],{"width":2108},[1497,9918,9919,9921],{},[1493,9920,9900],{},[1680,9922,9923],{},"22",[1506,9925,1508],{},[1506,9927,1888],{},[1680,9929,4007],{},[1506,9931,1559],{"separator":1041},[1912,9933],{"width":2108},[1497,9935,9936,9938],{},[1493,9937,9900],{},[1680,9939,6797],{},[1506,9941,1508],{},[1506,9943,1888],{},[1680,9945,1682],{},[1506,9947,1559],{"separator":1041},[1912,9949],{"width":2108},[1493,9951,9952],{},"det",[1506,9954,7574],{},[1493,9956,9900],{},[1506,9958,1508],{},[1680,9960,9961],{},"16",[1506,9963,1888],{},[1680,9965,1682],{},[1506,9967,1508],{},[1680,9969,9787],{},[1506,9971,2796],{},[1680,9973,1871],{},[1988,9975,1990],{},[1506,9977,2111],{},[1988,9979,1990],{},[1988,9981,9982],{},"maximum",[1528,9984,9985],{"encoding":1530},"H_{11} = -4 \u003C 0, \\quad H_{22} = -4, \\quad H_{12} = -1, \\quad \\det H = 16 - 1 = 15 > 0 \\;\\Longrightarrow\\; \\text{maximum}",[1304,9987,9989,9990],{"id":9988},"b-pro-p112p218p_1-12-p_2-18","(b) Pro ",[1035,9991,9993],{"className":9992},[1480],[1482,9994,9995],{"xmlns":1484},[1487,9996,9997,10025],{},[1490,9998,9999,10007,10009,10011,10013,10021,10023],{},[1697,10000,10001,10003,10005],{},[1493,10002,1501],{},[1680,10004,1682],{},[1506,10006,2287],{},[1506,10008,1508],{},[1680,10010,6797],{},[1506,10012,1559],{"separator":1041},[1697,10014,10015,10017,10019],{},[1493,10016,1501],{},[1680,10018,1691],{},[1506,10020,2287],{},[1506,10022,1508],{},[1680,10024,9319],{},[1528,10026,9322],{"encoding":1530},[1035,10028,10030],{"className":10029},[1480],[1482,10031,10032],{"xmlns":1484,"display":1485},[1487,10033,10034,10110],{},[1490,10035,10036,10044,10046,10059,10061,10067,10069,10071,10073,10075,10083,10085,10098,10100,10106,10108],{},[1697,10037,10038,10040,10042],{},[1493,10039,1520],{},[1680,10041,1682],{},[1506,10043,2287],{},[1506,10045,1508],{},[1510,10047,10048,10057],{},[1490,10049,10050,10053,10055],{},[1680,10051,10052],{},"48",[1506,10054,1888],{},[1680,10056,9319],{},[1680,10058,9787],{},[1506,10060,1508],{},[1510,10062,10063,10065],{},[1680,10064,6956],{},[1680,10066,9787],{},[1506,10068,1508],{},[1680,10070,1691],{},[1506,10072,1559],{"separator":1041},[1912,10074],{"width":1914},[1697,10076,10077,10079,10081],{},[1493,10078,1520],{},[1680,10080,1691],{},[1506,10082,2287],{},[1506,10084,1508],{},[1510,10086,10087,10096],{},[1490,10088,10089,10092,10094],{},[1680,10090,10091],{},"72",[1506,10093,1888],{},[1680,10095,6797],{},[1680,10097,9787],{},[1506,10099,1508],{},[1510,10101,10102,10104],{},[1680,10103,4965],{},[1680,10105,9787],{},[1506,10107,1508],{},[1680,10109,4007],{},[1528,10111,10112],{"encoding":1530},"Q_1^* = \\frac{48 - 18}{15} = \\frac{30}{15} = 2, \\qquad Q_2^* = \\frac{72 - 12}{15} = \\frac{60}{15} = 4",[1035,10114,10116],{"className":10115},[1480],[1482,10117,10118],{"xmlns":1484,"display":1485},[1487,10119,10120,10198],{},[1490,10121,10122,10124,10130,10132,10134,10136,10138,10140,10142,10144,10146,10148,10150,10152,10154,10156,10158,10160,10162,10164,10166,10168,10170,10172,10174,10176,10178,10180,10182,10184,10186,10188],{},[1493,10123,1501],{},[2315,10125,10126,10128],{},[1493,10127,1995],{},[1506,10129,2287],{},[1506,10131,1508],{},[1680,10133,6797],{},[1506,10135,1714],{},[1680,10137,1691],{},[1506,10139,2162],{},[1680,10141,9319],{},[1506,10143,1714],{},[1680,10145,4007],{},[1506,10147,1888],{},[1506,10149,1553],{"stretchy":1552},[1680,10151,1691],{},[1506,10153,1714],{},[1680,10155,4007],{},[1506,10157,2162],{},[1680,10159,1691],{},[1506,10161,1714],{},[1680,10163,4007],{},[1506,10165,2162],{},[1680,10167,1691],{},[1506,10169,1714],{},[1680,10171,9961],{},[1506,10173,1564],{"stretchy":1552},[1506,10175,1508],{},[1680,10177,7201],{},[1506,10179,2162],{},[1680,10181,10091],{},[1506,10183,1888],{},[1680,10185,10052],{},[1506,10187,1508],{},[1976,10189,10190],{"notation":1978},[1869,10191,10192],{"scriptlevel":1871,"displaystyle":1552},[1869,10193,10194],{"scriptlevel":1871,"displaystyle":1552},[1869,10195,10196],{"scriptlevel":1871,"displaystyle":1041},[1680,10197,10052],{},[1528,10199,10200],{"encoding":1530},"PR^* = 12 \\cdot 2 + 18 \\cdot 4 - (2 \\cdot 4 + 2 \\cdot 4 + 2 \\cdot 16) = 24 + 72 - 48 = \\boxed{48}",[1023,10202,10204,10248],{"className":10203,"dataCallout":582},[1026,1186],[1030,10205,10207,10210,10211,10247],{"className":10206},[1033],[1035,10208],{"className":10209,"ariaHidden":1041},[1038,1193,1040],"Proč ",[1035,10212,10214],{"className":10213},[1480],[1482,10215,10216],{"xmlns":1484},[1487,10217,10218,10244],{},[1490,10219,10220,10222,10228,10230,10236,10238],{},[1680,10221,4007],{},[1497,10223,10224,10226],{},[1493,10225,1520],{},[1680,10227,1682],{},[1506,10229,2162],{},[1497,10231,10232,10234],{},[1493,10233,1520],{},[1680,10235,1691],{},[1506,10237,1508],{},[1497,10239,10240,10242],{},[1493,10241,1501],{},[1680,10243,1682],{},[1528,10245,10246],{"encoding":1530},"4 Q_1 + Q_2 = P_1","?",[1030,10249,10250,10251,10268,10269,10315,10316,10346],{},"Levou stranu lze číst jako „mezní náklady na ",[1035,10252,10254],{"className":10253},[1480],[1482,10255,10256],{"xmlns":1484},[1487,10257,10258,10266],{},[1490,10259,10260],{},[1497,10261,10262,10264],{},[1493,10263,1520],{},[1680,10265,1682],{},[1528,10267,6702],{"encoding":1530},"\" — ",[1035,10270,10272],{"className":10271},[1480],[1482,10273,10274],{"xmlns":1484},[1487,10275,10276,10312],{},[1490,10277,10278,10280,10282,10284,10286,10288,10294,10296,10298,10304,10306],{},[1493,10279,1517],{"mathvariant":1516},[1493,10281,5289],{},[1493,10283,1998],{},[1493,10285,1709],{"mathvariant":1516},[1493,10287,1517],{"mathvariant":1516},[1497,10289,10290,10292],{},[1493,10291,1520],{},[1680,10293,1682],{},[1506,10295,1508],{},[1680,10297,4007],{},[1497,10299,10300,10302],{},[1493,10301,1520],{},[1680,10303,1682],{},[1506,10305,2162],{},[1497,10307,10308,10310],{},[1493,10309,1520],{},[1680,10311,1691],{},[1528,10313,10314],{"encoding":1530},"\\partial TC \u002F \\partial Q_1 = 4 Q_1 + Q_2",". V dokonalé konkurenci je MR_i = P_i. Podmínka ",[1035,10317,10319],{"className":10318},[1480],[1482,10320,10321],{"xmlns":1484},[1487,10322,10323,10343],{},[1490,10324,10325,10327,10333,10335,10337],{},[1493,10326,1495],{},[1497,10328,10329,10331],{},[1493,10330,1995],{},[1493,10332,6277],{},[1506,10334,1508],{},[1493,10336,1495],{},[1497,10338,10339,10341],{},[1493,10340,1998],{},[1493,10342,6277],{},[1528,10344,10345],{"encoding":1530},"MR_i = MC_i"," (princip max zisku) na obou trzích dá výše uvedenou soustavu.",[1246,10348],{},[1065,10350,10352,10353,10355],{"id":10351},"z4q4-40-b-is-lm-totožné-se-z3q4","Z4\u002FQ4 ",[1035,10354,1144],{}," — IS-LM (totožné se Z3\u002FQ4)",[1030,10357,10358],{},"Stejné parametry, stejný postup, stejné výsledky:",[1035,10360,10362],{"className":10361},[1480],[1482,10363,10364],{"xmlns":1484,"display":1485},[1487,10365,10366,10426],{},[1490,10367,10368,10374,10376,10378,10380,10382,10388,10390,10392,10394,10396,10398,10400,10402,10404],{},[2315,10369,10370,10372],{},[1493,10371,7740],{},[1493,10373,2711],{},[1506,10375,1508],{},[1680,10377,4007],{},[1506,10379,1559],{"separator":1041},[1912,10381],{"width":2108},[2315,10383,10384,10386],{},[1493,10385,1791],{},[1493,10387,2711],{},[1506,10389,1508],{},[1680,10391,8207],{},[1506,10393,1559],{"separator":1041},[1912,10395],{"width":2108},[1493,10397,2976],{"mathvariant":1516},[1493,10399,7740],{},[1506,10401,2343],{},[1680,10403,8461],{},[1490,10405,10406,10409,10415,10417,10423],{},[1988,10407,10408],{}," (p",[2178,10410,10411,10413],{"accent":1041},[1988,10412,7740],{},[1506,10414,8576],{},[1988,10416,8579],{},[2178,10418,10419,10421],{"accent":1041},[1988,10420,8584],{},[1506,10422,8576],{},[1988,10424,10425],{}," 0,5455)",[1528,10427,10428],{"encoding":1530},"r^E = 4, \\quad Y^E = 1800, \\quad \\Delta r \\approx 0{,}48 \\text{ (přesně 0,5455)}",[1030,10430,10431],{},[1047,10432,10433],{},"Viz Z3\u002FQ4 výše.",[1246,10435],{},[1019,10437,10439],{"id":10438},"zadání-5","Zadání 5",[1065,10441,10443,10444,10446],{"id":10442},"z5q1-10-b-ac-funkce-totožné-se-z3q1","Z5\u002FQ1 ",[1035,10445,1102],{}," — AC funkce (totožné se Z3\u002FQ1)",[1030,10448,10449,10450],{},"(a) ANO; (b) NE; (c) NE; (d) NE; (e) ANO. ",[1047,10451,10452],{},"Viz Z3\u002FQ1.",[1246,10454],{},[1065,10456,10458,10459,10461],{"id":10457},"z5q2-20-b-mrtslk","Z5\u002FQ2 ",[1035,10460,1116],{}," — MRTS(L,K)",[1030,10463,10464,10466],{},[1047,10465,1263],{}," Definujte mezní míru technické substituce a interpretujte MRTS(10,100) = 15.",[1304,10468,1476],{"id":10469},"definice-3",[1035,10471,10473],{"className":10472},[1480],[1482,10474,10475],{"xmlns":1484,"display":1485},[1487,10476,10477,10553],{},[1490,10478,10479],{},[1976,10480,10481],{"notation":1978},[1869,10482,10483],{"scriptlevel":1871,"displaystyle":1552},[1869,10484,10485],{"scriptlevel":1871,"displaystyle":1552},[1869,10486,10487],{"scriptlevel":1871,"displaystyle":1041},[1490,10488,10489,10491,10493,10495,10497,10499,10501,10523,10525,10551],{},[1988,10490,1990],{},[1493,10492,1495],{},[1493,10494,1995],{},[1493,10496,5289],{},[1493,10498,2001],{},[1506,10500,1508],{},[1510,10502,10503,10513],{},[1490,10504,10505,10507],{},[1493,10506,1495],{},[1497,10508,10509,10511],{},[1493,10510,1501],{},[1493,10512,1556],{},[1490,10514,10515,10517],{},[1493,10516,1495],{},[1497,10518,10519,10521],{},[1493,10520,1501],{},[1493,10522,1504],{},[1506,10524,1508],{},[1510,10526,10527,10539],{},[1490,10528,10529,10531,10533,10535,10537],{},[1493,10530,1517],{"mathvariant":1516},[1493,10532,1520],{},[1493,10534,1709],{"mathvariant":1516},[1493,10536,1517],{"mathvariant":1516},[1493,10538,1556],{},[1490,10540,10541,10543,10545,10547,10549],{},[1493,10542,1517],{"mathvariant":1516},[1493,10544,1520],{},[1493,10546,1709],{"mathvariant":1516},[1493,10548,1517],{"mathvariant":1516},[1493,10550,1504],{},[1988,10552,1990],{},[1528,10554,10555],{"encoding":1530},"\\boxed{\\; MRTS = \\frac{MP_L}{MP_K} = \\frac{\\partial Q \u002F \\partial L}{\\partial Q \u002F \\partial K} \\;}",[1030,10557,1295,10558,10561],{},[1052,10559,6836],{"className":10560,"dataFsResolvedFilePath":1572,"href":1573},[1055]," (vzorec 5.14).",[1304,10563,10565],{"id":10564},"interpretace-mrts10100-15","Interpretace MRTS(10,100) = 15",[1030,10567,10568,10569,10599,10600,10603],{},"Na hladině ",[1035,10570,10572],{"className":10571},[1480],[1482,10573,10574],{"xmlns":1484},[1487,10575,10576,10596],{},[1490,10577,10578,10580,10582,10584,10586,10588,10590,10592,10594],{},[1506,10579,1553],{"stretchy":1552},[1493,10581,1556],{},[1506,10583,1508],{},[1680,10585,1775],{},[1506,10587,1559],{"separator":1041},[1493,10589,1504],{},[1506,10591,1508],{},[1680,10593,2916],{},[1506,10595,1564],{"stretchy":1552},[1528,10597,10598],{"encoding":1530},"(L = 10, K = 100)"," lze ",[1047,10601,10602],{},"1 jednotku práce nahradit přibližně 15 jednotkami kapitálu"," se zachovanou produkcí (pohyb po izokvantě).",[1030,10605,10606,10607,2632],{},"Ekvivalentně: poklesne-li práce o 1 pracovníka, musíme pro udržení produkce přidat ",[1047,10608,10609],{},"~15 jednotek kapitálu",[1030,10611,6707,10612,6711,10615,2632],{},[1047,10613,10614],{},"sklon izokvanty",[1035,10616,10618],{"className":10617},[1480],[1482,10619,10620],{"xmlns":1484},[1487,10621,10622,10640],{},[1490,10623,10624,10626,10628,10630,10632,10634,10636,10638],{},[1506,10625,1888],{},[1493,10627,1495],{},[1493,10629,1995],{},[1493,10631,5289],{},[1493,10633,2001],{},[1506,10635,1508],{},[1506,10637,1888],{},[1680,10639,9787],{},[1528,10641,10642],{"encoding":1530},"-MRTS = -15",[1023,10644,10646,10653],{"className":10645,"dataCallout":582},[1026,1186],[1030,10647,10649,10652],{"className":10648},[1033],[1035,10650],{"className":10651,"ariaHidden":1041},[1038,1193,1040],"MRTS vs. MRCS",[1030,10654,10655,10656,10659],{},"Stejný matematický koncept jako MRCS u užitečnosti — ",[1047,10657,10658],{},"podíl mezních veličin = sklon vrstevnice",". MRCS pro indiferenční křivky (užitečnost), MRTS pro izokvanty (produkce).",[1246,10661],{},[1065,10663,10665,10666,10668],{"id":10664},"z5q3-30-b-max-produkce-totožné-se-z3q3","Z5\u002FQ3 ",[1035,10667,1130],{}," — Max produkce (totožné se Z3\u002FQ3)",[1030,10670,10671,10672,10704,10705,2632],{},"(a) ",[1035,10673,10675],{"className":10674},[1480],[1482,10676,10677],{"xmlns":1484},[1487,10678,10679,10701],{},[1490,10680,10681,10683,10685,10687,10689,10691,10697,10699],{},[1493,10682,1556],{},[1506,10684,1508],{},[1680,10686,6956],{},[1506,10688,1559],{"separator":1041},[1493,10690,3633],{},[1497,10692,10693,10695],{},[1493,10694,1501],{},[1493,10696,1556],{},[1506,10698,1508],{},[1680,10700,7047],{},[1528,10702,10703],{"encoding":1530},"L = 30, AP_L = 180","; (b) MP_L(30) = 180 = AP_L(30) ✓; (c) ",[1035,10706,10708],{"className":10707},[1480],[1482,10709,10710],{"xmlns":1484},[1487,10711,10712,10738],{},[1490,10713,10714,10716,10718,10720,10722,10730,10732,10734,10736],{},[1493,10715,1556],{},[1506,10717,1508],{},[1680,10719,7380],{},[1506,10721,1559],{"separator":1041},[1497,10723,10724,10726,10728],{},[1493,10725,1520],{},[1493,10727,7571],{},[1506,10729,7574],{},[1506,10731,1508],{},[1680,10733,7508],{},[1988,10735,5016],{},[1680,10737,5765],{},[1528,10739,10740],{"encoding":1530},"L = 40, Q_{\\max} = 6\\,400",[1030,10742,10743],{},[1047,10744,10745],{},"Viz Z3\u002FQ3.",[1246,10747],{},[1065,10749,10751,10752,10754],{"id":10750},"z5q4-40-b-firma-s-pevnými-mc-a-lineárním-mr","Z5\u002FQ4 ",[1035,10753,1144],{}," — Firma s pevnými MC a lineárním MR",[1030,10756,10757,1656,10759,1732,10779,1732,10801,10827],{},[1047,10758,1263],{},[1035,10760,10762],{"className":10761},[1480],[1482,10763,10764],{"xmlns":1484},[1487,10765,10766,10776],{},[1490,10767,10768,10770,10772,10774],{},[1493,10769,1495],{},[1493,10771,1998],{},[1506,10773,1508],{},[1680,10775,8436],{},[1528,10777,10778],{"encoding":1530},"MC = 20",[1035,10780,10782],{"className":10781},[1480],[1482,10783,10784],{"xmlns":1484},[1487,10785,10786,10798],{},[1490,10787,10788,10791,10793,10795],{},[1493,10789,10790],{},"F",[1493,10792,1998],{},[1506,10794,1508],{},[1680,10796,10797],{},"120",[1528,10799,10800],{"encoding":1530},"FC = 120",[1035,10802,10804],{"className":10803},[1480],[1482,10805,10806],{"xmlns":1484},[1487,10807,10808,10824],{},[1490,10809,10810,10812,10814,10816,10818,10820,10822],{},[1493,10811,1495],{},[1493,10813,1995],{},[1506,10815,1508],{},[1680,10817,2916],{},[1506,10819,1888],{},[1680,10821,8436],{},[1493,10823,1520],{},[1528,10825,10826],{"encoding":1530},"MR = 100 - 20Q",".\n(a) TR a poptávka. (b) TC. (c) Max TR + maximum. (d) Body zvratu. (e) Max zisku + maximum. (f) Náčrt.",[1030,10829,10830,10832,10833,2632],{},[1047,10831,1832],{}," Integrace MR a MC + standardní úkony ",[1052,10834,820],{"className":10835,"dataFsResolvedFilePath":1299,"href":1300},[1055],[1304,10837,10839],{"id":10838},"a-tr-a-dq","(a) TR a D(Q)",[1035,10841,10843],{"className":10842},[1480],[1482,10844,10845],{"xmlns":1484,"display":1485},[1487,10846,10847,10939],{},[1490,10848,10849,10851,10853,10855,10858,10860,10862,10864,10866,10868,10870,10872,10874,10876,10878,10880,10882,10884,10886,10888,10890,10892,10894,10896,10898,10900,10906,10908,10923,10925,10927,10929,10931,10933,10935,10937],{},[1493,10850,5289],{},[1493,10852,1995],{},[1506,10854,1508],{},[1506,10856,10857],{},"∫",[1493,10859,1495],{},[1493,10861,1995],{},[1988,10863,5016],{},[1493,10865,3384],{},[1493,10867,1520],{},[1506,10869,1508],{},[1506,10871,10857],{},[1506,10873,1553],{"stretchy":1552},[1680,10875,2916],{},[1506,10877,1888],{},[1680,10879,8436],{},[1493,10881,1520],{},[1506,10883,1564],{"stretchy":1552},[1988,10885,5016],{},[1493,10887,3384],{},[1493,10889,1520],{},[1506,10891,1508],{},[1680,10893,2916],{},[1493,10895,1520],{},[1506,10897,1888],{},[1680,10899,1775],{},[2315,10901,10902,10904],{},[1493,10903,1520],{},[1680,10905,1691],{},[1912,10907],{"width":2108},[1490,10909,10910,10913,10920],{},[1988,10911,10912],{},"(konstanta = 0, nebo",[2178,10914,10915,10918],{"accent":1041},[1988,10916,10917],{},"t",[1506,10919,8576],{},[1988,10921,10922],{}," ",[1493,10924,5289],{},[1493,10926,1995],{},[1506,10928,1553],{"stretchy":1552},[1680,10930,1871],{},[1506,10932,1564],{"stretchy":1552},[1506,10934,1508],{},[1680,10936,1871],{},[1506,10938,1564],{"stretchy":1552},[1528,10940,10941],{"encoding":1530},"TR = \\int MR \\, dQ = \\int (100 - 20Q) \\, dQ = 100Q - 10Q^2 \\quad \\text{(konstanta = 0, neboť } TR(0) = 0)",[1035,10943,10945],{"className":10944},[1480],[1482,10946,10947],{"xmlns":1484,"display":1485},[1487,10948,10949,10995],{},[1490,10950,10951,10953,10955,10957,10959,10961,10963,10965,10975,10977],{},[1493,10952,1501],{},[1506,10954,1508],{},[1493,10956,3712],{},[1506,10958,1553],{"stretchy":1552},[1493,10960,1520],{},[1506,10962,1564],{"stretchy":1552},[1506,10964,1508],{},[1510,10966,10967,10973],{},[1490,10968,10969,10971],{},[1493,10970,5289],{},[1493,10972,1995],{},[1493,10974,1520],{},[1506,10976,1508],{},[1976,10978,10979],{"notation":1978},[1869,10980,10981],{"scriptlevel":1871,"displaystyle":1552},[1869,10982,10983],{"scriptlevel":1871,"displaystyle":1552},[1869,10984,10985],{"scriptlevel":1871,"displaystyle":1041},[1490,10986,10987,10989,10991,10993],{},[1680,10988,2916],{},[1506,10990,1888],{},[1680,10992,1775],{},[1493,10994,1520],{},[1528,10996,10997],{"encoding":1530},"P = D(Q) = \\frac{TR}{Q} = \\boxed{100 - 10 Q}",[1304,10999,11001],{"id":11000},"b-tc","(b) TC",[1035,11003,11005],{"className":11004},[1480],[1482,11006,11007],{"xmlns":1484,"display":1485},[1487,11008,11009,11045],{},[1490,11010,11011,11013,11015,11017,11019,11021,11023,11025,11027,11029,11031,11033,11035,11037,11039,11041,11043],{},[1493,11012,5289],{},[1493,11014,1998],{},[1506,11016,1508],{},[1506,11018,10857],{},[1493,11020,1495],{},[1493,11022,1998],{},[1988,11024,5016],{},[1493,11026,3384],{},[1493,11028,1520],{},[1506,11030,2162],{},[1493,11032,10790],{},[1493,11034,1998],{},[1506,11036,1508],{},[1680,11038,8436],{},[1493,11040,1520],{},[1506,11042,2162],{},[1680,11044,10797],{},[1528,11046,11047],{"encoding":1530},"TC = \\int MC \\, dQ + FC = 20 Q + 120",[1304,11049,11051],{"id":11050},"c-max-tr","(c) Max TR",[1030,11053,11054,11074,11075],{},[1035,11055,11057],{"className":11056},[1480],[1482,11058,11059],{"xmlns":1484},[1487,11060,11061,11071],{},[1490,11062,11063,11065,11067,11069],{},[1493,11064,1495],{},[1493,11066,1995],{},[1506,11068,1508],{},[1680,11070,1871],{},[1528,11072,11073],{"encoding":1530},"MR = 0",": ",[1035,11076,11078],{"className":11077},[1480],[1482,11079,11080],{"xmlns":1484},[1487,11081,11082,11108],{},[1490,11083,11084,11086,11088,11090,11092,11094,11096,11098,11104,11106],{},[1680,11085,2916],{},[1506,11087,1888],{},[1680,11089,8436],{},[1493,11091,1520],{},[1506,11093,1508],{},[1680,11095,1871],{},[1506,11097,2183],{},[1497,11099,11100,11102],{},[1493,11101,1520],{},[1680,11103,1682],{},[1506,11105,1508],{},[1680,11107,1752],{},[1528,11109,11110],{"encoding":1530},"100 - 20Q = 0 \\Rightarrow Q_1 = 5",[1035,11112,11114],{"className":11113},[1480],[1482,11115,11116],{"xmlns":1484,"display":1485},[1487,11117,11118,11158],{},[1490,11119,11120,11122,11130,11132,11134,11136,11138,11140,11142,11144,11146,11148],{},[1493,11121,5289],{},[1497,11123,11124,11126,11128],{},[1493,11125,1995],{},[1493,11127,7571],{},[1506,11129,7574],{},[1506,11131,1508],{},[1680,11133,2916],{},[1506,11135,1714],{},[1680,11137,1752],{},[1506,11139,1888],{},[1680,11141,1775],{},[1506,11143,1714],{},[1680,11145,2309],{},[1506,11147,1508],{},[1976,11149,11150],{"notation":1978},[1869,11151,11152],{"scriptlevel":1871,"displaystyle":1552},[1869,11153,11154],{"scriptlevel":1871,"displaystyle":1552},[1869,11155,11156],{"scriptlevel":1871,"displaystyle":1041},[1680,11157,8140],{},[1528,11159,11160],{"encoding":1530},"TR_{\\max} = 100 \\cdot 5 - 10 \\cdot 25 = \\boxed{250}",[1304,11162,11164],{"id":11163},"d-body-zvratu-pr-0","(d) Body zvratu (PR = 0)",[1035,11166,11168],{"className":11167},[1480],[1482,11169,11170],{"xmlns":1484,"display":1485},[1487,11171,11172,11239],{},[1490,11173,11174,11176,11178,11180,11182,11184,11186,11188,11190,11192,11194,11196,11198,11200,11206,11208,11210,11212,11214,11216,11218,11220,11222,11228,11230,11233,11235,11237],{},[1493,11175,1501],{},[1493,11177,1995],{},[1506,11179,1508],{},[1493,11181,5289],{},[1493,11183,1995],{},[1506,11185,1888],{},[1493,11187,5289],{},[1493,11189,1998],{},[1506,11191,1508],{},[1680,11193,2916],{},[1493,11195,1520],{},[1506,11197,1888],{},[1680,11199,1775],{},[2315,11201,11202,11204],{},[1493,11203,1520],{},[1680,11205,1691],{},[1506,11207,1888],{},[1680,11209,8436],{},[1493,11211,1520],{},[1506,11213,1888],{},[1680,11215,10797],{},[1506,11217,1508],{},[1506,11219,1888],{},[1680,11221,1775],{},[2315,11223,11224,11226],{},[1493,11225,1520],{},[1680,11227,1691],{},[1506,11229,2162],{},[1680,11231,11232],{},"80",[1493,11234,1520],{},[1506,11236,1888],{},[1680,11238,10797],{},[1528,11240,11241],{"encoding":1530},"PR = TR - TC = 100Q - 10Q^2 - 20Q - 120 = -10 Q^2 + 80 Q - 120",[1035,11243,11245],{"className":11244},[1480],[1482,11246,11247],{"xmlns":1484,"display":1485},[1487,11248,11249,11309],{},[1490,11250,11251,11253,11255,11257,11259,11261,11264,11266,11272,11274,11276,11278,11280,11282,11284,11286,11288,11290,11292,11294,11296],{},[1493,11252,1501],{},[1493,11254,1995],{},[1506,11256,1508],{},[1680,11258,1871],{},[1988,11260,1990],{},[1506,11262,11263],{},"⟺",[1988,11265,1990],{},[2315,11267,11268,11270],{},[1493,11269,1520],{},[1680,11271,1691],{},[1506,11273,1888],{},[1680,11275,6138],{},[1493,11277,1520],{},[1506,11279,2162],{},[1680,11281,6797],{},[1506,11283,1508],{},[1680,11285,1871],{},[1988,11287,1990],{},[1506,11289,2111],{},[1988,11291,1990],{},[1493,11293,1520],{},[1506,11295,1508],{},[1510,11297,11298,11307],{},[1490,11299,11300,11302,11305],{},[1680,11301,6138],{},[1506,11303,11304],{},"±",[1680,11306,4007],{},[1680,11308,1691],{},[1528,11310,11311],{"encoding":1530},"PR = 0 \\;\\Longleftrightarrow\\; Q^2 - 8Q + 12 = 0 \\;\\Longrightarrow\\; Q = \\frac{8 \\pm 4}{2}",[1035,11313,11315],{"className":11314},[1480],[1482,11316,11317],{"xmlns":1484,"display":1485},[1487,11318,11319,11360],{},[1490,11320,11321],{},[1976,11322,11323],{"notation":1978},[1869,11324,11325],{"scriptlevel":1871,"displaystyle":1552},[1869,11326,11327],{"scriptlevel":1871,"displaystyle":1552},[1869,11328,11329],{"scriptlevel":1871,"displaystyle":1041},[1490,11330,11331,11333,11339,11341,11343,11345,11347,11354,11356,11358],{},[1988,11332,1990],{},[1497,11334,11335,11337],{},[1493,11336,1520],{},[1493,11338,3633],{},[1506,11340,1508],{},[1680,11342,1691],{},[1506,11344,1559],{"separator":1041},[1912,11346],{"width":2108},[1497,11348,11349,11351],{},[1493,11350,1520],{},[1493,11352,11353],{},"B",[1506,11355,1508],{},[1680,11357,7508],{},[1988,11359,1990],{},[1528,11361,11362],{"encoding":1530},"\\boxed{\\; Q_A = 2, \\quad Q_B = 6 \\;}",[1304,11364,11366],{"id":11365},"e-max-zisku","(e) Max zisku",[1030,11368,11369,11074,11391],{},[1035,11370,11372],{"className":11371},[1480],[1482,11373,11374],{"xmlns":1484},[1487,11375,11376,11388],{},[1490,11377,11378,11380,11382,11384,11386],{},[1493,11379,1495],{},[1493,11381,1995],{},[1506,11383,1508],{},[1493,11385,1495],{},[1493,11387,1998],{},[1528,11389,11390],{"encoding":1530},"MR = MC",[1035,11392,11394],{"className":11393},[1480],[1482,11395,11396],{"xmlns":1484},[1487,11397,11398,11424],{},[1490,11399,11400,11402,11404,11406,11408,11410,11412,11414,11420,11422],{},[1680,11401,2916],{},[1506,11403,1888],{},[1680,11405,8436],{},[1493,11407,1520],{},[1506,11409,1508],{},[1680,11411,8436],{},[1506,11413,2183],{},[1497,11415,11416,11418],{},[1493,11417,1520],{},[1680,11419,1691],{},[1506,11421,1508],{},[1680,11423,4007],{},[1528,11425,11426],{"encoding":1530},"100 - 20Q = 20 \\Rightarrow Q_2 = 4",[1035,11428,11430],{"className":11429},[1480],[1482,11431,11432],{"xmlns":1484,"display":1485},[1487,11433,11434,11496],{},[1490,11435,11436,11438,11440,11442,11444,11446,11448,11450,11452,11454,11456,11458,11460,11462,11464,11466,11468,11470,11472,11475,11477,11480,11482,11484,11486],{},[1493,11437,1501],{},[1493,11439,1995],{},[1506,11441,1553],{"stretchy":1552},[1680,11443,4007],{},[1506,11445,1564],{"stretchy":1552},[1506,11447,1508],{},[1506,11449,1888],{},[1680,11451,1775],{},[1506,11453,1714],{},[1680,11455,9961],{},[1506,11457,2162],{},[1680,11459,11232],{},[1506,11461,1714],{},[1680,11463,4007],{},[1506,11465,1888],{},[1680,11467,10797],{},[1506,11469,1508],{},[1506,11471,1888],{},[1680,11473,11474],{},"160",[1506,11476,2162],{},[1680,11478,11479],{},"320",[1506,11481,1888],{},[1680,11483,10797],{},[1506,11485,1508],{},[1976,11487,11488],{"notation":1978},[1869,11489,11490],{"scriptlevel":1871,"displaystyle":1552},[1869,11491,11492],{"scriptlevel":1871,"displaystyle":1552},[1869,11493,11494],{"scriptlevel":1871,"displaystyle":1041},[1680,11495,7380],{},[1528,11497,11498],{"encoding":1530},"PR(4) = -10 \\cdot 16 + 80 \\cdot 4 - 120 = -160 + 320 - 120 = \\boxed{40}",[1304,11500,11502],{"id":11501},"f-náčrt","(f) Náčrt",[1030,11504,11505],{},"Klíčové body, které by měly být v grafu:",[1073,11507,11508,11521],{},[1076,11509,11510],{},[1079,11511,11512,11515,11518],{},[1082,11513,11514],{},"Křivka",[1082,11516,11517],{},"Tvar",[1082,11519,11520],{},"Klíčové body",[1092,11522,11523,11579,11613,11667,11732,11761],{},[1079,11524,11525,11528,11531],{},[1097,11526,11527],{},"TR(Q)",[1097,11529,11530],{},"parabola obrácená dolů",[1097,11532,11533,11534,11556,11557],{},"kořeny ",[1035,11535,11537],{"className":11536},[1480],[1482,11538,11539],{"xmlns":1484},[1487,11540,11541,11553],{},[1490,11542,11543,11545,11547,11549,11551],{},[1493,11544,1520],{},[1506,11546,1508],{},[1680,11548,1871],{},[1506,11550,1559],{"separator":1041},[1680,11552,1775],{},[1528,11554,11555],{"encoding":1530},"Q = 0, 10","; vrchol ",[1035,11558,11560],{"className":11559},[1480],[1482,11561,11562],{"xmlns":1484},[1487,11563,11564,11576],{},[1490,11565,11566,11568,11570,11572,11574],{},[1506,11567,1553],{"stretchy":1552},[1680,11569,1752],{},[1506,11571,1559],{"separator":1041},[1680,11573,8140],{},[1506,11575,1564],{"stretchy":1552},[1528,11577,11578],{"encoding":1530},"(5, 250)",[1079,11580,11581,11584,11587],{},[1097,11582,11583],{},"TC(Q)",[1097,11585,11586],{},"rostoucí přímka",[1097,11588,11589,11590,11612],{},"průsečík s osou: ",[1035,11591,11593],{"className":11592},[1480],[1482,11594,11595],{"xmlns":1484},[1487,11596,11597,11609],{},[1490,11598,11599,11601,11603,11605,11607],{},[1506,11600,1553],{"stretchy":1552},[1680,11602,1871],{},[1506,11604,1559],{"separator":1041},[1680,11606,10797],{},[1506,11608,1564],{"stretchy":1552},[1528,11610,11611],{"encoding":1530},"(0, 120)","; sklon 20",[1079,11614,11615,11618,11620],{},[1097,11616,11617],{},"PR(Q)",[1097,11619,11530],{},[1097,11621,11533,11622,11644,11645],{},[1035,11623,11625],{"className":11624},[1480],[1482,11626,11627],{"xmlns":1484},[1487,11628,11629,11641],{},[1490,11630,11631,11633,11635,11637,11639],{},[1493,11632,1520],{},[1506,11634,1508],{},[1680,11636,1691],{},[1506,11638,1559],{"separator":1041},[1680,11640,7508],{},[1528,11642,11643],{"encoding":1530},"Q = 2, 6"," (body zvratu); vrchol ",[1035,11646,11648],{"className":11647},[1480],[1482,11649,11650],{"xmlns":1484},[1487,11651,11652,11664],{},[1490,11653,11654,11656,11658,11660,11662],{},[1506,11655,1553],{"stretchy":1552},[1680,11657,4007],{},[1506,11659,1559],{"separator":1041},[1680,11661,7380],{},[1506,11663,1564],{"stretchy":1552},[1528,11665,11666],{"encoding":1530},"(4, 40)",[1079,11668,11669,11672,11675],{},[1097,11670,11671],{},"MR(Q)",[1097,11673,11674],{},"klesající přímka",[1097,11676,11589,11677,11699,11700,11713,11714],{},[1035,11678,11680],{"className":11679},[1480],[1482,11681,11682],{"xmlns":1484},[1487,11683,11684,11696],{},[1490,11685,11686,11688,11690,11692,11694],{},[1506,11687,1553],{"stretchy":1552},[1680,11689,1871],{},[1506,11691,1559],{"separator":1041},[1680,11693,2916],{},[1506,11695,1564],{"stretchy":1552},[1528,11697,11698],{"encoding":1530},"(0, 100)","; sklon −20; protíná osu ",[1035,11701,11703],{"className":11702},[1480],[1482,11704,11705],{"xmlns":1484},[1487,11706,11707,11711],{},[1490,11708,11709],{},[1493,11710,1520],{},[1528,11712,1520],{"encoding":1530}," v bodě ",[1035,11715,11717],{"className":11716},[1480],[1482,11718,11719],{"xmlns":1484},[1487,11720,11721,11729],{},[1490,11722,11723,11725,11727],{},[1493,11724,1520],{},[1506,11726,1508],{},[1680,11728,1752],{},[1528,11730,11731],{"encoding":1530},"Q = 5",[1079,11733,11734,11737,11740],{},[1097,11735,11736],{},"MC(Q)",[1097,11738,11739],{},"konstanta",[1097,11741,11742,11743],{},"vodorovná přímka v ",[1035,11744,11746],{"className":11745},[1480],[1482,11747,11748],{"xmlns":1484},[1487,11749,11750,11758],{},[1490,11751,11752,11754,11756],{},[1493,11753,1501],{},[1506,11755,1508],{},[1680,11757,8436],{},[1528,11759,11760],{"encoding":1530},"P = 20",[1079,11762,11763,11766,11768],{},[1097,11764,11765],{},"D(Q)",[1097,11767,11674],{},[1097,11769,11770],{},"sklon −10 (poloviční oproti MR)",[1030,11772,11773,1656,11776,11798,11799,11833,11834,11856],{},[1047,11774,11775],{},"Vyznačit:",[1035,11777,11779],{"className":11778},[1480],[1482,11780,11781],{"xmlns":1484},[1487,11782,11783,11795],{},[1490,11784,11785,11791,11793],{},[1497,11786,11787,11789],{},[1493,11788,1520],{},[1680,11790,1682],{},[1506,11792,1508],{},[1680,11794,1752],{},[1528,11796,11797],{"encoding":1530},"Q_1 = 5"," (max TR — tam, kde MR protíná osu Q); ",[1035,11800,11802],{"className":11801},[1480],[1482,11803,11804],{"xmlns":1484},[1487,11805,11806,11830],{},[1490,11807,11808,11814,11816,11818,11820,11826,11828],{},[1497,11809,11810,11812],{},[1493,11811,1520],{},[1493,11813,3633],{},[1506,11815,1508],{},[1680,11817,1691],{},[1506,11819,1559],{"separator":1041},[1497,11821,11822,11824],{},[1493,11823,1520],{},[1493,11825,11353],{},[1506,11827,1508],{},[1680,11829,7508],{},[1528,11831,11832],{"encoding":1530},"Q_A = 2, Q_B = 6"," (body zvratu — TR = TC); ",[1035,11835,11837],{"className":11836},[1480],[1482,11838,11839],{"xmlns":1484},[1487,11840,11841,11853],{},[1490,11842,11843,11849,11851],{},[1497,11844,11845,11847],{},[1493,11846,1520],{},[1680,11848,1691],{},[1506,11850,1508],{},[1680,11852,4007],{},[1528,11854,11855],{"encoding":1530},"Q_2 = 4"," (max zisku — průsečík MR a MC).",[1023,11858,11860,11867],{"className":11859,"dataCallout":582},[1026,1186],[1030,11861,11863,11866],{"className":11862},[1033],[1035,11864],{"className":11865,"ariaHidden":1041},[1038,1193,1040],"Geometrický vztah",[1030,11868,11869,11890,11891,1656,11894,1586,11916,11938,11939,11969,11970,11991,11992,11995],{},[1035,11870,11872],{"className":11871},[1480],[1482,11873,11874],{"xmlns":1484},[1487,11875,11876,11888],{},[1490,11877,11878,11884,11886],{},[1497,11879,11880,11882],{},[1493,11881,1520],{},[1680,11883,1691],{},[1506,11885,1508],{},[1680,11887,4007],{},[1528,11889,11855],{"encoding":1530}," leží ",[1047,11892,11893],{},"mezi",[1035,11895,11897],{"className":11896},[1480],[1482,11898,11899],{"xmlns":1484},[1487,11900,11901,11913],{},[1490,11902,11903,11909,11911],{},[1497,11904,11905,11907],{},[1493,11906,1520],{},[1493,11908,3633],{},[1506,11910,1508],{},[1680,11912,1691],{},[1528,11914,11915],{"encoding":1530},"Q_A = 2",[1035,11917,11919],{"className":11918},[1480],[1482,11920,11921],{"xmlns":1484},[1487,11922,11923,11935],{},[1490,11924,11925,11931,11933],{},[1497,11926,11927,11929],{},[1493,11928,1520],{},[1493,11930,11353],{},[1506,11932,1508],{},[1680,11934,7508],{},[1528,11936,11937],{"encoding":1530},"Q_B = 6"," — uvnitř ziskového intervalu, blízko jeho středu (přesně středem: ",[1035,11940,11942],{"className":11941},[1480],[1482,11943,11944],{"xmlns":1484},[1487,11945,11946,11966],{},[1490,11947,11948,11950,11952,11954,11956,11958,11960,11962,11964],{},[1506,11949,1553],{"stretchy":1552},[1680,11951,1691],{},[1506,11953,2162],{},[1680,11955,7508],{},[1506,11957,1564],{"stretchy":1552},[1493,11959,1709],{"mathvariant":1516},[1680,11961,1691],{},[1506,11963,1508],{},[1680,11965,4007],{},[1528,11967,11968],{"encoding":1530},"(2+6)\u002F2 = 4",", neboť PR je kvadratická parabola). Maximum TR (",[1035,11971,11973],{"className":11972},[1480],[1482,11974,11975],{"xmlns":1484},[1487,11976,11977,11989],{},[1490,11978,11979,11985,11987],{},[1497,11980,11981,11983],{},[1493,11982,1520],{},[1680,11984,1682],{},[1506,11986,1508],{},[1680,11988,1752],{},[1528,11990,11797],{"encoding":1530},") leží ",[1047,11993,11994],{},"vpravo"," od max zisku — protože tam už náklady rostou rychleji než příjem.",[1246,11997],{},[1019,11999,12001],{"id":12000},"zadání-6","Zadání 6",[1065,12003,12005,12006,12008],{"id":12004},"z6q1-10-b-tr-funkce","Z6\u002FQ1 ",[1035,12007,1102],{}," — TR funkce",[1030,12010,12011,12013],{},[1047,12012,1263],{}," (a) TR = 100 − 3Q; (b) TR = 12Q − Q²; (c) TR = 1000 − Q²; (d) TR = Q(100 − 2Q²); (e) TR = 10Q + Q².",[1030,12015,12016,12018],{},[1047,12017,1832],{}," Stejný jako Z1\u002FQ1 — TR(0) = 0 a P klesající.",[1073,12020,12021,12035],{},[1076,12022,12023],{},[1079,12024,12025,12027,12029,12031,12033],{},[1082,12026],{},[1082,12028,1318],{},[1082,12030,1321],{},[1082,12032,1501],{},[1082,12034,1327],{},[1092,12036,12037,12054,12070,12087,12103],{},[1079,12038,12039,12041,12044,12048,12050],{},[1097,12040,1334],{},[1097,12042,12043],{},"100 − 3Q",[1097,12045,1398,12046,1402],{},[1047,12047,2916],{},[1097,12049,1405],{},[1097,12051,12052],{},[1047,12053,1387],{},[1079,12055,12056,12058,12061,12063,12066],{},[1097,12057,1353],{},[1097,12059,12060],{},"12Q − Q²",[1097,12062,1340],{},[1097,12064,12065],{},"12 − Q (klesá) ✓",[1097,12067,12068],{},[1047,12069,1348],{},[1079,12071,12072,12074,12077,12081,12083],{},[1097,12073,1370],{},[1097,12075,12076],{},"1000 − Q²",[1097,12078,1398,12079,1402],{},[1047,12080,1401],{},[1097,12082,1405],{},[1097,12084,12085],{},[1047,12086,1387],{},[1079,12088,12089,12091,12094,12096,12099],{},[1097,12090,1392],{},[1097,12092,12093],{},"Q(100 − 2Q²) = 100Q − 2Q³",[1097,12095,1340],{},[1097,12097,12098],{},"100 − 2Q² (klesá pro Q>0) ✓",[1097,12100,12101],{},[1047,12102,1348],{},[1079,12104,12105,12107,12110,12112,12117],{},[1097,12106,1414],{},[1097,12108,12109],{},"10Q + Q²",[1097,12111,1340],{},[1097,12113,12114,12115,1382],{},"10 + Q (",[1047,12116,7685],{},[1097,12118,12119],{},[1047,12120,1387],{},[1246,12122],{},[1065,12124,12126,12127,12129],{"id":12125},"z6q2-20-b-mpk20900-15","Z6\u002FQ2 ",[1035,12128,1116],{}," — MPK(20,900) = 15",[1030,12131,12132,12134,12135,2632],{},[1047,12133,1476],{}," (jako Z1\u002FQ2): ",[1035,12136,12138],{"className":12137},[1480],[1482,12139,12140],{"xmlns":1484},[1487,12141,12142,12164],{},[1490,12143,12144,12146,12152,12154,12156,12158,12160,12162],{},[1493,12145,1495],{},[1497,12147,12148,12150],{},[1493,12149,1501],{},[1493,12151,1504],{},[1506,12153,1508],{},[1493,12155,1517],{"mathvariant":1516},[1493,12157,1520],{},[1493,12159,1709],{"mathvariant":1516},[1493,12161,1517],{"mathvariant":1516},[1493,12163,1504],{},[1528,12165,12166],{"encoding":1530},"MP_K = \\partial Q \u002F \\partial K",[1030,12168,12169,12172,12173,12191,12192,12210,12211,12214],{},[1047,12170,12171],{},"Interpretace:"," Na hladině ",[1035,12174,12176],{"className":12175},[1480],[1482,12177,12178],{"xmlns":1484},[1487,12179,12180,12188],{},[1490,12181,12182,12184,12186],{},[1493,12183,1556],{},[1506,12185,1508],{},[1680,12187,8436],{},[1528,12189,12190],{"encoding":1530},"L = 20"," pracovníků, ",[1035,12193,12195],{"className":12194},[1480],[1482,12196,12197],{"xmlns":1484},[1487,12198,12199,12207],{},[1490,12200,12201,12203,12205],{},[1493,12202,1504],{},[1506,12204,1508],{},[1680,12206,7032],{},[1528,12208,12209],{"encoding":1530},"K = 900"," jednotek kapitálu se produkce přibližně ",[1047,12212,12213],{},"zvýší o 15 jednotek",", jestliže se kapitál zvýší o 1 jednotku (z 900 na 901), při neměnné práci. Další jednotka kapitálu přidá v daném bodě ~15 jednotek produkce.",[1246,12216],{},[1065,12218,12220,12221,12223,12224,12258],{"id":12219},"z6q3-30-b-mezní-náklady-mc5010qq2mc-50-10q-q2-fc-10","Z6\u002FQ3 ",[1035,12222,1130],{}," — Mezní náklady ",[1035,12225,12227],{"className":12226},[1480],[1482,12228,12229],{"xmlns":1484},[1487,12230,12231,12255],{},[1490,12232,12233,12235,12237,12239,12241,12243,12245,12247,12249],{},[1493,12234,1495],{},[1493,12236,1998],{},[1506,12238,1508],{},[1680,12240,2292],{},[1506,12242,1888],{},[1680,12244,1775],{},[1493,12246,1520],{},[1506,12248,2162],{},[2315,12250,12251,12253],{},[1493,12252,1520],{},[1680,12254,1691],{},[1528,12256,12257],{"encoding":1530},"MC = 50 - 10Q + Q^2",", FC = 10",[1030,12260,12261,12263],{},[1047,12262,1263],{}," (a) Stanovte TC a rychlost změny TC při Q = 20. (b) Min MC. (c) ΔMC při Q: 20→30, porovnejte s přesným.",[1304,12265,12267],{"id":12266},"a-tc-a-rychlost-při-q-20","(a) TC a rychlost při Q = 20",[1035,12269,12271],{"className":12270},[1480],[1482,12272,12273],{"xmlns":1484,"display":1485},[1487,12274,12275,12367],{},[1490,12276,12277,12279,12281,12283,12285,12287,12289,12291,12293,12295,12297,12299,12301,12303,12305,12307,12309,12311,12313,12315,12317,12323,12325,12327,12329,12331,12333,12335,12337,12339,12341,12343,12345,12351,12353,12363,12365],{},[1493,12278,5289],{},[1493,12280,1998],{},[1506,12282,1508],{},[1506,12284,10857],{},[1493,12286,1495],{},[1493,12288,1998],{},[1988,12290,5016],{},[1493,12292,3384],{},[1493,12294,1520],{},[1506,12296,2162],{},[1493,12298,10790],{},[1493,12300,1998],{},[1506,12302,1508],{},[1506,12304,10857],{},[1506,12306,1553],{"stretchy":1552},[1680,12308,2292],{},[1506,12310,1888],{},[1680,12312,1775],{},[1493,12314,1520],{},[1506,12316,2162],{},[2315,12318,12319,12321],{},[1493,12320,1520],{},[1680,12322,1691],{},[1506,12324,1564],{"stretchy":1552},[1988,12326,5016],{},[1493,12328,3384],{},[1493,12330,1520],{},[1506,12332,2162],{},[1680,12334,1775],{},[1506,12336,1508],{},[1680,12338,2292],{},[1493,12340,1520],{},[1506,12342,1888],{},[1680,12344,1752],{},[2315,12346,12347,12349],{},[1493,12348,1520],{},[1680,12350,1691],{},[1506,12352,2162],{},[1510,12354,12355,12361],{},[2315,12356,12357,12359],{},[1493,12358,1520],{},[1680,12360,3201],{},[1680,12362,3201],{},[1506,12364,2162],{},[1680,12366,1775],{},[1528,12368,12369],{"encoding":1530},"TC = \\int MC \\, dQ + FC = \\int (50 - 10Q + Q^2) \\, dQ + 10 = 50Q - 5Q^2 + \\frac{Q^3}{3} + 10",[1030,12371,12372,12375],{},[1047,12373,12374],{},"Rychlost změny TC"," = mezní náklady = MC(Q):",[1035,12377,12379],{"className":12378},[1480],[1482,12380,12381],{"xmlns":1484,"display":1485},[1487,12382,12383,12435],{},[1490,12384,12385,12387,12393,12395,12397,12399,12401,12403,12405,12407,12409,12411,12413,12415,12417,12419,12421,12423,12425],{},[1493,12386,5289],{},[2315,12388,12389,12391],{},[1493,12390,1998],{},[1506,12392,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,12394,1553],{"stretchy":1552},[1680,12396,8436],{},[1506,12398,1564],{"stretchy":1552},[1506,12400,1508],{},[1493,12402,1495],{},[1493,12404,1998],{},[1506,12406,1553],{"stretchy":1552},[1680,12408,8436],{},[1506,12410,1564],{"stretchy":1552},[1506,12412,1508],{},[1680,12414,2292],{},[1506,12416,1888],{},[1680,12418,5263],{},[1506,12420,2162],{},[1680,12422,5765],{},[1506,12424,1508],{},[1976,12426,12427],{"notation":1978},[1869,12428,12429],{"scriptlevel":1871,"displaystyle":1552},[1869,12430,12431],{"scriptlevel":1871,"displaystyle":1552},[1869,12432,12433],{"scriptlevel":1871,"displaystyle":1041},[1680,12434,8140],{},[1528,12436,12437],{"encoding":1530},"TC'(20) = MC(20) = 50 - 200 + 400 = \\boxed{250}",[1030,12439,12440,12441,2632],{},"Při produkci 20 jednotek se celkové náklady mění ",[1047,12442,12443],{},"rychlostí 250 peněžních jednotek na další jednotku produkce",[1030,12445,12446,12447,7909],{},"(Pro úplnost: ",[1035,12448,12450],{"className":12449},[1480],[1482,12451,12452],{"xmlns":1484},[1487,12453,12454,12496],{},[1490,12455,12456,12458,12460,12462,12464,12466,12468,12470,12472,12474,12476,12479,12481,12483,12485,12487,12489,12491,12493],{},[1493,12457,5289],{},[1493,12459,1998],{},[1506,12461,1553],{"stretchy":1552},[1680,12463,8436],{},[1506,12465,1564],{"stretchy":1552},[1506,12467,1508],{},[1680,12469,1401],{},[1506,12471,1888],{},[1680,12473,8113],{},[1506,12475,2162],{},[1680,12477,12478],{},"8000",[1493,12480,1709],{"mathvariant":1516},[1680,12482,3201],{},[1506,12484,2162],{},[1680,12486,1775],{},[1506,12488,2343],{},[1680,12490,1682],{},[1988,12492,5016],{},[1680,12494,12495],{},"676,67",[1528,12497,12498],{"encoding":1530},"TC(20) = 1000 - 2000 + 8000\u002F3 + 10 \\approx 1\\,676{,}67",[1304,12500,12502],{"id":12501},"b-min-mc","(b) Min MC",[1035,12504,12506],{"className":12505},[1480],[1482,12507,12508],{"xmlns":1484,"display":1485},[1487,12509,12510,12552],{},[1490,12511,12512,12514,12520,12522,12524,12526,12528,12530,12532,12534,12536,12538,12540,12542,12548,12550],{},[1493,12513,1495],{},[2315,12515,12516,12518],{},[1493,12517,1998],{},[1506,12519,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,12521,1508],{},[1506,12523,1888],{},[1680,12525,1775],{},[1506,12527,2162],{},[1680,12529,1691],{},[1493,12531,1520],{},[1506,12533,1508],{},[1680,12535,1871],{},[1988,12537,1990],{},[1506,12539,2111],{},[1988,12541,1990],{},[2315,12543,12544,12546],{},[1493,12545,1520],{},[1506,12547,2287],{},[1506,12549,1508],{},[1680,12551,1752],{},[1528,12553,12554],{"encoding":1530},"MC' = -10 + 2Q = 0 \\;\\Longrightarrow\\; Q^* = 5",[1030,12556,12557,12595],{},[1035,12558,12560],{"className":12559},[1480],[1482,12561,12562],{"xmlns":1484},[1487,12563,12564,12592],{},[1490,12565,12566,12568,12578,12580,12582,12584,12586,12588,12590],{},[1493,12567,1495],{},[2315,12569,12570,12572],{},[1493,12571,1998],{},[1490,12573,12574,12576],{},[1506,12575,6927],{"mathvariant":1516},[1506,12577,6927],{"mathvariant":1516},[1506,12579,1553],{"stretchy":1552},[1680,12581,1752],{},[1506,12583,1564],{"stretchy":1552},[1506,12585,1508],{},[1680,12587,1691],{},[1506,12589,2796],{},[1680,12591,1871],{},[1528,12593,12594],{"encoding":1530},"MC''(5) = 2 > 0"," → minimum.",[1035,12597,12599],{"className":12598},[1480],[1482,12600,12601],{"xmlns":1484,"display":1485},[1487,12602,12603,12639],{},[1490,12604,12605,12607,12609,12611,12613,12615,12617,12619,12621,12623,12625,12627,12629],{},[1493,12606,1495],{},[1493,12608,1998],{},[1506,12610,1553],{"stretchy":1552},[1680,12612,1752],{},[1506,12614,1564],{"stretchy":1552},[1506,12616,1508],{},[1680,12618,2292],{},[1506,12620,1888],{},[1680,12622,2292],{},[1506,12624,2162],{},[1680,12626,2309],{},[1506,12628,1508],{},[1976,12630,12631],{"notation":1978},[1869,12632,12633],{"scriptlevel":1871,"displaystyle":1552},[1869,12634,12635],{"scriptlevel":1871,"displaystyle":1552},[1869,12636,12637],{"scriptlevel":1871,"displaystyle":1041},[1680,12638,2309],{},[1528,12640,12641],{"encoding":1530},"MC(5) = 50 - 50 + 25 = \\boxed{25}",[1304,12643,12645],{"id":12644},"c-δmc-při-q-20-30","(c) ΔMC při Q: 20 → 30",[1030,12647,12648],{},[1047,12649,2964],{},[1035,12651,12653],{"className":12652},[1480],[1482,12654,12655],{"xmlns":1484,"display":1485},[1487,12656,12657,12721],{},[1490,12658,12659,12661,12663,12665,12667,12669,12675,12677,12679,12681,12683,12685,12687,12689,12691,12693,12695,12697,12699,12701,12703,12705,12707,12709,12711,12713,12715,12717,12719],{},[1493,12660,2976],{"mathvariant":1516},[1493,12662,1495],{},[1493,12664,1998],{},[1506,12666,2343],{},[1493,12668,1495],{},[2315,12670,12671,12673],{},[1493,12672,1998],{},[1506,12674,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,12676,1553],{"stretchy":1552},[1493,12678,1520],{},[1506,12680,1564],{"stretchy":1552},[1506,12682,1714],{},[1493,12684,2976],{"mathvariant":1516},[1493,12686,1520],{},[1506,12688,1508],{},[1506,12690,1553],{"stretchy":1552},[1506,12692,1888],{},[1680,12694,1775],{},[1506,12696,2162],{},[1680,12698,1691],{},[1506,12700,1714],{},[1680,12702,8436],{},[1506,12704,1564],{"stretchy":1552},[1506,12706,1714],{},[1680,12708,1775],{},[1506,12710,1508],{},[1680,12712,6956],{},[1506,12714,1714],{},[1680,12716,1775],{},[1506,12718,1508],{},[1680,12720,5231],{},[1528,12722,12723],{"encoding":1530},"\\Delta MC \\approx MC'(Q) \\cdot \\Delta Q = (-10 + 2 \\cdot 20) \\cdot 10 = 30 \\cdot 10 = 300",[1030,12725,12726],{},[1047,12727,3029],{},[1035,12729,12731],{"className":12730},[1480],[1482,12732,12733],{"xmlns":1484,"display":1485},[1487,12734,12735,12782],{},[1490,12736,12737,12739,12741,12743,12745,12747,12749,12751,12753,12755,12757,12759,12761,12764,12766,12768,12770,12772,12774,12776,12778,12780],{},[1493,12738,1495],{},[1493,12740,1998],{},[1506,12742,1553],{"stretchy":1552},[1680,12744,6956],{},[1506,12746,1564],{"stretchy":1552},[1506,12748,1508],{},[1680,12750,2292],{},[1506,12752,1888],{},[1680,12754,5231],{},[1506,12756,2162],{},[1680,12758,7032],{},[1506,12760,1508],{},[1680,12762,12763],{},"650",[1506,12765,6065],{"separator":1041},[1912,12767],{"width":2108},[1493,12769,1495],{},[1493,12771,1998],{},[1506,12773,1553],{"stretchy":1552},[1680,12775,8436],{},[1506,12777,1564],{"stretchy":1552},[1506,12779,1508],{},[1680,12781,8140],{},[1528,12783,12784],{"encoding":1530},"MC(30) = 50 - 300 + 900 = 650; \\quad MC(20) = 250",[1035,12786,12788],{"className":12787},[1480],[1482,12789,12790],{"xmlns":1484,"display":1485},[1487,12791,12792,12832],{},[1490,12793,12794,12796,12798,12820,12822,12824,12826,12828,12830],{},[1493,12795,2976],{"mathvariant":1516},[1493,12797,1495],{},[1497,12799,12800,12802],{},[1493,12801,1998],{},[1490,12803,12804,12806,12812,12814],{},[1988,12805,1030],{},[2178,12807,12808,12810],{"accent":1041},[1988,12809,7740],{},[1506,12811,8576],{},[1988,12813,8579],{},[2178,12815,12816,12818],{"accent":1041},[1988,12817,8584],{},[1506,12819,3055],{},[1506,12821,1508],{},[1680,12823,12763],{},[1506,12825,1888],{},[1680,12827,8140],{},[1506,12829,1508],{},[1680,12831,5765],{},[1528,12833,12834],{"encoding":1530},"\\Delta MC_{\\text{přesné}} = 650 - 250 = 400",[1030,12836,12837,12839,12840,12843,12844,12864],{},[1047,12838,8607],{}," aproximace 300 vs. přesných 400 → ",[1047,12841,12842],{},"chyba 25 %",". Důvod: ",[1035,12845,12847],{"className":12846},[1480],[1482,12848,12849],{"xmlns":1484},[1487,12850,12851,12861],{},[1490,12852,12853,12855,12857,12859],{},[1493,12854,2976],{"mathvariant":1516},[1493,12856,1520],{},[1506,12858,1508],{},[1680,12860,1775],{},[1528,12862,12863],{"encoding":1530},"\\Delta Q = 10"," je velký krok, MC je kvadratická (nelineární), takže lineární aproximace systematicky podhodnocuje (druhá derivace je kladná).",[1023,12866,12868,12875],{"className":12867,"dataCallout":1155},[1026,1154],[1030,12869,12871,12874],{"className":12870},[1033],[1035,12872],{"className":12873,"ariaHidden":1041},[1038,1162,1040],"Diferenciál v kvadratické funkci",[1030,12876,12877,12878,12919,12920,12982,12983,13029,13030,13050,13051,1732,13069,13087,13088,13110],{},"Pro funkci ",[1035,12879,12881],{"className":12880},[1480],[1482,12882,12883],{"xmlns":1484},[1487,12884,12885,12916],{},[1490,12886,12887,12890,12892,12894,12896,12898,12900,12906,12908,12910,12912,12914],{},[1493,12888,12889],{},"f",[1506,12891,1553],{"stretchy":1552},[1493,12893,1520],{},[1506,12895,1564],{"stretchy":1552},[1506,12897,1508],{},[1493,12899,1052],{},[2315,12901,12902,12904],{},[1493,12903,1520],{},[1680,12905,1691],{},[1506,12907,2162],{},[1493,12909,2394],{},[1493,12911,1520],{},[1506,12913,2162],{},[1493,12915,8730],{},[1528,12917,12918],{"encoding":1530},"f(Q) = aQ^2 + bQ + c"," platí: ",[1035,12921,12923],{"className":12922},[1480],[1482,12924,12925],{"xmlns":1484},[1487,12926,12927,12979],{},[1490,12928,12929,12931,12933,12935,12937,12939,12941,12943,12945,12947,12949,12951,12953,12955,12957,12959,12961,12963,12965,12967,12969,12971,12973],{},[1493,12930,12889],{},[1506,12932,1553],{"stretchy":1552},[1493,12934,1520],{},[1506,12936,2162],{},[1493,12938,2976],{"mathvariant":1516},[1506,12940,1564],{"stretchy":1552},[1506,12942,1888],{},[1493,12944,12889],{},[1506,12946,1553],{"stretchy":1552},[1493,12948,1520],{},[1506,12950,1564],{"stretchy":1552},[1506,12952,1508],{},[1506,12954,1553],{"stretchy":1552},[1680,12956,1691],{},[1493,12958,1052],{},[1493,12960,1520],{},[1506,12962,2162],{},[1493,12964,2394],{},[1506,12966,1564],{"stretchy":1552},[1493,12968,2976],{"mathvariant":1516},[1506,12970,2162],{},[1493,12972,1052],{},[2315,12974,12975,12977],{},[1493,12976,2976],{"mathvariant":1516},[1680,12978,1691],{},[1528,12980,12981],{"encoding":1530},"f(Q + \\Delta) - f(Q) = (2aQ + b) \\Delta + a \\Delta^2",".\nLineární aproximace zachytí jen první člen (",[1035,12984,12986],{"className":12985},[1480],[1482,12987,12988],{"xmlns":1484},[1487,12989,12990,13026],{},[1490,12991,12992,12998,13000,13002,13004,13006,13008,13010,13012,13014,13016,13018,13020,13022,13024],{},[2315,12993,12994,12996],{},[1493,12995,12889],{},[1506,12997,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,12999,1553],{"stretchy":1552},[1493,13001,1520],{},[1506,13003,1564],{"stretchy":1552},[1506,13005,1714],{},[1493,13007,2976],{"mathvariant":1516},[1506,13009,1508],{},[1506,13011,1553],{"stretchy":1552},[1680,13013,1691],{},[1493,13015,1052],{},[1493,13017,1520],{},[1506,13019,2162],{},[1493,13021,2394],{},[1506,13023,1564],{"stretchy":1552},[1493,13025,2976],{"mathvariant":1516},[1528,13027,13028],{"encoding":1530},"f'(Q) \\cdot \\Delta = (2aQ + b) \\Delta","), zatímco kvadratický člen ",[1035,13031,13033],{"className":13032},[1480],[1482,13034,13035],{"xmlns":1484},[1487,13036,13037,13047],{},[1490,13038,13039,13041],{},[1493,13040,1052],{},[2315,13042,13043,13045],{},[1493,13044,2976],{"mathvariant":1516},[1680,13046,1691],{},[1528,13048,13049],{"encoding":1530},"a \\Delta^2"," vypadne.\nZde: ",[1035,13052,13054],{"className":13053},[1480],[1482,13055,13056],{"xmlns":1484},[1487,13057,13058,13066],{},[1490,13059,13060,13062,13064],{},[1493,13061,1052],{},[1506,13063,1508],{},[1680,13065,1682],{},[1528,13067,13068],{"encoding":1530},"a = 1",[1035,13070,13072],{"className":13071},[1480],[1482,13073,13074],{"xmlns":1484},[1487,13075,13076,13084],{},[1490,13077,13078,13080,13082],{},[1493,13079,2976],{"mathvariant":1516},[1506,13081,1508],{},[1680,13083,1775],{},[1528,13085,13086],{"encoding":1530},"\\Delta = 10"," → vynechaný člen ",[1035,13089,13091],{"className":13090},[1480],[1482,13092,13093],{"xmlns":1484},[1487,13094,13095,13107],{},[1490,13096,13097,13099,13101,13103,13105],{},[1680,13098,1682],{},[1506,13100,1714],{},[1680,13102,2916],{},[1506,13104,1508],{},[1680,13106,2916],{},[1528,13108,13109],{"encoding":1530},"1 \\cdot 100 = 100",", což přesně odpovídá rozdílu (400 − 300 = 100). ✓",[1246,13112],{},[1065,13114,13116,13117,13119],{"id":13115},"z6q4-40-b-model-c-i-jako-z1q4-s-odlišným-e","Z6\u002FQ4 ",[1035,13118,1144],{}," — Model C-I (jako Z1\u002FQ4 s odlišným (e))",[1030,13121,13122],{},[1047,13123,13124],{},"(a)–(d) totožné se Z1\u002FQ4:",[1203,13126,13127,13171,13174,13199],{},[1206,13128,13129],{},[1035,13130,13132],{"className":13131},[1480],[1482,13133,13134],{"xmlns":1484},[1487,13135,13136,13168],{},[1490,13137,13138,13144,13146,13148,13150,13152,13154,13156,13158,13160,13162,13164,13166],{},[2315,13139,13140,13142],{},[1493,13141,1791],{},[1493,13143,2711],{},[1506,13145,1508],{},[1506,13147,1553],{"stretchy":1552},[1493,13149,2394],{},[1506,13151,2162],{},[1493,13153,2662],{},[1506,13155,1564],{"stretchy":1552},[1493,13157,1709],{"mathvariant":1516},[1506,13159,1553],{"stretchy":1552},[1680,13161,1682],{},[1506,13163,1888],{},[1493,13165,1052],{},[1506,13167,1564],{"stretchy":1552},[1528,13169,13170],{"encoding":1530},"Y^E = (b + I)\u002F(1 - a)",[1206,13172,13173],{},"∂Y\u002F∂a > 0, ∂Y\u002F∂b > 0, ∂Y\u002F∂I > 0",[1206,13175,13176,13177],{},"(c) ",[1035,13178,13180],{"className":13179},[1480],[1482,13181,13182],{"xmlns":1484},[1487,13183,13184,13196],{},[1490,13185,13186,13192,13194],{},[2315,13187,13188,13190],{},[1493,13189,1791],{},[1493,13191,2711],{},[1506,13193,1508],{},[1680,13195,2952],{},[1528,13197,13198],{"encoding":1530},"Y^E = 1375",[1206,13200,13201],{},"(d) ΔI = 100 → ΔY = 125 (přesné = přibližné, lineární v I)",[1304,13203,13205],{"id":13204},"e-da-01-db-2-di-10","(e) da = −0,1; db = 2; dI = 10",[1030,13207,13208,13211],{},[1047,13209,13210],{},"Aproximace"," (multiplikátory v hladině (c) jako u Z1\u002FQ4):",[1035,13213,13215],{"className":13214},[1480],[1482,13216,13217],{"xmlns":1484,"display":1485},[1487,13218,13219,13256],{},[1490,13220,13221,13223,13225,13227,13229,13231,13233,13235,13238,13240,13242,13244,13246,13248,13250,13252,13254],{},[1493,13222,2976],{"mathvariant":1516},[1493,13224,1791],{},[1506,13226,2343],{},[1680,13228,3171],{},[1506,13230,1714],{},[1506,13232,1553],{"stretchy":1552},[1506,13234,1888],{},[1680,13236,13237],{},"0,1",[1506,13239,1564],{"stretchy":1552},[1506,13241,2162],{},[1680,13243,3196],{},[1506,13245,1714],{},[1680,13247,1691],{},[1506,13249,2162],{},[1680,13251,3196],{},[1506,13253,1714],{},[1680,13255,1775],{},[1528,13257,13258],{"encoding":1530},"\\Delta Y \\approx 1718{,}75 \\cdot (-0{,}1) + 1{,}25 \\cdot 2 + 1{,}25 \\cdot 10",[1035,13260,13262],{"className":13261},[1480],[1482,13263,13264],{"xmlns":1484,"display":1485},[1487,13265,13266,13301],{},[1490,13267,13268,13270,13272,13275,13277,13280,13282,13284,13286],{},[1506,13269,1508],{},[1506,13271,1888],{},[1680,13273,13274],{},"171,875",[1506,13276,2162],{},[1680,13278,13279],{},"2,5",[1506,13281,2162],{},[1680,13283,3252],{},[1506,13285,1508],{},[1976,13287,13288],{"notation":1978},[1869,13289,13290],{"scriptlevel":1871,"displaystyle":1552},[1869,13291,13292],{"scriptlevel":1871,"displaystyle":1552},[1869,13293,13294],{"scriptlevel":1871,"displaystyle":1041},[1490,13295,13296,13298],{},[1506,13297,1888],{},[1680,13299,13300],{},"156,875",[1528,13302,13303],{"encoding":1530},"= -171{,}875 + 2{,}5 + 12{,}5 = \\boxed{-156{,}875}",[1030,13305,13306,13308],{},[1047,13307,3273],{}," (a → 0,1; b → 102; I → 1010):",[1035,13310,13312],{"className":13311},[1480],[1482,13313,13314],{"xmlns":1484,"display":1485},[1487,13315,13316,13374],{},[1490,13317,13318,13334,13336,13355,13357,13365,13367,13369,13371],{},[1697,13319,13320,13322,13332],{},[1493,13321,1791],{},[1490,13323,13324,13326],{},[1988,13325,3047],{},[2178,13327,13328,13330],{"accent":1041},[1988,13329,3052],{},[1506,13331,3055],{},[1493,13333,2711],{},[1506,13335,1508],{},[1510,13337,13338,13347],{},[1490,13339,13340,13343,13345],{},[1680,13341,13342],{},"102",[1506,13344,2162],{},[1680,13346,3313],{},[1490,13348,13349,13351,13353],{},[1680,13350,1682],{},[1506,13352,1888],{},[1680,13354,13237],{},[1506,13356,1508],{},[1510,13358,13359,13362],{},[1680,13360,13361],{},"1112",[1680,13363,13364],{},"0,9",[1506,13366,2343],{},[1680,13368,1682],{},[1988,13370,5016],{},[1680,13372,13373],{},"235,56",[1528,13375,13376],{"encoding":1530},"Y^E_{\\text{nový}} = \\frac{102 + 1010}{1 - 0{,}1} = \\frac{1112}{0{,}9} \\approx 1\\,235{,}56",[1035,13378,13380],{"className":13379},[1480],[1482,13381,13382],{"xmlns":1484,"display":1485},[1487,13383,13384,13429],{},[1490,13385,13386,13388,13410,13412,13414,13416,13418,13420,13422,13424,13426],{},[1493,13387,2976],{"mathvariant":1516},[1497,13389,13390,13392],{},[1493,13391,1791],{},[1490,13393,13394,13396,13402,13404],{},[1988,13395,1030],{},[2178,13397,13398,13400],{"accent":1041},[1988,13399,7740],{},[1506,13401,8576],{},[1988,13403,8579],{},[2178,13405,13406,13408],{"accent":1041},[1988,13407,8584],{},[1506,13409,3055],{},[1506,13411,1508],{},[1680,13413,1682],{},[1988,13415,5016],{},[1680,13417,13373],{},[1506,13419,1888],{},[1680,13421,2952],{},[1506,13423,2343],{},[1506,13425,1888],{},[1680,13427,13428],{},"139,44",[1528,13430,13431],{"encoding":1530},"\\Delta Y_{\\text{přesné}} = 1\\,235{,}56 - 1375 \\approx -139{,}44",[1030,13433,13434,13436,13437,13459,13460,13482],{},[1047,13435,8607],{}," aproximace −156,875 vs. přesných −139,44 → chyba ~12 %. Změna ",[1035,13438,13440],{"className":13439},[1480],[1482,13441,13442],{"xmlns":1484},[1487,13443,13444,13456],{},[1490,13445,13446,13448,13450,13452,13454],{},[1493,13447,3384],{},[1493,13449,1052],{},[1506,13451,1508],{},[1506,13453,1888],{},[1680,13455,13237],{},[1528,13457,13458],{"encoding":1530},"da = -0{,}1"," je menší než v Z1\u002FQ4 (tam ",[1035,13461,13463],{"className":13462},[1480],[1482,13464,13465],{"xmlns":1484},[1487,13466,13467,13479],{},[1490,13468,13469,13471,13473,13475,13477],{},[1493,13470,3384],{},[1493,13472,1052],{},[1506,13474,1508],{},[1506,13476,2162],{},[1680,13478,2929],{},[1528,13480,13481],{"encoding":1530},"da = +0{,}2","), proto i chyba aproximace je menší.",[1023,13484,13486,13493,13546],{"className":13485,"dataCallout":582},[1026,1186],[1030,13487,13489,13492],{"className":13488},[1033],[1035,13490],{"className":13491,"ariaHidden":1041},[1038,1193,1040],"Srovnání Z1\u002FQ4(e) a Z6\u002FQ4(e)",[1073,13494,13495,13513],{},[1076,13496,13497],{},[1079,13498,13499,13502,13505,13507,13510],{},[1082,13500,13501],{},"Změna",[1082,13503,13504],{},"da",[1082,13506,13210],{},[1082,13508,13509],{},"Přesné",[1082,13511,13512],{},"Chyba",[1092,13514,13515,13529],{},[1079,13516,13517,13520,13523,13525,13527],{},[1097,13518,13519],{},"Z1\u002FQ4(e)",[1097,13521,13522],{},"+0,2",[1097,13524,3265],{},[1097,13526,3352],{},[1097,13528,3371],{},[1079,13530,13531,13534,13537,13540,13543],{},[1097,13532,13533],{},"Z6\u002FQ4(e)",[1097,13535,13536],{},"−0,1",[1097,13538,13539],{},"−156,9",[1097,13541,13542],{},"−139,4",[1097,13544,13545],{},"12 %",[1030,13547,13548,13549,13569],{},"Větší ",[1035,13550,13552],{"className":13551},[1480],[1482,13553,13554],{"xmlns":1484},[1487,13555,13556,13566],{},[1490,13557,13558,13560,13562,13564],{},[1493,13559,8620],{"mathvariant":1516},[1493,13561,3384],{},[1493,13563,1052],{},[1493,13565,8620],{"mathvariant":1516},[1528,13567,13568],{"encoding":1530},"|da|"," → větší chyba lineárního přibližení.",[1246,13571],{},[1019,13573,13575],{"id":13574},"zadání-7","Zadání 7",[1065,13577,13579,13580,13582],{"id":13578},"z7q1-10-b-funkce-úspor","Z7\u002FQ1 ",[1035,13581,1102],{}," — Funkce úspor",[1030,13584,13585,13587],{},[1047,13586,1263],{}," (a) S = 0,3Y − 50; (b) S = 2,5Y − 20; (c) S = 0,3Y + 50; (d) S = −0,3Y − 150; (e) S = 0,03Y − 100.",[1030,13589,13590,13592,13593,13625],{},[1047,13591,1832],{}," Lineární model úspor je ",[1035,13594,13596],{"className":13595},[1480],[1482,13597,13598],{"xmlns":1484},[1487,13599,13600,13622],{},[1490,13601,13602,13604,13606,13608,13610,13612,13614,13616,13618,13620],{},[1493,13603,2001],{},[1506,13605,1508],{},[1506,13607,1553],{"stretchy":1552},[1680,13609,1682],{},[1506,13611,1888],{},[1493,13613,1052],{},[1506,13615,1564],{"stretchy":1552},[1493,13617,1791],{},[1506,13619,1888],{},[1493,13621,2394],{},[1528,13623,13624],{"encoding":1530},"S = (1 - a)Y - b"," kde 0 \u003C a \u003C 1, b > 0. Tedy:",[1203,13627,13628,13634],{},[1206,13629,13630,13633],{},[1047,13631,13632],{},"MPS = 1 − a ∈ (0, 1)"," (sklon kladný, ale menší než 1);",[1206,13635,13636,13669],{},[1047,13637,13638,13639],{},"autonomní úspory ",[1035,13640,13642],{"className":13641},[1480],[1482,13643,13644],{"xmlns":1484},[1487,13645,13646,13666],{},[1490,13647,13648,13650,13652,13654,13656,13658,13660,13662,13664],{},[1493,13649,2001],{},[1506,13651,1553],{"stretchy":1552},[1680,13653,1871],{},[1506,13655,1564],{"stretchy":1552},[1506,13657,1508],{},[1506,13659,1888],{},[1493,13661,2394],{},[1506,13663,3961],{},[1680,13665,1871],{},[1528,13667,13668],{"encoding":1530},"S(0) = -b \u003C 0"," (záporné, neboť b > 0).",[1030,13671,1295,13672,13677],{},[1052,13673,13676],{"className":13674,"dataFsResolvedFilePath":2622,"href":13675},[1055],"\u002Fwiki\u002Fnarodni-duchod#Spotřeba a úspory","Spotřeba a úspory"," (vzorec 7.4).",[1304,13679,1307],{"id":13680},"rozbor-3",[1073,13682,13683,13699],{},[1076,13684,13685],{},[1079,13686,13687,13689,13691,13694,13697],{},[1082,13688],{},[1082,13690,1318],{},[1082,13692,13693],{},"MPS",[1082,13695,13696],{},"S(0)",[1082,13698,1327],{},[1092,13700,13701,13718,13736,13755,13773],{},[1079,13702,13703,13705,13708,13711,13714],{},[1097,13704,1334],{},[1097,13706,13707],{},"0,3Y − 50",[1097,13709,13710],{},"0,3 ∈ (0,1) ✓",[1097,13712,13713],{},"−50 \u003C 0 ✓",[1097,13715,13716],{},[1047,13717,1348],{},[1079,13719,13720,13722,13725,13730,13732],{},[1097,13721,1353],{},[1097,13723,13724],{},"2,5Y − 20",[1097,13726,13727,1402],{},[1047,13728,13729],{},"2,5 > 1",[1097,13731,1405],{},[1097,13733,13734],{},[1047,13735,1387],{},[1079,13737,13738,13740,13743,13746,13751],{},[1097,13739,1370],{},[1097,13741,13742],{},"0,3Y + 50",[1097,13744,13745],{},"0,3 ✓",[1097,13747,13748,1402],{},[1047,13749,13750],{},"+50 > 0",[1097,13752,13753],{},[1047,13754,1387],{},[1079,13756,13757,13759,13762,13767,13769],{},[1097,13758,1392],{},[1097,13760,13761],{},"−0,3Y − 150",[1097,13763,13764,1402],{},[1047,13765,13766],{},"−0,3 \u003C 0",[1097,13768,1405],{},[1097,13770,13771],{},[1047,13772,1387],{},[1079,13774,13775,13777,13780,13783,13786],{},[1097,13776,1414],{},[1097,13778,13779],{},"0,03Y − 100",[1097,13781,13782],{},"0,03 ∈ (0,1) ✓",[1097,13784,13785],{},"−100 \u003C 0 ✓",[1097,13787,13788],{},[1047,13789,1348],{},[1030,13791,13792,13794],{},[1047,13793,8917],{}," MPS = 2,5 by znamenalo MPC = 1 − 2,5 = −1,5 — záporná spotřeba na další korunu důchodu, ekonomicky nesmysl.",[1030,13796,13797,13799,13800,13818],{},[1047,13798,1431],{}," Kladné autonomní úspory implikují ",[1035,13801,13803],{"className":13802},[1480],[1482,13804,13805],{"xmlns":1484},[1487,13806,13807,13815],{},[1490,13808,13809,13811,13813],{},[1493,13810,2394],{},[1506,13812,3961],{},[1680,13814,1871],{},[1528,13816,13817],{"encoding":1530},"b \u003C 0",", tj. autonomní spotřeba C(0) = b \u003C 0 — také nesmysl.",[1030,13820,13821,13823],{},[1047,13822,1437],{}," Záporné MPS znamená, že s růstem důchodu úspory klesají — porušuje princip „úspory rostou s důchodem\".",[1023,13825,13827,13834],{"className":13826,"dataCallout":1443},[1026,1442],[1030,13828,13830,13833],{"className":13829},[1033],[1035,13831],{"className":13832,"ariaHidden":1041},[1038,1450,1040],"Filtr v 5 sekundách",[1276,13835,13836,13839],{},[1206,13837,13838],{},"Sklon (koeficient u Y) musí být v intervalu (0, 1).",[1206,13840,13841],{},"Absolutní člen musí být záporný (= autonomní úspory \u003C 0).\nPokud něco z toho neplatí, není to standardní funkce úspor.",[1246,13843],{},[1065,13845,13847,13848,13850],{"id":13846},"z7q2-20-b-mrcs-zadání-píše-mrts-ale-formulace-je-mrcs","Z7\u002FQ2 ",[1035,13849,1116],{}," — MRCS (zadání píše MRTS, ale formulace je MRCS)",[1030,13852,13853,13855],{},[1047,13854,1121],{}," stejné jako Z3\u002FQ2.",[1030,13857,13858,1656,13861,2632],{},[1047,13859,13860],{},"Vzorec:",[1035,13862,13864],{"className":13863},[1480],[1482,13865,13866],{"xmlns":1484},[1487,13867,13868,13898],{},[1490,13869,13870,13872,13874,13876,13878,13880,13882,13888,13890,13892],{},[1493,13871,1495],{},[1493,13873,1995],{},[1493,13875,1998],{},[1493,13877,2001],{},[1506,13879,1508],{},[1493,13881,1495],{},[1497,13883,13884,13886],{},[1493,13885,1668],{},[1680,13887,1682],{},[1493,13889,1709],{"mathvariant":1516},[1493,13891,1495],{},[1497,13893,13894,13896],{},[1493,13895,1668],{},[1680,13897,1691],{},[1528,13899,9084],{"encoding":1530},[1030,13901,13902,13905,13906,9103,13923,13940],{},[1047,13903,13904],{},"MRCS(100,200) = 5:"," spotřebitel je ochoten obětovat 5 jednotek ",[1035,13907,13909],{"className":13908},[1480],[1482,13910,13911],{"xmlns":1484},[1487,13912,13913,13921],{},[1490,13914,13915],{},[1497,13916,13917,13919],{},[1493,13918,1520],{},[1680,13920,1691],{},[1528,13922,6683],{"encoding":1530},[1035,13924,13926],{"className":13925},[1480],[1482,13927,13928],{"xmlns":1484},[1487,13929,13930,13938],{},[1490,13931,13932],{},[1497,13933,13934,13936],{},[1493,13935,1520],{},[1680,13937,1682],{},[1528,13939,6702],{"encoding":1530}," navíc se zachovanou užitečností.",[1023,13942,13944,13951],{"className":13943,"dataCallout":1155},[1026,1154],[1030,13945,13947,13950],{"className":13946},[1033],[1035,13948],{"className":13949,"ariaHidden":1041},[1038,1162,1040],"Pozor na formulaci úlohy",[1030,13952,13953,13954,13957,13958,13961,13962,13965],{},"Zadání uvádí „mezní míru technické substituce MRCS\" — kombinace pojmu ",[1176,13955,13956],{},"technické substituce"," (MRTS, produkce) a symbolu ",[1176,13959,13960],{},"MRCS"," (komoditní substituce, užitečnost). Pokud by byla otázka ",[1047,13963,13964],{},"MRTS(L,K) = 5",", znamenalo by to: 1 jednotku práce lze nahradit 5 jednotkami kapitálu se zachovanou produkcí. Ostatní obsah úlohy se kryje.",[1246,13967],{},[1065,13969,13971,13972,13974],{"id":13970},"z7q3-30-b-tržní-rovnováha-s-nelineární-nabídkou","Z7\u002FQ3 ",[1035,13973,1130],{}," — Tržní rovnováha s nelineární nabídkou",[1030,13976,13977,1656,13979,1732,14009,14041,14042,14060,14061,14079,14080,14098],{},[1047,13978,1263],{},[1035,13980,13982],{"className":13981},[1480],[1482,13983,13984],{"xmlns":1484},[1487,13985,13986,14006],{},[1490,13987,13988,13990,13992,13994,13996,13998,14000,14002,14004],{},[1493,13989,3712],{},[1506,13991,1553],{"stretchy":1552},[1493,13993,1520],{},[1506,13995,1564],{"stretchy":1552},[1506,13997,1508],{},[1680,13999,9319],{},[1506,14001,1888],{},[1680,14003,1691],{},[1493,14005,1520],{},[1528,14007,14008],{"encoding":1530},"D(Q) = 18 - 2Q",[1035,14010,14012],{"className":14011},[1480],[1482,14013,14014],{"xmlns":1484},[1487,14015,14016,14038],{},[1490,14017,14018,14020,14022,14024,14026,14028,14030,14032],{},[1493,14019,2001],{},[1506,14021,1553],{"stretchy":1552},[1493,14023,1520],{},[1506,14025,1564],{"stretchy":1552},[1506,14027,1508],{},[1680,14029,3201],{},[1506,14031,2162],{},[2315,14033,14034,14036],{},[1493,14035,1520],{},[1680,14037,1691],{},[1528,14039,14040],{"encoding":1530},"S(Q) = 3 + Q^2",".\n(a) ",[1035,14043,14045],{"className":14044},[1480],[1482,14046,14047],{"xmlns":1484},[1487,14048,14049,14057],{},[1490,14050,14051],{},[2315,14052,14053,14055],{},[1493,14054,1520],{},[1493,14056,2711],{},[1528,14058,14059],{"encoding":1530},"Q^E"," + náčrt; (b) elasticita poptávky při ",[1035,14062,14064],{"className":14063},[1480],[1482,14065,14066],{"xmlns":1484},[1487,14067,14068,14076],{},[1490,14069,14070,14072,14074],{},[1493,14071,1501],{},[1506,14073,1508],{},[1680,14075,1775],{},[1528,14077,14078],{"encoding":1530},"P = 10","; (c) ",[1035,14081,14083],{"className":14082},[1480],[1482,14084,14085],{"xmlns":1484},[1487,14086,14087,14095],{},[1490,14088,14089],{},[2315,14090,14091,14093],{},[1493,14092,1520],{},[1506,14094,2287],{},[1528,14096,14097],{"encoding":1530},"Q^*"," pro max TR; (d) přebytek spotřebitele a výrobce při rovnovážném množství.",[1304,14100,14102],{"id":14101},"a-rovnovážné-množství","(a) Rovnovážné množství",[1035,14104,14106],{"className":14105},[1480],[1482,14107,14108],{"xmlns":1484,"display":1485},[1487,14109,14110,14158],{},[1490,14111,14112,14114,14116,14118,14120,14122,14124,14126,14132,14134,14136,14138,14144,14146,14148,14150,14152,14154,14156],{},[1680,14113,9319],{},[1506,14115,1888],{},[1680,14117,1691],{},[1493,14119,1520],{},[1506,14121,1508],{},[1680,14123,3201],{},[1506,14125,2162],{},[2315,14127,14128,14130],{},[1493,14129,1520],{},[1680,14131,1691],{},[1988,14133,1990],{},[1506,14135,2111],{},[1988,14137,1990],{},[2315,14139,14140,14142],{},[1493,14141,1520],{},[1680,14143,1691],{},[1506,14145,2162],{},[1680,14147,1691],{},[1493,14149,1520],{},[1506,14151,1888],{},[1680,14153,9787],{},[1506,14155,1508],{},[1680,14157,1871],{},[1528,14159,14160],{"encoding":1530},"18 - 2Q = 3 + Q^2 \\;\\Longrightarrow\\; Q^2 + 2Q - 15 = 0",[1035,14162,14164],{"className":14163},[1480],[1482,14165,14166],{"xmlns":1484,"display":1485},[1487,14167,14168,14234],{},[1490,14169,14170,14172,14174,14196,14198,14212,14214,14216,14218,14220,14222,14224,14226,14228,14230,14232],{},[1493,14171,1520],{},[1506,14173,1508],{},[1510,14175,14176,14194],{},[1490,14177,14178,14180,14182,14184],{},[1506,14179,1888],{},[1680,14181,1691],{},[1506,14183,11304],{},[2324,14185,14186],{},[1490,14187,14188,14190,14192],{},[1680,14189,4007],{},[1506,14191,2162],{},[1680,14193,4965],{},[1680,14195,1691],{},[1506,14197,1508],{},[1510,14199,14200,14210],{},[1490,14201,14202,14204,14206,14208],{},[1506,14203,1888],{},[1680,14205,1691],{},[1506,14207,11304],{},[1680,14209,6138],{},[1680,14211,1691],{},[1988,14213,1990],{},[1506,14215,2111],{},[1988,14217,1990],{},[1493,14219,1520],{},[1506,14221,1508],{},[1680,14223,3201],{},[1988,14225,7373],{},[1493,14227,1520],{},[1506,14229,1508],{},[1506,14231,1888],{},[1680,14233,1752],{},[1528,14235,14236],{"encoding":1530},"Q = \\frac{-2 \\pm \\sqrt{4 + 60}}{2} = \\frac{-2 \\pm 8}{2} \\;\\Longrightarrow\\; Q = 3 \\text{ nebo } Q = -5",[1035,14238,14240],{"className":14239},[1480],[1482,14241,14242],{"xmlns":1484,"display":1485},[1487,14243,14244,14292],{},[1490,14245,14246],{},[1976,14247,14248],{"notation":1978},[1869,14249,14250],{"scriptlevel":1871,"displaystyle":1552},[1869,14251,14252],{"scriptlevel":1871,"displaystyle":1552},[1869,14253,14254],{"scriptlevel":1871,"displaystyle":1041},[1490,14255,14256,14258,14264,14266,14268,14270,14272,14278,14280,14282,14284,14286,14288,14290],{},[1988,14257,1990],{},[2315,14259,14260,14262],{},[1493,14261,1520],{},[1493,14263,2711],{},[1506,14265,1508],{},[1680,14267,3201],{},[1506,14269,1559],{"separator":1041},[1912,14271],{"width":2108},[2315,14273,14274,14276],{},[1493,14275,1501],{},[1493,14277,2711],{},[1506,14279,1508],{},[1680,14281,9319],{},[1506,14283,1888],{},[1680,14285,7508],{},[1506,14287,1508],{},[1680,14289,6797],{},[1988,14291,1990],{},[1528,14293,14294],{"encoding":1530},"\\boxed{\\; Q^E = 3, \\quad P^E = 18 - 6 = 12 \\;}",[1030,14296,14297,14300,14301,2632],{},[1047,14298,14299],{},"Náčrt:"," D je klesající přímka z (0, 18) do (9, 0); S je rostoucí parabola z (0, 3); průsečík v ",[1035,14302,14304],{"className":14303},[1480],[1482,14305,14306],{"xmlns":1484},[1487,14307,14308,14324],{},[1490,14309,14310,14312,14315,14317,14319,14321],{},[1493,14311,2711],{},[1506,14313,14314],{"stretchy":1552},"[",[1680,14316,3201],{},[1506,14318,1559],{"separator":1041},[1680,14320,6797],{},[1506,14322,14323],{"stretchy":1552},"]",[1528,14325,14326],{"encoding":1530},"E[3, 12]",[1304,14328,14330],{"id":14329},"b-elasticita-poptávky-při-p-10","(b) Elasticita poptávky při P = 10",[1030,14332,14333,14334,1732,14377,14413,14414,11074,14431,2632],{},"Inverze: ",[1035,14335,14337],{"className":14336},[1480],[1482,14338,14339],{"xmlns":1484},[1487,14340,14341,14374],{},[1490,14342,14343,14345,14347,14349,14351,14353,14355,14357,14359,14361,14363,14366,14368,14370,14372],{},[1493,14344,1520],{},[1506,14346,1508],{},[1506,14348,1553],{"stretchy":1552},[1680,14350,9319],{},[1506,14352,1888],{},[1493,14354,1501],{},[1506,14356,1564],{"stretchy":1552},[1493,14358,1709],{"mathvariant":1516},[1680,14360,1691],{},[1506,14362,1508],{},[1680,14364,14365],{},"9",[1506,14367,1888],{},[1493,14369,1501],{},[1493,14371,1709],{"mathvariant":1516},[1680,14373,1691],{},[1528,14375,14376],{"encoding":1530},"Q = (18 - P)\u002F2 = 9 - P\u002F2",[1035,14378,14380],{"className":14379},[1480],[1482,14381,14382],{"xmlns":1484},[1487,14383,14384,14410],{},[1490,14385,14386,14400,14402,14404],{},[1510,14387,14388,14394],{},[1490,14389,14390,14392],{},[1493,14391,3384],{},[1493,14393,1520],{},[1490,14395,14396,14398],{},[1493,14397,3384],{},[1493,14399,1501],{},[1506,14401,1508],{},[1506,14403,1888],{},[1510,14405,14406,14408],{},[1680,14407,1682],{},[1680,14409,1691],{},[1528,14411,14412],{"encoding":1530},"\\frac{dQ}{dP} = -\\frac{1}{2}",". Při ",[1035,14415,14417],{"className":14416},[1480],[1482,14418,14419],{"xmlns":1484},[1487,14420,14421,14429],{},[1490,14422,14423,14425,14427],{},[1493,14424,1501],{},[1506,14426,1508],{},[1680,14428,1775],{},[1528,14430,14078],{"encoding":1530},[1035,14432,14434],{"className":14433},[1480],[1482,14435,14436],{"xmlns":1484},[1487,14437,14438,14446],{},[1490,14439,14440,14442,14444],{},[1493,14441,1520],{},[1506,14443,1508],{},[1680,14445,4007],{},[1528,14447,14448],{"encoding":1530},"Q = 4",[1035,14450,14452],{"className":14451},[1480],[1482,14453,14454],{"xmlns":1484,"display":1485},[1487,14455,14456,14526],{},[1490,14457,14458,14460,14462,14464,14470,14472,14486,14488,14490,14496,14498,14514,14516],{},[1493,14459,2711],{},[1506,14461,1508],{},[1506,14463,1888],{},[1510,14465,14466,14468],{},[1493,14467,1501],{},[1493,14469,1520],{},[1506,14471,1714],{},[1510,14473,14474,14480],{},[1490,14475,14476,14478],{},[1493,14477,3384],{},[1493,14479,1520],{},[1490,14481,14482,14484],{},[1493,14483,3384],{},[1493,14485,1501],{},[1506,14487,1508],{},[1506,14489,1888],{},[1510,14491,14492,14494],{},[1680,14493,1775],{},[1680,14495,4007],{},[1506,14497,1714],{},[1490,14499,14500,14502,14504,14512],{},[1506,14501,1553],{"fence":1041},[1506,14503,1888],{},[1869,14505,14506],{"scriptlevel":1871,"displaystyle":1552},[1510,14507,14508,14510],{},[1680,14509,1682],{},[1680,14511,1691],{},[1506,14513,1564],{"fence":1041},[1506,14515,1508],{},[1976,14517,14518],{"notation":1978},[1869,14519,14520],{"scriptlevel":1871,"displaystyle":1552},[1869,14521,14522],{"scriptlevel":1871,"displaystyle":1552},[1869,14523,14524],{"scriptlevel":1871,"displaystyle":1041},[1680,14525,3196],{},[1528,14527,14528],{"encoding":1530},"E = -\\frac{P}{Q} \\cdot \\frac{dQ}{dP} = -\\frac{10}{4} \\cdot \\left(-\\tfrac{1}{2}\\right) = \\boxed{1{,}25}",[1030,14530,14531,1656,14534,14552,14553,14556],{},[1047,14532,14533],{},"Klasifikace:",[1035,14535,14537],{"className":14536},[1480],[1482,14538,14539],{"xmlns":1484},[1487,14540,14541,14549],{},[1490,14542,14543,14545,14547],{},[1493,14544,2711],{},[1506,14546,2796],{},[1680,14548,1682],{},[1528,14550,14551],{"encoding":1530},"E > 1"," → ",[1047,14554,14555],{},"elastická poptávka",". Snížení ceny zvýší celkový příjem.",[1304,14558,11051],{"id":14559},"c-max-tr-1",[1035,14561,14563],{"className":14562},[1480],[1482,14564,14565],{"xmlns":1484,"display":1485},[1487,14566,14567,14613],{},[1490,14568,14569,14571,14573,14575,14577,14579,14581,14583,14585,14587,14589,14591,14593,14595,14597,14599,14601,14603,14605,14607],{},[1493,14570,5289],{},[1493,14572,1995],{},[1506,14574,1508],{},[1493,14576,1501],{},[1506,14578,1714],{},[1493,14580,1520],{},[1506,14582,1508],{},[1506,14584,1553],{"stretchy":1552},[1680,14586,9319],{},[1506,14588,1888],{},[1680,14590,1691],{},[1493,14592,1520],{},[1506,14594,1564],{"stretchy":1552},[1493,14596,1520],{},[1506,14598,1508],{},[1680,14600,9319],{},[1493,14602,1520],{},[1506,14604,1888],{},[1680,14606,1691],{},[2315,14608,14609,14611],{},[1493,14610,1520],{},[1680,14612,1691],{},[1528,14614,14615],{"encoding":1530},"TR = P \\cdot Q = (18 - 2Q) Q = 18Q - 2 Q^2",[1035,14617,14619],{"className":14618},[1480],[1482,14620,14621],{"xmlns":1484,"display":1485},[1487,14622,14623,14660],{},[1490,14624,14625,14627,14629,14631,14633,14635,14637,14639,14641,14643,14645,14647,14649,14655,14657],{},[1493,14626,1495],{},[1493,14628,1995],{},[1506,14630,1508],{},[1680,14632,9319],{},[1506,14634,1888],{},[1680,14636,4007],{},[1493,14638,1520],{},[1506,14640,1508],{},[1680,14642,1871],{},[1988,14644,1990],{},[1506,14646,2111],{},[1988,14648,1990],{},[2315,14650,14651,14653],{},[1493,14652,1520],{},[1506,14654,2287],{},[1506,14656,1508],{},[1680,14658,14659],{},"4,5",[1528,14661,14662],{"encoding":1530},"MR = 18 - 4Q = 0 \\;\\Longrightarrow\\; Q^* = 4{,}5",[1035,14664,14666],{"className":14665},[1480],[1482,14667,14668],{"xmlns":1484,"display":1485},[1487,14669,14670,14721],{},[1490,14671,14672,14674,14682,14684,14686,14688,14690,14692,14694,14696,14699,14701,14704,14706,14709,14711],{},[1493,14673,5289],{},[1497,14675,14676,14678,14680],{},[1493,14677,1995],{},[1493,14679,7571],{},[1506,14681,7574],{},[1506,14683,1508],{},[1680,14685,9319],{},[1506,14687,1714],{},[1680,14689,14659],{},[1506,14691,1888],{},[1680,14693,1691],{},[1506,14695,1714],{},[1680,14697,14698],{},"20,25",[1506,14700,1508],{},[1680,14702,14703],{},"81",[1506,14705,1888],{},[1680,14707,14708],{},"40,5",[1506,14710,1508],{},[1976,14712,14713],{"notation":1978},[1869,14714,14715],{"scriptlevel":1871,"displaystyle":1552},[1869,14716,14717],{"scriptlevel":1871,"displaystyle":1552},[1869,14718,14719],{"scriptlevel":1871,"displaystyle":1041},[1680,14720,14708],{},[1528,14722,14723],{"encoding":1530},"TR_{\\max} = 18 \\cdot 4{,}5 - 2 \\cdot 20{,}25 = 81 - 40{,}5 = \\boxed{40{,}5}",[1304,14725,14727,14728],{"id":14726},"d-přebytky-při-qe3pe12qe-3-pe-12","(d) Přebytky při ",[1035,14729,14731],{"className":14730},[1480],[1482,14732,14733],{"xmlns":1484},[1487,14734,14735,14759],{},[1490,14736,14737,14743,14745,14747,14749,14755,14757],{},[2315,14738,14739,14741],{},[1493,14740,1520],{},[1493,14742,2711],{},[1506,14744,1508],{},[1680,14746,3201],{},[1506,14748,1559],{"separator":1041},[2315,14750,14751,14753],{},[1493,14752,1501],{},[1493,14754,2711],{},[1506,14756,1508],{},[1680,14758,6797],{},[1528,14760,14761],{"encoding":1530},"Q^E = 3, P^E = 12",[1030,14763,14764],{},[1047,14765,14766],{},"Přebytek spotřebitele:",[1035,14768,14770],{"className":14769},[1480],[1482,14771,14772],{"xmlns":1484,"display":1485},[1487,14773,14774,14876],{},[1490,14775,14776,14778,14780,14782,14790,14792,14794,14796,14798,14800,14802,14804,14806,14808,14810,14812,14814,14816,14818,14842,14844,14847,14849,14851,14854,14856,14858,14860,14862,14864,14866],{},[1493,14777,1998],{},[1493,14779,2001],{},[1506,14781,1508],{},[1697,14783,14784,14786,14788],{},[1506,14785,10857],{},[1680,14787,1871],{},[1680,14789,3201],{},[1506,14791,1553],{"stretchy":1552},[1680,14793,9319],{},[1506,14795,1888],{},[1680,14797,1691],{},[1493,14799,1520],{},[1506,14801,1564],{"stretchy":1552},[1988,14803,5016],{},[1493,14805,3384],{},[1493,14807,1520],{},[1506,14809,1888],{},[1680,14811,6797],{},[1506,14813,1714],{},[1680,14815,3201],{},[1506,14817,1508],{},[1697,14819,14820,14838,14840],{},[1490,14821,14822,14824,14826,14828,14830,14836],{},[1506,14823,14314],{"fence":1041},[1680,14825,9319],{},[1493,14827,1520],{},[1506,14829,1888],{},[2315,14831,14832,14834],{},[1493,14833,1520],{},[1680,14835,1691],{},[1506,14837,14323],{"fence":1041},[1680,14839,1871],{},[1680,14841,3201],{},[1506,14843,1888],{},[1680,14845,14846],{},"36",[1506,14848,1508],{},[1506,14850,1553],{"stretchy":1552},[1680,14852,14853],{},"54",[1506,14855,1888],{},[1680,14857,14365],{},[1506,14859,1564],{"stretchy":1552},[1506,14861,1888],{},[1680,14863,14846],{},[1506,14865,1508],{},[1976,14867,14868],{"notation":1978},[1869,14869,14870],{"scriptlevel":1871,"displaystyle":1552},[1869,14871,14872],{"scriptlevel":1871,"displaystyle":1552},[1869,14873,14874],{"scriptlevel":1871,"displaystyle":1041},[1680,14875,14365],{},[1528,14877,14878],{"encoding":1530},"CS = \\int_0^3 (18 - 2Q) \\, dQ - 12 \\cdot 3 = \\left[18Q - Q^2\\right]_0^3 - 36 = (54 - 9) - 36 = \\boxed{9}",[1030,14880,14881],{},[1047,14882,14883],{},"Přebytek výrobce:",[1035,14885,14887],{"className":14886},[1480],[1482,14888,14889],{"xmlns":1484,"display":1485},[1487,14890,14891,14997],{},[1490,14892,14893,14895,14897,14899,14901,14903,14905,14907,14915,14917,14919,14921,14927,14929,14931,14933,14935,14937,14939,14941,14969,14971,14973,14975,14977,14979,14981,14983,14985,14987],{},[1493,14894,1501],{},[1493,14896,2001],{},[1506,14898,1508],{},[1680,14900,6797],{},[1506,14902,1714],{},[1680,14904,3201],{},[1506,14906,1888],{},[1697,14908,14909,14911,14913],{},[1506,14910,10857],{},[1680,14912,1871],{},[1680,14914,3201],{},[1506,14916,1553],{"stretchy":1552},[1680,14918,3201],{},[1506,14920,2162],{},[2315,14922,14923,14925],{},[1493,14924,1520],{},[1680,14926,1691],{},[1506,14928,1564],{"stretchy":1552},[1988,14930,5016],{},[1493,14932,3384],{},[1493,14934,1520],{},[1506,14936,1508],{},[1680,14938,14846],{},[1506,14940,1888],{},[1697,14942,14943,14965,14967],{},[1490,14944,14945,14947,14949,14951,14953,14963],{},[1506,14946,14314],{"fence":1041},[1680,14948,3201],{},[1493,14950,1520],{},[1506,14952,2162],{},[1510,14954,14955,14961],{},[2315,14956,14957,14959],{},[1493,14958,1520],{},[1680,14960,3201],{},[1680,14962,3201],{},[1506,14964,14323],{"fence":1041},[1680,14966,1871],{},[1680,14968,3201],{},[1506,14970,1508],{},[1680,14972,14846],{},[1506,14974,1888],{},[1506,14976,1553],{"stretchy":1552},[1680,14978,14365],{},[1506,14980,2162],{},[1680,14982,14365],{},[1506,14984,1564],{"stretchy":1552},[1506,14986,1508],{},[1976,14988,14989],{"notation":1978},[1869,14990,14991],{"scriptlevel":1871,"displaystyle":1552},[1869,14992,14993],{"scriptlevel":1871,"displaystyle":1552},[1869,14994,14995],{"scriptlevel":1871,"displaystyle":1041},[1680,14996,9319],{},[1528,14998,14999],{"encoding":1530},"PS = 12 \\cdot 3 - \\int_0^3 (3 + Q^2) \\, dQ = 36 - \\left[3Q + \\frac{Q^3}{3}\\right]_0^3 = 36 - (9 + 9) = \\boxed{18}",[1030,15001,15002],{},[1047,15003,15004],{},"Geometricky:",[1203,15006,15007,15071],{},[1206,15008,15009,15010,15029,15030,15048,15049,2632],{},"CS = plocha mezi křivkou ",[1035,15011,15013],{"className":15012},[1480],[1482,15014,15015],{"xmlns":1484},[1487,15016,15017,15027],{},[1490,15018,15019,15021,15023,15025],{},[1493,15020,3712],{},[1506,15022,1553],{"stretchy":1552},[1493,15024,1520],{},[1506,15026,1564],{"stretchy":1552},[1528,15028,11765],{"encoding":1530}," (klesající přímka shora) a vodorovnou linií ",[1035,15031,15033],{"className":15032},[1480],[1482,15034,15035],{"xmlns":1484},[1487,15036,15037,15045],{},[1490,15038,15039,15041,15043],{},[1493,15040,1501],{},[1506,15042,1508],{},[1680,15044,6797],{},[1528,15046,15047],{"encoding":1530},"P = 12"," na intervalu ",[1035,15050,15052],{"className":15051},[1480],[1482,15053,15054],{"xmlns":1484},[1487,15055,15056,15068],{},[1490,15057,15058,15060,15062,15064,15066],{},[1506,15059,14314],{"stretchy":1552},[1680,15061,1871],{},[1506,15063,1559],{"separator":1041},[1680,15065,3201],{},[1506,15067,14323],{"stretchy":1552},[1528,15069,15070],{"encoding":1530},"[0, 3]",[1206,15072,15073,15074,15091,15092,15112,15113,2632],{},"PS = plocha mezi vodorovnou linií ",[1035,15075,15077],{"className":15076},[1480],[1482,15078,15079],{"xmlns":1484},[1487,15080,15081,15089],{},[1490,15082,15083,15085,15087],{},[1493,15084,1501],{},[1506,15086,1508],{},[1680,15088,6797],{},[1528,15090,15047],{"encoding":1530}," (shora) a křivkou ",[1035,15093,15095],{"className":15094},[1480],[1482,15096,15097],{"xmlns":1484},[1487,15098,15099,15109],{},[1490,15100,15101,15103,15105,15107],{},[1493,15102,2001],{},[1506,15104,1553],{"stretchy":1552},[1493,15106,1520],{},[1506,15108,1564],{"stretchy":1552},[1528,15110,15111],{"encoding":1530},"S(Q)"," (rostoucí parabola zdola) na intervalu ",[1035,15114,15116],{"className":15115},[1480],[1482,15117,15118],{"xmlns":1484},[1487,15119,15120,15132],{},[1490,15121,15122,15124,15126,15128,15130],{},[1506,15123,14314],{"stretchy":1552},[1680,15125,1871],{},[1506,15127,1559],{"separator":1041},[1680,15129,3201],{},[1506,15131,14323],{"stretchy":1552},[1528,15133,15070],{"encoding":1530},[1030,15135,15136,15137,15169],{},"Celkový blahobyt ",[1035,15138,15140],{"className":15139},[1480],[1482,15141,15142],{"xmlns":1484},[1487,15143,15144,15166],{},[1490,15145,15146,15149,15151,15153,15155,15157,15159,15161,15163],{},[1493,15147,15148],{},"W",[1506,15150,1508],{},[1493,15152,1998],{},[1493,15154,2001],{},[1506,15156,2162],{},[1493,15158,1501],{},[1493,15160,2001],{},[1506,15162,1508],{},[1680,15164,15165],{},"27",[1528,15167,15168],{"encoding":1530},"W = CS + PS = 27"," — čistý přínos trhu pro obě strany dohromady.",[1246,15171],{},[1065,15173,15175,15176,15178],{"id":15174},"z7q4-40-b-vícefaktorová-poptávka-po-kašmírových-ponožkách","Z7\u002FQ4 ",[1035,15177,1144],{}," — Vícefaktorová poptávka po kašmírových ponožkách",[1030,15180,15181,1656,15183,15223,15224,15241,15242,15284],{},[1047,15182,1263],{},[1035,15184,15186],{"className":15185},[1480],[1482,15187,15188],{"xmlns":1484},[1487,15189,15190,15220],{},[1490,15191,15192,15194,15196,15198,15200,15202,15204,15206,15208,15214,15216,15218],{},[1493,15193,1520],{},[1506,15195,1508],{},[1680,15197,1401],{},[1506,15199,1888],{},[1680,15201,5765],{},[1493,15203,1501],{},[1506,15205,2162],{},[1680,15207,5263],{},[1497,15209,15210,15212],{},[1493,15211,1501],{},[1493,15213,3633],{},[1506,15215,2162],{},[1680,15217,3687],{},[1493,15219,1791],{},[1528,15221,15222],{"encoding":1530},"Q = 1000 - 400P + 200 P_A + 0{,}5 Y"," (Q = páry kašmírových; P = cena kašmír; ",[1035,15225,15227],{"className":15226},[1480],[1482,15228,15229],{"xmlns":1484},[1487,15230,15231,15239],{},[1490,15232,15233],{},[1497,15234,15235,15237],{},[1493,15236,1501],{},[1493,15238,3633],{},[1528,15240,3862],{"encoding":1530}," = cena vlna; Y = důchod).\n",[1035,15243,15245],{"className":15244},[1480],[1482,15246,15247],{"xmlns":1484},[1487,15248,15249,15281],{},[1490,15250,15251,15253,15255,15257,15259,15265,15267,15269,15271,15273,15275,15277,15279],{},[1493,15252,1501],{},[1506,15254,1508],{},[1680,15256,1775],{},[1506,15258,1559],{"separator":1041},[1497,15260,15261,15263],{},[1493,15262,1501],{},[1493,15264,3633],{},[1506,15266,1508],{},[1680,15268,1752],{},[1506,15270,1559],{"separator":1041},[1493,15272,1791],{},[1506,15274,1508],{},[1680,15276,8436],{},[1988,15278,5016],{},[1680,15280,5608],{},[1528,15282,15283],{"encoding":1530},"P = 10, P_A = 5, Y = 20\\,000",".\n(a) Q. (b) E_P, E_PA, E_Y + charakter. (c) Substitut\u002Fkomplement, normální\u002Fpodřadné. (d) ΔQ % při ΔP% = +1, ΔPA% = −3, ΔY% = +20.",[1030,15286,15287,15289,15290,15295],{},[1047,15288,1832],{}," Vícefaktorové elasticity (",[1052,15291,15294],{"className":15292,"dataFsResolvedFilePath":3807,"href":15293},[1055],"\u002Fwiki\u002Felasticita#Vícefaktorový model","vzorce 4.18–4.20",") + procentní aproximace (4.21).",[1304,15297,15299],{"id":15298},"a-q-na-hladině","(a) Q na hladině",[1035,15301,15303],{"className":15302},[1480],[1482,15304,15305],{"xmlns":1484,"display":1485},[1487,15306,15307,15382],{},[1490,15308,15309,15311,15313,15315,15317,15319,15321,15323,15325,15327,15329,15331,15333,15335,15337,15339,15341,15343,15345,15347,15349,15352,15354,15356,15358,15360,15362,15364,15366],{},[1493,15310,1520],{},[1506,15312,1508],{},[1680,15314,1401],{},[1506,15316,1888],{},[1680,15318,5765],{},[1506,15320,1714],{},[1680,15322,1775],{},[1506,15324,2162],{},[1680,15326,5263],{},[1506,15328,1714],{},[1680,15330,1752],{},[1506,15332,2162],{},[1680,15334,3687],{},[1506,15336,1714],{},[1680,15338,8436],{},[1988,15340,5016],{},[1680,15342,5608],{},[1506,15344,1508],{},[1680,15346,1401],{},[1506,15348,1888],{},[1680,15350,15351],{},"4000",[1506,15353,2162],{},[1680,15355,1401],{},[1506,15357,2162],{},[1680,15359,1775],{},[1988,15361,5016],{},[1680,15363,5608],{},[1506,15365,1508],{},[1976,15367,15368],{"notation":1978},[1869,15369,15370],{"scriptlevel":1871,"displaystyle":1552},[1869,15371,15372],{"scriptlevel":1871,"displaystyle":1552},[1869,15373,15374],{"scriptlevel":1871,"displaystyle":1041},[1490,15375,15376,15378,15380],{},[1680,15377,6138],{},[1988,15379,5016],{},[1680,15381,5608],{},[1528,15383,15384],{"encoding":1530},"Q = 1000 - 400 \\cdot 10 + 200 \\cdot 5 + 0{,}5 \\cdot 20\\,000 = 1000 - 4000 + 1000 + 10\\,000 = \\boxed{8\\,000}",[1304,15386,15388],{"id":15387},"b-elasticity","(b) Elasticity",[1030,15390,15391],{},[1047,15392,15393],{},"Cenová:",[1035,15395,15397],{"className":15396},[1480],[1482,15398,15399],{"xmlns":1484,"display":1485},[1487,15400,15401,15499],{},[1490,15402,15403,15417,15419,15421,15423,15425,15427,15433,15435,15437,15443,15445,15459,15461,15463,15469,15471,15473,15475,15477,15479,15481,15487,15489],{},[1510,15404,15405,15411],{},[1490,15406,15407,15409],{},[1493,15408,1517],{"mathvariant":1516},[1493,15410,1520],{},[1490,15412,15413,15415],{},[1493,15414,1517],{"mathvariant":1516},[1493,15416,1501],{},[1506,15418,1508],{},[1506,15420,1888],{},[1680,15422,5765],{},[1506,15424,1559],{"separator":1041},[1912,15426],{"width":2108},[1497,15428,15429,15431],{},[1493,15430,2711],{},[1493,15432,1501],{},[1506,15434,1508],{},[1506,15436,1888],{},[1510,15438,15439,15441],{},[1493,15440,1501],{},[1493,15442,1520],{},[1506,15444,1714],{},[1510,15446,15447,15453],{},[1490,15448,15449,15451],{},[1493,15450,1517],{"mathvariant":1516},[1493,15452,1520],{},[1490,15454,15455,15457],{},[1493,15456,1517],{"mathvariant":1516},[1493,15458,1501],{},[1506,15460,1508],{},[1506,15462,1888],{},[1510,15464,15465,15467],{},[1680,15466,1775],{},[1680,15468,12478],{},[1506,15470,1714],{},[1506,15472,1553],{"stretchy":1552},[1506,15474,1888],{},[1680,15476,5765],{},[1506,15478,1564],{"stretchy":1552},[1506,15480,1508],{},[1510,15482,15483,15485],{},[1680,15484,15351],{},[1680,15486,12478],{},[1506,15488,1508],{},[1976,15490,15491],{"notation":1978},[1869,15492,15493],{"scriptlevel":1871,"displaystyle":1552},[1869,15494,15495],{"scriptlevel":1871,"displaystyle":1552},[1869,15496,15497],{"scriptlevel":1871,"displaystyle":1041},[1680,15498,3687],{},[1528,15500,15501],{"encoding":1530},"\\frac{\\partial Q}{\\partial P} = -400, \\quad E_P = -\\frac{P}{Q} \\cdot \\frac{\\partial Q}{\\partial P} = -\\frac{10}{8000} \\cdot (-400) = \\frac{4000}{8000} = \\boxed{0{,}5}",[1030,15503,15504,15505,15508],{},"→ ",[1047,15506,15507],{},"neelastická"," (0 \u003C E_P \u003C 1).",[1030,15510,15511],{},[1047,15512,15513],{},"Křížově-cenová:",[1035,15515,15517],{"className":15516},[1480],[1482,15518,15519],{"xmlns":1484,"display":1485},[1487,15520,15521,15618],{},[1490,15522,15523,15541,15543,15545,15547,15549,15551,15561,15563,15573,15575,15593,15595,15601,15603,15605,15607],{},[1510,15524,15525,15531],{},[1490,15526,15527,15529],{},[1493,15528,1517],{"mathvariant":1516},[1493,15530,1520],{},[1490,15532,15533,15535],{},[1493,15534,1517],{"mathvariant":1516},[1497,15536,15537,15539],{},[1493,15538,1501],{},[1493,15540,3633],{},[1506,15542,1508],{},[1506,15544,2162],{},[1680,15546,5263],{},[1506,15548,1559],{"separator":1041},[1912,15550],{"width":2108},[1497,15552,15553,15555],{},[1493,15554,2711],{},[1497,15556,15557,15559],{},[1493,15558,1501],{},[1493,15560,3633],{},[1506,15562,1508],{},[1510,15564,15565,15571],{},[1497,15566,15567,15569],{},[1493,15568,1501],{},[1493,15570,3633],{},[1493,15572,1520],{},[1506,15574,1714],{},[1510,15576,15577,15583],{},[1490,15578,15579,15581],{},[1493,15580,1517],{"mathvariant":1516},[1493,15582,1520],{},[1490,15584,15585,15587],{},[1493,15586,1517],{"mathvariant":1516},[1497,15588,15589,15591],{},[1493,15590,1501],{},[1493,15592,3633],{},[1506,15594,1508],{},[1510,15596,15597,15599],{},[1680,15598,1752],{},[1680,15600,12478],{},[1506,15602,1714],{},[1680,15604,5263],{},[1506,15606,1508],{},[1976,15608,15609],{"notation":1978},[1869,15610,15611],{"scriptlevel":1871,"displaystyle":1552},[1869,15612,15613],{"scriptlevel":1871,"displaystyle":1552},[1869,15614,15615],{"scriptlevel":1871,"displaystyle":1041},[1680,15616,15617],{},"0,125",[1528,15619,15620],{"encoding":1530},"\\frac{\\partial Q}{\\partial P_A} = +200, \\quad E_{P_A} = \\frac{P_A}{Q} \\cdot \\frac{\\partial Q}{\\partial P_A} = \\frac{5}{8000} \\cdot 200 = \\boxed{0{,}125}",[1030,15622,15623],{},[1047,15624,15625],{},"Důchodová:",[1035,15627,15629],{"className":15628},[1480],[1482,15630,15631],{"xmlns":1484,"display":1485},[1487,15632,15633,15719],{},[1490,15634,15635,15649,15651,15653,15655,15657,15659,15665,15667,15673,15675,15689,15691,15703,15705,15707,15709],{},[1510,15636,15637,15643],{},[1490,15638,15639,15641],{},[1493,15640,1517],{"mathvariant":1516},[1493,15642,1520],{},[1490,15644,15645,15647],{},[1493,15646,1517],{"mathvariant":1516},[1493,15648,1791],{},[1506,15650,1508],{},[1506,15652,2162],{},[1680,15654,3687],{},[1506,15656,1559],{"separator":1041},[1912,15658],{"width":2108},[1497,15660,15661,15663],{},[1493,15662,2711],{},[1493,15664,1791],{},[1506,15666,1508],{},[1510,15668,15669,15671],{},[1493,15670,1791],{},[1493,15672,1520],{},[1506,15674,1714],{},[1510,15676,15677,15683],{},[1490,15678,15679,15681],{},[1493,15680,1517],{"mathvariant":1516},[1493,15682,1520],{},[1490,15684,15685,15687],{},[1493,15686,1517],{"mathvariant":1516},[1493,15688,1791],{},[1506,15690,1508],{},[1510,15692,15693,15701],{},[1490,15694,15695,15697,15699],{},[1680,15696,8436],{},[1988,15698,5016],{},[1680,15700,5608],{},[1680,15702,12478],{},[1506,15704,1714],{},[1680,15706,3687],{},[1506,15708,1508],{},[1976,15710,15711],{"notation":1978},[1869,15712,15713],{"scriptlevel":1871,"displaystyle":1552},[1869,15714,15715],{"scriptlevel":1871,"displaystyle":1552},[1869,15716,15717],{"scriptlevel":1871,"displaystyle":1041},[1680,15718,3196],{},[1528,15720,15721],{"encoding":1530},"\\frac{\\partial Q}{\\partial Y} = +0{,}5, \\quad E_Y = \\frac{Y}{Q} \\cdot \\frac{\\partial Q}{\\partial Y} = \\frac{20\\,000}{8000} \\cdot 0{,}5 = \\boxed{1{,}25}",[1304,15723,15725],{"id":15724},"c-charakterizace","(c) Charakterizace",[1203,15727,15728,15765],{},[1206,15729,15730,15760,15761,15764],{},[1035,15731,15733],{"className":15732},[1480],[1482,15734,15735],{"xmlns":1484},[1487,15736,15737,15757],{},[1490,15738,15739,15749,15751,15753,15755],{},[1497,15740,15741,15743],{},[1493,15742,2711],{},[1497,15744,15745,15747],{},[1493,15746,1501],{},[1493,15748,3633],{},[1506,15750,1508],{},[1680,15752,15617],{},[1506,15754,2796],{},[1680,15756,1871],{},[1528,15758,15759],{"encoding":1530},"E_{P_A} = 0{,}125 > 0"," → vlna je ",[1047,15762,15763],{},"substitut"," kašmíru (zdraží-li se vlněné ponožky, lidé kupují víc kašmírových).",[1206,15766,15767,15793,15794,15797,15798,14552,15820,15823],{},[1035,15768,15770],{"className":15769},[1480],[1482,15771,15772],{"xmlns":1484},[1487,15773,15774,15790],{},[1490,15775,15776,15782,15784,15786,15788],{},[1497,15777,15778,15780],{},[1493,15779,2711],{},[1493,15781,1791],{},[1506,15783,1508],{},[1680,15785,3196],{},[1506,15787,2796],{},[1680,15789,1871],{},[1528,15791,15792],{"encoding":1530},"E_Y = 1{,}25 > 0"," → kašmír je ",[1047,15795,15796],{},"normální zboží",". Navíc ",[1035,15799,15801],{"className":15800},[1480],[1482,15802,15803],{"xmlns":1484},[1487,15804,15805,15817],{},[1490,15806,15807,15813,15815],{},[1497,15808,15809,15811],{},[1493,15810,2711],{},[1493,15812,1791],{},[1506,15814,2796],{},[1680,15816,1682],{},[1528,15818,15819],{"encoding":1530},"E_Y > 1",[1047,15821,15822],{},"luxusní zboží"," (s růstem důchodu roste spotřeba rychleji než důchod).",[1304,15825,15827],{"id":15826},"d-δq-při-současných-změnách","(d) ΔQ % při současných změnách",[1030,15829,15830,15831],{},"Vzorec: ",[1035,15832,15834],{"className":15833},[1480],[1482,15835,15836],{"xmlns":1484},[1487,15837,15838,15905],{},[1490,15839,15840,15842,15844,15847,15849,15851,15857,15859,15861,15863,15865,15867,15877,15879,15881,15887,15889,15891,15897,15899,15901,15903],{},[1493,15841,2976],{"mathvariant":1516},[1493,15843,1520],{},[1493,15845,15846],{"mathvariant":1516},"%",[1506,15848,2343],{},[1506,15850,1888],{},[1497,15852,15853,15855],{},[1493,15854,2711],{},[1493,15856,1501],{},[1506,15858,1714],{},[1493,15860,2976],{"mathvariant":1516},[1493,15862,1501],{},[1493,15864,15846],{"mathvariant":1516},[1506,15866,2162],{},[1497,15868,15869,15871],{},[1493,15870,2711],{},[1497,15872,15873,15875],{},[1493,15874,1501],{},[1493,15876,3633],{},[1506,15878,1714],{},[1493,15880,2976],{"mathvariant":1516},[1497,15882,15883,15885],{},[1493,15884,1501],{},[1493,15886,3633],{},[1493,15888,15846],{"mathvariant":1516},[1506,15890,2162],{},[1497,15892,15893,15895],{},[1493,15894,2711],{},[1493,15896,1791],{},[1506,15898,1714],{},[1493,15900,2976],{"mathvariant":1516},[1493,15902,1791],{},[1493,15904,15846],{"mathvariant":1516},[1528,15906,15907],{"encoding":1530},"\\Delta Q\\% \\approx -E_P \\cdot \\Delta P\\% + E_{P_A} \\cdot \\Delta P_A\\% + E_Y \\cdot \\Delta Y\\%",[1035,15909,15911],{"className":15910},[1480],[1482,15912,15913],{"xmlns":1484,"display":1485},[1487,15914,15915,15955],{},[1490,15916,15917,15919,15921,15923,15925,15927,15929,15931,15933,15935,15937,15939,15941,15943,15945,15947,15949,15951,15953],{},[1493,15918,2976],{"mathvariant":1516},[1493,15920,1520],{},[1493,15922,15846],{"mathvariant":1516},[1506,15924,2343],{},[1506,15926,1888],{},[1680,15928,3687],{},[1506,15930,1714],{},[1680,15932,1682],{},[1506,15934,2162],{},[1680,15936,15617],{},[1506,15938,1714],{},[1506,15940,1553],{"stretchy":1552},[1506,15942,1888],{},[1680,15944,3201],{},[1506,15946,1564],{"stretchy":1552},[1506,15948,2162],{},[1680,15950,3196],{},[1506,15952,1714],{},[1680,15954,8436],{},[1528,15956,15957],{"encoding":1530},"\\Delta Q\\% \\approx -0{,}5 \\cdot 1 + 0{,}125 \\cdot (-3) + 1{,}25 \\cdot 20",[1035,15959,15961],{"className":15960},[1480],[1482,15962,15963],{"xmlns":1484,"display":1485},[1487,15964,15965,16001],{},[1490,15966,15967,15969,15971,15973,15975,15978,15980,15982,15984],{},[1506,15968,1508],{},[1506,15970,1888],{},[1680,15972,3687],{},[1506,15974,1888],{},[1680,15976,15977],{},"0,375",[1506,15979,2162],{},[1680,15981,2309],{},[1506,15983,1508],{},[1976,15985,15986],{"notation":1978},[1869,15987,15988],{"scriptlevel":1871,"displaystyle":1552},[1869,15989,15990],{"scriptlevel":1871,"displaystyle":1552},[1869,15991,15992],{"scriptlevel":1871,"displaystyle":1041},[1490,15993,15994,15996,15999],{},[1506,15995,2162],{},[1680,15997,15998],{},"24,125",[1493,16000,15846],{"mathvariant":1516},[1528,16002,16003],{"encoding":1530},"= -0{,}5 - 0{,}375 + 25 = \\boxed{+24{,}125 \\%}",[1030,16005,16006,16008,16009,16012],{},[1047,16007,12171],{}," dominuje ",[1047,16010,16011],{},"důchodový efekt"," — 20 % růst důchodu krát luxusní elasticita 1,25 = 25 procentních bodů růstu Q. Cenové efekty (zdražení kašmíru, zlevnění vlny) sotva tlumí o necelé procento.",[1246,16014],{},[1019,16016,16018],{"id":16017},"zadání-8","Zadání 8",[1065,16020,16022,16023,13582],{"id":16021},"z8q1-10-b-funkce-úspor","Z8\u002FQ1 ",[1035,16024,1102],{},[1030,16026,16027,16029],{},[1047,16028,1263],{}," (a) S = 0,2Y − 50; (b) S = 50 − 0,3Y; (c) S = 1,2Y − 10; (d) S = 0,4Y − 10; (e) S = 100 + 0,4Y.",[1030,16031,16032,16035],{},[1047,16033,16034],{},"Stejná pravidla"," jako Z7\u002FQ1.",[1073,16037,16038,16052],{},[1076,16039,16040],{},[1079,16041,16042,16044,16046,16048,16050],{},[1082,16043],{},[1082,16045,1318],{},[1082,16047,13693],{},[1082,16049,13696],{},[1082,16051,1327],{},[1092,16053,16054,16070,16088,16106,16123],{},[1079,16055,16056,16058,16061,16064,16066],{},[1097,16057,1334],{},[1097,16059,16060],{},"0,2Y − 50",[1097,16062,16063],{},"0,2 ∈ (0,1) ✓",[1097,16065,13713],{},[1097,16067,16068],{},[1047,16069,1348],{},[1079,16071,16072,16074,16077,16082,16084],{},[1097,16073,1353],{},[1097,16075,16076],{},"−0,3Y + 50",[1097,16078,16079,1402],{},[1047,16080,16081],{},"−0,3",[1097,16083,1405],{},[1097,16085,16086],{},[1047,16087,1387],{},[1079,16089,16090,16092,16095,16100,16102],{},[1097,16091,1370],{},[1097,16093,16094],{},"1,2Y − 10",[1097,16096,16097,1402],{},[1047,16098,16099],{},"1,2 > 1",[1097,16101,1405],{},[1097,16103,16104],{},[1047,16105,1387],{},[1079,16107,16108,16110,16113,16116,16119],{},[1097,16109,1392],{},[1097,16111,16112],{},"0,4Y − 10",[1097,16114,16115],{},"0,4 ✓",[1097,16117,16118],{},"−10 \u003C 0 ✓",[1097,16120,16121],{},[1047,16122,1348],{},[1079,16124,16125,16127,16130,16132,16137],{},[1097,16126,1414],{},[1097,16128,16129],{},"0,4Y + 100",[1097,16131,16115],{},[1097,16133,16134,1402],{},[1047,16135,16136],{},"+100 > 0",[1097,16138,16139],{},[1047,16140,1387],{},[1246,16142],{},[1065,16144,16146,16147,16149],{"id":16145},"z8q2-20-b-mrts10100-15","Z8\u002FQ2 ",[1035,16148,1116],{}," — MRTS(10,100) = 15",[1030,16151,16152,1656,16155,16195],{},[1047,16153,16154],{},"Identické se Z5\u002FQ2.",[1035,16156,16158],{"className":16157},[1480],[1482,16159,16160],{"xmlns":1484},[1487,16161,16162,16192],{},[1490,16163,16164,16166,16168,16170,16172,16174,16176,16182,16184,16186],{},[1493,16165,1495],{},[1493,16167,1995],{},[1493,16169,5289],{},[1493,16171,2001],{},[1506,16173,1508],{},[1493,16175,1495],{},[1497,16177,16178,16180],{},[1493,16179,1501],{},[1493,16181,1556],{},[1493,16183,1709],{"mathvariant":1516},[1493,16185,1495],{},[1497,16187,16188,16190],{},[1493,16189,1501],{},[1493,16191,1504],{},[1528,16193,16194],{"encoding":1530},"MRTS = MP_L\u002FMP_K",". MRTS(10,100) = 15 znamená, že 1 jednotku práce lze nahradit ~15 jednotkami kapitálu se zachovanou produkcí.",[1246,16197],{},[1065,16199,16201,16202,16204],{"id":16200},"z8q3-30-b-min-výdajů-totožné-se-z2q3","Z8\u002FQ3 ",[1035,16203,1130],{}," — Min výdajů (totožné se Z2\u002FQ3)",[1035,16206,16208],{"className":16207},[1480],[1482,16209,16210],{"xmlns":1484,"display":1485},[1487,16211,16212,16310],{},[1490,16213,16214,16222,16224,16226,16228,16240,16242,16244,16246,16248,16256,16258,16260,16262,16274,16276,16278,16280,16282,16288,16290,16292,16294,16306,16308],{},[1697,16215,16216,16218,16220],{},[1493,16217,1520],{},[1680,16219,1682],{},[1506,16221,2287],{},[1506,16223,1508],{},[1680,16225,4007],{},[1506,16227,1714],{},[2315,16229,16230,16232],{},[1680,16231,1752],{},[1490,16233,16234,16236,16238],{},[1680,16235,1691],{},[1493,16237,1709],{"mathvariant":1516},[1680,16239,3201],{},[1506,16241,2343],{},[1680,16243,4865],{},[1506,16245,1559],{"separator":1041},[1912,16247],{"width":2108},[1697,16249,16250,16252,16254],{},[1493,16251,1520],{},[1680,16253,1691],{},[1506,16255,2287],{},[1506,16257,1508],{},[1680,16259,1775],{},[1506,16261,1714],{},[2315,16263,16264,16266],{},[1680,16265,1752],{},[1490,16267,16268,16270,16272],{},[1680,16269,1691],{},[1493,16271,1709],{"mathvariant":1516},[1680,16273,3201],{},[1506,16275,2343],{},[1680,16277,4900],{},[1506,16279,1559],{"separator":1041},[1912,16281],{"width":2108},[2315,16283,16284,16286],{},[1493,16285,2711],{},[1506,16287,2287],{},[1506,16289,1508],{},[1680,16291,4965],{},[1506,16293,1714],{},[2315,16295,16296,16298],{},[1680,16297,1752],{},[1490,16299,16300,16302,16304],{},[1680,16301,1691],{},[1493,16303,1709],{"mathvariant":1516},[1680,16305,3201],{},[1506,16307,2343],{},[1680,16309,4984],{},[1528,16311,16312],{"encoding":1530},"Q_1^* = 4 \\cdot 5^{2\u002F3} \\approx 11{,}696, \\quad Q_2^* = 10 \\cdot 5^{2\u002F3} \\approx 29{,}240, \\quad E^* = 60 \\cdot 5^{2\u002F3} \\approx 175{,}44",[1030,16314,16315],{},[1047,16316,16317],{},"Viz Z2\u002FQ3.",[1246,16319],{},[1065,16321,16323,16324,16326],{"id":16322},"z8q4-40-b-kašmírové-ponožky-totožné-se-z7q4","Z8\u002FQ4 ",[1035,16325,1144],{}," — Kašmírové ponožky (totožné se Z7\u002FQ4)",[1030,16328,16329,16351,16352,16374,16375,16401,16402,16424,16425,2632],{},[1035,16330,16332],{"className":16331},[1480],[1482,16333,16334],{"xmlns":1484},[1487,16335,16336,16348],{},[1490,16337,16338,16340,16342,16344,16346],{},[1493,16339,1520],{},[1506,16341,1508],{},[1680,16343,6138],{},[1988,16345,5016],{},[1680,16347,5608],{},[1528,16349,16350],{"encoding":1530},"Q = 8\\,000","; ",[1035,16353,16355],{"className":16354},[1480],[1482,16356,16357],{"xmlns":1484},[1487,16358,16359,16371],{},[1490,16360,16361,16367,16369],{},[1497,16362,16363,16365],{},[1493,16364,2711],{},[1493,16366,1501],{},[1506,16368,1508],{},[1680,16370,3687],{},[1528,16372,16373],{"encoding":1530},"E_P = 0{,}5"," (neelastická); ",[1035,16376,16378],{"className":16377},[1480],[1482,16379,16380],{"xmlns":1484},[1487,16381,16382,16398],{},[1490,16383,16384,16394,16396],{},[1497,16385,16386,16388],{},[1493,16387,2711],{},[1497,16389,16390,16392],{},[1493,16391,1501],{},[1493,16393,3633],{},[1506,16395,1508],{},[1680,16397,15617],{},[1528,16399,16400],{"encoding":1530},"E_{P_A} = 0{,}125"," (substitut); ",[1035,16403,16405],{"className":16404},[1480],[1482,16406,16407],{"xmlns":1484},[1487,16408,16409,16421],{},[1490,16410,16411,16417,16419],{},[1497,16412,16413,16415],{},[1493,16414,2711],{},[1493,16416,1791],{},[1506,16418,1508],{},[1680,16420,3196],{},[1528,16422,16423],{"encoding":1530},"E_Y = 1{,}25"," (normální\u002Fluxusní); ",[1035,16426,16428],{"className":16427},[1480],[1482,16429,16430],{"xmlns":1484},[1487,16431,16432,16448],{},[1490,16433,16434,16436,16438,16440,16442,16444,16446],{},[1493,16435,2976],{"mathvariant":1516},[1493,16437,1520],{},[1493,16439,15846],{"mathvariant":1516},[1506,16441,2343],{},[1506,16443,2162],{},[1680,16445,15998],{},[1493,16447,15846],{"mathvariant":1516},[1528,16449,16450],{"encoding":1530},"\\Delta Q\\% \\approx +24{,}125 \\%",[1030,16452,16453],{},[1047,16454,16455],{},"Viz Z7\u002FQ4.",[1246,16457],{},[1019,16459,16461],{"id":16460},"závěrečné-shrnutí-pro-studium","Závěrečné shrnutí pro studium",[1065,16463,16465],{"id":16464},"mapa-úloh-topiky","Mapa úloh × topiky",[1073,16467,16468,16483],{},[1076,16469,16470],{},[1079,16471,16472,16475,16477,16479,16481],{},[1082,16473,16474],{},"Zadání",[1082,16476,1099],{},[1082,16478,1113],{},[1082,16480,1127],{},[1082,16482,1141],{},[1092,16484,16485,16501,16517,16531,16546,16562,16576,16592],{},[1079,16486,16487,16489,16492,16495,16498],{},[1097,16488,1682],{},[1097,16490,16491],{},"TR",[1097,16493,16494],{},"MPK",[1097,16496,16497],{},"max U",[1097,16499,16500],{},"C-I",[1079,16502,16503,16505,16508,16511,16514],{},[1097,16504,1691],{},[1097,16506,16507],{},"nabídka",[1097,16509,16510],{},"E_PA",[1097,16512,16513],{},"min E",[1097,16515,16516],{},"cenová diskriminace",[1079,16518,16519,16521,16524,16526,16528],{},[1097,16520,3201],{},[1097,16522,16523],{},"AC",[1097,16525,13960],{},[1097,16527,7628],{},[1097,16529,16530],{},"IS-LM",[1079,16532,16533,16535,16538,16540,16543],{},[1097,16534,4007],{},[1097,16536,16537],{},"páry poptávky",[1097,16539,13960],{},[1097,16541,16542],{},"max zisku 2 zboží",[1097,16544,16545],{},"IS-LM (= Z3)",[1079,16547,16548,16550,16553,16556,16559],{},[1097,16549,1752],{},[1097,16551,16552],{},"AC (= Z3)",[1097,16554,16555],{},"MRTS",[1097,16557,16558],{},"max produkce (= Z3)",[1097,16560,16561],{},"TR\u002FTC firmy",[1079,16563,16564,16566,16568,16570,16573],{},[1097,16565,7508],{},[1097,16567,16491],{},[1097,16569,16494],{},[1097,16571,16572],{},"mezní náklady",[1097,16574,16575],{},"C-I (≈ Z1)",[1079,16577,16578,16581,16584,16586,16589],{},[1097,16579,16580],{},"7",[1097,16582,16583],{},"úspory",[1097,16585,13960],{},[1097,16587,16588],{},"rovnováha trhu",[1097,16590,16591],{},"vícefaktorová",[1079,16593,16594,16596,16598,16600,16603],{},[1097,16595,6138],{},[1097,16597,16583],{},[1097,16599,16555],{},[1097,16601,16602],{},"min E (= Z2)",[1097,16604,16605],{},"vícefaktorová (= Z7)",[1065,16607,16609],{"id":16608},"klíčové-vzorce-které-musíš-znát","Klíčové vzorce, které musíš znát",[1276,16611,16612,16624,16630,16639,16686,16692,16702,16738],{},[1206,16613,16614,16617,16618,16623],{},[1047,16615,16616],{},"TR = P·Q, MR = TR'(Q), MC = TC'(Q)"," — derivace celkových veličin (viz ",[1052,16619,102],{"className":16620,"dataFsResolvedFilePath":16621,"href":16622},[1055],"topics\u002Fderivace.md","\u002Fwiki\u002Fderivace",").",[1206,16625,16626,16629],{},[1047,16627,16628],{},"AC = MC v min AC; AVC = MC v min AVC; MR = MC v max zisku"," — tři optimalizační principy firmy.",[1206,16631,16632,16635,16636,16638],{},[1047,16633,16634],{},"MRCS = MU₁\u002FMU₂ = P₁\u002FP₂"," v optimu spotřebitele; ",[1047,16637,16194],{}," sklon izokvanty.",[1206,16640,16641,16644,16645,1656,16648,2632],{},[1047,16642,16643],{},"Y^E = (b + I)\u002F(1 − a)"," — model C-I; ",[1047,16646,16647],{},"Keynesův multiplikátor",[1035,16649,16651],{"className":16650},[1480],[1482,16652,16653],{"xmlns":1484},[1487,16654,16655,16683],{},[1490,16656,16657,16659,16661,16663,16665,16667,16669,16671,16673,16675,16677,16679,16681],{},[1493,16658,1517],{"mathvariant":1516},[1493,16660,1791],{},[1493,16662,1709],{"mathvariant":1516},[1493,16664,1517],{"mathvariant":1516},[1493,16666,2662],{},[1506,16668,1508],{},[1680,16670,1682],{},[1493,16672,1709],{"mathvariant":1516},[1506,16674,1553],{"stretchy":1552},[1680,16676,1682],{},[1506,16678,1888],{},[1493,16680,1052],{},[1506,16682,1564],{"stretchy":1552},[1528,16684,16685],{"encoding":1530},"\\partial Y \u002F \\partial I = 1\u002F(1-a)",[1206,16687,16688,16691],{},[1047,16689,16690],{},"r^E = (q − n)\u002F(m − p)"," — IS-LM po dosazení.",[1206,16693,16694,16697,16698,16701],{},[1047,16695,16696],{},"Δf ≈ f'(x) Δx"," (jedna proměnná) nebo ",[1047,16699,16700],{},"df = ∑(∂f\u002F∂xᵢ) dxᵢ"," (více proměnných) — diferenciál.",[1206,16703,16704,16707,16708,2632],{},[1047,16705,16706],{},"E = −(P\u002FQ)·(dQ\u002FdP)"," — cenová elasticita; vícefaktorové analogicky pro ",[1035,16709,16711],{"className":16710},[1480],[1482,16712,16713],{"xmlns":1484},[1487,16714,16715,16735],{},[1490,16716,16717,16727,16729],{},[1497,16718,16719,16721],{},[1493,16720,2711],{},[1497,16722,16723,16725],{},[1493,16724,1501],{},[1493,16726,3633],{},[1506,16728,1559],{"separator":1041},[1497,16730,16731,16733],{},[1493,16732,2711],{},[1493,16734,1791],{},[1528,16736,16737],{"encoding":1530},"E_{P_A}, E_Y",[1206,16739,16740,16743],{},[1047,16741,16742],{},"CS = ∫₀^Q D dQ − P Q;  PS = P Q − ∫₀^Q S dQ"," — přebytky.",[1065,16745,16747],{"id":16746},"kdy-je-aproximace-přesná-a-kdy-ne","Kdy je aproximace přesná a kdy ne",[1203,16749,16750,16864],{},[1206,16751,16752,16755,16756,16759,16760,16802,16803,1586,16816,16829,16830,16846,16847,16863],{},[1047,16753,16754],{},"Přesná"," = aproximace pro ",[1047,16757,16758],{},"lineární"," funkce (např. ",[1035,16761,16763],{"className":16762},[1480],[1482,16764,16765],{"xmlns":1484},[1487,16766,16767,16799],{},[1490,16768,16769,16775,16777,16779,16781,16783,16785,16787,16789,16791,16793,16795,16797],{},[2315,16770,16771,16773],{},[1493,16772,1791],{},[1493,16774,2711],{},[1506,16776,1508],{},[1506,16778,1553],{"stretchy":1552},[1493,16780,2394],{},[1506,16782,2162],{},[1493,16784,2662],{},[1506,16786,1564],{"stretchy":1552},[1493,16788,1709],{"mathvariant":1516},[1506,16790,1553],{"stretchy":1552},[1680,16792,1682],{},[1506,16794,1888],{},[1493,16796,1052],{},[1506,16798,1564],{"stretchy":1552},[1528,16800,16801],{"encoding":1530},"Y^E = (b+I)\u002F(1-a)"," je lineární v ",[1035,16804,16806],{"className":16805},[1480],[1482,16807,16808],{"xmlns":1484},[1487,16809,16810,16814],{},[1490,16811,16812],{},[1493,16813,2394],{},[1528,16815,2394],{"encoding":1530},[1035,16817,16819],{"className":16818},[1480],[1482,16820,16821],{"xmlns":1484},[1487,16822,16823,16827],{},[1490,16824,16825],{},[1493,16826,2662],{},[1528,16828,2662],{"encoding":1530}," — tedy diferenciál pro samotné ",[1035,16831,16833],{"className":16832},[1480],[1482,16834,16835],{"xmlns":1484},[1487,16836,16837,16843],{},[1490,16838,16839,16841],{},[1493,16840,2976],{"mathvariant":1516},[1493,16842,2394],{},[1528,16844,16845],{"encoding":1530},"\\Delta b"," nebo ",[1035,16848,16850],{"className":16849},[1480],[1482,16851,16852],{"xmlns":1484},[1487,16853,16854,16860],{},[1490,16855,16856,16858],{},[1493,16857,2976],{"mathvariant":1516},[1493,16859,2662],{},[1528,16861,16862],{"encoding":1530},"\\Delta I"," je přesný).",[1206,16865,16866,16755,16869,16872,16873,16876,16877],{},[1047,16867,16868],{},"Přibližná",[1047,16870,16871],{},"nelineární"," funkce nebo ",[1047,16874,16875],{},"velké"," perturbace. Příklady chyb v tomto materiálu:\n",[1203,16878,16879,16902,16938,16962],{},[1206,16880,16881,16882,16901],{},"Z1\u002FQ4(e): ",[1035,16883,16885],{"className":16884},[1480],[1482,16886,16887],{"xmlns":1484},[1487,16888,16889,16899],{},[1490,16890,16891,16893,16895,16897],{},[1493,16892,3384],{},[1493,16894,1052],{},[1506,16896,1508],{},[1680,16898,2929],{},[1528,16900,3393],{"encoding":1530}," → chyba 25 %",[1206,16903,16904,16905,16937],{},"Z3\u002FQ4(d): ",[1035,16906,16908],{"className":16907},[1480],[1482,16909,16910],{"xmlns":1484},[1487,16911,16912,16934],{},[1490,16913,16914,16916,16918,16920,16922,16924,16926,16928,16930,16932],{},[1493,16915,3384],{},[1493,16917,1030],{},[1506,16919,1508],{},[1506,16921,1888],{},[1680,16923,8436],{},[1506,16925,1559],{"separator":1041},[1493,16927,3384],{},[1493,16929,7774],{},[1506,16931,1508],{},[1680,16933,1775],{},[1528,16935,16936],{"encoding":1530},"dp = -20, dm = 10"," → chyba 12 %",[1206,16939,16940,16941,16961],{},"Z6\u002FQ3(c): ",[1035,16942,16944],{"className":16943},[1480],[1482,16945,16946],{"xmlns":1484},[1487,16947,16948,16958],{},[1490,16949,16950,16952,16954,16956],{},[1493,16951,3384],{},[1493,16953,1520],{},[1506,16955,1508],{},[1680,16957,1775],{},[1528,16959,16960],{"encoding":1530},"dQ = 10"," pro kvadratické MC → chyba 25 %",[1206,16963,16964,16965,16937],{},"Z6\u002FQ4(e): ",[1035,16966,16968],{"className":16967},[1480],[1482,16969,16970],{"xmlns":1484},[1487,16971,16972,16984],{},[1490,16973,16974,16976,16978,16980,16982],{},[1493,16975,3384],{},[1493,16977,1052],{},[1506,16979,1508],{},[1506,16981,1888],{},[1680,16983,13237],{},[1528,16985,13458],{"encoding":1530},[1023,16987,16989,16996],{"className":16988,"dataCallout":1443},[1026,1442],[1030,16990,16992,16995],{"className":16991},[1033],[1035,16993],{"className":16994,"ariaHidden":1041},[1038,1450,1040],"Heuristika pro zkoušku",[1030,16997,16998,16999,17002,17003,17006],{},"Když relativní změna parametru přesahuje ",[1047,17000,17001],{},"5–10 %",", očekávej, že lineární aproximace ",[1047,17004,17005],{},"podhodnotí nebo nadhodnotí"," přesný výsledek. V odpovědi vždy uveď obě hodnoty a krátce komentuj.",[1065,17008,17010],{"id":17009},"postup-řešení-dle-typu-úlohy","Postup řešení dle typu úlohy",[1023,17012,17014,17021],{"className":17013,"dataCallout":1443},[1026,1442],[1030,17015,17017,17020],{"className":17016},[1033],[1035,17018],{"className":17019,"ariaHidden":1041},[1038,1450,1040],"Q1 (10 b) — kvalitativní rozhodování",[1276,17022,17023,17030],{},[1206,17024,17025,17026,17029],{},"Vyber ",[1047,17027,17028],{},"2–3 podmínky",", které funkce daného typu musí splnit.",[1206,17031,17032,17033,17036],{},"Pro každou variantu odpověz „ano\u002Fne\" a stručně ",[1047,17034,17035],{},"zdůvodni"," (dosazením do podmínky).",[1023,17038,17040,17047],{"className":17039,"dataCallout":1443},[1026,1442],[1030,17041,17043,17046],{"className":17042},[1033],[1035,17044],{"className":17045,"ariaHidden":1041},[1038,1450,1040],"Q2 (20 b) — definice + interpretace",[1276,17048,17049,17055,17061],{},[1206,17050,17051,17054],{},[1047,17052,17053],{},"Vzorec"," definice (parciální derivace).",[1206,17056,17057,17060],{},[1047,17058,17059],{},"Slovní interpretace"," numerické hodnoty: „při hladině X přidání 1 jednotky Y změní Z přibližně o ...\".",[1206,17062,17063,17064,17067],{},"Případně ",[1047,17065,17066],{},"znaménko \u002F typ vztahu"," (substitut\u002Fkomplement, normální\u002Fpodřadné, optimální\u002Fpřesycený).",[1023,17069,17071,17078],{"className":17070,"dataCallout":1443},[1026,1442],[1030,17072,17074,17077],{"className":17073},[1033],[1035,17075],{"className":17076,"ariaHidden":1041},[1038,1450,1040],"Q3 (30 b) — optimalizace",[1276,17079,17080,17086,17096,17102],{},[1206,17081,17082,17085],{},[1047,17083,17084],{},"Identifikuj typ:"," max U \u002F min E \u002F max produkce \u002F max zisku (i 2-zbožového) \u002F rovnováha trhu.",[1206,17087,17088,17091,17092,17095],{},[1047,17089,17090],{},"Lagrange"," (pro vázanou) nebo ",[1047,17093,17094],{},"přímá derivace = 0"," (volná).",[1206,17097,17098,17101],{},[1047,17099,17100],{},"Vyřeš soustavu"," (typicky 2 rovnice).",[1206,17103,17104,17107],{},[1047,17105,17106],{},"Dopočítej"," výsledné veličiny (užitečnost, výdaje, produkce, zisk, přebytky).",[1023,17109,17111,17118],{"className":17110,"dataCallout":1443},[1026,1442],[1030,17112,17114,17117],{"className":17113},[1033],[1035,17115],{"className":17116,"ariaHidden":1041},[1038,1450,1040],"Q4 (40 b) — komplexní makroekonomický nebo strategický model",[1276,17119,17120,17126,17132,17138,17144],{},[1206,17121,17122,17125],{},[1047,17123,17124],{},"Sestav rovnice"," ze zadání (rovnováha + funkce spotřeby\u002Finvestic \u002F poptávka + náklady \u002F IS + LM).",[1206,17127,17128,17131],{},[1047,17129,17130],{},"Řeš soustavu"," → redukovaný tvar.",[1206,17133,17134,17137],{},[1047,17135,17136],{},"Dosaď čísla"," → rovnovážné hodnoty.",[1206,17139,17140,17143],{},[1047,17141,17142],{},"Multiplikátory"," = parciální derivace redukovaného tvaru.",[1206,17145,17146,17149,17150,17153],{},[1047,17147,17148],{},"Aproximace změn"," přes diferenciál; ",[1047,17151,17152],{},"porovnej s přesným"," výsledkem.",[1246,17155],{},[1065,17157,17159],{"id":17158},"navigace","Navigace",[1203,17161,17162,17172,17180,17203,17234,17245],{},[1206,17163,17164,1656,17167],{},[1047,17165,17166],{},"Kompletní přehled vzorců:",[1052,17168,17171],{"className":17169,"dataFsResolvedFilePath":2629,"href":17170},[1055],"\u002Fwiki\u002Fimek-vzorce-prehled","ImeK — kompletní přehled vzorců",[1206,17173,17174,1656,17177],{},[1047,17175,17176],{},"Kurz:",[1052,17178,10],{"className":17179,"dataFsResolvedFilePath":1056,"href":1057},[1055],[1206,17181,17182,1656,17185,1732,17191,1732,17197],{},[1047,17183,17184],{},"Souhrny přednášek:",[1052,17186,17190],{"className":17187,"dataFsResolvedFilePath":17188,"href":17189},[1055],"summaries\u002Fimek-blok-01.md","\u002Fwiki\u002Fimek-blok-01","Kalkul a mikroekonomie",[1052,17192,17196],{"className":17193,"dataFsResolvedFilePath":17194,"href":17195},[1055],"summaries\u002Fimek-blok-02.md","\u002Fwiki\u002Fimek-blok-02","Elasticita a produkce",[1052,17198,17202],{"className":17199,"dataFsResolvedFilePath":17200,"href":17201},[1055],"summaries\u002Fimek-blok-03.md","\u002Fwiki\u002Fimek-blok-03","Užitečnost a národní důchod",[1206,17204,17205,1656,17208,1732,17212,1732,17215,1732,17219,1732,17222,1732,17225,1732,17228],{},[1047,17206,17207],{},"Mikroekonomie:",[1052,17209,17211],{"className":17210,"dataFsResolvedFilePath":3487,"href":3488},[1055],"Poptávka a nabídka",[1052,17213,1301],{"className":17214,"dataFsResolvedFilePath":1299,"href":1300},[1055],[1052,17216,17218],{"className":17217,"dataFsResolvedFilePath":3807,"href":3808},[1055],"Elasticita",[1052,17220,6836],{"className":17221,"dataFsResolvedFilePath":1572,"href":1573},[1055],[1052,17223,6615],{"className":17224,"dataFsResolvedFilePath":6613,"href":6614},[1055],[1052,17226,1843],{"className":17227,"dataFsResolvedFilePath":1841,"href":1842},[1055],[1052,17229,17233],{"className":17230,"dataFsResolvedFilePath":17231,"href":17232},[1055],"topics\u002Fprebytek-spotrebitele-vyrobce.md","\u002Fwiki\u002Fprebytek-spotrebitele-vyrobce","Přebytky",[1206,17235,17236,1656,17239,1732,17242],{},[1047,17237,17238],{},"Makroekonomie:",[1052,17240,2624],{"className":17241,"dataFsResolvedFilePath":2622,"href":2623},[1055],[1052,17243,7756],{"className":17244,"dataFsResolvedFilePath":7754,"href":7755},[1055],[1206,17246,17247,1656,17250,1732,17253,1732,17259,1732,17262],{},[1047,17248,17249],{},"Matematický aparát:",[1052,17251,3506],{"className":17252,"dataFsResolvedFilePath":16621,"href":16622},[1055],[1052,17254,17258],{"className":17255,"dataFsResolvedFilePath":17256,"href":17257},[1055],"topics\u002Fintegral.md","\u002Fwiki\u002Fintegral","Integrál",[1052,17260,9472],{"className":17261,"dataFsResolvedFilePath":9470,"href":9471},[1055],[1052,17263,17267],{"className":17264,"dataFsResolvedFilePath":17265,"href":17266},[1055],"topics\u002Flagrangeova-metoda.md","\u002Fwiki\u002Flagrangeova-metoda","Lagrangeova metoda",{"title":17269,"searchDepth":141,"depth":141,"links":17270},"",[17271,17272,17276,17283,17290,17298,17302,17308,17315,17321,17325,17330,17337,17344,17348,17350,17356,17358,17360,17365,17367,17376,17378,17380,17386,17390,17394,17396,17404,17411,17413,17415,17417,17419,17420,17421,17422,17423],{"id":1067,"depth":141,"text":1068},{"id":1254,"depth":141,"text":17273,"children":17274},"Z1\u002FQ1 10 b — Které funkce mohou být TR(Q)?",[17275],{"id":1306,"depth":96,"text":1307},{"id":1463,"depth":141,"text":17277,"children":17278},"Z1\u002FQ2 20 b — Mezní produkt kapitálu MPK",[17279,17280,17281,17282],{"id":1475,"depth":96,"text":1476},{"id":1578,"depth":96,"text":1579},{"id":1600,"depth":96,"text":1601},{"id":1613,"depth":96,"text":1614},{"id":1647,"depth":141,"text":17284,"children":17285},"Z1\u002FQ3 30 b — Maximalizace užitečnosti",[17286,17287,17288,17289],{"id":1847,"depth":96,"text":1848},{"id":2049,"depth":96,"text":2050},{"id":2141,"depth":96,"text":2142},{"id":2256,"depth":96,"text":2257},{"id":2604,"depth":141,"text":17291,"children":17292},"Z1\u002FQ4 40 b — Model C-I",[17293,17294,17295,17296,17297],{"id":2635,"depth":96,"text":2636},{"id":2737,"depth":96,"text":2738},{"id":2891,"depth":96,"text":2892},{"id":2958,"depth":96,"text":2959},{"id":3128,"depth":96,"text":3129},{"id":3465,"depth":141,"text":17299,"children":17300},"Z2\u002FQ1 10 b — Které funkce mohou být nabídka?",[17301],{"id":3492,"depth":96,"text":3493},{"id":3609,"depth":141,"text":17303,"children":17304},"Z2\u002FQ2 20 b — Křížová cenová elasticita poptávky EPAE_{P_A}",[17305,17306],{"id":3693,"depth":96,"text":1476},{"id":3813,"depth":96,"text":17307},"Interpretace EPA=0,5E_{P_A} = 0{,}5",{"id":3971,"depth":141,"text":17309,"children":17310},"Z2\u002FQ3 30 b — Minimalizace výdajů",[17311,17312,17313,17314],{"id":4220,"depth":96,"text":1848},{"id":4441,"depth":96,"text":2050},{"id":4510,"depth":96,"text":4511},{"id":4812,"depth":96,"text":4813},{"id":5203,"depth":141,"text":17316,"children":17317},"Z2\u002FQ4 40 b — Cenová diskriminace",[17318,17319,17320],{"id":5355,"depth":96,"text":5356},{"id":5706,"depth":96,"text":5707},{"id":6150,"depth":96,"text":6151},{"id":6299,"depth":141,"text":17322,"children":17323},"Z3\u002FQ1 10 b — Které funkce mohou být AC(Q)?",[17324],{"id":6325,"depth":96,"text":1307},{"id":6461,"depth":141,"text":17326,"children":17327},"Z3\u002FQ2 20 b — MRCS(L,K) — vlastně MRCS(Q₁,Q₂)",[17328,17329],{"id":6513,"depth":96,"text":1476},{"id":6619,"depth":96,"text":6620},{"id":6761,"depth":141,"text":17331,"children":17332},"Z3\u002FQ3 30 b — Maximalizace produkce a produktivity",[17333,17335,17336],{"id":6840,"depth":96,"text":17334},"(a) Max produktivity práce (APLAP_L)",{"id":7152,"depth":96,"text":7153},{"id":7296,"depth":96,"text":7297},{"id":7709,"depth":141,"text":17338,"children":17339},"Z3\u002FQ4 40 b — IS-LM analýza",[17340,17341,17342,17343],{"id":7759,"depth":96,"text":2636},{"id":7912,"depth":96,"text":7913},{"id":8084,"depth":96,"text":8085},{"id":8244,"depth":96,"text":8245},{"id":8672,"depth":141,"text":17345,"children":17346},"Z4\u002FQ1 10 b — Páry funkcí poptávky ve dvoukomoditním trhu",[17347],{"id":8779,"depth":96,"text":1307},{"id":9034,"depth":141,"text":17349},"Z4\u002FQ2 20 b — MRCS interpretace",{"id":9126,"depth":141,"text":17351,"children":17352},"Z4\u002FQ3 30 b — Firma s dvěma zbožími v dokonalé konkurenci",[17353,17354],{"id":9478,"depth":96,"text":9479},{"id":9988,"depth":96,"text":17355},"(b) Pro P1∗=12,P2∗=18P_1^* = 12, P_2^* = 18",{"id":10351,"depth":141,"text":17357},"Z4\u002FQ4 40 b — IS-LM (totožné se Z3\u002FQ4)",{"id":10442,"depth":141,"text":17359},"Z5\u002FQ1 10 b — AC funkce (totožné se Z3\u002FQ1)",{"id":10457,"depth":141,"text":17361,"children":17362},"Z5\u002FQ2 20 b — MRTS(L,K)",[17363,17364],{"id":10469,"depth":96,"text":1476},{"id":10564,"depth":96,"text":10565},{"id":10664,"depth":141,"text":17366},"Z5\u002FQ3 30 b — Max produkce (totožné se Z3\u002FQ3)",{"id":10750,"depth":141,"text":17368,"children":17369},"Z5\u002FQ4 40 b — Firma s pevnými MC a lineárním MR",[17370,17371,17372,17373,17374,17375],{"id":10838,"depth":96,"text":10839},{"id":11000,"depth":96,"text":11001},{"id":11050,"depth":96,"text":11051},{"id":11163,"depth":96,"text":11164},{"id":11365,"depth":96,"text":11366},{"id":11501,"depth":96,"text":11502},{"id":12004,"depth":141,"text":17377},"Z6\u002FQ1 10 b — TR funkce",{"id":12125,"depth":141,"text":17379},"Z6\u002FQ2 20 b — MPK(20,900) = 15",{"id":12219,"depth":141,"text":17381,"children":17382},"Z6\u002FQ3 30 b — Mezní náklady MC=50−10Q+Q2MC = 50 - 10Q + Q^2, FC = 10",[17383,17384,17385],{"id":12266,"depth":96,"text":12267},{"id":12501,"depth":96,"text":12502},{"id":12644,"depth":96,"text":12645},{"id":13115,"depth":141,"text":17387,"children":17388},"Z6\u002FQ4 40 b — Model C-I (jako Z1\u002FQ4 s odlišným (e))",[17389],{"id":13204,"depth":96,"text":13205},{"id":13578,"depth":141,"text":17391,"children":17392},"Z7\u002FQ1 10 b — Funkce úspor",[17393],{"id":13680,"depth":96,"text":1307},{"id":13846,"depth":141,"text":17395},"Z7\u002FQ2 20 b — MRCS (zadání píše MRTS, ale formulace je MRCS)",{"id":13970,"depth":141,"text":17397,"children":17398},"Z7\u002FQ3 30 b — Tržní rovnováha s nelineární nabídkou",[17399,17400,17401,17402],{"id":14101,"depth":96,"text":14102},{"id":14329,"depth":96,"text":14330},{"id":14559,"depth":96,"text":11051},{"id":14726,"depth":96,"text":17403},"(d) Přebytky při QE=3,PE=12Q^E = 3, P^E = 12",{"id":15174,"depth":141,"text":17405,"children":17406},"Z7\u002FQ4 40 b — Vícefaktorová poptávka po kašmírových ponožkách",[17407,17408,17409,17410],{"id":15298,"depth":96,"text":15299},{"id":15387,"depth":96,"text":15388},{"id":15724,"depth":96,"text":15725},{"id":15826,"depth":96,"text":15827},{"id":16021,"depth":141,"text":17412},"Z8\u002FQ1 10 b — Funkce úspor",{"id":16145,"depth":141,"text":17414},"Z8\u002FQ2 20 b — MRTS(10,100) = 15",{"id":16200,"depth":141,"text":17416},"Z8\u002FQ3 30 b — Min výdajů (totožné se Z2\u002FQ3)",{"id":16322,"depth":141,"text":17418},"Z8\u002FQ4 40 b — Kašmírové ponožky (totožné se Z7\u002FQ4)",{"id":16464,"depth":141,"text":16465},{"id":16608,"depth":141,"text":16609},{"id":16746,"depth":141,"text":16747},{"id":17009,"depth":141,"text":17010},{"id":17158,"depth":141,"text":17159},null,"2026-04-27","md",{},true,"\u002Foutputs\u002Fimek-zkouska-priprava",{"title":1014,"description":17269},[17432],"raw\u002Fimek\u002FImeK_Zadani-zkousky_final.pdf","outputs\u002Fimek-zkouska-priprava",[9,343,828,28,53],"output","o0uT4j2ugcp_ooeZEvuemOxdvKLezFCecu5-I_35edE","outputs",{"zapisku":11,"topics":17439,"summaries":58,"outputs":141},15,[17441,19278,26104,27635,28481,32435,34029,43331,51851,65154,69294,86820,98512,106964,107245],{"id":17442,"title":17443,"body":17444,"course":9,"courses":17424,"created":19266,"description":19267,"extension":17426,"meta":19268,"navigation":17428,"path":19269,"seo":19270,"sources":19271,"stem":19273,"tags":19274,"type":19275,"updated":19276,"__hash__":19277},"topics\u002Ftopics\u002Fderivace.md","Derivace, diferenciál a extrémy funkcí jedné proměnné",{"type":1016,"value":17445,"toc":19249},[17446,17449,17468,17472,17549,17552,17675,17818,17820,17900,17904,17963,18011,18020,18024,18158,18206,18210,18249,18315,18384,18390,18394,18430,18501,18504,18580,18626,18670,18674,18678,18748,18752,18802,18879,18886,18889,18941,19209,19211],[1019,17447,17443],{"id":17448},"derivace-diferenciál-a-extrémy-funkcí-jedné-proměnné",[1030,17450,17451,17452,17456,17457,17460,17461,17464,17465,2632],{},"Matematický aparát kurzu ",[1052,17453,17455],{"className":17454,"dataFsResolvedFilePath":1056,"href":1057},[1055],"ImeK",". Bez derivace se neobejdou ",[1047,17458,17459],{},"mezní veličiny"," (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde ",[1047,17462,17463],{},"maximalizace zisku"," ani ",[1047,17466,17467],{},"minimalizace nákladů",[1065,17469,17471],{"id":17470},"funkce-a-polynomy","Funkce a polynomy",[1030,17473,17474,17475,17500,17501,17514,17515,17528,17529,2632],{},"Funkce jedné proměnné ",[1035,17476,17478],{"className":17477},[1480],[1482,17479,17480],{"xmlns":1484},[1487,17481,17482,17497],{},[1490,17483,17484,17486,17488,17490,17492,17495],{},[1493,17485,3052],{},[1506,17487,1508],{},[1493,17489,12889],{},[1506,17491,1553],{"stretchy":1552},[1493,17493,17494],{},"x",[1506,17496,1564],{"stretchy":1552},[1528,17498,17499],{"encoding":1530},"y = f(x)"," — předpis závislosti ",[1035,17502,17504],{"className":17503},[1480],[1482,17505,17506],{"xmlns":1484},[1487,17507,17508,17512],{},[1490,17509,17510],{},[1493,17511,17494],{},[1528,17513,17494],{"encoding":1530}," (nezávislá) → ",[1035,17516,17518],{"className":17517},[1480],[1482,17519,17520],{"xmlns":1484},[1487,17521,17522,17526],{},[1490,17523,17524],{},[1493,17525,3052],{},[1528,17527,3052],{"encoding":1530}," (závislá). Hodnota v bodě: ",[1035,17530,17532],{"className":17531},[1480],[1482,17533,17534],{"xmlns":1484},[1487,17535,17536,17546],{},[1490,17537,17538,17540,17542,17544],{},[1493,17539,12889],{},[1506,17541,1553],{"stretchy":1552},[1493,17543,1052],{},[1506,17545,1564],{"stretchy":1552},[1528,17547,17548],{"encoding":1530},"f(a)",[1030,17550,17551],{},"Polynomy:",[1203,17553,17554,17585,17625],{},[1206,17555,17556],{},[1276,17557,17558],{},[1206,17559,17560,17561],{},"stupně: ",[1035,17562,17564],{"className":17563},[1480],[1482,17565,17566],{"xmlns":1484},[1487,17567,17568,17582],{},[1490,17569,17570,17572,17574,17576,17578,17580],{},[1493,17571,3052],{},[1506,17573,1508],{},[1493,17575,1052],{},[1493,17577,17494],{},[1506,17579,2162],{},[1493,17581,2394],{},[1528,17583,17584],{"encoding":1530},"y = ax + b",[1206,17586,17587],{},[1276,17588,17589],{"start":141},[1206,17590,17560,17591],{},[1035,17592,17594],{"className":17593},[1480],[1482,17595,17596],{"xmlns":1484},[1487,17597,17598,17622],{},[1490,17599,17600,17602,17604,17606,17612,17614,17616,17618,17620],{},[1493,17601,3052],{},[1506,17603,1508],{},[1493,17605,1052],{},[2315,17607,17608,17610],{},[1493,17609,17494],{},[1680,17611,1691],{},[1506,17613,2162],{},[1493,17615,2394],{},[1493,17617,17494],{},[1506,17619,2162],{},[1493,17621,8730],{},[1528,17623,17624],{"encoding":1530},"y = ax^2 + bx + c",[1206,17626,17627],{},[1276,17628,17629],{"start":96},[1206,17630,17560,17631],{},[1035,17632,17634],{"className":17633},[1480],[1482,17635,17636],{"xmlns":1484},[1487,17637,17638,17672],{},[1490,17639,17640,17642,17644,17646,17652,17654,17656,17662,17664,17666,17668,17670],{},[1493,17641,3052],{},[1506,17643,1508],{},[1493,17645,1052],{},[2315,17647,17648,17650],{},[1493,17649,17494],{},[1680,17651,3201],{},[1506,17653,2162],{},[1493,17655,2394],{},[2315,17657,17658,17660],{},[1493,17659,17494],{},[1680,17661,1691],{},[1506,17663,2162],{},[1493,17665,8730],{},[1493,17667,17494],{},[1506,17669,2162],{},[1493,17671,3384],{},[1528,17673,17674],{"encoding":1530},"y = ax^3 + bx^2 + cx + d",[1030,17676,17677,1656,17680,17734,17735,17771,17772,2632],{},[1047,17678,17679],{},"Příklad rozkladu:",[1035,17681,17683],{"className":17682},[1480],[1482,17684,17685],{"xmlns":1484},[1487,17686,17687,17731],{},[1490,17688,17689,17691,17693,17699,17701,17703,17705,17707,17709,17711,17713,17715,17717,17719,17721,17723,17725,17727,17729],{},[1493,17690,3052],{},[1506,17692,1508],{},[2315,17694,17695,17697],{},[1493,17696,17494],{},[1680,17698,1691],{},[1506,17700,1888],{},[1680,17702,1752],{},[1493,17704,17494],{},[1506,17706,2162],{},[1680,17708,7508],{},[1506,17710,1508],{},[1506,17712,1553],{"stretchy":1552},[1493,17714,17494],{},[1506,17716,1888],{},[1680,17718,1691],{},[1506,17720,1564],{"stretchy":1552},[1506,17722,1553],{"stretchy":1552},[1493,17724,17494],{},[1506,17726,1888],{},[1680,17728,3201],{},[1506,17730,1564],{"stretchy":1552},[1528,17732,17733],{"encoding":1530},"y = x^2 - 5x + 6 = (x-2)(x-3)",", kořeny ",[1035,17736,17738],{"className":17737},[1480],[1482,17739,17740],{"xmlns":1484},[1487,17741,17742,17768],{},[1490,17743,17744,17750,17752,17754,17756,17758,17764,17766],{},[1497,17745,17746,17748],{},[1493,17747,17494],{},[1680,17749,1682],{},[1506,17751,1508],{},[1680,17753,1691],{},[1506,17755,1559],{"separator":1041},[1988,17757,10922],{},[1497,17759,17760,17762],{},[1493,17761,17494],{},[1680,17763,1691],{},[1506,17765,1508],{},[1680,17767,3201],{},[1528,17769,17770],{"encoding":1530},"x_1 = 2,\\ x_2 = 3",". Vrcholový tvar ",[1035,17773,17775],{"className":17774},[1480],[1482,17776,17777],{"xmlns":1484},[1487,17778,17779,17815],{},[1490,17780,17781,17783,17785,17787,17789,17791,17799,17805,17807],{},[1493,17782,3052],{},[1506,17784,1508],{},[1506,17786,1553],{"stretchy":1552},[1493,17788,17494],{},[1506,17790,1888],{},[1869,17792,17793],{"scriptlevel":1871,"displaystyle":1552},[1510,17794,17795,17797],{},[1680,17796,1752],{},[1680,17798,1691],{},[2315,17800,17801,17803],{},[1506,17802,1564],{"stretchy":1552},[1680,17804,1691],{},[1506,17806,1888],{},[1869,17808,17809],{"scriptlevel":1871,"displaystyle":1552},[1510,17810,17811,17813],{},[1680,17812,1682],{},[1680,17814,4007],{},[1528,17816,17817],{"encoding":1530},"y = (x - \\tfrac{5}{2})^2 - \\tfrac{1}{4}",[1065,17819,3506],{"id":102},[1030,17821,17822,17823,16846,17847,17875,17876,2632],{},"Označení ",[1035,17824,17826],{"className":17825},[1480],[1482,17827,17828],{"xmlns":1484},[1487,17829,17830,17844],{},[1490,17831,17832,17838,17840,17842],{},[2315,17833,17834,17836],{},[1493,17835,12889],{},[1506,17837,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,17839,1553],{"stretchy":1552},[1493,17841,17494],{},[1506,17843,1564],{"stretchy":1552},[1528,17845,17846],{"encoding":1530},"f'(x)",[1035,17848,17850],{"className":17849},[1480],[1482,17851,17852],{"xmlns":1484},[1487,17853,17854,17872],{},[1490,17855,17856],{},[1869,17857,17858],{"scriptlevel":1871,"displaystyle":1041},[1510,17859,17860,17866],{},[1490,17861,17862,17864],{},[1493,17863,3384],{},[1493,17865,3052],{},[1490,17867,17868,17870],{},[1493,17869,3384],{},[1493,17871,17494],{},[1528,17873,17874],{"encoding":1530},"\\dfrac{dy}{dx}",". Hodnota v bodě: ",[1035,17877,17879],{"className":17878},[1480],[1482,17880,17881],{"xmlns":1484},[1487,17882,17883,17897],{},[1490,17884,17885,17891,17893,17895],{},[2315,17886,17887,17889],{},[1493,17888,12889],{},[1506,17890,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,17892,1553],{"stretchy":1552},[1493,17894,1052],{},[1506,17896,1564],{"stretchy":1552},[1528,17898,17899],{"encoding":1530},"f'(a)",[1304,17901,17903],{"id":17902},"geometrická-interpretace","Geometrická interpretace",[1030,17905,17906,17929,17930,17933,17934,17962],{},[1035,17907,17909],{"className":17908},[1480],[1482,17910,17911],{"xmlns":1484},[1487,17912,17913,17927],{},[1490,17914,17915,17921,17923,17925],{},[2315,17916,17917,17919],{},[1493,17918,12889],{},[1506,17920,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,17922,1553],{"stretchy":1552},[1493,17924,1052],{},[1506,17926,1564],{"stretchy":1552},[1528,17928,17899],{"encoding":1530}," = ",[1047,17931,17932],{},"sklon tečny"," ke grafu funkce v bodě ",[1035,17935,17937],{"className":17936},[1480],[1482,17938,17939],{"xmlns":1484},[1487,17940,17941,17959],{},[1490,17942,17943,17945,17947,17949,17951,17953,17955,17957],{},[1506,17944,14314],{"stretchy":1552},[1493,17946,1052],{},[1506,17948,1559],{"separator":1041},[1493,17950,12889],{},[1506,17952,1553],{"stretchy":1552},[1493,17954,1052],{},[1506,17956,1564],{"stretchy":1552},[1506,17958,14323],{"stretchy":1552},[1528,17960,17961],{"encoding":1530},"[a, f(a)]",". Rovnice tečny:",[1035,17964,17966],{"className":17965},[1480],[1482,17967,17968],{"xmlns":1484,"display":1485},[1487,17969,17970,18008],{},[1490,17971,17972,17974,17976,17978,17980,17982,17984,17986,17992,17994,17996,17998,18000,18002,18004,18006],{},[1493,17973,3052],{},[1506,17975,1888],{},[1493,17977,12889],{},[1506,17979,1553],{"stretchy":1552},[1493,17981,1052],{},[1506,17983,1564],{"stretchy":1552},[1506,17985,1508],{},[2315,17987,17988,17990],{},[1493,17989,12889],{},[1506,17991,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,17993,1553],{"stretchy":1552},[1493,17995,1052],{},[1506,17997,1564],{"stretchy":1552},[1506,17999,1553],{"stretchy":1552},[1493,18001,17494],{},[1506,18003,1888],{},[1493,18005,1052],{},[1506,18007,1564],{"stretchy":1552},[1528,18009,18010],{"encoding":1530},"y - f(a) = f'(a)(x - a)",[1030,18012,18013],{},[18014,18015],"img",{"alt":18016,"className":18017,"src":18019},"imek-derivace-tecna",[1055,18018],"wikilink-broken","\u002Fwiki-assets\u002Fimek-derivace-tecna.jpeg",[1304,18021,18023],{"id":18022},"inženýrská-interpretace","Inženýrská interpretace",[1030,18025,18026,17929,18049,1656,18052,18065,18066,11713,18079,18097,18098,18111,18112,18125,18126,18139,18140,1274],{},[1035,18027,18029],{"className":18028},[1480],[1482,18030,18031],{"xmlns":1484},[1487,18032,18033,18047],{},[1490,18034,18035,18041,18043,18045],{},[2315,18036,18037,18039],{},[1493,18038,12889],{},[1506,18040,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,18042,1553],{"stretchy":1552},[1493,18044,1052],{},[1506,18046,1564],{"stretchy":1552},[1528,18048,17899],{"encoding":1530},[1047,18050,18051],{},"rychlost změny",[1035,18053,18055],{"className":18054},[1480],[1482,18056,18057],{"xmlns":1484},[1487,18058,18059,18063],{},[1490,18060,18061],{},[1493,18062,3052],{},[1528,18064,3052],{"encoding":1530}," vzhledem k ",[1035,18067,18069],{"className":18068},[1480],[1482,18070,18071],{"xmlns":1484},[1487,18072,18073,18077],{},[1490,18074,18075],{},[1493,18076,17494],{},[1528,18078,17494],{"encoding":1530},[1035,18080,18082],{"className":18081},[1480],[1482,18083,18084],{"xmlns":1484},[1487,18085,18086,18094],{},[1490,18087,18088,18090,18092],{},[1493,18089,17494],{},[1506,18091,1508],{},[1493,18093,1052],{},[1528,18095,18096],{"encoding":1530},"x = a","; přibližná změna ",[1035,18099,18101],{"className":18100},[1480],[1482,18102,18103],{"xmlns":1484},[1487,18104,18105,18109],{},[1490,18106,18107],{},[1493,18108,3052],{},[1528,18110,3052],{"encoding":1530}," při změně ",[1035,18113,18115],{"className":18114},[1480],[1482,18116,18117],{"xmlns":1484},[1487,18118,18119,18123],{},[1490,18120,18121],{},[1493,18122,17494],{},[1528,18124,17494],{"encoding":1530}," z ",[1035,18127,18129],{"className":18128},[1480],[1482,18130,18131],{"xmlns":1484},[1487,18132,18133,18137],{},[1490,18134,18135],{},[1493,18136,1052],{},[1528,18138,1052],{"encoding":1530}," na ",[1035,18141,18143],{"className":18142},[1480],[1482,18144,18145],{"xmlns":1484},[1487,18146,18147,18155],{},[1490,18148,18149,18151,18153],{},[1493,18150,1052],{},[1506,18152,2162],{},[1680,18154,1682],{},[1528,18156,18157],{"encoding":1530},"a+1",[1035,18159,18161],{"className":18160},[1480],[1482,18162,18163],{"xmlns":1484,"display":1485},[1487,18164,18165,18203],{},[1490,18166,18167,18169,18171,18173,18175,18177,18179,18181,18183,18185,18187,18189,18191,18197,18199,18201],{},[1493,18168,12889],{},[1506,18170,1553],{"stretchy":1552},[1493,18172,1052],{},[1506,18174,2162],{},[1680,18176,1682],{},[1506,18178,1564],{"stretchy":1552},[1506,18180,2343],{},[1493,18182,12889],{},[1506,18184,1553],{"stretchy":1552},[1493,18186,1052],{},[1506,18188,1564],{"stretchy":1552},[1506,18190,2162],{},[2315,18192,18193,18195],{},[1493,18194,12889],{},[1506,18196,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,18198,1553],{"stretchy":1552},[1493,18200,1052],{},[1506,18202,1564],{"stretchy":1552},[1528,18204,18205],{"encoding":1530},"f(a+1) \\approx f(a) + f'(a)",[1304,18207,18209],{"id":18208},"příklad-mezní-náklady","Příklad — mezní náklady",[1030,18211,18212,18213,2632],{},"Celkové náklady ",[1035,18214,18216],{"className":18215},[1480],[1482,18217,18218],{"xmlns":1484},[1487,18219,18220,18246],{},[1490,18221,18222,18224,18226,18228,18230,18232,18234,18236,18238,18240],{},[1493,18223,5289],{},[1493,18225,1998],{},[1506,18227,1508],{},[1680,18229,1401],{},[1506,18231,2162],{},[1680,18233,1691],{},[1493,18235,1520],{},[1506,18237,2162],{},[1680,18239,13237],{},[2315,18241,18242,18244],{},[1493,18243,1520],{},[1680,18245,1691],{},[1528,18247,18248],{"encoding":1530},"TC = 1000 + 2Q + 0{,}1 Q^2",[1030,18250,18251,18252,18288,18289,2632],{},"Mezní náklady: ",[1035,18253,18255],{"className":18254},[1480],[1482,18256,18257],{"xmlns":1484},[1487,18258,18259,18285],{},[1490,18260,18261,18263,18265,18267,18269,18275,18277,18279,18281,18283],{},[1493,18262,1495],{},[1493,18264,1998],{},[1506,18266,1508],{},[1493,18268,5289],{},[2315,18270,18271,18273],{},[1493,18272,1998],{},[1506,18274,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,18276,1508],{},[1680,18278,1691],{},[1506,18280,2162],{},[1680,18282,2929],{},[1493,18284,1520],{},[1528,18286,18287],{"encoding":1530},"MC = TC' = 2 + 0{,}2 Q",", takže ",[1035,18290,18292],{"className":18291},[1480],[1482,18293,18294],{"xmlns":1484},[1487,18295,18296,18312],{},[1490,18297,18298,18300,18302,18304,18306,18308,18310],{},[1493,18299,1495],{},[1493,18301,1998],{},[1506,18303,1553],{"stretchy":1552},[1680,18305,1775],{},[1506,18307,1564],{"stretchy":1552},[1506,18309,1508],{},[1680,18311,4007],{},[1528,18313,18314],{"encoding":1530},"MC(10) = 4",[1030,18316,18317,1656,18320,18367,18368,1656,18371,2632],{},[1047,18318,18319],{},"Skutečný přírůstek:",[1035,18321,18323],{"className":18322},[1480],[1482,18324,18325],{"xmlns":1484},[1487,18326,18327,18364],{},[1490,18328,18329,18331,18333,18335,18337,18339,18341,18343,18345,18347,18349,18351,18353,18355,18357,18359,18361],{},[1493,18330,2976],{"mathvariant":1516},[1493,18332,5289],{},[1493,18334,1998],{},[1506,18336,1508],{},[1493,18338,5289],{},[1493,18340,1998],{},[1506,18342,1553],{"stretchy":1552},[1680,18344,8542],{},[1506,18346,1564],{"stretchy":1552},[1506,18348,1888],{},[1493,18350,5289],{},[1493,18352,1998],{},[1506,18354,1553],{"stretchy":1552},[1680,18356,1775],{},[1506,18358,1564],{"stretchy":1552},[1506,18360,1508],{},[1680,18362,18363],{},"4,2",[1528,18365,18366],{"encoding":1530},"\\Delta TC = TC(11) - TC(10) = 4{,}2",". ",[1047,18369,18370],{},"Přibližný (lineární):",[1035,18372,18374],{"className":18373},[1480],[1482,18375,18376],{"xmlns":1484},[1487,18377,18378,18382],{},[1490,18379,18380],{},[1680,18381,4007],{},[1528,18383,4007],{"encoding":1530},[1030,18385,18386,18387,7909],{},"(Viz aplikace v ",[1052,18388,820],{"className":18389,"dataFsResolvedFilePath":1299,"href":1300},[1055],[1065,18391,18393],{"id":18392},"diferenciál","Diferenciál",[1035,18395,18397],{"className":18396},[1480],[1482,18398,18399],{"xmlns":1484,"display":1485},[1487,18400,18401,18427],{},[1490,18402,18403,18405,18407,18409,18415,18417,18419,18421,18423,18425],{},[1493,18404,3384],{},[1493,18406,12889],{},[1506,18408,1508],{},[2315,18410,18411,18413],{},[1493,18412,12889],{},[1506,18414,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,18416,1553],{"stretchy":1552},[1493,18418,17494],{},[1506,18420,1564],{"stretchy":1552},[1988,18422,5016],{},[1493,18424,3384],{},[1493,18426,17494],{},[1528,18428,18429],{"encoding":1530},"df = f'(x)\\, dx",[1030,18431,18432,18433,12919,18449,18497,18498,2632],{},"Pro malá ",[1035,18434,18436],{"className":18435},[1480],[1482,18437,18438],{"xmlns":1484},[1487,18439,18440,18446],{},[1490,18441,18442,18444],{},[1493,18443,3384],{},[1493,18445,17494],{},[1528,18447,18448],{"encoding":1530},"dx",[1035,18450,18452],{"className":18451},[1480],[1482,18453,18454],{"xmlns":1484},[1487,18455,18456,18494],{},[1490,18457,18458,18460,18462,18464,18466,18468,18470,18472,18474,18476,18478,18480,18482,18484,18486,18488,18490,18492],{},[1493,18459,2976],{"mathvariant":1516},[1493,18461,12889],{},[1506,18463,1508],{},[1493,18465,12889],{},[1506,18467,1553],{"stretchy":1552},[1493,18469,17494],{},[1506,18471,2162],{},[1493,18473,3384],{},[1493,18475,17494],{},[1506,18477,1564],{"stretchy":1552},[1506,18479,1888],{},[1493,18481,12889],{},[1506,18483,1553],{"stretchy":1552},[1493,18485,17494],{},[1506,18487,1564],{"stretchy":1552},[1506,18489,2343],{},[1493,18491,3384],{},[1493,18493,12889],{},[1528,18495,18496],{"encoding":1530},"\\Delta f = f(x + dx) - f(x) \\approx df",". Diferenciál je ",[1047,18499,18500],{},"lineární odhad přírůstku",[1304,18502,3910],{"id":18503},"příklad",[1030,18505,18506,18536,18537,18559,18560,18579],{},[1035,18507,18509],{"className":18508},[1480],[1482,18510,18511],{"xmlns":1484},[1487,18512,18513,18533],{},[1490,18514,18515,18517,18519,18521,18523,18525,18527],{},[1493,18516,5289],{},[1493,18518,1998],{},[1506,18520,1508],{},[1680,18522,2916],{},[1506,18524,2162],{},[1680,18526,13237],{},[2315,18528,18529,18531],{},[1493,18530,1520],{},[1680,18532,1691],{},[1528,18534,18535],{"encoding":1530},"TC = 100 + 0{,}1 Q^2",", odhad změny při ",[1035,18538,18540],{"className":18539},[1480],[1482,18541,18542],{"xmlns":1484},[1487,18543,18544,18556],{},[1490,18545,18546,18548,18550,18552,18554],{},[1493,18547,1520],{},[1506,18549,1274],{},[1680,18551,2292],{},[1506,18553,6380],{},[1680,18555,4965],{},[1528,18557,18558],{"encoding":1530},"Q: 50 \\to 60"," (tj. ",[1035,18561,18563],{"className":18562},[1480],[1482,18564,18565],{"xmlns":1484},[1487,18566,18567,18577],{},[1490,18568,18569,18571,18573,18575],{},[1493,18570,3384],{},[1493,18572,1520],{},[1506,18574,1508],{},[1680,18576,1775],{},[1528,18578,16960],{"encoding":1530},"):",[1035,18581,18583],{"className":18582},[1480],[1482,18584,18585],{"xmlns":1484,"display":1485},[1487,18586,18587,18623],{},[1490,18588,18589,18591,18593,18595,18597,18599,18601,18603,18605,18607,18609,18611,18613,18615,18617,18619,18621],{},[1493,18590,3384],{},[1493,18592,5289],{},[1493,18594,1998],{},[1506,18596,1508],{},[1680,18598,2929],{},[1493,18600,1520],{},[1506,18602,1714],{},[1493,18604,3384],{},[1493,18606,1520],{},[1506,18608,1508],{},[1680,18610,2929],{},[1506,18612,1714],{},[1680,18614,2292],{},[1506,18616,1714],{},[1680,18618,1775],{},[1506,18620,1508],{},[1680,18622,2916],{},[1528,18624,18625],{"encoding":1530},"dTC = 0{,}2 Q \\cdot dQ = 0{,}2 \\cdot 50 \\cdot 10 = 100",[1030,18627,18628,18629,18652,18653,18669],{},"Přesná změna: ",[1035,18630,18632],{"className":18631},[1480],[1482,18633,18634],{"xmlns":1484},[1487,18635,18636,18649],{},[1490,18637,18638,18640,18642,18644,18646],{},[1493,18639,2976],{"mathvariant":1516},[1493,18641,5289],{},[1493,18643,1998],{},[1506,18645,1508],{},[1680,18647,18648],{},"110",[1528,18650,18651],{"encoding":1530},"\\Delta TC = 110",". Lineární odhad mírně podstřeluje, protože ",[1035,18654,18656],{"className":18655},[1480],[1482,18657,18658],{"xmlns":1484},[1487,18659,18660,18666],{},[1490,18661,18662,18664],{},[1493,18663,5289],{},[1493,18665,1998],{},[1528,18667,18668],{"encoding":1530},"TC"," je konvexní.",[1065,18671,18673],{"id":18672},"extrémy-funkce-jedné-proměnné","Extrémy funkce jedné proměnné",[1304,18675,18677],{"id":18676},"nutná-podmínka","Nutná podmínka",[1030,18679,18680,18681,11713,18701,18714,18715,18743,18744,18747],{},"Má-li ",[1035,18682,18684],{"className":18683},[1480],[1482,18685,18686],{"xmlns":1484},[1487,18687,18688,18698],{},[1490,18689,18690,18692,18694,18696],{},[1493,18691,12889],{},[1506,18693,1553],{"stretchy":1552},[1493,18695,17494],{},[1506,18697,1564],{"stretchy":1552},[1528,18699,18700],{"encoding":1530},"f(x)",[1035,18702,18704],{"className":18703},[1480],[1482,18705,18706],{"xmlns":1484},[1487,18707,18708,18712],{},[1490,18709,18710],{},[1493,18711,1052],{},[1528,18713,1052],{"encoding":1530}," extrém, pak ",[1035,18716,18718],{"className":18717},[1480],[1482,18719,18720],{"xmlns":1484},[1487,18721,18722,18740],{},[1490,18723,18724,18730,18732,18734,18736,18738],{},[2315,18725,18726,18728],{},[1493,18727,12889],{},[1506,18729,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,18731,1553],{"stretchy":1552},[1493,18733,1052],{},[1506,18735,1564],{"stretchy":1552},[1506,18737,1508],{},[1680,18739,1871],{},[1528,18741,18742],{"encoding":1530},"f'(a) = 0",". Body splňující tuto podmínku se nazývají ",[1047,18745,18746],{},"stacionární"," (podezřelé) body.",[1304,18749,18751],{"id":18750},"postačující-podmínka","Postačující podmínka",[1030,18753,18754,18755,18768,18769,1274],{},"Pro stacionární bod ",[1035,18756,18758],{"className":18757},[1480],[1482,18759,18760],{"xmlns":1484},[1487,18761,18762,18766],{},[1490,18763,18764],{},[1493,18765,1052],{},[1528,18767,1052],{"encoding":1530},", je-li ",[1035,18770,18772],{"className":18771},[1480],[1482,18773,18774],{"xmlns":1484},[1487,18775,18776,18799],{},[1490,18777,18778,18788,18790,18792,18794,18797],{},[2315,18779,18780,18782],{},[1493,18781,12889],{},[1490,18783,18784,18786],{},[1506,18785,6927],{"mathvariant":1516},[1506,18787,6927],{"mathvariant":1516},[1506,18789,1553],{"stretchy":1552},[1493,18791,1052],{},[1506,18793,1564],{"stretchy":1552},[1506,18795,18796],{"mathvariant":1516},"≠",[1680,18798,1871],{},[1528,18800,18801],{"encoding":1530},"f''(a) \\neq 0",[1203,18803,18804,18842],{},[1206,18805,18806,18838,18839],{},[1035,18807,18809],{"className":18808},[1480],[1482,18810,18811],{"xmlns":1484},[1487,18812,18813,18835],{},[1490,18814,18815,18825,18827,18829,18831,18833],{},[2315,18816,18817,18819],{},[1493,18818,12889],{},[1490,18820,18821,18823],{},[1506,18822,6927],{"mathvariant":1516},[1506,18824,6927],{"mathvariant":1516},[1506,18826,1553],{"stretchy":1552},[1493,18828,1052],{},[1506,18830,1564],{"stretchy":1552},[1506,18832,2796],{},[1680,18834,1871],{},[1528,18836,18837],{"encoding":1530},"f''(a) > 0"," ⇒ ",[1047,18840,18841],{},"lokální minimum",[1206,18843,18844,18838,18876],{},[1035,18845,18847],{"className":18846},[1480],[1482,18848,18849],{"xmlns":1484},[1487,18850,18851,18873],{},[1490,18852,18853,18863,18865,18867,18869,18871],{},[2315,18854,18855,18857],{},[1493,18856,12889],{},[1490,18858,18859,18861],{},[1506,18860,6927],{"mathvariant":1516},[1506,18862,6927],{"mathvariant":1516},[1506,18864,1553],{"stretchy":1552},[1493,18866,1052],{},[1506,18868,1564],{"stretchy":1552},[1506,18870,3961],{},[1680,18872,1871],{},[1528,18874,18875],{"encoding":1530},"f''(a) \u003C 0",[1047,18877,18878],{},"lokální maximum",[1030,18880,18881],{},[18014,18882],{"alt":18883,"className":18884,"src":18885},"imek-extremy-1d",[1055,18018],"\u002Fwiki-assets\u002Fimek-extremy-1d.jpeg",[1304,18887,3910],{"id":18888},"příklad-1",[1030,18890,18891],{},[1035,18892,18894],{"className":18893},[1480],[1482,18895,18896],{"xmlns":1484},[1487,18897,18898,18938],{},[1490,18899,18900,18902,18904,18906,18908,18910,18912,18918,18920,18922,18928,18930,18932,18934,18936],{},[1493,18901,12889],{},[1506,18903,1553],{"stretchy":1552},[1493,18905,17494],{},[1506,18907,1564],{"stretchy":1552},[1506,18909,1508],{},[1680,18911,1691],{},[2315,18913,18914,18916],{},[1493,18915,17494],{},[1680,18917,3201],{},[1506,18919,1888],{},[1680,18921,3201],{},[2315,18923,18924,18926],{},[1493,18925,17494],{},[1680,18927,1691],{},[1506,18929,1888],{},[1680,18931,6797],{},[1493,18933,17494],{},[1506,18935,2162],{},[1680,18937,3201],{},[1528,18939,18940],{"encoding":1530},"f(x) = 2x^3 - 3x^2 - 12x + 3",[1203,18942,18943,19054,19094,19155],{},[1206,18944,18945,19017,19018],{},[1035,18946,18948],{"className":18947},[1480],[1482,18949,18950],{"xmlns":1484},[1487,18951,18952,19014],{},[1490,18953,18954,18960,18962,18964,18966,18968,18970,18976,18978,18980,18982,18984,18986,18988,18990,18992,18994,18996,18998,19000,19002,19004,19006,19008,19010,19012],{},[2315,18955,18956,18958],{},[1493,18957,12889],{},[1506,18959,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,18961,1553],{"stretchy":1552},[1493,18963,17494],{},[1506,18965,1564],{"stretchy":1552},[1506,18967,1508],{},[1680,18969,7508],{},[2315,18971,18972,18974],{},[1493,18973,17494],{},[1680,18975,1691],{},[1506,18977,1888],{},[1680,18979,7508],{},[1493,18981,17494],{},[1506,18983,1888],{},[1680,18985,6797],{},[1506,18987,1508],{},[1680,18989,7508],{},[1506,18991,1553],{"stretchy":1552},[1493,18993,17494],{},[1506,18995,2162],{},[1680,18997,1682],{},[1506,18999,1564],{"stretchy":1552},[1506,19001,1553],{"stretchy":1552},[1493,19003,17494],{},[1506,19005,1888],{},[1680,19007,1691],{},[1506,19009,1564],{"stretchy":1552},[1506,19011,1508],{},[1680,19013,1871],{},[1528,19015,19016],{"encoding":1530},"f'(x) = 6x^2 - 6x - 12 = 6(x+1)(x-2) = 0"," ⇒ S.B. ",[1035,19019,19021],{"className":19020},[1480],[1482,19022,19023],{"xmlns":1484},[1487,19024,19025,19051],{},[1490,19026,19027,19033,19035,19037,19039,19041,19047,19049],{},[1497,19028,19029,19031],{},[1493,19030,17494],{},[1680,19032,1682],{},[1506,19034,1508],{},[1506,19036,1888],{},[1680,19038,1682],{},[1506,19040,1559],{"separator":1041},[1497,19042,19043,19045],{},[1493,19044,17494],{},[1680,19046,1691],{},[1506,19048,1508],{},[1680,19050,1691],{},[1528,19052,19053],{"encoding":1530},"x_1 = -1, x_2 = 2",[1206,19055,19056],{},[1035,19057,19059],{"className":19058},[1480],[1482,19060,19061],{"xmlns":1484},[1487,19062,19063,19091],{},[1490,19064,19065,19075,19077,19079,19081,19083,19085,19087,19089],{},[2315,19066,19067,19069],{},[1493,19068,12889],{},[1490,19070,19071,19073],{},[1506,19072,6927],{"mathvariant":1516},[1506,19074,6927],{"mathvariant":1516},[1506,19076,1553],{"stretchy":1552},[1493,19078,17494],{},[1506,19080,1564],{"stretchy":1552},[1506,19082,1508],{},[1680,19084,6797],{},[1493,19086,17494],{},[1506,19088,1888],{},[1680,19090,7508],{},[1528,19092,19093],{"encoding":1530},"f''(x) = 12x - 6",[1206,19095,19096,18838,19136,19138,19139],{},[1035,19097,19099],{"className":19098},[1480],[1482,19100,19101],{"xmlns":1484},[1487,19102,19103,19133],{},[1490,19104,19105,19115,19117,19119,19121,19123,19125,19127,19129,19131],{},[2315,19106,19107,19109],{},[1493,19108,12889],{},[1490,19110,19111,19113],{},[1506,19112,6927],{"mathvariant":1516},[1506,19114,6927],{"mathvariant":1516},[1506,19116,1553],{"stretchy":1552},[1506,19118,1888],{},[1680,19120,1682],{},[1506,19122,1564],{"stretchy":1552},[1506,19124,1508],{},[1506,19126,1888],{},[1680,19128,9319],{},[1506,19130,3961],{},[1680,19132,1871],{},[1528,19134,19135],{"encoding":1530},"f''(-1) = -18 \u003C 0",[1047,19137,9982],{}," v ",[1035,19140,19142],{"className":19141},[1480],[1482,19143,19144],{"xmlns":1484},[1487,19145,19146,19152],{},[1490,19147,19148,19150],{},[1506,19149,1888],{},[1680,19151,1682],{},[1528,19153,19154],{"encoding":1530},"-1",[1206,19156,19157,18838,19193,19138,19196],{},[1035,19158,19160],{"className":19159},[1480],[1482,19161,19162],{"xmlns":1484},[1487,19163,19164,19190],{},[1490,19165,19166,19176,19178,19180,19182,19184,19186,19188],{},[2315,19167,19168,19170],{},[1493,19169,12889],{},[1490,19171,19172,19174],{},[1506,19173,6927],{"mathvariant":1516},[1506,19175,6927],{"mathvariant":1516},[1506,19177,1553],{"stretchy":1552},[1680,19179,1691],{},[1506,19181,1564],{"stretchy":1552},[1506,19183,1508],{},[1680,19185,9319],{},[1506,19187,2796],{},[1680,19189,1871],{},[1528,19191,19192],{"encoding":1530},"f''(2) = 18 > 0",[1047,19194,19195],{},"minimum",[1035,19197,19199],{"className":19198},[1480],[1482,19200,19201],{"xmlns":1484},[1487,19202,19203,19207],{},[1490,19204,19205],{},[1680,19206,1691],{},[1528,19208,1691],{"encoding":1530},[1065,19210,17159],{"id":17158},[1203,19212,19213,19224,19232],{},[1206,19214,19215,1656,19218],{},[1047,19216,19217],{},"Předchozí:",[1052,19219,19223],{"className":19220,"dataFsResolvedFilePath":19221,"href":19222},[1055],"topics\u002Fzaklady-matematicke-ekonomie.md","\u002Fwiki\u002Fzaklady-matematicke-ekonomie","Základy matematické ekonomie",[1206,19225,19226,1656,19229],{},[1047,19227,19228],{},"Navazující:",[1052,19230,17258],{"className":19231,"dataFsResolvedFilePath":17256,"href":17257},[1055],[1206,19233,19234,1656,19237,19240,19241,19244,19245,19248],{},[1047,19235,19236],{},"Souvislosti:",[1052,19238,9472],{"className":19239,"dataFsResolvedFilePath":9470,"href":9471},[1055]," (rozšíření na 2D), ",[1052,19242,1301],{"className":19243,"dataFsResolvedFilePath":1299,"href":1300},[1055]," (aplikace mezních veličin), ",[1052,19246,17218],{"className":19247,"dataFsResolvedFilePath":3807,"href":3808},[1055]," (procentní citlivost přes derivaci)",{"title":17269,"searchDepth":141,"depth":141,"links":19250},[19251,19252,19257,19260,19265],{"id":17470,"depth":141,"text":17471},{"id":102,"depth":141,"text":3506,"children":19253},[19254,19255,19256],{"id":17902,"depth":96,"text":17903},{"id":18022,"depth":96,"text":18023},{"id":18208,"depth":96,"text":18209},{"id":18392,"depth":141,"text":18393,"children":19258},[19259],{"id":18503,"depth":96,"text":3910},{"id":18672,"depth":141,"text":18673,"children":19261},[19262,19263,19264],{"id":18676,"depth":96,"text":18677},{"id":18750,"depth":96,"text":18751},{"id":18888,"depth":96,"text":3910},{"id":17158,"depth":141,"text":17159},"2026-04-20","Matematický aparát kurzu ImeK. Bez derivace se neobejdou mezní veličiny (mezní náklady, mezní příjem, mezní užitečnost), bez extrémů se neobejde maximalizace zisku ani minimalizace nákladů.",{},"\u002Ftopics\u002Fderivace",{"title":17443,"description":19267},[19272],"raw\u002Fimek\u002FKS_prvni_blok.pdf","topics\u002Fderivace",[9,102,173,524,698],"topic","2026-04-25","YW_ULxZWZQ9J6PW_r0bs1Oybsylsppc_UzncDCSP3mo",{"id":19279,"title":3809,"body":19280,"course":9,"courses":17424,"created":26093,"description":17269,"extension":17426,"meta":26094,"navigation":17428,"path":26095,"seo":26096,"sources":26097,"stem":26100,"tags":26101,"type":19275,"updated":26102,"__hash__":26103},"topics\u002Ftopics\u002Felasticita.md",{"type":1016,"value":19281,"toc":26066},[19282,19285,19309,19313,19338,19342,19383,19469,19511,19515,19540,19547,19551,19561,19577,19581,19609,19671,19726,19802,19805,19892,19919,20020,20116,20280,20572,20576,20656,20662,20666,20762,20826,20993,20997,21075,21106,21133,21196,21228,21304,21389,21393,21456,21515,21518,21583,21697,21778,21821,21825,21871,21878,22194,22199,22223,22252,22322,22419,22423,22430,22437,22507,22625,22707,22710,22799,23130,23134,23296,23304,23440,23448,23686,23694,23697,23702,23958,23962,24134,24266,24303,24343,24346,24475,24562,24580,24584,24591,24666,24726,24729,24753,24756,24829,24832,24895,24898,24902,24939,24995,25181,25185,25256,25309,25316,25320,25385,25525,25529,25604,25640,25645,25821,25828,25831,25835,25838,26048,26055,26059,26062],[1019,19283,3809],{"id":19284},"elasticita-poptávky-a-nabídky",[1023,19286,19288,19294],{"className":19287,"dataCallout":1028},[1026,1027],[1030,19289,19291,1042],{"className":19290},[1033],[1035,19292],{"className":19293,"ariaHidden":1041},[1038,1039,1040],[1030,19295,19296,19298,19299,19302,19303,1586,19306,2632],{},[1047,19297,17218],{}," je bezrozměrná míra toho, o kolik procent přibližně zareaguje jedna veličina na jednoprocentní změnu veličiny jiné. Studujeme ji proto, abychom mohli kvantitativně rozhodovat o cenové politice (kdy cenu snížit, kdy zvýšit) a charakterizovat povahu zboží. V kapitole rozlišujeme tři typy: ",[1047,19300,19301],{},"cenovou elasticitu poptávky"," (a nabídky), ",[1047,19304,19305],{},"křížově-cenovou elasticitu",[1047,19307,19308],{},"důchodovou elasticitu",[1065,19310,19312],{"id":19311},"úvod-motivace","Úvod — motivace",[1030,19314,19315,19316,19318,19319,19322,19323,19326,19327,19330,19331,19334,19335,16623],{},"Termín ",[1176,19317,79],{}," (alternativně ",[1176,19320,19321],{},"pružnost",") patří ke klíčovým pojmům ekonomické teorie. Slouží ke ",[1047,19324,19325],{},"kvantifikaci citlivosti (míry) odezvy"," jisté veličiny na změnu veličiny jiné. Bezprostředně nás zajímá citlivost množství (poptávaného či nabízeného) na změnu ceny zboží, což vede k pojmům ",[1176,19328,19329],{},"cenové elasticity poptávky"," (resp. ",[1176,19332,19333],{},"nabídky","). Matematickým modelem míry citlivosti je elasticita funkce (viz ",[1052,19336,3506],{"className":19337,"dataFsResolvedFilePath":16621,"href":16622},[1055],[1304,19339,19341],{"id":19340},"srovnání-trh-1-vs-trh-2","Srovnání Trh 1 vs Trh 2",[1030,19343,19344,19345,19363,19364,19382],{},"Uvažujme dvě různá tržní prostředí. Zboží má na obou trzích stejnou cenu ",[1035,19346,19348],{"className":19347},[1480],[1482,19349,19350],{"xmlns":1484},[1487,19351,19352,19360],{},[1490,19353,19354,19356,19358],{},[1493,19355,1501],{},[1506,19357,1508],{},[1680,19359,1775],{},[1528,19361,19362],{"encoding":1530},"P=10"," a při této ceně se prodá ",[1035,19365,19367],{"className":19366},[1480],[1482,19368,19369],{"xmlns":1484},[1487,19370,19371,19379],{},[1490,19372,19373,19375,19377],{},[1493,19374,1520],{},[1506,19376,1508],{},[1680,19378,2916],{},[1528,19380,19381],{"encoding":1530},"Q=100"," jednotek. Prodejce sníží cenu z 10 na 9:",[1203,19384,19385,19427],{},[1206,19386,19387,19390,19391,19426],{},[1047,19388,19389],{},"Trh 1"," zareaguje zvýšením množství na 110 ",[1035,19392,19394],{"className":19393},[1480],[1482,19395,19396],{"xmlns":1484},[1487,19397,19398,19423],{},[1490,19399,19400,19402,19404,19406,19408,19410,19412,19414,19416,19418,19420],{},[1988,19401,1990],{},[1506,19403,2183],{},[1988,19405,1990],{},[1493,19407,5289],{},[1493,19409,1995],{},[1506,19411,1508],{},[1680,19413,14365],{},[1506,19415,1714],{},[1680,19417,18648],{},[1506,19419,1508],{},[1680,19421,19422],{},"990",[1528,19424,19425],{"encoding":1530},"\\;\\Rightarrow\\; TR = 9\\cdot 110 = 990"," (pokles z 1000).",[1206,19428,19429,19432,19433,19468],{},[1047,19430,19431],{},"Trh 2"," zareaguje zvýšením množství na 120 ",[1035,19434,19436],{"className":19435},[1480],[1482,19437,19438],{"xmlns":1484},[1487,19439,19440,19465],{},[1490,19441,19442,19444,19446,19448,19450,19452,19454,19456,19458,19460,19462],{},[1988,19443,1990],{},[1506,19445,2183],{},[1988,19447,1990],{},[1493,19449,5289],{},[1493,19451,1995],{},[1506,19453,1508],{},[1680,19455,14365],{},[1506,19457,1714],{},[1680,19459,10797],{},[1506,19461,1508],{},[1680,19463,19464],{},"1080",[1528,19466,19467],{"encoding":1530},"\\;\\Rightarrow\\; TR = 9\\cdot 120 = 1080"," (růst z 1000).",[1030,19470,19471,19472,19475,19476,19479,19480,19483,19484,19487,19488,19490,19491,19506,19507,19510],{},"Závěr: snížení ceny bylo na Trhu 1 ",[1047,19473,19474],{},"nerozumné",", na Trhu 2 ",[1047,19477,19478],{},"rozumné",". Trh 2 je ",[1047,19481,19482],{},"relativně citlivý"," na změnu ceny — říkáme, že poptávka je ",[1176,19485,19486],{},"elastická"," a snížení ceny je „překompenzováno\" zvýšením poptávaného množství. Na Trhu 1 je poptávka ",[1176,19489,15507],{}," a vyššího ",[1035,19492,19494],{"className":19493},[1480],[1482,19495,19496],{"xmlns":1484},[1487,19497,19498,19504],{},[1490,19499,19500,19502],{},[1493,19501,5289],{},[1493,19503,1995],{},[1528,19505,16491],{"encoding":1530}," lze naopak dosáhnout ",[1176,19508,19509],{},"zvýšením"," ceny.",[1304,19512,19514],{"id":19513},"hypotéza-41","Hypotéza 4.1",[19516,19517,19518],"blockquote",{},[1030,19519,19520,19521],{},"Aby nedošlo k poklesu celkového příjmu, musí být procentní růst poptávaného množství alespoň takový, jaký je procentní pokles jeho ceny. ",[1035,19522,19524],{"className":19523},[1480],[1482,19525,19526],{"xmlns":1484},[1487,19527,19528,19537],{},[1490,19529,19530,19532,19535],{},[1506,19531,1553],{"stretchy":1552},[1680,19533,19534],{},"4.1",[1506,19536,1564],{"stretchy":1552},[1528,19538,19539],{"encoding":1530},"(4.1)",[1030,19541,19542,19543,19546],{},"Rozhodující nejsou nominální změny (jsou měřeny v různých jednotkách), nýbrž ",[1047,19544,19545],{},"procentní změny"," obou faktorů.",[1065,19548,19550],{"id":19549},"pojem-elasticity","Pojem elasticity",[1030,19552,19553,19554,19556,19557,19560],{},"Obecně ",[1047,19555,79],{}," jedné veličiny vzhledem k druhé kvantifikuje, o kolik procent se první veličina přibližně změní, když se druhá veličina změní o 1 %. Jde o ",[1047,19558,19559],{},"bezrozměrnou veličinu"," — nezávislou na jednotkách, ve kterých jsou proměnné měřeny.",[1023,19562,19564,19570],{"className":19563,"dataCallout":582},[1026,1186],[1030,19565,19567,6749],{"className":19566},[1033],[1035,19568],{"className":19569,"ariaHidden":1041},[1038,1193,1040],[1030,19571,19572,19573,19576],{},"Elasticitu lze číst jako ",[1047,19574,19575],{},"procentní odpověď na procentní podnět",". Místo „o kolik kusů se změní prodej, když zlevním o korunu\" (což závisí na jednotkách) se ptáme „o kolik procent se změní prodej, když zlevním o 1 %\". Tato procentní citlivost je univerzální a umožňuje srovnávat zboží různých řádů i měn.",[1065,19578,19580],{"id":19579},"cenová-elasticita-poptávky-jednofaktorový-model","Cenová elasticita poptávky — jednofaktorový model",[1030,19582,19583,19584,19608],{},"Nechť ",[1035,19585,19587],{"className":19586},[1480],[1482,19588,19589],{"xmlns":1484},[1487,19590,19591,19605],{},[1490,19592,19593,19595,19597,19599,19601,19603],{},[1493,19594,1520],{},[1506,19596,1508],{},[1493,19598,3712],{},[1506,19600,1553],{"stretchy":1552},[1493,19602,1501],{},[1506,19604,1564],{"stretchy":1552},[1528,19606,19607],{"encoding":1530},"Q = D(P)"," je funkce poptávky (ceteris paribus). Zkoumáme podíl procentních změn",[1035,19610,19612],{"className":19611},[1480],[1482,19613,19614],{"xmlns":1484,"display":1485},[1487,19615,19616,19668],{},[19617,19618,19620],"mtable",{"width":19619},"100%",[19621,19622,19623,19627,19661,19663],"mtr",{},[19624,19625],"mtd",{"width":19626},"50%",[19624,19628,19629],{},[1490,19630,19631,19637,19639,19641,19659],{},[2315,19632,19633,19635],{},[1493,19634,2711],{},[1493,19636,3633],{},[1506,19638,1508],{},[1506,19640,1888],{},[1510,19642,19643,19651],{},[1490,19644,19645,19647,19649],{},[1493,19646,2976],{"mathvariant":1516},[1493,19648,1520],{},[1493,19650,15846],{"mathvariant":1516},[1490,19652,19653,19655,19657],{},[1493,19654,2976],{"mathvariant":1516},[1493,19656,1501],{},[1493,19658,15846],{"mathvariant":1516},[1493,19660,2632],{"mathvariant":1516},[19624,19662],{"width":19626},[19624,19664,19665],{},[1988,19666,19667],{},"(4.2)",[1528,19669,19670],{"encoding":1530},"E^A = -\\frac{\\Delta Q\\%}{\\Delta P\\%}. \\tag{4.2}",[1030,19672,19673,19674,1586,19690,19706,19707,19725],{},"Znaménko minus je korekce: změny ",[1035,19675,19677],{"className":19676},[1480],[1482,19678,19679],{"xmlns":1484},[1487,19680,19681,19687],{},[1490,19682,19683,19685],{},[1493,19684,2976],{"mathvariant":1516},[1493,19686,1520],{},[1528,19688,19689],{"encoding":1530},"\\Delta Q",[1035,19691,19693],{"className":19692},[1480],[1482,19694,19695],{"xmlns":1484},[1487,19696,19697,19703],{},[1490,19698,19699,19701],{},[1493,19700,2976],{"mathvariant":1516},[1493,19702,1501],{},[1528,19704,19705],{"encoding":1530},"\\Delta P"," mají vždy opačná znaménka, takže bez korekce by ",[1035,19708,19710],{"className":19709},[1480],[1482,19711,19712],{"xmlns":1484},[1487,19713,19714,19722],{},[1490,19715,19716],{},[2315,19717,19718,19720],{},[1493,19719,2711],{},[1493,19721,3633],{},[1528,19723,19724],{"encoding":1530},"E^A"," bylo záporné; pro pohodlí pracujeme s nezápornými hodnotami. Pro procentní změny platí",[1035,19727,19729],{"className":19728},[1480],[1482,19730,19731],{"xmlns":1484,"display":1485},[1487,19732,19733,19799],{},[19617,19734,19735],{"width":19619},[19621,19736,19737,19739,19792,19794],{},[19624,19738],{"width":19626},[19624,19740,19741],{},[1490,19742,19743,19745,19747,19749,19751,19761,19763,19765,19767,19769,19771,19773,19775,19777,19787,19789],{},[1493,19744,2976],{"mathvariant":1516},[1493,19746,1520],{},[1493,19748,15846],{"mathvariant":1516},[1506,19750,1508],{},[1510,19752,19753,19759],{},[1490,19754,19755,19757],{},[1493,19756,2976],{"mathvariant":1516},[1493,19758,1520],{},[1493,19760,1520],{},[1506,19762,1714],{},[1680,19764,2916],{},[1506,19766,1559],{"separator":1041},[1912,19768],{"width":1914},[1493,19770,2976],{"mathvariant":1516},[1493,19772,1501],{},[1493,19774,15846],{"mathvariant":1516},[1506,19776,1508],{},[1510,19778,19779,19785],{},[1490,19780,19781,19783],{},[1493,19782,2976],{"mathvariant":1516},[1493,19784,1501],{},[1493,19786,1501],{},[1506,19788,1714],{},[1680,19790,19791],{},"100.",[19624,19793],{"width":19626},[19624,19795,19796],{},[1988,19797,19798],{},"(4.3)",[1528,19800,19801],{"encoding":1530},"\\Delta Q\\% = \\frac{\\Delta Q}{Q}\\cdot 100, \\qquad \\Delta P\\% = \\frac{\\Delta P}{P}\\cdot 100. \\tag{4.3}",[1030,19803,19804],{},"Po dosazení:",[1035,19806,19808],{"className":19807},[1480],[1482,19809,19810],{"xmlns":1484,"display":1485},[1487,19811,19812,19889],{},[19617,19813,19814],{"width":19619},[19621,19815,19816,19818,19882,19884],{},[19624,19817],{"width":19626},[19624,19819,19820],{},[1490,19821,19822,19828,19830,19832,19854,19856,19858,19864,19866,19880],{},[2315,19823,19824,19826],{},[1493,19825,2711],{},[1493,19827,3633],{},[1506,19829,1508],{},[1506,19831,1888],{},[1510,19833,19834,19844],{},[1510,19835,19836,19842],{},[1490,19837,19838,19840],{},[1493,19839,2976],{"mathvariant":1516},[1493,19841,1520],{},[1493,19843,1520],{},[1510,19845,19846,19852],{},[1490,19847,19848,19850],{},[1493,19849,2976],{"mathvariant":1516},[1493,19851,1501],{},[1493,19853,1501],{},[1506,19855,1508],{},[1506,19857,1888],{},[1510,19859,19860,19862],{},[1493,19861,1501],{},[1493,19863,1520],{},[1506,19865,1714],{},[1510,19867,19868,19874],{},[1490,19869,19870,19872],{},[1493,19871,2976],{"mathvariant":1516},[1493,19873,1520],{},[1490,19875,19876,19878],{},[1493,19877,2976],{"mathvariant":1516},[1493,19879,1501],{},[1493,19881,2632],{"mathvariant":1516},[19624,19883],{"width":19626},[19624,19885,19886],{},[1988,19887,19888],{},"(4.4)",[1528,19890,19891],{"encoding":1530},"E^A = -\\frac{\\frac{\\Delta Q}{Q}}{\\frac{\\Delta P}{P}} = -\\frac{P}{Q}\\cdot \\frac{\\Delta Q}{\\Delta P}. \\tag{4.4}",[1030,19893,19894,19895,19915,19916,19918],{},"Limitním přechodem ",[1035,19896,19898],{"className":19897},[1480],[1482,19899,19900],{"xmlns":1484},[1487,19901,19902,19912],{},[1490,19903,19904,19906,19908,19910],{},[1493,19905,2976],{"mathvariant":1516},[1493,19907,1501],{},[1506,19909,6380],{},[1680,19911,1871],{},[1528,19913,19914],{"encoding":1530},"\\Delta P \\to 0"," získáme definici ",[1047,19917,19329],{}," (price elasticity of demand):",[1035,19920,19922],{"className":19921},[1480],[1482,19923,19924],{"xmlns":1484,"display":1485},[1487,19925,19926,20017],{},[19617,19927,19928],{"width":19619},[19621,19929,19930,19932,20010,20012],{},[19624,19931],{"width":19626},[19624,19933,19934],{},[1976,19935,19936],{"notation":1978},[1869,19937,19938],{"scriptlevel":1871,"displaystyle":1552},[1869,19939,19940],{"scriptlevel":1871,"displaystyle":1552},[1869,19941,19942],{"scriptlevel":1871,"displaystyle":1041},[1490,19943,19944,19946,19948,19950,19952,19954,19956,19958,19960,19962,19968,19970,19984,19986,19988,19994,19996,20002,20004,20006,20008],{},[1988,19945,1990],{},[1493,19947,2711],{},[1506,19949,1508],{},[1493,19951,2711],{},[1506,19953,1553],{"stretchy":1552},[1493,19955,1501],{},[1506,19957,1564],{"stretchy":1552},[1506,19959,1508],{},[1506,19961,1888],{},[1510,19963,19964,19966],{},[1493,19965,1501],{},[1493,19967,1520],{},[1506,19969,1714],{},[1510,19971,19972,19978],{},[1490,19973,19974,19976],{},[1493,19975,3384],{"mathvariant":1516},[1493,19977,1520],{},[1490,19979,19980,19982],{},[1493,19981,3384],{"mathvariant":1516},[1493,19983,1501],{},[1506,19985,1508],{},[1506,19987,1888],{},[1510,19989,19990,19992],{},[1493,19991,1501],{},[1493,19993,1520],{},[1988,19995,5016],{},[2315,19997,19998,20000],{},[1493,19999,1520],{},[1506,20001,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,20003,1553],{"stretchy":1552},[1493,20005,1501],{},[1506,20007,1564],{"stretchy":1552},[1988,20009,1990],{},[19624,20011],{"width":19626},[19624,20013,20014],{},[1988,20015,20016],{},"(4.5)",[1528,20018,20019],{"encoding":1530},"\\boxed{\\;E = E(P) = -\\frac{P}{Q}\\cdot \\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{Q}\\,Q'(P)\\;} \\tag{4.5}",[1030,20021,20022,20023,20046,20047,3397,20069,20093,20094,20115],{},"kde ",[1035,20024,20026],{"className":20025},[1480],[1482,20027,20028],{"xmlns":1484},[1487,20029,20030,20044],{},[1490,20031,20032,20034,20036,20038,20040,20042],{},[1493,20033,1520],{},[1506,20035,1508],{},[1493,20037,3712],{},[1506,20039,1553],{"stretchy":1552},[1493,20041,1501],{},[1506,20043,1564],{"stretchy":1552},[1528,20045,19607],{"encoding":1530},". Pro pevnou cenu ",[1035,20048,20050],{"className":20049},[1480],[1482,20051,20052],{"xmlns":1484},[1487,20053,20054,20066],{},[1490,20055,20056,20058,20060],{},[1493,20057,1501],{},[1506,20059,1508],{},[2315,20061,20062,20064],{},[1493,20063,1501],{},[1506,20065,2287],{},[1528,20067,20068],{"encoding":1530},"P = P^*",[1035,20070,20072],{"className":20071},[1480],[1482,20073,20074],{"xmlns":1484},[1487,20075,20076,20090],{},[1490,20077,20078,20080,20082,20088],{},[1493,20079,2711],{},[1506,20081,1553],{"stretchy":1552},[2315,20083,20084,20086],{},[1493,20085,1501],{},[1506,20087,2287],{},[1506,20089,1564],{"stretchy":1552},[1528,20091,20092],{"encoding":1530},"E(P^*)"," nazývá ",[1176,20095,20096,20097],{},"elasticita poptávky při ceně ",[1035,20098,20100],{"className":20099},[1480],[1482,20101,20102],{"xmlns":1484},[1487,20103,20104,20112],{},[1490,20105,20106],{},[2315,20107,20108,20110],{},[1493,20109,1501],{},[1506,20111,2287],{},[1528,20113,20114],{"encoding":1530},"P^*"," a je to vždy nezáporné číslo.",[1023,20117,20119,20126],{"className":20118,"dataCallout":1155},[1026,1154],[1030,20120,20122,20125],{"className":20121},[1033],[1035,20123],{"className":20124,"ariaHidden":1041},[1038,1162,1040],"Pozor na znaménko",[1030,20127,20128,20129,20147,20148,20176,20177,20206,20207,1732,20224,1732,20242,20260,20261,20276,20277,2632],{},"V (4.5) je ",[1047,20130,20131,20132],{},"explicitní ",[1035,20133,20135],{"className":20134},[1480],[1482,20136,20137],{"xmlns":1484},[1487,20138,20139,20145],{},[1490,20140,20141,20143],{},[1506,20142,1888],{},[1680,20144,1682],{},[1528,20146,19154],{"encoding":1530}," právě proto, že ",[1035,20149,20151],{"className":20150},[1480],[1482,20152,20153],{"xmlns":1484},[1487,20154,20155,20173],{},[1490,20156,20157,20163,20165,20167,20169,20171],{},[2315,20158,20159,20161],{},[1493,20160,1520],{},[1506,20162,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,20164,1553],{"stretchy":1552},[1493,20166,1501],{},[1506,20168,1564],{"stretchy":1552},[1506,20170,3961],{},[1680,20172,1871],{},[1528,20174,20175],{"encoding":1530},"Q'(P) \u003C 0"," (poptávka klesá s cenou). Díky korekčnímu znaménku je výsledné ",[1035,20178,20180],{"className":20179},[1480],[1482,20181,20182],{"xmlns":1484},[1487,20183,20184,20203],{},[1490,20185,20186,20188,20190,20196,20198,20201],{},[1493,20187,2711],{},[1506,20189,1553],{"stretchy":1552},[2315,20191,20192,20194],{},[1493,20193,1501],{},[1506,20195,2287],{},[1506,20197,1564],{"stretchy":1552},[1506,20199,20200],{},"≥",[1680,20202,1871],{},[1528,20204,20205],{"encoding":1530},"E(P^*) \\ge 0"," a s touto nezápornou konvencí pracuje celá klasifikace ",[1035,20208,20210],{"className":20209},[1480],[1482,20211,20212],{"xmlns":1484},[1487,20213,20214,20222],{},[1490,20215,20216,20218,20220],{},[1493,20217,2711],{},[1506,20219,2796],{},[1680,20221,1682],{},[1528,20223,14551],{"encoding":1530},[1035,20225,20227],{"className":20226},[1480],[1482,20228,20229],{"xmlns":1484},[1487,20230,20231,20239],{},[1490,20232,20233,20235,20237],{},[1493,20234,2711],{},[1506,20236,3961],{},[1680,20238,1682],{},[1528,20240,20241],{"encoding":1530},"E \u003C 1",[1035,20243,20245],{"className":20244},[1480],[1482,20246,20247],{"xmlns":1484},[1487,20248,20249,20257],{},[1490,20250,20251,20253,20255],{},[1493,20252,2711],{},[1506,20254,1508],{},[1680,20256,1682],{},[1528,20258,20259],{"encoding":1530},"E = 1",". V některých starších pramenech se ",[1035,20262,20264],{"className":20263},[1480],[1482,20265,20266],{"xmlns":1484},[1487,20267,20268,20274],{},[1490,20269,20270,20272],{},[1506,20271,1888],{},[1680,20273,1682],{},[1528,20275,19154],{"encoding":1530}," vynechává a uvádějí se záporné hodnoty; obsah pojmu se tím nemění, ale srovnávat hodnoty napříč zdroji je třeba opatrně. Pokud narazíte na zápornou hodnotu, pracujte s ",[1047,20278,20279],{},"absolutní hodnotou",[1023,20281,20283,20304],{"className":20282,"dataCallout":1443},[1026,1442],[1030,20284,20286,20289,20290,20303],{"className":20285},[1033],[1035,20287],{"className":20288,"ariaHidden":1041},[1038,1450,1040],"Postup: jak spočítat ",[1035,20291,20293],{"className":20292},[1480],[1482,20294,20295],{"xmlns":1484},[1487,20296,20297,20301],{},[1490,20298,20299],{},[1493,20300,2711],{},[1528,20302,2711],{"encoding":1530}," v bodě",[1276,20305,20306,20358,20397,20450,20515],{},[1206,20307,20308,20309,20332,20333,20357],{},"Zapište ",[1035,20310,20312],{"className":20311},[1480],[1482,20313,20314],{"xmlns":1484},[1487,20315,20316,20330],{},[1490,20317,20318,20320,20322,20324,20326,20328],{},[1493,20319,1520],{},[1506,20321,1508],{},[1493,20323,3712],{},[1506,20325,1553],{"stretchy":1552},[1493,20327,1501],{},[1506,20329,1564],{"stretchy":1552},[1528,20331,19607],{"encoding":1530},". Pokud je poptávka zadaná jako ",[1035,20334,20336],{"className":20335},[1480],[1482,20337,20338],{"xmlns":1484},[1487,20339,20340,20354],{},[1490,20341,20342,20344,20346,20348,20350,20352],{},[1493,20343,1501],{},[1506,20345,1508],{},[1493,20347,3712],{},[1506,20349,1553],{"stretchy":1552},[1493,20351,1520],{},[1506,20353,1564],{"stretchy":1552},[1528,20355,20356],{"encoding":1530},"P = D(Q)",", použijte vztah (4.9).",[1206,20359,20360,20361,2632],{},"Spočítejte derivaci ",[1035,20362,20364],{"className":20363},[1480],[1482,20365,20366],{"xmlns":1484},[1487,20367,20368,20394],{},[1490,20369,20370,20376,20378,20380,20382,20384,20386,20388,20390,20392],{},[2315,20371,20372,20374],{},[1493,20373,1520],{},[1506,20375,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,20377,1553],{"stretchy":1552},[1493,20379,1501],{},[1506,20381,1564],{"stretchy":1552},[1506,20383,1508],{},[1493,20385,3384],{"mathvariant":1516},[1493,20387,1520],{},[1493,20389,1709],{"mathvariant":1516},[1493,20391,3384],{"mathvariant":1516},[1493,20393,1501],{},[1528,20395,20396],{"encoding":1530},"Q'(P) = \\mathrm{d}Q\u002F\\mathrm{d}P",[1206,20398,20399,20400,20417,20418,2632],{},"Dosaďte zadanou cenu ",[1035,20401,20403],{"className":20402},[1480],[1482,20404,20405],{"xmlns":1484},[1487,20406,20407,20415],{},[1490,20408,20409],{},[2315,20410,20411,20413],{},[1493,20412,1501],{},[1506,20414,2287],{},[1528,20416,20114],{"encoding":1530}," a dopočítejte odpovídající ",[1035,20419,20421],{"className":20420},[1480],[1482,20422,20423],{"xmlns":1484},[1487,20424,20425,20447],{},[1490,20426,20427,20433,20435,20437,20439,20445],{},[2315,20428,20429,20431],{},[1493,20430,1520],{},[1506,20432,2287],{},[1506,20434,1508],{},[1493,20436,3712],{},[1506,20438,1553],{"stretchy":1552},[2315,20440,20441,20443],{},[1493,20442,1501],{},[1506,20444,2287],{},[1506,20446,1564],{"stretchy":1552},[1528,20448,20449],{"encoding":1530},"Q^* = D(P^*)",[1206,20451,20452,20453,2632],{},"Dosaďte do (4.5): ",[1035,20454,20456],{"className":20455},[1480],[1482,20457,20458],{"xmlns":1484},[1487,20459,20460,20512],{},[1490,20461,20462,20464,20466,20472,20474,20476,20478,20494,20496,20502,20504,20510],{},[1493,20463,2711],{},[1506,20465,1553],{"stretchy":1552},[2315,20467,20468,20470],{},[1493,20469,1501],{},[1506,20471,2287],{},[1506,20473,1564],{"stretchy":1552},[1506,20475,1508],{},[1506,20477,1888],{},[1869,20479,20480],{"scriptlevel":1871,"displaystyle":1041},[1510,20481,20482,20488],{},[2315,20483,20484,20486],{},[1493,20485,1501],{},[1506,20487,2287],{},[2315,20489,20490,20492],{},[1493,20491,1520],{},[1506,20493,2287],{},[1988,20495,5016],{},[2315,20497,20498,20500],{},[1493,20499,1520],{},[1506,20501,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,20503,1553],{"stretchy":1552},[2315,20505,20506,20508],{},[1493,20507,1501],{},[1506,20509,2287],{},[1506,20511,1564],{"stretchy":1552},[1528,20513,20514],{"encoding":1530},"E(P^*) = -\\dfrac{P^*}{Q^*}\\,Q'(P^*)",[1206,20516,20517,20518,20535,20536,20553,20554,20571],{},"Klasifikujte: ",[1035,20519,20521],{"className":20520},[1480],[1482,20522,20523],{"xmlns":1484},[1487,20524,20525,20533],{},[1490,20526,20527,20529,20531],{},[1493,20528,2711],{},[1506,20530,2796],{},[1680,20532,1682],{},[1528,20534,14551],{"encoding":1530}," elastická, ",[1035,20537,20539],{"className":20538},[1480],[1482,20540,20541],{"xmlns":1484},[1487,20542,20543,20551],{},[1490,20544,20545,20547,20549],{},[1493,20546,2711],{},[1506,20548,1508],{},[1680,20550,1682],{},[1528,20552,20259],{"encoding":1530}," jednotková, ",[1035,20555,20557],{"className":20556},[1480],[1482,20558,20559],{"xmlns":1484},[1487,20560,20561,20569],{},[1490,20562,20563,20565,20567],{},[1493,20564,2711],{},[1506,20566,3961],{},[1680,20568,1682],{},[1528,20570,20241],{"encoding":1530}," neelastická.",[1304,20573,20575],{"id":20574},"interpretace-46","Interpretace (4.6)",[19516,20577,20578],{},[1030,20579,20580,20581,20604,20605,20618,20619,20636,20637],{},"Číslo ",[1035,20582,20584],{"className":20583},[1480],[1482,20585,20586],{"xmlns":1484},[1487,20587,20588,20602],{},[1490,20589,20590,20592,20594,20600],{},[1493,20591,2711],{},[1506,20593,1553],{"stretchy":1552},[2315,20595,20596,20598],{},[1493,20597,1501],{},[1506,20599,2287],{},[1506,20601,1564],{"stretchy":1552},[1528,20603,20092],{"encoding":1530}," udává, o kolik % se přibližně změní poptávané množství ",[1035,20606,20608],{"className":20607},[1480],[1482,20609,20610],{"xmlns":1484},[1487,20611,20612,20616],{},[1490,20613,20614],{},[1493,20615,1520],{},[1528,20617,1520],{"encoding":1530},", jestliže se cena ",[1035,20620,20622],{"className":20621},[1480],[1482,20623,20624],{"xmlns":1484},[1487,20625,20626,20634],{},[1490,20627,20628],{},[2315,20629,20630,20632],{},[1493,20631,1501],{},[1506,20633,2287],{},[1528,20635,20114],{"encoding":1530}," změní o 1 %. ",[1035,20638,20640],{"className":20639},[1480],[1482,20641,20642],{"xmlns":1484},[1487,20643,20644,20653],{},[1490,20645,20646,20648,20651],{},[1506,20647,1553],{"stretchy":1552},[1680,20649,20650],{},"4.6",[1506,20652,1564],{"stretchy":1552},[1528,20654,20655],{"encoding":1530},"(4.6)",[1030,20657,20658,20661],{},[1047,20659,20660],{},"Historicky:"," úvahy vedoucí k hypotéze (4.1) formuloval již Cournot (1838), dnešní vymezení se připisuje Marshallovi (1881).",[1304,20663,20665],{"id":20664},"příklad-41","Příklad 4.1",[1030,20667,20668,20669,20703,20704,1732,20728,1274],{},"Poptávka ",[1035,20670,20672],{"className":20671},[1480],[1482,20673,20674],{"xmlns":1484},[1487,20675,20676,20700],{},[1490,20677,20678,20680,20682,20684,20686,20688,20690,20692,20694,20696,20698],{},[1493,20679,1501],{},[1506,20681,1508],{},[1493,20683,3712],{},[1506,20685,1553],{"stretchy":1552},[1493,20687,1520],{},[1506,20689,1564],{"stretchy":1552},[1506,20691,1508],{},[1680,20693,2292],{},[1506,20695,1888],{},[1680,20697,1691],{},[1493,20699,1520],{},[1528,20701,20702],{"encoding":1530},"P = D(Q) = 50 - 2Q",". Vyjádříme ",[1035,20705,20707],{"className":20706},[1480],[1482,20708,20709],{"xmlns":1484},[1487,20710,20711,20725],{},[1490,20712,20713,20715,20717,20719,20721,20723],{},[1493,20714,1520],{},[1506,20716,1508],{},[1680,20718,2309],{},[1506,20720,1888],{},[1680,20722,3687],{},[1493,20724,1501],{},[1528,20726,20727],{"encoding":1530},"Q = 25 - 0{,}5P",[1035,20729,20731],{"className":20730},[1480],[1482,20732,20733],{"xmlns":1484},[1487,20734,20735,20759],{},[1490,20736,20737,20753,20755,20757],{},[1869,20738,20739],{"scriptlevel":1871,"displaystyle":1041},[1510,20740,20741,20747],{},[1490,20742,20743,20745],{},[1493,20744,3384],{"mathvariant":1516},[1493,20746,1520],{},[1490,20748,20749,20751],{},[1493,20750,3384],{"mathvariant":1516},[1493,20752,1501],{},[1506,20754,1508],{},[1506,20756,1888],{},[1680,20758,3687],{},[1528,20760,20761],{"encoding":1530},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -0{,}5",[1035,20763,20765],{"className":20764},[1480],[1482,20766,20767],{"xmlns":1484,"display":1485},[1487,20768,20769,20823],{},[1490,20770,20771,20773,20775,20777,20791,20793,20795,20797,20799,20801,20803,20821],{},[1493,20772,2711],{},[1506,20774,1508],{},[1506,20776,1888],{},[1510,20778,20779,20781],{},[1493,20780,1501],{},[1490,20782,20783,20785,20787,20789],{},[1680,20784,2309],{},[1506,20786,1888],{},[1680,20788,3687],{},[1493,20790,1501],{},[1506,20792,1714],{},[1506,20794,1553],{"stretchy":1552},[1506,20796,1888],{},[1680,20798,3687],{},[1506,20800,1564],{"stretchy":1552},[1506,20802,1508],{},[1510,20804,20805,20811],{},[1490,20806,20807,20809],{},[1680,20808,3687],{},[1493,20810,1501],{},[1490,20812,20813,20815,20817,20819],{},[1680,20814,2309],{},[1506,20816,1888],{},[1680,20818,3687],{},[1493,20820,1501],{},[1493,20822,2632],{"mathvariant":1516},[1528,20824,20825],{"encoding":1530},"E = -\\frac{P}{25-0{,}5P}\\cdot(-0{,}5) = \\frac{0{,}5P}{25-0{,}5P}.",[1030,20827,20828,20829,1732,20853,1732,20883,1732,20907,20931,20932,20955,20956,18139,20974,16623],{},"Potom ",[1035,20830,20832],{"className":20831},[1480],[1482,20833,20834],{"xmlns":1484},[1487,20835,20836,20850],{},[1490,20837,20838,20840,20842,20844,20846,20848],{},[1493,20839,2711],{},[1506,20841,1553],{"stretchy":1552},[1680,20843,1871],{},[1506,20845,1564],{"stretchy":1552},[1506,20847,1508],{},[1680,20849,1871],{},[1528,20851,20852],{"encoding":1530},"E(0)=0",[1035,20854,20856],{"className":20855},[1480],[1482,20857,20858],{"xmlns":1484},[1487,20859,20860,20880],{},[1490,20861,20862,20864,20866,20868,20870,20872],{},[1493,20863,2711],{},[1506,20865,1553],{"stretchy":1552},[1680,20867,1775],{},[1506,20869,1564],{"stretchy":1552},[1506,20871,1508],{},[1869,20873,20874],{"scriptlevel":1871,"displaystyle":1552},[1510,20875,20876,20878],{},[1680,20877,1682],{},[1680,20879,4007],{},[1528,20881,20882],{"encoding":1530},"E(10)=\\tfrac{1}{4}",[1035,20884,20886],{"className":20885},[1480],[1482,20887,20888],{"xmlns":1484},[1487,20889,20890,20904],{},[1490,20891,20892,20894,20896,20898,20900,20902],{},[1493,20893,2711],{},[1506,20895,1553],{"stretchy":1552},[1680,20897,2309],{},[1506,20899,1564],{"stretchy":1552},[1506,20901,1508],{},[1680,20903,1682],{},[1528,20905,20906],{"encoding":1530},"E(25)=1",[1035,20908,20910],{"className":20909},[1480],[1482,20911,20912],{"xmlns":1484},[1487,20913,20914,20928],{},[1490,20915,20916,20918,20920,20922,20924,20926],{},[1493,20917,2711],{},[1506,20919,1553],{"stretchy":1552},[1680,20921,7380],{},[1506,20923,1564],{"stretchy":1552},[1506,20925,1508],{},[1680,20927,4007],{},[1528,20929,20930],{"encoding":1530},"E(40)=4",". Např. ",[1035,20933,20935],{"className":20934},[1480],[1482,20936,20937],{"xmlns":1484},[1487,20938,20939,20953],{},[1490,20940,20941,20943,20945,20947,20949,20951],{},[1493,20942,2711],{},[1506,20944,1553],{"stretchy":1552},[1680,20946,7380],{},[1506,20948,1564],{"stretchy":1552},[1506,20950,1508],{},[1680,20952,4007],{},[1528,20954,20930],{"encoding":1530}," znamená, že zvýšení ceny o 1 % (z 40 na 40,4) způsobí pokles množství o 4 % (z ",[1035,20957,20959],{"className":20958},[1480],[1482,20960,20961],{"xmlns":1484},[1487,20962,20963,20971],{},[1490,20964,20965,20967,20969],{},[1493,20966,1520],{},[1506,20968,1508],{},[1680,20970,1752],{},[1528,20972,20973],{"encoding":1530},"Q=5",[1035,20975,20977],{"className":20976},[1480],[1482,20978,20979],{"xmlns":1484},[1487,20980,20981,20990],{},[1490,20982,20983,20985,20987],{},[1493,20984,1520],{},[1506,20986,1508],{},[1680,20988,20989],{},"4,8",[1528,20991,20992],{"encoding":1530},"Q=4{,}8",[1304,20994,20996],{"id":20995},"oblouková-průměrná-vs-bodová-okamžitá-elasticita","Oblouková (průměrná) vs. bodová (okamžitá) elasticita",[1203,20998,20999,21055],{},[1206,21000,21001,21004,21005,21022,21023,2632],{},[1047,21002,21003],{},"Oblouková"," (průměrná) elasticita: výraz ",[1035,21006,21008],{"className":21007},[1480],[1482,21009,21010],{"xmlns":1484},[1487,21011,21012,21020],{},[1490,21013,21014],{},[2315,21015,21016,21018],{},[1493,21017,2711],{},[1493,21019,3633],{},[1528,21021,19724],{"encoding":1530}," ze (4.4) vztažený k intervalu ",[1035,21024,21026],{"className":21025},[1480],[1482,21027,21028],{"xmlns":1484},[1487,21029,21030,21052],{},[1490,21031,21032,21035,21037,21039,21041,21043,21045,21047,21049],{},[1506,21033,21034],{"stretchy":1552},"⟨",[1493,21036,1501],{},[1506,21038,1559],{"separator":1041},[1988,21040,5016],{},[1493,21042,1501],{},[1506,21044,2162],{},[1493,21046,2976],{"mathvariant":1516},[1493,21048,1501],{},[1506,21050,21051],{"stretchy":1552},"⟩",[1528,21053,21054],{"encoding":1530},"\\langle P,\\, P+\\Delta P\\rangle",[1206,21056,21057,21060,21061,21074],{},[1047,21058,21059],{},"Bodová"," (okamžitá) elasticita: ",[1035,21062,21064],{"className":21063},[1480],[1482,21065,21066],{"xmlns":1484},[1487,21067,21068,21072],{},[1490,21069,21070],{},[1493,21071,2711],{},[1528,21073,2711],{"encoding":1530}," dle (4.5) — výchozí pojem dále v textu.",[1304,21076,21078,21079,21092,21093],{"id":21077},"výpočet-je-li-dáno-pp-jako-funkce-qq","Výpočet, je-li dáno ",[1035,21080,21082],{"className":21081},[1480],[1482,21083,21084],{"xmlns":1484},[1487,21085,21086,21090],{},[1490,21087,21088],{},[1493,21089,1501],{},[1528,21091,1501],{"encoding":1530}," jako funkce ",[1035,21094,21096],{"className":21095},[1480],[1482,21097,21098],{"xmlns":1484},[1487,21099,21100,21104],{},[1490,21101,21102],{},[1493,21103,1520],{},[1528,21105,1520],{"encoding":1530},[1030,21107,21108,21109,21132],{},"Pokud je poptávka zadaná ve tvaru ",[1035,21110,21112],{"className":21111},[1480],[1482,21113,21114],{"xmlns":1484},[1487,21115,21116,21130],{},[1490,21117,21118,21120,21122,21124,21126,21128],{},[1493,21119,1501],{},[1506,21121,1508],{},[1493,21123,3712],{},[1506,21125,1553],{"stretchy":1552},[1493,21127,1520],{},[1506,21129,1564],{"stretchy":1552},[1528,21131,20356],{"encoding":1530},", využijeme vztah pro derivaci inverzní funkce",[1035,21134,21136],{"className":21135},[1480],[1482,21137,21138],{"xmlns":1484,"display":1485},[1487,21139,21140,21193],{},[19617,21141,21142],{"width":19619},[19621,21143,21144,21146,21186,21188],{},[19624,21145],{"width":19626},[19624,21147,21148],{},[1490,21149,21150,21164,21166,21184],{},[1510,21151,21152,21158],{},[1490,21153,21154,21156],{},[1493,21155,3384],{"mathvariant":1516},[1493,21157,1520],{},[1490,21159,21160,21162],{},[1493,21161,3384],{"mathvariant":1516},[1493,21163,1501],{},[1506,21165,1508],{},[1510,21167,21168,21170],{},[1680,21169,1682],{},[1510,21171,21172,21178],{},[1490,21173,21174,21176],{},[1493,21175,3384],{"mathvariant":1516},[1493,21177,1501],{},[1490,21179,21180,21182],{},[1493,21181,3384],{"mathvariant":1516},[1493,21183,1520],{},[1493,21185,2632],{"mathvariant":1516},[19624,21187],{"width":19626},[19624,21189,21190],{},[1988,21191,21192],{},"(4.9)",[1528,21194,21195],{"encoding":1530},"\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = \\frac{1}{\\frac{\\mathrm{d}P}{\\mathrm{d}Q}}. \\tag{4.9}",[1030,21197,21198,1656,21201,21227],{},[1047,21199,21200],{},"Příklad 4.3.",[1035,21202,21204],{"className":21203},[1480],[1482,21205,21206],{"xmlns":1484},[1487,21207,21208,21224],{},[1490,21209,21210,21212,21214,21216,21218],{},[1493,21211,1501],{},[1506,21213,1508],{},[1680,21215,2916],{},[1506,21217,1888],{},[2315,21219,21220,21222],{},[1493,21221,1520],{},[1680,21223,1691],{},[1528,21225,21226],{"encoding":1530},"P = 100 - Q^2",", ptáme se na elasticitu při ceně 36. Dostáváme",[1035,21229,21231],{"className":21230},[1480],[1482,21232,21233],{"xmlns":1484,"display":1485},[1487,21234,21235,21301],{},[1490,21236,21237,21239,21241,21243,21259,21261,21273,21275,21299],{},[1493,21238,2711],{},[1506,21240,1508],{},[1506,21242,1888],{},[1510,21244,21245,21257],{},[1490,21246,21247,21249,21251],{},[1680,21248,2916],{},[1506,21250,1888],{},[2315,21252,21253,21255],{},[1493,21254,1520],{},[1680,21256,1691],{},[1493,21258,1520],{},[1506,21260,1714],{},[1510,21262,21263,21265],{},[1680,21264,1682],{},[1490,21266,21267,21269,21271],{},[1506,21268,1888],{},[1680,21270,1691],{},[1493,21272,1520],{},[1506,21274,1508],{},[1510,21276,21277,21289],{},[1490,21278,21279,21281,21283],{},[1680,21280,2916],{},[1506,21282,1888],{},[2315,21284,21285,21287],{},[1493,21286,1520],{},[1680,21288,1691],{},[1490,21290,21291,21293],{},[1680,21292,1691],{},[2315,21294,21295,21297],{},[1493,21296,1520],{},[1680,21298,1691],{},[1493,21300,2632],{"mathvariant":1516},[1528,21302,21303],{"encoding":1530},"E = -\\frac{100-Q^2}{Q}\\cdot \\frac{1}{-2Q} = \\frac{100-Q^2}{2Q^2}.",[1030,21305,21306,21307,21333,21334,21352,21353,2632],{},"Z rovnice ",[1035,21308,21310],{"className":21309},[1480],[1482,21311,21312],{"xmlns":1484},[1487,21313,21314,21330],{},[1490,21315,21316,21318,21320,21326,21328],{},[1680,21317,2916],{},[1506,21319,1888],{},[2315,21321,21322,21324],{},[1493,21323,1520],{},[1680,21325,1691],{},[1506,21327,1508],{},[1680,21329,14846],{},[1528,21331,21332],{"encoding":1530},"100 - Q^2 = 36"," plyne ",[1035,21335,21337],{"className":21336},[1480],[1482,21338,21339],{"xmlns":1484},[1487,21340,21341,21349],{},[1490,21342,21343,21345,21347],{},[1493,21344,1520],{},[1506,21346,1508],{},[1680,21348,6138],{},[1528,21350,21351],{"encoding":1530},"Q = 8",", tedy ",[1035,21354,21356],{"className":21355},[1480],[1482,21357,21358],{"xmlns":1484},[1487,21359,21360,21386],{},[1490,21361,21362,21364,21366,21368,21370,21372,21381,21383],{},[1493,21363,2711],{},[1506,21365,1553],{"stretchy":1552},[1680,21367,6138],{},[1506,21369,1564],{"stretchy":1552},[1506,21371,1508],{},[1869,21373,21374],{"scriptlevel":1871,"displaystyle":1552},[1510,21375,21376,21378],{},[1680,21377,14846],{},[1680,21379,21380],{},"128",[1506,21382,1508],{},[1680,21384,21385],{},"0,281",[1528,21387,21388],{"encoding":1530},"E(8) = \\tfrac{36}{128} = 0{,}281",[1304,21390,21392],{"id":21391},"přibližné-změny","Přibližné změny",[1030,21394,21395,21396,21432,21433,21455],{},"Diferenciál ",[1035,21397,21399],{"className":21398},[1480],[1482,21400,21401],{"xmlns":1484},[1487,21402,21403,21429],{},[1490,21404,21405,21407,21409,21411,21417,21419,21421,21423,21425,21427],{},[1493,21406,3384],{"mathvariant":1516},[1493,21408,1520],{},[1506,21410,1508],{},[2315,21412,21413,21415],{},[1493,21414,1520],{},[1506,21416,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,21418,1553],{"stretchy":1552},[1493,21420,1501],{},[1506,21422,1564],{"stretchy":1552},[1988,21424,5016],{},[1493,21426,3384],{"mathvariant":1516},[1493,21428,1501],{},[1528,21430,21431],{"encoding":1530},"\\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P"," s ",[1035,21434,21436],{"className":21435},[1480],[1482,21437,21438],{"xmlns":1484},[1487,21439,21440,21452],{},[1490,21441,21442,21444,21446,21448,21450],{},[1493,21443,3384],{"mathvariant":1516},[1493,21445,1501],{},[1506,21447,1508],{},[1493,21449,2976],{"mathvariant":1516},[1493,21451,1501],{},[1528,21453,21454],{"encoding":1530},"\\mathrm{d}P = \\Delta P"," dává nominální odhad",[1035,21457,21459],{"className":21458},[1480],[1482,21460,21461],{"xmlns":1484,"display":1485},[1487,21462,21463,21512],{},[19617,21464,21465],{"width":19619},[19621,21466,21467,21469,21505,21507],{},[19624,21468],{"width":19626},[19624,21470,21471],{},[1490,21472,21473,21475,21477,21479,21481,21483,21485,21491,21493,21495,21497,21499,21501,21503],{},[1493,21474,2976],{"mathvariant":1516},[1493,21476,1520],{},[1506,21478,2343],{},[1493,21480,3384],{"mathvariant":1516},[1493,21482,1520],{},[1506,21484,1508],{},[2315,21486,21487,21489],{},[1493,21488,1520],{},[1506,21490,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,21492,1553],{"stretchy":1552},[1493,21494,1501],{},[1506,21496,1564],{"stretchy":1552},[1988,21498,5016],{},[1493,21500,3384],{"mathvariant":1516},[1493,21502,1501],{},[1493,21504,2632],{"mathvariant":1516},[19624,21506],{"width":19626},[19624,21508,21509],{},[1988,21510,21511],{},"(4.10)",[1528,21513,21514],{"encoding":1530},"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P. \\tag{4.10}",[1030,21516,21517],{},"Po přechodu na procentní změny (vztah (4.3)):",[1035,21519,21521],{"className":21520},[1480],[1482,21522,21523],{"xmlns":1484,"display":1485},[1487,21524,21525,21580],{},[19617,21526,21527],{"width":19619},[19621,21528,21529,21531,21573,21575],{},[19624,21530],{"width":19626},[19624,21532,21533],{},[1976,21534,21535],{"notation":1978},[1869,21536,21537],{"scriptlevel":1871,"displaystyle":1552},[1869,21538,21539],{"scriptlevel":1871,"displaystyle":1552},[1869,21540,21541],{"scriptlevel":1871,"displaystyle":1041},[1490,21542,21543,21545,21547,21549,21551,21553,21555,21557,21559,21561,21563,21565,21567,21569,21571],{},[1988,21544,1990],{},[1493,21546,2976],{"mathvariant":1516},[1493,21548,1520],{},[1493,21550,15846],{"mathvariant":1516},[1506,21552,2343],{},[1506,21554,1888],{},[1493,21556,2711],{},[1506,21558,1553],{"stretchy":1552},[1493,21560,1501],{},[1506,21562,1564],{"stretchy":1552},[1988,21564,5016],{},[1493,21566,2976],{"mathvariant":1516},[1493,21568,1501],{},[1493,21570,15846],{"mathvariant":1516},[1988,21572,1990],{},[19624,21574],{"width":19626},[19624,21576,21577],{},[1988,21578,21579],{},"(4.11)",[1528,21581,21582],{"encoding":1530},"\\boxed{\\;\\Delta Q\\% \\approx -E(P)\\,\\Delta P\\%\\;} \\tag{4.11}",[1030,21584,21585,1656,21588,21623,21624,21643,21644,21678,21679,21696],{},[1047,21586,21587],{},"Příklad 4.5.",[1035,21589,21591],{"className":21590},[1480],[1482,21592,21593],{"xmlns":1484},[1487,21594,21595,21620],{},[1490,21596,21597,21599,21601,21603,21609,21611,21613,21615,21617],{},[1493,21598,1501],{},[1506,21600,1508],{},[1506,21602,1888],{},[2315,21604,21605,21607],{},[1493,21606,1520],{},[1680,21608,1691],{},[1506,21610,1888],{},[1680,21612,4007],{},[1493,21614,1520],{},[1506,21616,2162],{},[1680,21618,21619],{},"96",[1528,21621,21622],{"encoding":1530},"P = -Q^2 - 4Q + 96",", cena ",[1035,21625,21627],{"className":21626},[1480],[1482,21628,21629],{"xmlns":1484},[1487,21630,21631,21640],{},[1490,21632,21633,21635,21637],{},[1493,21634,1501],{},[1506,21636,1508],{},[1680,21638,21639],{},"51",[1528,21641,21642],{"encoding":1530},"P=51",". Z rovnice ",[1035,21645,21647],{"className":21646},[1480],[1482,21648,21649],{"xmlns":1484},[1487,21650,21651,21675],{},[1490,21652,21653,21655,21657,21659,21665,21667,21669,21671,21673],{},[1680,21654,21639],{},[1506,21656,1508],{},[1506,21658,1888],{},[2315,21660,21661,21663],{},[1493,21662,1520],{},[1680,21664,1691],{},[1506,21666,1888],{},[1680,21668,4007],{},[1493,21670,1520],{},[1506,21672,2162],{},[1680,21674,21619],{},[1528,21676,21677],{"encoding":1530},"51 = -Q^2-4Q+96"," volíme (kladný kořen) ",[1035,21680,21682],{"className":21681},[1480],[1482,21683,21684],{"xmlns":1484},[1487,21685,21686,21694],{},[1490,21687,21688,21690,21692],{},[1493,21689,1520],{},[1506,21691,1508],{},[1680,21693,1752],{},[1528,21695,20973],{"encoding":1530},". Elasticita:",[1035,21698,21700],{"className":21699},[1480],[1482,21701,21702],{"xmlns":1484,"display":1485},[1487,21703,21704,21775],{},[1490,21705,21706,21708,21710,21748,21750,21752,21754,21756,21758,21760,21762,21769,21772],{},[1493,21707,2711],{},[1506,21709,1508],{},[1510,21711,21712,21732],{},[1490,21713,21714,21716,21722,21724,21726,21728,21730],{},[1506,21715,1888],{},[2315,21717,21718,21720],{},[1493,21719,1520],{},[1680,21721,1691],{},[1506,21723,1888],{},[1680,21725,4007],{},[1493,21727,1520],{},[1506,21729,2162],{},[1680,21731,21619],{},[1490,21733,21734,21736,21738,21740,21742,21744,21746],{},[1493,21735,1520],{},[1506,21737,1553],{"stretchy":1552},[1680,21739,1691],{},[1493,21741,1520],{},[1506,21743,2162],{},[1680,21745,4007],{},[1506,21747,1564],{"stretchy":1552},[1506,21749,1559],{"separator":1041},[1912,21751],{"width":1914},[1493,21753,2711],{},[1506,21755,1553],{"stretchy":1552},[1680,21757,1752],{},[1506,21759,1564],{"stretchy":1552},[1506,21761,1508],{},[1510,21763,21764,21766],{},[1680,21765,21639],{},[1680,21767,21768],{},"70",[1506,21770,21771],{},"≐",[1680,21773,21774],{},"0,728.",[1528,21776,21777],{"encoding":1530},"E = \\frac{-Q^2-4Q+96}{Q(2Q+4)}, \\qquad E(5) = \\frac{51}{70} \\doteq 0{,}728.",[1030,21779,21780,21781,2632],{},"Jde o neelastickou poptávku. Zvýší-li se cena o 2 %, pak ",[1035,21782,21784],{"className":21783},[1480],[1482,21785,21786],{"xmlns":1484},[1487,21787,21788,21818],{},[1490,21789,21790,21792,21794,21796,21798,21800,21803,21805,21807,21809,21811,21814,21816],{},[1493,21791,2976],{"mathvariant":1516},[1493,21793,1520],{},[1493,21795,15846],{"mathvariant":1516},[1506,21797,2343],{},[1506,21799,1888],{},[1680,21801,21802],{},"0,728",[1506,21804,1714],{},[1680,21806,1691],{},[1506,21808,1508],{},[1506,21810,1888],{},[1680,21812,21813],{},"1,456",[1988,21815,5016],{},[1493,21817,15846],{"mathvariant":1516},[1528,21819,21820],{"encoding":1530},"\\Delta Q\\% \\approx -0{,}728\\cdot 2 = -1{,}456\\,\\%",[1065,21822,21824],{"id":21823},"klasifikace-elasticit-poptávky","Klasifikace elasticit poptávky",[1030,21826,21827,21828,21851,21852,1274],{},"V závislosti na hodnotě ",[1035,21829,21831],{"className":21830},[1480],[1482,21832,21833],{"xmlns":1484},[1487,21834,21835,21849],{},[1490,21836,21837,21839,21841,21847],{},[1493,21838,2711],{},[1506,21840,1553],{"stretchy":1552},[2315,21842,21843,21845],{},[1493,21844,1501],{},[1506,21846,2287],{},[1506,21848,1564],{"stretchy":1552},[1528,21850,20092],{"encoding":1530}," mluvíme o poptávce podle následující tabulky ",[1035,21853,21855],{"className":21854},[1480],[1482,21856,21857],{"xmlns":1484},[1487,21858,21859,21868],{},[1490,21860,21861,21863,21866],{},[1506,21862,1553],{"stretchy":1552},[1680,21864,21865],{},"4.7",[1506,21867,1564],{"stretchy":1552},[1528,21869,21870],{"encoding":1530},"(4.7)",[1030,21872,21873],{},[18014,21874],{"alt":21875,"className":21876,"src":21877},"imek-typy-elasticity-5panelu",[1055,18018],"\u002Fwiki-assets\u002Fimek-typy-elasticity-5panelu.jpeg",[1073,21879,21880,21919],{},[1076,21881,21882],{},[1079,21883,21884,21910,21913,21916],{},[1082,21885,21886,21887],{},"Hodnota ",[1035,21888,21890],{"className":21889},[1480],[1482,21891,21892],{"xmlns":1484},[1487,21893,21894,21908],{},[1490,21895,21896,21898,21900,21906],{},[1493,21897,2711],{},[1506,21899,1553],{"stretchy":1552},[2315,21901,21902,21904],{},[1493,21903,1501],{},[1506,21905,2287],{},[1506,21907,1564],{"stretchy":1552},[1528,21909,20092],{"encoding":1530},[1082,21911,21912],{},"Typ poptávky",[1082,21914,21915],{},"Termín",[1082,21917,21918],{},"Význam",[1092,21920,21921,21954,22016,22091,22148],{},[1079,21922,21923,21943,21948,21951],{},[1097,21924,21925],{},[1035,21926,21928],{"className":21927},[1480],[1482,21929,21930],{"xmlns":1484},[1487,21931,21932,21940],{},[1490,21933,21934,21936,21938],{},[1493,21935,2711],{},[1506,21937,1508],{},[1680,21939,1871],{},[1528,21941,21942],{"encoding":1530},"E = 0",[1097,21944,21945],{},[1047,21946,21947],{},"dokonale neelastická",[1097,21949,21950],{},"perfectly inelastic",[1097,21952,21953],{},"množství se nemění bez ohledu na cenu",[1079,21955,21956,21980,21984,21987],{},[1097,21957,21958],{},[1035,21959,21961],{"className":21960},[1480],[1482,21962,21963],{"xmlns":1484},[1487,21964,21965,21977],{},[1490,21966,21967,21969,21971,21973,21975],{},[1680,21968,1871],{},[1506,21970,3961],{},[1493,21972,2711],{},[1506,21974,3961],{},[1680,21976,1682],{},[1528,21978,21979],{"encoding":1530},"0 \u003C E \u003C 1",[1097,21981,21982],{},[1047,21983,15507],{},[1097,21985,21986],{},"inelastic",[1097,21988,21989,22002,22003],{},[1035,21990,21992],{"className":21991},[1480],[1482,21993,21994],{"xmlns":1484},[1487,21995,21996,22000],{},[1490,21997,21998],{},[1493,21999,1520],{},[1528,22001,1520],{"encoding":1530}," se mění pomaleji než ",[1035,22004,22006],{"className":22005},[1480],[1482,22007,22008],{"xmlns":1484},[1487,22009,22010,22014],{},[1490,22011,22012],{},[1493,22013,1501],{},[1528,22015,1501],{"encoding":1530},[1079,22017,22018,22037,22042,22045],{},[1097,22019,22020],{},[1035,22021,22023],{"className":22022},[1480],[1482,22024,22025],{"xmlns":1484},[1487,22026,22027,22035],{},[1490,22028,22029,22031,22033],{},[1493,22030,2711],{},[1506,22032,1508],{},[1680,22034,1682],{},[1528,22036,20259],{"encoding":1530},[1097,22038,22039],{},[1047,22040,22041],{},"jednotkově elastická",[1097,22043,22044],{},"unit elastic",[1097,22046,22047,22060,22061,22074,22075,22090],{},[1035,22048,22050],{"className":22049},[1480],[1482,22051,22052],{"xmlns":1484},[1487,22053,22054,22058],{},[1490,22055,22056],{},[1493,22057,1520],{},[1528,22059,1520],{"encoding":1530}," i ",[1035,22062,22064],{"className":22063},[1480],[1482,22065,22066],{"xmlns":1484},[1487,22067,22068,22072],{},[1490,22069,22070],{},[1493,22071,1501],{},[1528,22073,1501],{"encoding":1530}," se mění stejně rychle; ",[1035,22076,22078],{"className":22077},[1480],[1482,22079,22080],{"xmlns":1484},[1487,22081,22082,22088],{},[1490,22083,22084,22086],{},[1493,22085,5289],{},[1493,22087,1995],{},[1528,22089,16491],{"encoding":1530}," má maximum",[1079,22092,22093,22112,22116,22119],{},[1097,22094,22095],{},[1035,22096,22098],{"className":22097},[1480],[1482,22099,22100],{"xmlns":1484},[1487,22101,22102,22110],{},[1490,22103,22104,22106,22108],{},[1493,22105,2711],{},[1506,22107,2796],{},[1680,22109,1682],{},[1528,22111,14551],{"encoding":1530},[1097,22113,22114],{},[1047,22115,19486],{},[1097,22117,22118],{},"elastic",[1097,22120,22121,22134,22135],{},[1035,22122,22124],{"className":22123},[1480],[1482,22125,22126],{"xmlns":1484},[1487,22127,22128,22132],{},[1490,22129,22130],{},[1493,22131,1520],{},[1528,22133,1520],{"encoding":1530}," se mění rychleji než ",[1035,22136,22138],{"className":22137},[1480],[1482,22139,22140],{"xmlns":1484},[1487,22141,22142,22146],{},[1490,22143,22144],{},[1493,22145,1501],{},[1528,22147,1501],{"encoding":1530},[1079,22149,22150,22170,22175,22178],{},[1097,22151,22152],{},[1035,22153,22155],{"className":22154},[1480],[1482,22156,22157],{"xmlns":1484},[1487,22158,22159,22167],{},[1490,22160,22161,22163,22165],{},[1493,22162,2711],{},[1506,22164,6380],{},[1493,22166,6383],{"mathvariant":1516},[1528,22168,22169],{"encoding":1530},"E \\to \\infty",[1097,22171,22172],{},[1047,22173,22174],{},"dokonale elastická",[1097,22176,22177],{},"perfectly elastic",[1097,22179,22180,22181],{},"sebemenší změna ceny úplně mění ",[1035,22182,22184],{"className":22183},[1480],[1482,22185,22186],{"xmlns":1484},[1487,22187,22188,22192],{},[1490,22189,22190],{},[1493,22191,1520],{},[1528,22193,1520],{"encoding":1530},[1030,22195,22196],{},[1047,22197,22198],{},"Pravidlo růstu elasticity s cenou:",[19516,22200,22201],{},[1030,22202,22203,22204],{},"S rostoucí cenou elasticita poptávky roste. ",[1035,22205,22207],{"className":22206},[1480],[1482,22208,22209],{"xmlns":1484},[1487,22210,22211,22220],{},[1490,22212,22213,22215,22218],{},[1506,22214,1553],{"stretchy":1552},[1680,22216,22217],{},"4.8",[1506,22219,1564],{"stretchy":1552},[1528,22221,22222],{"encoding":1530},"(4.8)",[1030,22224,22225,22226,22229,22230,22233,22234,22251],{},"Z toho plyne, že při ",[1176,22227,22228],{},"dostatečně nízkých"," cenách je poptávka neelastická a při ",[1176,22231,22232],{},"dostatečně vysokých"," elastická. Existuje tedy cena ",[1035,22235,22237],{"className":22236},[1480],[1482,22238,22239],{"xmlns":1484},[1487,22240,22241,22249],{},[1490,22242,22243],{},[2315,22244,22245,22247],{},[1493,22246,1501],{},[1506,22248,2287],{},[1528,22250,20114],{"encoding":1530},", při které je poptávka jednotkově elastická, a ta rozděluje reálné cenové rozpětí na obě zóny.",[1023,22253,22255,22262],{"className":22254,"dataCallout":1443},[1026,1442],[1030,22256,22258,22261],{"className":22257},[1033],[1035,22259],{"className":22260,"ariaHidden":1041},[1038,1450,1040],"Postup: jak klasifikovat poptávku",[1276,22263,22264,22291,22294],{},[1206,22265,22266,22267,22290],{},"Spočítejte ",[1035,22268,22270],{"className":22269},[1480],[1482,22271,22272],{"xmlns":1484},[1487,22273,22274,22288],{},[1490,22275,22276,22278,22280,22286],{},[1493,22277,2711],{},[1506,22279,1553],{"stretchy":1552},[2315,22281,22282,22284],{},[1493,22283,1501],{},[1506,22285,2287],{},[1506,22287,1564],{"stretchy":1552},[1528,22289,20092],{"encoding":1530}," dle (4.5).",[1206,22292,22293],{},"Porovnejte s jedničkou (viz tabulka výše).",[1206,22295,22296,22297,22321],{},"Chcete-li najít hranici mezi elastickou a neelastickou zónou, řešte rovnici ",[1035,22298,22300],{"className":22299},[1480],[1482,22301,22302],{"xmlns":1484},[1487,22303,22304,22318],{},[1490,22305,22306,22308,22310,22312,22314,22316],{},[1493,22307,2711],{},[1506,22309,1553],{"stretchy":1552},[1493,22311,1501],{},[1506,22313,1564],{"stretchy":1552},[1506,22315,1508],{},[1680,22317,1682],{},[1528,22319,22320],{"encoding":1530},"E(P) = 1"," a výsledek porovnejte s reálným cenovým rozpětím.",[1030,22323,22324,22327,22328,22345,22346,22364,22365,22392,22393,2632],{},[1047,22325,22326],{},"Příklad 4.2."," Pro poptávku z Příkladu 4.1: ",[1035,22329,22331],{"className":22330},[1480],[1482,22332,22333],{"xmlns":1484},[1487,22334,22335,22343],{},[1490,22336,22337,22339,22341],{},[1493,22338,2711],{},[1506,22340,1508],{},[1680,22342,1682],{},[1528,22344,20259],{"encoding":1530}," pro ",[1035,22347,22349],{"className":22348},[1480],[1482,22350,22351],{"xmlns":1484},[1487,22352,22353,22361],{},[1490,22354,22355,22357,22359],{},[1493,22356,1501],{},[1506,22358,1508],{},[1680,22360,2309],{},[1528,22362,22363],{"encoding":1530},"P = 25",". Podle (4.8) je poptávka neelastická pro ",[1035,22366,22368],{"className":22367},[1480],[1482,22369,22370],{"xmlns":1484},[1487,22371,22372,22389],{},[1490,22373,22374,22376,22379,22381,22383,22385,22387],{},[1493,22375,1501],{},[1506,22377,22378],{},"∈",[1506,22380,21034],{"stretchy":1552},[1680,22382,1871],{},[1506,22384,1559],{"separator":1041},[1680,22386,2309],{},[1506,22388,1564],{"stretchy":1552},[1528,22390,22391],{"encoding":1530},"P \\in \\langle 0, 25)"," a elastická pro ",[1035,22394,22396],{"className":22395},[1480],[1482,22397,22398],{"xmlns":1484},[1487,22399,22400,22416],{},[1490,22401,22402,22404,22406,22408,22410,22412,22414],{},[1493,22403,1501],{},[1506,22405,22378],{},[1506,22407,1553],{"stretchy":1552},[1680,22409,2309],{},[1506,22411,1559],{"separator":1041},[1680,22413,2292],{},[1506,22415,21051],{"stretchy":1552},[1528,22417,22418],{"encoding":1530},"P \\in (25, 50\\rangle",[1065,22420,22422],{"id":22421},"elasticita-a-celkový-příjem","Elasticita a celkový příjem",[1030,22424,22425],{},[18014,22426],{"alt":22427,"className":22428,"src":22429},"imek-elasticita-tr",[1055,18018],"\u002Fwiki-assets\u002Fimek-elasticita-tr.jpeg",[1030,22431,22432],{},[18014,22433],{"alt":22434,"className":22435,"src":22436},"imek-elasticita-podel-linearni-poptavky",[1055,18018],"\u002Fwiki-assets\u002Fimek-elasticita-podel-linearni-poptavky.jpeg",[1030,22438,22439,22440,22490,22491,22506],{},"Pro celkový příjem platí ",[1035,22441,22443],{"className":22442},[1480],[1482,22444,22445],{"xmlns":1484},[1487,22446,22447,22487],{},[1490,22448,22449,22451,22453,22455,22457,22459,22461,22463,22465,22467,22469,22471,22473,22475,22477,22479,22481,22483,22485],{},[1493,22450,5289],{},[1493,22452,1995],{},[1506,22454,1508],{},[1493,22456,5289],{},[1493,22458,1995],{},[1506,22460,1553],{"stretchy":1552},[1493,22462,1520],{},[1506,22464,1564],{"stretchy":1552},[1506,22466,1508],{},[1493,22468,1501],{},[1506,22470,1714],{},[1493,22472,1520],{},[1506,22474,1508],{},[1493,22476,1520],{},[1506,22478,1714],{},[1493,22480,3712],{},[1506,22482,1553],{"stretchy":1552},[1493,22484,1520],{},[1506,22486,1564],{"stretchy":1552},[1528,22488,22489],{"encoding":1530},"TR = TR(Q) = P\\cdot Q = Q\\cdot D(Q)",". Pro mezní příjem ",[1035,22492,22494],{"className":22493},[1480],[1482,22495,22496],{"xmlns":1484},[1487,22497,22498,22504],{},[1490,22499,22500,22502],{},[1493,22501,1495],{},[1493,22503,1995],{},[1528,22505,6258],{"encoding":1530}," odvodíme:",[1035,22508,22510],{"className":22509},[1480],[1482,22511,22512],{"xmlns":1484,"display":1485},[1487,22513,22514,22622],{},[1490,22515,22516,22518,22520,22522,22524,22530,22532,22534,22536,22538,22540,22542,22544,22546,22548,22550,22552,22558,22560,22562,22564,22566,22568,22570,22572,22586,22588,22590],{},[1493,22517,1495],{},[1493,22519,1995],{},[1506,22521,1508],{},[1493,22523,5289],{},[2315,22525,22526,22528],{},[1493,22527,1995],{},[1506,22529,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,22531,1553],{"stretchy":1552},[1493,22533,1520],{},[1506,22535,1564],{"stretchy":1552},[1506,22537,1508],{},[1493,22539,3712],{},[1506,22541,1553],{"stretchy":1552},[1493,22543,1520],{},[1506,22545,1564],{"stretchy":1552},[1506,22547,2162],{},[1493,22549,1520],{},[1988,22551,5016],{},[2315,22553,22554,22556],{},[1493,22555,3712],{},[1506,22557,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,22559,1553],{"stretchy":1552},[1493,22561,1520],{},[1506,22563,1564],{"stretchy":1552},[1506,22565,1508],{},[1493,22567,1501],{},[1506,22569,2162],{},[1493,22571,1520],{},[1510,22573,22574,22580],{},[1490,22575,22576,22578],{},[1493,22577,3384],{"mathvariant":1516},[1493,22579,1501],{},[1490,22581,22582,22584],{},[1493,22583,3384],{"mathvariant":1516},[1493,22585,1520],{},[1506,22587,1508],{},[1493,22589,1501],{},[1490,22591,22592,22594,22596,22598,22604,22606,22620],{},[1506,22593,1553],{"fence":1041},[1680,22595,1682],{},[1506,22597,2162],{},[1510,22599,22600,22602],{},[1493,22601,1520],{},[1493,22603,1501],{},[1506,22605,1714],{},[1510,22607,22608,22614],{},[1490,22609,22610,22612],{},[1493,22611,3384],{"mathvariant":1516},[1493,22613,1501],{},[1490,22615,22616,22618],{},[1493,22617,3384],{"mathvariant":1516},[1493,22619,1520],{},[1506,22621,1564],{"fence":1041},[1528,22623,22624],{"encoding":1530},"MR = TR'(Q) = D(Q) + Q\\,D'(Q) = P + Q\\frac{\\mathrm{d}P}{\\mathrm{d}Q} = P\\left(1 + \\frac{Q}{P}\\cdot\\frac{\\mathrm{d}P}{\\mathrm{d}Q}\\right)",[1035,22626,22628],{"className":22627},[1480],[1482,22629,22630],{"xmlns":1484,"display":1485},[1487,22631,22632,22704],{},[1490,22633,22634,22636,22638,22680,22682,22684],{},[1506,22635,1508],{},[1493,22637,1501],{},[1490,22639,22640,22642,22644,22646,22678],{},[1506,22641,1553],{"fence":1041},[1680,22643,1682],{},[1506,22645,2162],{},[1510,22647,22648,22650],{},[1680,22649,1682],{},[1490,22651,22652,22660,22662],{},[1869,22653,22654],{"scriptlevel":1871,"displaystyle":1552},[1510,22655,22656,22658],{},[1493,22657,1501],{},[1493,22659,1520],{},[1506,22661,1714],{},[1869,22663,22664],{"scriptlevel":1871,"displaystyle":1552},[1510,22665,22666,22672],{},[1490,22667,22668,22670],{},[1493,22669,3384],{"mathvariant":1516},[1493,22671,1520],{},[1490,22673,22674,22676],{},[1493,22675,3384],{"mathvariant":1516},[1493,22677,1501],{},[1506,22679,1564],{"fence":1041},[1506,22681,1508],{},[1493,22683,1501],{},[1490,22685,22686,22688,22690,22692,22702],{},[1506,22687,1553],{"fence":1041},[1680,22689,1682],{},[1506,22691,2162],{},[1510,22693,22694,22696],{},[1680,22695,1682],{},[1490,22697,22698,22700],{},[1506,22699,1888],{},[1493,22701,2711],{},[1506,22703,1564],{"fence":1041},[1528,22705,22706],{"encoding":1530},"= P\\left(1 + \\frac{1}{\\tfrac{P}{Q}\\cdot\\tfrac{\\mathrm{d}Q}{\\mathrm{d}P}}\\right) = P\\left(1 + \\frac{1}{-E}\\right)",[1030,22708,22709],{},"a tedy",[1035,22711,22713],{"className":22712},[1480],[1482,22714,22715],{"xmlns":1484,"display":1485},[1487,22716,22717,22796],{},[19617,22718,22719],{"width":19619},[19621,22720,22721,22723,22789,22791],{},[19624,22722],{"width":19626},[19624,22724,22725],{},[1976,22726,22727],{"notation":1978},[1869,22728,22729],{"scriptlevel":1871,"displaystyle":1552},[1869,22730,22731],{"scriptlevel":1871,"displaystyle":1552},[1869,22732,22733],{"scriptlevel":1871,"displaystyle":1041},[1490,22734,22735,22737,22739,22741,22743,22745,22761,22763,22765,22767,22769,22771,22787],{},[1988,22736,1990],{},[1493,22738,1495],{},[1493,22740,1995],{},[1506,22742,1508],{},[1493,22744,1501],{},[1490,22746,22747,22749,22751,22753,22759],{},[1506,22748,1553],{"fence":1041},[1680,22750,1682],{},[1506,22752,1888],{},[1510,22754,22755,22757],{},[1680,22756,1682],{},[1493,22758,2711],{},[1506,22760,1564],{"fence":1041},[1506,22762,1508],{},[1493,22764,3712],{},[1506,22766,1553],{"stretchy":1552},[1493,22768,1520],{},[1506,22770,1564],{"stretchy":1552},[1490,22772,22773,22775,22777,22779,22785],{},[1506,22774,1553],{"fence":1041},[1680,22776,1682],{},[1506,22778,1888],{},[1510,22780,22781,22783],{},[1680,22782,1682],{},[1493,22784,2711],{},[1506,22786,1564],{"fence":1041},[1988,22788,1990],{},[19624,22790],{"width":19626},[19624,22792,22793],{},[1988,22794,22795],{},"(4.12)",[1528,22797,22798],{"encoding":1530},"\\boxed{\\;MR = P\\left(1 - \\frac{1}{E}\\right) = D(Q)\\left(1 - \\frac{1}{E}\\right)\\;} \\tag{4.12}",[1023,22800,22802,22843,22875,23124],{"className":22801,"dataCallout":582},[1026,1186],[1030,22803,22805,22808,22809],{"className":22804},[1033],[1035,22806],{"className":22807,"ariaHidden":1041},[1038,1193,1040],"Intuice: vztah ",[1035,22810,22812],{"className":22811},[1480],[1482,22813,22814],{"xmlns":1484},[1487,22815,22816,22840],{},[1490,22817,22818,22820,22822,22824,22826,22828,22830,22832,22834,22836,22838],{},[1493,22819,1495],{},[1493,22821,1995],{},[1506,22823,1508],{},[1493,22825,1501],{},[1506,22827,1553],{"stretchy":1552},[1680,22829,1682],{},[1506,22831,1888],{},[1680,22833,1682],{},[1493,22835,1709],{"mathvariant":1516},[1493,22837,2711],{},[1506,22839,1564],{"stretchy":1552},[1528,22841,22842],{"encoding":1530},"MR = P(1 - 1\u002FE)",[1030,22844,22845,22846,22861,22862,1274],{},"Vztah (4.12) je „most\" mezi elasticitou a mezním příjmem — znaménko ",[1035,22847,22849],{"className":22848},[1480],[1482,22850,22851],{"xmlns":1484},[1487,22852,22853,22859],{},[1490,22854,22855,22857],{},[1493,22856,1495],{},[1493,22858,1995],{},[1528,22860,6258],{"encoding":1530}," jednoznačně určuje hodnota ",[1035,22863,22865],{"className":22864},[1480],[1482,22866,22867],{"xmlns":1484},[1487,22868,22869,22873],{},[1490,22870,22871],{},[1493,22872,2711],{},[1528,22874,2711],{"encoding":1530},[1203,22876,22877,22987,23055],{},[1206,22878,22879,22896,22897,1656,22911,1656,22937,1656,22950,22970,22971,22986],{},[1035,22880,22882],{"className":22881},[1480],[1482,22883,22884],{"xmlns":1484},[1487,22885,22886,22894],{},[1490,22887,22888,22890,22892],{},[1493,22889,2711],{},[1506,22891,2796],{},[1680,22893,1682],{},[1528,22895,14551],{"encoding":1530}," (elastická) ",[1035,22898,22900],{"className":22899},[1480],[1482,22901,22902],{"xmlns":1484},[1487,22903,22904,22908],{},[1490,22905,22906],{},[1506,22907,2183],{},[1528,22909,22910],{"encoding":1530},"\\Rightarrow",[1035,22912,22914],{"className":22913},[1480],[1482,22915,22916],{"xmlns":1484},[1487,22917,22918,22934],{},[1490,22919,22920,22922,22924,22926,22928,22930,22932],{},[1680,22921,1682],{},[1506,22923,1888],{},[1680,22925,1682],{},[1493,22927,1709],{"mathvariant":1516},[1493,22929,2711],{},[1506,22931,2796],{},[1680,22933,1871],{},[1528,22935,22936],{"encoding":1530},"1 - 1\u002FE > 0",[1035,22938,22940],{"className":22939},[1480],[1482,22941,22942],{"xmlns":1484},[1487,22943,22944,22948],{},[1490,22945,22946],{},[1506,22947,2183],{},[1528,22949,22910],{"encoding":1530},[1035,22951,22953],{"className":22952},[1480],[1482,22954,22955],{"xmlns":1484},[1487,22956,22957,22967],{},[1490,22958,22959,22961,22963,22965],{},[1493,22960,1495],{},[1493,22962,1995],{},[1506,22964,2796],{},[1680,22966,1871],{},[1528,22968,22969],{"encoding":1530},"MR > 0"," — ",[1035,22972,22974],{"className":22973},[1480],[1482,22975,22976],{"xmlns":1484},[1487,22977,22978,22984],{},[1490,22979,22980,22982],{},[1493,22981,5289],{},[1493,22983,1995],{},[1528,22985,16491],{"encoding":1530}," roste s množstvím, tj. klesá s cenou.",[1206,22988,22989,23006,23007,1656,23020,22970,23039,23054],{},[1035,22990,22992],{"className":22991},[1480],[1482,22993,22994],{"xmlns":1484},[1487,22995,22996,23004],{},[1490,22997,22998,23000,23002],{},[1493,22999,2711],{},[1506,23001,1508],{},[1680,23003,1682],{},[1528,23005,20259],{"encoding":1530}," (jednotková) ",[1035,23008,23010],{"className":23009},[1480],[1482,23011,23012],{"xmlns":1484},[1487,23013,23014,23018],{},[1490,23015,23016],{},[1506,23017,2183],{},[1528,23019,22910],{"encoding":1530},[1035,23021,23023],{"className":23022},[1480],[1482,23024,23025],{"xmlns":1484},[1487,23026,23027,23037],{},[1490,23028,23029,23031,23033,23035],{},[1493,23030,1495],{},[1493,23032,1995],{},[1506,23034,1508],{},[1680,23036,1871],{},[1528,23038,11073],{"encoding":1530},[1035,23040,23042],{"className":23041},[1480],[1482,23043,23044],{"xmlns":1484},[1487,23045,23046,23052],{},[1490,23047,23048,23050],{},[1493,23049,5289],{},[1493,23051,1995],{},[1528,23053,16491],{"encoding":1530}," je extrém (maximum).",[1206,23056,23057,23074,23075,1656,23088,22970,23108,23123],{},[1035,23058,23060],{"className":23059},[1480],[1482,23061,23062],{"xmlns":1484},[1487,23063,23064,23072],{},[1490,23065,23066,23068,23070],{},[1493,23067,2711],{},[1506,23069,3961],{},[1680,23071,1682],{},[1528,23073,20241],{"encoding":1530}," (neelastická) ",[1035,23076,23078],{"className":23077},[1480],[1482,23079,23080],{"xmlns":1484},[1487,23081,23082,23086],{},[1490,23083,23084],{},[1506,23085,2183],{},[1528,23087,22910],{"encoding":1530},[1035,23089,23091],{"className":23090},[1480],[1482,23092,23093],{"xmlns":1484},[1487,23094,23095,23105],{},[1490,23096,23097,23099,23101,23103],{},[1493,23098,1495],{},[1493,23100,1995],{},[1506,23102,3961],{},[1680,23104,1871],{},[1528,23106,23107],{"encoding":1530},"MR \u003C 0",[1035,23109,23111],{"className":23110},[1480],[1482,23112,23113],{"xmlns":1484},[1487,23114,23115,23121],{},[1490,23116,23117,23119],{},[1493,23118,5289],{},[1493,23120,1995],{},[1528,23122,16491],{"encoding":1530}," klesá s množstvím, tj. roste s cenou.",[1030,23125,23126,23127,2632],{},"Viz také ",[1052,23128,1301],{"className":23129,"dataFsResolvedFilePath":1299,"href":1300},[1055],[1304,23131,23133],{"id":23132},"pravidla-13-odvození-z-412","Pravidla 1–3 (odvození z (4.12))",[1030,23135,23136,23156,23157,23183,23184,23199,23200,23213,23214,23227,23228,23241,23242,23258,23259,1656,23274,23276,23277,23258,23293,2632],{},[1047,23137,23138,23139,16623],{},"(a) Poptávka elastická (",[1035,23140,23142],{"className":23141},[1480],[1482,23143,23144],{"xmlns":1484},[1487,23145,23146,23154],{},[1490,23147,23148,23150,23152],{},[1493,23149,2711],{},[1506,23151,2796],{},[1680,23153,1682],{},[1528,23155,14551],{"encoding":1530}," Z (4.12) plyne ",[1035,23158,23160],{"className":23159},[1480],[1482,23161,23162],{"xmlns":1484},[1487,23163,23164,23180],{},[1490,23165,23166,23168,23170,23172,23174,23176,23178],{},[1493,23167,1495],{},[1493,23169,1995],{},[1506,23171,1553],{"stretchy":1552},[1493,23173,1520],{},[1506,23175,1564],{"stretchy":1552},[1506,23177,2796],{},[1680,23179,1871],{},[1528,23181,23182],{"encoding":1530},"MR(Q) > 0",", a tedy celkový příjem ",[1035,23185,23187],{"className":23186},[1480],[1482,23188,23189],{"xmlns":1484},[1487,23190,23191,23197],{},[1490,23192,23193,23195],{},[1493,23194,5289],{},[1493,23196,1995],{},[1528,23198,16491],{"encoding":1530}," je rostoucí funkcí ",[1035,23201,23203],{"className":23202},[1480],[1482,23204,23205],{"xmlns":1484},[1487,23206,23207,23211],{},[1490,23208,23209],{},[1493,23210,1520],{},[1528,23212,1520],{"encoding":1530},". Avšak růst ",[1035,23215,23217],{"className":23216},[1480],[1482,23218,23219],{"xmlns":1484},[1487,23220,23221,23225],{},[1490,23222,23223],{},[1493,23224,1520],{},[1528,23226,1520],{"encoding":1530}," je odezvou na pokles ceny ",[1035,23229,23231],{"className":23230},[1480],[1482,23232,23233],{"xmlns":1484},[1487,23234,23235,23239],{},[1490,23236,23237],{},[1493,23238,1501],{},[1528,23240,1501],{"encoding":1530},". Tudíž s ",[1176,23243,23244,23245],{},"poklesem ceny ",[1035,23246,23248],{"className":23247},[1480],[1482,23249,23250],{"xmlns":1484},[1487,23251,23252,23256],{},[1490,23253,23254],{},[1493,23255,1501],{},[1528,23257,1501],{"encoding":1530}," celkový příjem ",[1035,23260,23262],{"className":23261},[1480],[1482,23263,23264],{"xmlns":1484},[1487,23265,23266,23272],{},[1490,23267,23268,23270],{},[1493,23269,5289],{},[1493,23271,1995],{},[1528,23273,16491],{"encoding":1530},[1176,23275,7685],{}," a s ",[1176,23278,23279,23280],{},"růstem ceny ",[1035,23281,23283],{"className":23282},[1480],[1482,23284,23285],{"xmlns":1484},[1487,23286,23287,23291],{},[1490,23288,23289],{},[1493,23290,1501],{},[1528,23292,1501],{"encoding":1530},[1176,23294,23295],{},"klesá",[19516,23297,23298],{},[1030,23299,23300,23303],{},[1047,23301,23302],{},"Pravidlo 1."," Je-li poptávka elastická, pak s poklesem ceny celkový příjem roste a s růstem ceny celkový příjem klesá.",[1030,23305,23306,23156,23326,1732,23352,23367,23368,23381,23382,23395,23396,23409,23410,23258,23423,1656,23438,2632],{},[1047,23307,23308,23309,16623],{},"(b) Poptávka neelastická (",[1035,23310,23312],{"className":23311},[1480],[1482,23313,23314],{"xmlns":1484},[1487,23315,23316,23324],{},[1490,23317,23318,23320,23322],{},[1493,23319,2711],{},[1506,23321,3961],{},[1680,23323,1682],{},[1528,23325,20241],{"encoding":1530},[1035,23327,23329],{"className":23328},[1480],[1482,23330,23331],{"xmlns":1484},[1487,23332,23333,23349],{},[1490,23334,23335,23337,23339,23341,23343,23345,23347],{},[1493,23336,1495],{},[1493,23338,1995],{},[1506,23340,1553],{"stretchy":1552},[1493,23342,1520],{},[1506,23344,1564],{"stretchy":1552},[1506,23346,3961],{},[1680,23348,1871],{},[1528,23350,23351],{"encoding":1530},"MR(Q) \u003C 0",[1035,23353,23355],{"className":23354},[1480],[1482,23356,23357],{"xmlns":1484},[1487,23358,23359,23365],{},[1490,23360,23361,23363],{},[1493,23362,5289],{},[1493,23364,1995],{},[1528,23366,16491],{"encoding":1530}," je klesající funkce ",[1035,23369,23371],{"className":23370},[1480],[1482,23372,23373],{"xmlns":1484},[1487,23374,23375,23379],{},[1490,23376,23377],{},[1493,23378,1520],{},[1528,23380,1520],{"encoding":1530},", tj. s růstem ",[1035,23383,23385],{"className":23384},[1480],[1482,23386,23387],{"xmlns":1484},[1487,23388,23389,23393],{},[1490,23390,23391],{},[1493,23392,1520],{},[1528,23394,1520],{"encoding":1530}," (s poklesem ceny ",[1035,23397,23399],{"className":23398},[1480],[1482,23400,23401],{"xmlns":1484},[1487,23402,23403,23407],{},[1490,23404,23405],{},[1493,23406,1501],{},[1528,23408,1501],{"encoding":1530},") celkový příjem klesá. S růstem ceny ",[1035,23411,23413],{"className":23412},[1480],[1482,23414,23415],{"xmlns":1484},[1487,23416,23417,23421],{},[1490,23418,23419],{},[1493,23420,1501],{},[1528,23422,1501],{"encoding":1530},[1035,23424,23426],{"className":23425},[1480],[1482,23427,23428],{"xmlns":1484},[1487,23429,23430,23436],{},[1490,23431,23432,23434],{},[1493,23433,5289],{},[1493,23435,1995],{},[1528,23437,16491],{"encoding":1530},[1176,23439,7685],{},[19516,23441,23442],{},[1030,23443,23444,23447],{},[1047,23445,23446],{},"Pravidlo 2."," Je-li poptávka neelastická, pak s poklesem ceny celkový příjem klesá a s růstem ceny celkový příjem roste.",[1030,23449,23450,23156,23470,23489,23490,23505,23506,23576,23577,1586,23605,23638,23639,21352,23667,23682,23683,2632],{},[1047,23451,23452,23453,16623],{},"(c) Jednotková elasticita (",[1035,23454,23456],{"className":23455},[1480],[1482,23457,23458],{"xmlns":1484},[1487,23459,23460,23468],{},[1490,23461,23462,23464,23466],{},[1493,23463,2711],{},[1506,23465,1508],{},[1680,23467,1682],{},[1528,23469,20259],{"encoding":1530},[1035,23471,23473],{"className":23472},[1480],[1482,23474,23475],{"xmlns":1484},[1487,23476,23477,23487],{},[1490,23478,23479,23481,23483,23485],{},[1493,23480,1495],{},[1493,23482,1995],{},[1506,23484,1508],{},[1680,23486,1871],{},[1528,23488,11073],{"encoding":1530}," — nutná podmínka extrému ",[1035,23491,23493],{"className":23492},[1480],[1482,23494,23495],{"xmlns":1484},[1487,23496,23497,23503],{},[1490,23498,23499,23501],{},[1493,23500,5289],{},[1493,23502,1995],{},[1528,23504,16491],{"encoding":1530},". Dále ",[1035,23507,23509],{"className":23508},[1480],[1482,23510,23511],{"xmlns":1484},[1487,23512,23513,23573],{},[1490,23514,23515,23517,23527,23529,23531,23537,23539,23545,23547,23549,23551,23553,23555,23557,23567,23569,23571],{},[1493,23516,5289],{},[2315,23518,23519,23521],{},[1493,23520,1995],{},[1490,23522,23523,23525],{},[1506,23524,6927],{"mathvariant":1516},[1506,23526,6927],{"mathvariant":1516},[1506,23528,1508],{},[1493,23530,1495],{},[2315,23532,23533,23535],{},[1493,23534,1995],{},[1506,23536,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,23538,1508],{},[2315,23540,23541,23543],{},[1493,23542,3712],{},[1506,23544,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,23546,1553],{"stretchy":1552},[1493,23548,1520],{},[1506,23550,1564],{"stretchy":1552},[1506,23552,2162],{},[1493,23554,1520],{},[1988,23556,5016],{},[2315,23558,23559,23561],{},[1493,23560,3712],{},[1490,23562,23563,23565],{},[1506,23564,6927],{"mathvariant":1516},[1506,23566,6927],{"mathvariant":1516},[1506,23568,1553],{"stretchy":1552},[1493,23570,1520],{},[1506,23572,1564],{"stretchy":1552},[1528,23574,23575],{"encoding":1530},"TR'' = MR' = D'(Q) + Q\\,D''(Q)","; za normálních podmínek ",[1035,23578,23580],{"className":23579},[1480],[1482,23581,23582],{"xmlns":1484},[1487,23583,23584,23602],{},[1490,23585,23586,23592,23594,23596,23598,23600],{},[2315,23587,23588,23590],{},[1493,23589,3712],{},[1506,23591,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,23593,1553],{"stretchy":1552},[1493,23595,1520],{},[1506,23597,1564],{"stretchy":1552},[1506,23599,3961],{},[1680,23601,1871],{},[1528,23603,23604],{"encoding":1530},"D'(Q) \u003C 0",[1035,23606,23608],{"className":23607},[1480],[1482,23609,23610],{"xmlns":1484},[1487,23611,23612,23635],{},[1490,23613,23614,23624,23626,23628,23630,23633],{},[2315,23615,23616,23618],{},[1493,23617,3712],{},[1490,23619,23620,23622],{},[1506,23621,6927],{"mathvariant":1516},[1506,23623,6927],{"mathvariant":1516},[1506,23625,1553],{"stretchy":1552},[1493,23627,1520],{},[1506,23629,1564],{"stretchy":1552},[1506,23631,23632],{},"≤",[1680,23634,1871],{},[1528,23636,23637],{"encoding":1530},"D''(Q) \\le 0",", odkud ",[1035,23640,23642],{"className":23641},[1480],[1482,23643,23644],{"xmlns":1484},[1487,23645,23646,23664],{},[1490,23647,23648,23650,23660,23662],{},[1493,23649,5289],{},[2315,23651,23652,23654],{},[1493,23653,1995],{},[1490,23655,23656,23658],{},[1506,23657,6927],{"mathvariant":1516},[1506,23659,6927],{"mathvariant":1516},[1506,23661,3961],{},[1680,23663,1871],{},[1528,23665,23666],{"encoding":1530},"TR'' \u003C 0",[1035,23668,23670],{"className":23669},[1480],[1482,23671,23672],{"xmlns":1484},[1487,23673,23674,23680],{},[1490,23675,23676,23678],{},[1493,23677,5289],{},[1493,23679,1995],{},[1528,23681,16491],{"encoding":1530}," nabývá ",[1047,23684,23685],{},"maxima",[19516,23687,23688],{},[1030,23689,23690,23693],{},[1047,23691,23692],{},"Pravidlo 3."," Celkový příjem nabývá maxima při ceně, pro kterou je poptávka jednotkově elastická.",[1030,23695,23696],{},"Tato tři pravidla potvrzují hypotézu (4.1) a jsou klíčem k regulaci ceny za účelem zvýšení (maximalizace) celkového příjmu.",[1030,23698,23699],{},[1047,23700,23701],{},"Souhrnná tabulka Pravidel 1–3:",[1073,23703,23704,23808],{},[1076,23705,23706],{},[1079,23707,23708,23711,23726,23743,23774,23805],{},[1082,23709,23710],{},"Charakter poptávky",[1082,23712,23713],{},[1035,23714,23716],{"className":23715},[1480],[1482,23717,23718],{"xmlns":1484},[1487,23719,23720,23724],{},[1490,23721,23722],{},[1493,23723,2711],{},[1528,23725,2711],{"encoding":1530},[1082,23727,23728],{},[1035,23729,23731],{"className":23730},[1480],[1482,23732,23733],{"xmlns":1484},[1487,23734,23735,23741],{},[1490,23736,23737,23739],{},[1493,23738,1495],{},[1493,23740,1995],{},[1528,23742,6258],{"encoding":1530},[1082,23744,23745,23746,1656,23759],{},"Pokles ceny ",[1035,23747,23749],{"className":23748},[1480],[1482,23750,23751],{"xmlns":1484},[1487,23752,23753,23757],{},[1490,23754,23755],{},[1506,23756,2183],{},[1528,23758,22910],{"encoding":1530},[1035,23760,23762],{"className":23761},[1480],[1482,23763,23764],{"xmlns":1484},[1487,23765,23766,23772],{},[1490,23767,23768,23770],{},[1493,23769,5289],{},[1493,23771,1995],{},[1528,23773,16491],{"encoding":1530},[1082,23775,23776,23777,1656,23790],{},"Růst ceny ",[1035,23778,23780],{"className":23779},[1480],[1482,23781,23782],{"xmlns":1484},[1487,23783,23784,23788],{},[1490,23785,23786],{},[1506,23787,2183],{},[1528,23789,22910],{"encoding":1530},[1035,23791,23793],{"className":23792},[1480],[1482,23794,23795],{"xmlns":1484},[1487,23796,23797,23803],{},[1490,23798,23799,23801],{},[1493,23800,5289],{},[1493,23802,1995],{},[1528,23804,16491],{"encoding":1530},[1082,23806,23807],{},"Doporučení",[1092,23809,23810,23859,23909],{},[1079,23811,23812,23814,23832,23850,23852,23854],{},[1097,23813,19486],{},[1097,23815,23816],{},[1035,23817,23819],{"className":23818},[1480],[1482,23820,23821],{"xmlns":1484},[1487,23822,23823,23829],{},[1490,23824,23825,23827],{},[1506,23826,2796],{},[1680,23828,1682],{},[1528,23830,23831],{"encoding":1530},"> 1",[1097,23833,23834],{},[1035,23835,23837],{"className":23836},[1480],[1482,23838,23839],{"xmlns":1484},[1487,23840,23841,23847],{},[1490,23842,23843,23845],{},[1506,23844,2796],{},[1680,23846,1871],{},[1528,23848,23849],{"encoding":1530},"> 0",[1097,23851,7685],{},[1097,23853,23295],{},[1097,23855,23856],{},[1047,23857,23858],{},"snížit cenu",[1079,23860,23861,23864,23882,23900,23902,23904],{},[1097,23862,23863],{},"jednotková",[1097,23865,23866],{},[1035,23867,23869],{"className":23868},[1480],[1482,23870,23871],{"xmlns":1484},[1487,23872,23873,23879],{},[1490,23874,23875,23877],{},[1506,23876,1508],{},[1680,23878,1682],{},[1528,23880,23881],{"encoding":1530},"= 1",[1097,23883,23884],{},[1035,23885,23887],{"className":23886},[1480],[1482,23888,23889],{"xmlns":1484},[1487,23890,23891,23897],{},[1490,23892,23893,23895],{},[1506,23894,1508],{},[1680,23896,1871],{},[1528,23898,23899],{"encoding":1530},"= 0",[1097,23901,9982],{},[1097,23903,9982],{},[1097,23905,23906],{},[1047,23907,23908],{},"držet cenu",[1079,23910,23911,23913,23931,23949,23951,23953],{},[1097,23912,15507],{},[1097,23914,23915],{},[1035,23916,23918],{"className":23917},[1480],[1482,23919,23920],{"xmlns":1484},[1487,23921,23922,23928],{},[1490,23923,23924,23926],{},[1506,23925,3961],{},[1680,23927,1682],{},[1528,23929,23930],{"encoding":1530},"\u003C 1",[1097,23932,23933],{},[1035,23934,23936],{"className":23935},[1480],[1482,23937,23938],{"xmlns":1484},[1487,23939,23940,23946],{},[1490,23941,23942,23944],{},[1506,23943,3961],{},[1680,23945,1871],{},[1528,23947,23948],{"encoding":1530},"\u003C 0",[1097,23950,23295],{},[1097,23952,7685],{},[1097,23954,23955],{},[1047,23956,23957],{},"zvýšit cenu",[1304,23959,23961],{"id":23960},"příklad-46-aplikace-pravidel-13","Příklad 4.6 — aplikace Pravidel 1–3",[1030,23963,23964,23965,23990,23991,24013,24014,24027,24028,24041,24042,8994,24055,21352,24081,24133],{},"Aplikujme pravidla 1–3 pro poptávku ",[1035,23966,23968],{"className":23967},[1480],[1482,23969,23970],{"xmlns":1484},[1487,23971,23972,23988],{},[1490,23973,23974,23976,23978,23980,23982],{},[1493,23975,1501],{},[1506,23977,1508],{},[1680,23979,2916],{},[1506,23981,1888],{},[2315,23983,23984,23986],{},[1493,23985,1520],{},[1680,23987,1691],{},[1528,23989,21226],{"encoding":1530},". Reálné cenové rozpětí je ",[1035,23992,23994],{"className":23993},[1480],[1482,23995,23996],{"xmlns":1484},[1487,23997,23998,24010],{},[1490,23999,24000,24002,24004,24006,24008],{},[1506,24001,21034],{"stretchy":1552},[1680,24003,1682],{},[1506,24005,1559],{"separator":1041},[1680,24007,2916],{},[1506,24009,21051],{"stretchy":1552},[1528,24011,24012],{"encoding":1530},"\\langle 1, 100\\rangle",". Pro výpočet elasticity vyjádříme ",[1035,24015,24017],{"className":24016},[1480],[1482,24018,24019],{"xmlns":1484},[1487,24020,24021,24025],{},[1490,24022,24023],{},[1493,24024,1520],{},[1528,24026,1520],{"encoding":1530}," jako funkci ",[1035,24029,24031],{"className":24030},[1480],[1482,24032,24033],{"xmlns":1484},[1487,24034,24035,24039],{},[1490,24036,24037],{},[1493,24038,1501],{},[1528,24040,1501],{"encoding":1530},"; pro nezáporné ",[1035,24043,24045],{"className":24044},[1480],[1482,24046,24047],{"xmlns":1484},[1487,24048,24049,24053],{},[1490,24050,24051],{},[1493,24052,1520],{},[1528,24054,1520],{"encoding":1530},[1035,24056,24058],{"className":24057},[1480],[1482,24059,24060],{"xmlns":1484},[1487,24061,24062,24078],{},[1490,24063,24064,24066,24068],{},[1493,24065,1520],{},[1506,24067,1508],{},[2324,24069,24070],{},[1490,24071,24072,24074,24076],{},[1680,24073,2916],{},[1506,24075,1888],{},[1493,24077,1501],{},[1528,24079,24080],{"encoding":1530},"Q = \\sqrt{100 - P}",[1035,24082,24084],{"className":24083},[1480],[1482,24085,24086],{"xmlns":1484},[1487,24087,24088,24130],{},[1490,24089,24090,24106,24108,24110],{},[1869,24091,24092],{"scriptlevel":1871,"displaystyle":1041},[1510,24093,24094,24100],{},[1490,24095,24096,24098],{},[1493,24097,3384],{"mathvariant":1516},[1493,24099,1520],{},[1490,24101,24102,24104],{},[1493,24103,3384],{"mathvariant":1516},[1493,24105,1501],{},[1506,24107,1508],{},[1506,24109,1888],{},[1869,24111,24112],{"scriptlevel":1871,"displaystyle":1041},[1510,24113,24114,24116],{},[1680,24115,1682],{},[1490,24117,24118,24120],{},[1680,24119,1691],{},[2324,24121,24122],{},[1490,24123,24124,24126,24128],{},[1680,24125,2916],{},[1506,24127,1888],{},[1493,24129,1501],{},[1528,24131,24132],{"encoding":1530},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\dfrac{1}{2\\sqrt{100-P}}",". Podle (4.5):",[1035,24135,24137],{"className":24136},[1480],[1482,24138,24139],{"xmlns":1484,"display":1485},[1487,24140,24141,24263],{},[1490,24142,24143,24145,24147,24149,24151,24153,24155,24161,24163,24177,24179,24181,24195,24197,24223,24225,24243,24245,24261],{},[1493,24144,2711],{},[1506,24146,1553],{"stretchy":1552},[1493,24148,1501],{},[1506,24150,1564],{"stretchy":1552},[1506,24152,1508],{},[1506,24154,1888],{},[1510,24156,24157,24159],{},[1493,24158,1501],{},[1493,24160,1520],{},[1506,24162,1714],{},[1510,24164,24165,24171],{},[1490,24166,24167,24169],{},[1493,24168,3384],{"mathvariant":1516},[1493,24170,1520],{},[1490,24172,24173,24175],{},[1493,24174,3384],{"mathvariant":1516},[1493,24176,1501],{},[1506,24178,1508],{},[1506,24180,1888],{},[1510,24182,24183,24185],{},[1493,24184,1501],{},[2324,24186,24187],{},[1490,24188,24189,24191,24193],{},[1680,24190,2916],{},[1506,24192,1888],{},[1493,24194,1501],{},[1506,24196,1714],{},[1490,24198,24199,24201,24203,24221],{},[1506,24200,1553],{"fence":1041},[1506,24202,1888],{},[1510,24204,24205,24207],{},[1680,24206,1682],{},[1490,24208,24209,24211],{},[1680,24210,1691],{},[2324,24212,24213],{},[1490,24214,24215,24217,24219],{},[1680,24216,2916],{},[1506,24218,1888],{},[1493,24220,1501],{},[1506,24222,1564],{"fence":1041},[1506,24224,1508],{},[1510,24226,24227,24229],{},[1493,24228,1501],{},[1490,24230,24231,24233,24235,24237,24239,24241],{},[1680,24232,1691],{},[1506,24234,1553],{"stretchy":1552},[1680,24236,2916],{},[1506,24238,1888],{},[1493,24240,1501],{},[1506,24242,1564],{"stretchy":1552},[1506,24244,1508],{},[1510,24246,24247,24253],{},[1490,24248,24249,24251],{},[1680,24250,3687],{},[1493,24252,1501],{},[1490,24254,24255,24257,24259],{},[1680,24256,2916],{},[1506,24258,1888],{},[1493,24260,1501],{},[1493,24262,2632],{"mathvariant":1516},[1528,24264,24265],{"encoding":1530},"E(P) = -\\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P} = -\\frac{P}{\\sqrt{100-P}}\\cdot\\left(-\\frac{1}{2\\sqrt{100-P}}\\right) = \\frac{P}{2(100-P)} = \\frac{0{,}5P}{100-P}.",[1030,24267,24268,24269,1274],{},"Stanovíme cenu, při které je poptávka jednotkově elastická. Řešíme ",[1035,24270,24272],{"className":24271},[1480],[1482,24273,24274],{"xmlns":1484},[1487,24275,24276,24300],{},[1490,24277,24278,24296,24298],{},[1869,24279,24280],{"scriptlevel":1871,"displaystyle":1041},[1510,24281,24282,24288],{},[1490,24283,24284,24286],{},[1680,24285,3687],{},[1493,24287,1501],{},[1490,24289,24290,24292,24294],{},[1680,24291,2916],{},[1506,24293,1888],{},[1493,24295,1501],{},[1506,24297,1508],{},[1680,24299,1682],{},[1528,24301,24302],{"encoding":1530},"\\dfrac{0{,}5P}{100-P} = 1",[1035,24304,24306],{"className":24305},[1480],[1482,24307,24308],{"xmlns":1484,"display":1485},[1487,24309,24310,24340],{},[1490,24311,24312,24318,24320,24326,24328,24331,24338],{},[2315,24313,24314,24316],{},[1493,24315,1501],{},[1506,24317,2287],{},[1506,24319,1508],{},[1510,24321,24322,24324],{},[1680,24323,5263],{},[1680,24325,3201],{},[1506,24327,21771],{},[1680,24329,24330],{},"66,",[2178,24332,24333,24335],{"accent":1041},[1680,24334,7508],{},[1506,24336,24337],{"stretchy":1041},"‾",[1493,24339,2632],{"mathvariant":1516},[1528,24341,24342],{"encoding":1530},"P^* = \\frac{200}{3} \\doteq 66{,}\\overline{6}.",[1030,24344,24345],{},"S využitím vlastnosti (4.8):",[1203,24347,24348,24393,24435],{},[1206,24349,24350,24351,24385,24386,24388,24389,24392],{},"Při cenách ",[1035,24352,24354],{"className":24353},[1480],[1482,24355,24356],{"xmlns":1484},[1487,24357,24358,24382],{},[1490,24359,24360,24362,24364,24366,24368,24370,24372,24374,24380],{},[1493,24361,1501],{},[1506,24363,22378],{},[1506,24365,21034],{"stretchy":1552},[1680,24367,1682],{},[1506,24369,6065],{"separator":1041},[1988,24371,5016],{},[1680,24373,24330],{},[2178,24375,24376,24378],{"accent":1041},[1680,24377,7508],{},[1506,24379,24337],{"stretchy":1041},[1506,24381,1564],{"stretchy":1552},[1528,24383,24384],{"encoding":1530},"P \\in \\langle 1;\\, 66{,}\\overline{6})"," je poptávka ",[1047,24387,15507],{}," — dle ",[1176,24390,24391],{},"Pravidla 2"," přiměřené zvýšení ceny zvýší celkový příjem.",[1206,24394,24350,24395,24385,24429,24388,24431,24434],{},[1035,24396,24398],{"className":24397},[1480],[1482,24399,24400],{"xmlns":1484},[1487,24401,24402,24426],{},[1490,24403,24404,24406,24408,24410,24412,24418,24420,24422,24424],{},[1493,24405,1501],{},[1506,24407,22378],{},[1506,24409,1553],{"stretchy":1552},[1680,24411,24330],{},[2178,24413,24414,24416],{"accent":1041},[1680,24415,7508],{},[1506,24417,24337],{"stretchy":1041},[1506,24419,6065],{"separator":1041},[1988,24421,5016],{},[1680,24423,2916],{},[1506,24425,21051],{"stretchy":1552},[1528,24427,24428],{"encoding":1530},"P \\in (66{,}\\overline{6};\\, 100\\rangle",[1047,24430,19486],{},[1176,24432,24433],{},"Pravidla 1"," přiměřené snížení ceny povede ke zvýšení celkového příjmu.",[1206,24436,24437,24438,24441,24442,24470,24471,24474],{},"Dle ",[1176,24439,24440],{},"Pravidla 3"," je při ceně ",[1035,24443,24445],{"className":24444},[1480],[1482,24446,24447],{"xmlns":1484},[1487,24448,24449,24467],{},[1490,24450,24451,24457,24459,24461],{},[2315,24452,24453,24455],{},[1493,24454,1501],{},[1506,24456,2287],{},[1506,24458,1508],{},[1680,24460,24330],{},[2178,24462,24463,24465],{"accent":1041},[1680,24464,7508],{},[1506,24466,24337],{"stretchy":1041},[1528,24468,24469],{"encoding":1530},"P^* = 66{,}\\overline{6}"," dosaženo ",[1047,24472,24473],{},"maxima celkového příjmu"," ve výši",[1035,24476,24478],{"className":24477},[1480],[1482,24479,24480],{"xmlns":1484,"display":1485},[1487,24481,24482,24559],{},[1490,24483,24484,24486,24488,24490,24496,24498,24500,24506,24508,24522,24524,24530,24532,24540,24542,24554,24556],{},[1493,24485,5289],{},[1493,24487,1995],{},[1506,24489,1553],{"stretchy":1552},[2315,24491,24492,24494],{},[1493,24493,1501],{},[1506,24495,2287],{},[1506,24497,1564],{"stretchy":1552},[1506,24499,1508],{},[2315,24501,24502,24504],{},[1493,24503,1501],{},[1506,24505,2287],{},[1506,24507,1714],{},[2324,24509,24510],{},[1490,24511,24512,24514,24516],{},[1680,24513,2916],{},[1506,24515,1888],{},[2315,24517,24518,24520],{},[1493,24519,1501],{},[1506,24521,2287],{},[1506,24523,1508],{},[1510,24525,24526,24528],{},[1680,24527,5263],{},[1680,24529,3201],{},[1506,24531,1714],{},[2324,24533,24534],{},[1510,24535,24536,24538],{},[1680,24537,2916],{},[1680,24539,3201],{},[1506,24541,1508],{},[1510,24543,24544,24546],{},[1680,24545,8113],{},[1490,24547,24548,24550],{},[1680,24549,3201],{},[2324,24551,24552],{},[1680,24553,3201],{},[1506,24555,21771],{},[1680,24557,24558],{},"384,9.",[1528,24560,24561],{"encoding":1530},"TR(P^*) = P^*\\cdot\\sqrt{100 - P^*} = \\frac{200}{3}\\cdot\\sqrt{\\frac{100}{3}} = \\frac{2000}{3\\sqrt{3}} \\doteq 384{,}9.",[1030,24563,24564,24565,2632],{},"Ke stejnému výsledku bychom dospěli přímým hledáním maxima funkce ",[1035,24566,24568],{"className":24567},[1480],[1482,24569,24570],{"xmlns":1484},[1487,24571,24572,24578],{},[1490,24573,24574,24576],{},[1493,24575,5289],{},[1493,24577,1995],{},[1528,24579,16491],{"encoding":1530},[1065,24581,24583],{"id":24582},"cenová-elasticita-nabídky","Cenová elasticita nabídky",[1030,24585,24586,24587,24590],{},"Analogicky se definuje ",[1047,24588,24589],{},"cenová elasticita nabídky"," (price elasticity of supply):",[1035,24592,24594],{"className":24593},[1480],[1482,24595,24596],{"xmlns":1484,"display":1485},[1487,24597,24598,24663],{},[19617,24599,24600],{"width":19619},[19621,24601,24602,24604,24656,24658],{},[19624,24603],{"width":19626},[19624,24605,24606],{},[1976,24607,24608],{"notation":1978},[1869,24609,24610],{"scriptlevel":1871,"displaystyle":1552},[1869,24611,24612],{"scriptlevel":1871,"displaystyle":1552},[1869,24613,24614],{"scriptlevel":1871,"displaystyle":1041},[1490,24615,24616,24618,24620,24622,24624,24626,24628,24630,24632,24638,24640,24654],{},[1988,24617,1990],{},[1493,24619,2711],{},[1506,24621,1508],{},[1493,24623,2711],{},[1506,24625,1553],{"stretchy":1552},[1493,24627,1501],{},[1506,24629,1564],{"stretchy":1552},[1506,24631,1508],{},[1510,24633,24634,24636],{},[1493,24635,1501],{},[1493,24637,1520],{},[1506,24639,1714],{},[1510,24641,24642,24648],{},[1490,24643,24644,24646],{},[1493,24645,3384],{"mathvariant":1516},[1493,24647,1520],{},[1490,24649,24650,24652],{},[1493,24651,3384],{"mathvariant":1516},[1493,24653,1501],{},[1988,24655,1990],{},[19624,24657],{"width":19626},[19624,24659,24660],{},[1988,24661,24662],{},"(4.13)",[1528,24664,24665],{"encoding":1530},"\\boxed{\\;E = E(P) = \\frac{P}{Q}\\cdot\\frac{\\mathrm{d}Q}{\\mathrm{d}P}\\;} \\tag{4.13}",[1030,24667,20022,24668,24692,24693,24725],{},[1035,24669,24671],{"className":24670},[1480],[1482,24672,24673],{"xmlns":1484},[1487,24674,24675,24689],{},[1490,24676,24677,24679,24681,24683,24685,24687],{},[1493,24678,1520],{},[1506,24680,1508],{},[1493,24682,2001],{},[1506,24684,1553],{"stretchy":1552},[1493,24686,1501],{},[1506,24688,1564],{"stretchy":1552},[1528,24690,24691],{"encoding":1530},"Q = S(P)"," je funkce nabídky. Protože nabídka je rostoucí, ",[1035,24694,24696],{"className":24695},[1480],[1482,24697,24698],{"xmlns":1484},[1487,24699,24700,24722],{},[1490,24701,24702,24718,24720],{},[1869,24703,24704],{"scriptlevel":1871,"displaystyle":1041},[1510,24705,24706,24712],{},[1490,24707,24708,24710],{},[1493,24709,3384],{"mathvariant":1516},[1493,24711,1520],{},[1490,24713,24714,24716],{},[1493,24715,3384],{"mathvariant":1516},[1493,24717,1501],{},[1506,24719,2796],{},[1680,24721,1871],{},[1528,24723,24724],{"encoding":1530},"\\dfrac{\\mathrm{d}Q}{\\mathrm{d}P} > 0",", a elasticita nabídky je vždy nezáporná — proto zde není znaménková korekce jako u poptávky.",[1030,24727,24728],{},"Klasifikace na elastickou \u002F jednotkově elastickou \u002F neelastickou je analogická jako u poptávky (tabulka (4.7)). Platí paralela k (4.8):",[19516,24730,24731],{},[1030,24732,24733,24734],{},"S rostoucí cenou elasticita nabídky roste. ",[1035,24735,24737],{"className":24736},[1480],[1482,24738,24739],{"xmlns":1484},[1487,24740,24741,24750],{},[1490,24742,24743,24745,24748],{},[1506,24744,1553],{"stretchy":1552},[1680,24746,24747],{},"4.14",[1506,24749,1564],{"stretchy":1552},[1528,24751,24752],{"encoding":1530},"(4.14)",[1030,24754,24755],{},"Pro nominální změny platí",[1035,24757,24759],{"className":24758},[1480],[1482,24760,24761],{"xmlns":1484,"display":1485},[1487,24762,24763,24826],{},[19617,24764,24765],{"width":19619},[19621,24766,24767,24769,24819,24821],{},[19624,24768],{"width":19626},[19624,24770,24771],{},[1490,24772,24773,24775,24777,24779,24781,24783,24785,24791,24793,24795,24797,24799,24801,24803,24805,24807,24809,24811,24813,24815,24817],{},[1493,24774,2976],{"mathvariant":1516},[1493,24776,1520],{},[1506,24778,2343],{},[1493,24780,3384],{"mathvariant":1516},[1493,24782,1520],{},[1506,24784,1508],{},[2315,24786,24787,24789],{},[1493,24788,1520],{},[1506,24790,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,24792,1553],{"stretchy":1552},[1493,24794,1501],{},[1506,24796,1564],{"stretchy":1552},[1988,24798,5016],{},[1493,24800,3384],{"mathvariant":1516},[1493,24802,1501],{},[1506,24804,1559],{"separator":1041},[1912,24806],{"width":1914},[1493,24808,3384],{"mathvariant":1516},[1493,24810,1501],{},[1506,24812,1508],{},[1493,24814,2976],{"mathvariant":1516},[1493,24816,1501],{},[1506,24818,1559],{"separator":1041},[19624,24820],{"width":19626},[19624,24822,24823],{},[1988,24824,24825],{},"(4.15)",[1528,24827,24828],{"encoding":1530},"\\Delta Q \\approx \\mathrm{d}Q = Q'(P)\\,\\mathrm{d}P, \\qquad \\mathrm{d}P = \\Delta P, \\tag{4.15}",[1030,24830,24831],{},"a pro procentní změny",[1035,24833,24835],{"className":24834},[1480],[1482,24836,24837],{"xmlns":1484,"display":1485},[1487,24838,24839,24892],{},[19617,24840,24841],{"width":19619},[19621,24842,24843,24845,24885,24887],{},[19624,24844],{"width":19626},[19624,24846,24847],{},[1976,24848,24849],{"notation":1978},[1869,24850,24851],{"scriptlevel":1871,"displaystyle":1552},[1869,24852,24853],{"scriptlevel":1871,"displaystyle":1552},[1869,24854,24855],{"scriptlevel":1871,"displaystyle":1041},[1490,24856,24857,24859,24861,24863,24865,24867,24869,24871,24873,24875,24877,24879,24881,24883],{},[1988,24858,1990],{},[1493,24860,2976],{"mathvariant":1516},[1493,24862,1520],{},[1493,24864,15846],{"mathvariant":1516},[1506,24866,2343],{},[1493,24868,2711],{},[1506,24870,1553],{"stretchy":1552},[1493,24872,1501],{},[1506,24874,1564],{"stretchy":1552},[1988,24876,5016],{},[1493,24878,2976],{"mathvariant":1516},[1493,24880,1501],{},[1493,24882,15846],{"mathvariant":1516},[1988,24884,1990],{},[19624,24886],{"width":19626},[19624,24888,24889],{},[1988,24890,24891],{},"(4.16)",[1528,24893,24894],{"encoding":1530},"\\boxed{\\;\\Delta Q\\% \\approx E(P)\\,\\Delta P\\%\\;} \\tag{4.16}",[1030,24896,24897],{},"(bez znaménka minus).",[1304,24899,24901],{"id":24900},"příklad-47","Příklad 4.7",[1030,24903,24904,24905,1274],{},"Nabídka ",[1035,24906,24908],{"className":24907},[1480],[1482,24909,24910],{"xmlns":1484},[1487,24911,24912,24936],{},[1490,24913,24914,24916,24918,24920,24926,24928,24930,24932,24934],{},[1493,24915,1520],{},[1506,24917,1508],{},[1680,24919,13237],{},[2315,24921,24922,24924],{},[1493,24923,1501],{},[1680,24925,1691],{},[1506,24927,2162],{},[1680,24929,1752],{},[1493,24931,1501],{},[1506,24933,2162],{},[1680,24935,5551],{},[1528,24937,24938],{"encoding":1530},"Q = 0{,}1P^2 + 5P + 150",[1035,24940,24942],{"className":24941},[1480],[1482,24943,24944],{"xmlns":1484,"display":1485},[1487,24945,24946,24992],{},[1490,24947,24948,24950,24952,24976,24978,24980,24982,24984,24986,24988,24990],{},[1493,24949,2711],{},[1506,24951,1508],{},[1510,24953,24954,24956],{},[1493,24955,1501],{},[1490,24957,24958,24960,24966,24968,24970,24972,24974],{},[1680,24959,13237],{},[2315,24961,24962,24964],{},[1493,24963,1501],{},[1680,24965,1691],{},[1506,24967,2162],{},[1680,24969,1752],{},[1493,24971,1501],{},[1506,24973,2162],{},[1680,24975,5551],{},[1988,24977,5016],{},[1506,24979,1553],{"stretchy":1552},[1680,24981,2929],{},[1493,24983,1501],{},[1506,24985,2162],{},[1680,24987,1752],{},[1506,24989,1564],{"stretchy":1552},[1493,24991,2632],{"mathvariant":1516},[1528,24993,24994],{"encoding":1530},"E = \\frac{P}{0{,}1P^2 + 5P + 150}\\,(0{,}2P + 5).",[1030,24996,20828,24997,1732,25027,1732,25053,25088,25089,25114,25115,25133,25134,2632],{},[1035,24998,25000],{"className":24999},[1480],[1482,25001,25002],{"xmlns":1484},[1487,25003,25004,25024],{},[1490,25005,25006,25008,25010,25012,25014,25016],{},[1493,25007,2711],{},[1506,25009,1553],{"stretchy":1552},[1680,25011,1775],{},[1506,25013,1564],{"stretchy":1552},[1506,25015,1508],{},[1869,25017,25018],{"scriptlevel":1871,"displaystyle":1552},[1510,25019,25020,25022],{},[1680,25021,1682],{},[1680,25023,3201],{},[1528,25025,25026],{"encoding":1530},"E(10) = \\tfrac{1}{3}",[1035,25028,25030],{"className":25029},[1480],[1482,25031,25032],{"xmlns":1484},[1487,25033,25034,25050],{},[1490,25035,25036,25038,25040,25044,25046,25048],{},[1493,25037,2711],{},[1506,25039,1553],{"stretchy":1552},[2324,25041,25042],{},[1680,25043,3076],{},[1506,25045,1564],{"stretchy":1552},[1506,25047,1508],{},[1680,25049,1682],{},[1528,25051,25052],{"encoding":1530},"E(\\sqrt{1500}) = 1",[1035,25054,25056],{"className":25055},[1480],[1482,25057,25058],{"xmlns":1484},[1487,25059,25060,25085],{},[1490,25061,25062,25064,25066,25068,25070,25072,25080,25082],{},[1493,25063,2711],{},[1506,25065,1553],{"stretchy":1552},[1680,25067,2916],{},[1506,25069,1564],{"stretchy":1552},[1506,25071,1508],{},[1869,25073,25074],{"scriptlevel":1871,"displaystyle":1552},[1510,25075,25076,25078],{},[1680,25077,2292],{},[1680,25079,6057],{},[1506,25081,21771],{},[1680,25083,25084],{},"1,515",[1528,25086,25087],{"encoding":1530},"E(100) = \\tfrac{50}{33} \\doteq 1{,}515",". Dle (4.14): pro ",[1035,25090,25092],{"className":25091},[1480],[1482,25093,25094],{"xmlns":1484},[1487,25095,25096,25111],{},[1490,25097,25098,25100,25102,25106,25108],{},[1493,25099,1501],{},[1506,25101,2796],{},[2324,25103,25104],{},[1680,25105,3076],{},[1506,25107,2343],{},[1680,25109,25110],{},"38,7",[1528,25112,25113],{"encoding":1530},"P > \\sqrt{1500} \\approx 38{,}7"," je nabídka elastická, pro ",[1035,25116,25118],{"className":25117},[1480],[1482,25119,25120],{"xmlns":1484},[1487,25121,25122,25130],{},[1490,25123,25124,25126,25128],{},[1493,25125,1501],{},[1506,25127,3961],{},[1680,25129,25110],{},[1528,25131,25132],{"encoding":1530},"P \u003C 38{,}7"," neelastická. Zvýší-li se cena z 10 o 20 %, pak ",[1035,25135,25137],{"className":25136},[1480],[1482,25138,25139],{"xmlns":1484},[1487,25140,25141,25178],{},[1490,25142,25143,25145,25147,25149,25151,25159,25161,25163,25165,25168,25174,25176],{},[1493,25144,2976],{"mathvariant":1516},[1493,25146,1520],{},[1493,25148,15846],{"mathvariant":1516},[1506,25150,2343],{},[1869,25152,25153],{"scriptlevel":1871,"displaystyle":1552},[1510,25154,25155,25157],{},[1680,25156,1682],{},[1680,25158,3201],{},[1506,25160,1714],{},[1680,25162,8436],{},[1506,25164,1508],{},[1680,25166,25167],{},"6,",[2178,25169,25170,25172],{"accent":1041},[1680,25171,7508],{},[1506,25173,24337],{"stretchy":1041},[1988,25175,5016],{},[1493,25177,15846],{"mathvariant":1516},[1528,25179,25180],{"encoding":1530},"\\Delta Q\\% \\approx \\tfrac{1}{3}\\cdot 20 = 6{,}\\overline{6}\\,\\%",[1065,25182,25184],{"id":25183},"vícefaktorový-model","Vícefaktorový model",[1030,25186,25187,25188,25201,25202,1656,25205,25218,25219,1656,25222,25239,25240,1656,25243,1274],{},"Předpokládejme, že poptávané množství ",[1035,25189,25191],{"className":25190},[1480],[1482,25192,25193],{"xmlns":1484},[1487,25194,25195,25199],{},[1490,25196,25197],{},[1493,25198,1520],{},[1528,25200,1520],{"encoding":1530}," závisí na ",[1047,25203,25204],{},"ceně základního zboží",[1035,25206,25208],{"className":25207},[1480],[1482,25209,25210],{"xmlns":1484},[1487,25211,25212,25216],{},[1490,25213,25214],{},[1493,25215,1501],{},[1528,25217,1501],{"encoding":1530},", na ",[1047,25220,25221],{},"ceně alternativního zboží",[1035,25223,25225],{"className":25224},[1480],[1482,25226,25227],{"xmlns":1484},[1487,25228,25229,25237],{},[1490,25230,25231],{},[1497,25232,25233,25235],{},[1493,25234,1501],{},[1493,25236,3633],{},[1528,25238,3862],{"encoding":1530}," a na ",[1047,25241,25242],{},"důchodu",[1035,25244,25246],{"className":25245},[1480],[1482,25247,25248],{"xmlns":1484},[1487,25249,25250,25254],{},[1490,25251,25252],{},[1493,25253,1791],{},[1528,25255,1791],{"encoding":1530},[1035,25257,25259],{"className":25258},[1480],[1482,25260,25261],{"xmlns":1484,"display":1485},[1487,25262,25263,25306],{},[19617,25264,25265],{"width":19619},[19621,25266,25267,25269,25299,25301],{},[19624,25268],{"width":19626},[19624,25270,25271],{},[1490,25272,25273,25275,25277,25279,25281,25283,25285,25291,25293,25295,25297],{},[1493,25274,1520],{},[1506,25276,1508],{},[1493,25278,3712],{},[1506,25280,1553],{"stretchy":1552},[1493,25282,1501],{},[1506,25284,1559],{"separator":1041},[1497,25286,25287,25289],{},[1493,25288,1501],{},[1493,25290,3633],{},[1506,25292,1559],{"separator":1041},[1493,25294,1791],{},[1506,25296,1564],{"stretchy":1552},[1493,25298,2632],{"mathvariant":1516},[19624,25300],{"width":19626},[19624,25302,25303],{},[1988,25304,25305],{},"(4.17)",[1528,25307,25308],{"encoding":1530},"Q = D(P, P_A, Y). \\tag{4.17}",[1030,25310,25311,25312,25315],{},"V analogii jednofaktorového modelu pracujeme s ",[1047,25313,25314],{},"parciálními derivacemi"," funkce poptávky.",[1304,25317,25319],{"id":25318},"cenová-elasticita-poptávky-vícefaktorová","Cenová elasticita poptávky (vícefaktorová)",[1035,25321,25323],{"className":25322},[1480],[1482,25324,25325],{"xmlns":1484,"display":1485},[1487,25326,25327,25382],{},[19617,25328,25329],{"width":19619},[19621,25330,25331,25333,25375,25377],{},[19624,25332],{"width":19626},[19624,25334,25335],{},[1976,25336,25337],{"notation":1978},[1869,25338,25339],{"scriptlevel":1871,"displaystyle":1552},[1869,25340,25341],{"scriptlevel":1871,"displaystyle":1552},[1869,25342,25343],{"scriptlevel":1871,"displaystyle":1041},[1490,25344,25345,25347,25353,25355,25357,25363,25365,25373],{},[1988,25346,1990],{},[1497,25348,25349,25351],{},[1493,25350,2711],{},[1493,25352,1501],{},[1506,25354,1508],{},[1506,25356,1888],{},[1510,25358,25359,25361],{},[1493,25360,1501],{},[1493,25362,1520],{},[1988,25364,5016],{},[1697,25366,25367,25369,25371],{},[1493,25368,1520],{},[1493,25370,1501],{},[1506,25372,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1988,25374,1990],{},[19624,25376],{"width":19626},[19624,25378,25379],{},[1988,25380,25381],{},"(4.18)",[1528,25383,25384],{"encoding":1530},"\\boxed{\\;E_P = -\\frac{P}{Q}\\,Q'_P\\;} \\tag{4.18}",[1030,25386,20022,25387,25407,25408,25421,25422,18367,25444,1656,25446,25492,25493,25506,25507,25524],{},[1035,25388,25390],{"className":25389},[1480],[1482,25391,25392],{"xmlns":1484},[1487,25393,25394,25404],{},[1490,25395,25396],{},[1697,25397,25398,25400,25402],{},[1493,25399,1520],{},[1493,25401,1501],{},[1506,25403,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,25405,25406],{"encoding":1530},"Q'_P"," je parciální derivace (4.17) podle ",[1035,25409,25411],{"className":25410},[1480],[1482,25412,25413],{"xmlns":1484},[1487,25414,25415,25419],{},[1490,25416,25417],{},[1493,25418,1501],{},[1528,25420,1501],{"encoding":1530},". Vždy ",[1035,25423,25425],{"className":25424},[1480],[1482,25426,25427],{"xmlns":1484},[1487,25428,25429,25441],{},[1490,25430,25431,25437,25439],{},[1497,25432,25433,25435],{},[1493,25434,2711],{},[1493,25436,1501],{},[1506,25438,20200],{},[1680,25440,1871],{},[1528,25442,25443],{"encoding":1530},"E_P \\ge 0",[1176,25445,12171],{},[1035,25447,25449],{"className":25448},[1480],[1482,25450,25451],{"xmlns":1484},[1487,25452,25453,25489],{},[1490,25454,25455,25461,25463,25469,25471,25479,25481,25487],{},[1497,25456,25457,25459],{},[1493,25458,2711],{},[1493,25460,1501],{},[1506,25462,1553],{"stretchy":1552},[2315,25464,25465,25467],{},[1493,25466,1501],{},[1506,25468,2287],{},[1506,25470,1559],{"separator":1041},[1697,25472,25473,25475,25477],{},[1493,25474,1501],{},[1493,25476,3633],{},[1506,25478,2287],{},[1506,25480,1559],{"separator":1041},[2315,25482,25483,25485],{},[1493,25484,1791],{},[1506,25486,2287],{},[1506,25488,1564],{"stretchy":1552},[1528,25490,25491],{"encoding":1530},"E_P(P^*, P_A^*, Y^*)"," udává přibližnou procentní změnu ",[1035,25494,25496],{"className":25495},[1480],[1482,25497,25498],{"xmlns":1484},[1487,25499,25500,25504],{},[1490,25501,25502],{},[1493,25503,1520],{},[1528,25505,1520],{"encoding":1530}," při 1% změně ",[1035,25508,25510],{"className":25509},[1480],[1482,25511,25512],{"xmlns":1484},[1487,25513,25514,25522],{},[1490,25515,25516],{},[2315,25517,25518,25520],{},[1493,25519,1501],{},[1506,25521,2287],{},[1528,25523,20114],{"encoding":1530},", ceteris paribus.",[1304,25526,25528],{"id":25527},"křížová-křížově-cenová-elasticita-poptávky","Křížová (křížově-cenová) elasticita poptávky",[1035,25530,25532],{"className":25531},[1480],[1482,25533,25534],{"xmlns":1484,"display":1485},[1487,25535,25536,25601],{},[19617,25537,25538],{"width":19619},[19621,25539,25540,25542,25594,25596],{},[19624,25541],{"width":19626},[19624,25543,25544],{},[1976,25545,25546],{"notation":1978},[1869,25547,25548],{"scriptlevel":1871,"displaystyle":1552},[1869,25549,25550],{"scriptlevel":1871,"displaystyle":1552},[1869,25551,25552],{"scriptlevel":1871,"displaystyle":1041},[1490,25553,25554,25556,25566,25568,25578,25580,25592],{},[1988,25555,1990],{},[1497,25557,25558,25560],{},[1493,25559,2711],{},[1497,25561,25562,25564],{},[1493,25563,1501],{},[1493,25565,3633],{},[1506,25567,1508],{},[1510,25569,25570,25576],{},[1497,25571,25572,25574],{},[1493,25573,1501],{},[1493,25575,3633],{},[1493,25577,1520],{},[1988,25579,5016],{},[1697,25581,25582,25584,25590],{},[1493,25583,1520],{},[1497,25585,25586,25588],{},[1493,25587,1501],{},[1493,25589,3633],{},[1506,25591,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1988,25593,1990],{},[19624,25595],{"width":19626},[19624,25597,25598],{},[1988,25599,25600],{},"(4.19)",[1528,25602,25603],{"encoding":1530},"\\boxed{\\;E_{P_A} = \\frac{P_A}{Q}\\,Q'_{P_A}\\;} \\tag{4.19}",[1030,25605,25606,25492,25608,25621,25622,25639],{},[1176,25607,12171],{},[1035,25609,25611],{"className":25610},[1480],[1482,25612,25613],{"xmlns":1484},[1487,25614,25615,25619],{},[1490,25616,25617],{},[1493,25618,1520],{},[1528,25620,1520],{"encoding":1530}," základního zboží při 1% změně ceny ",[1035,25623,25625],{"className":25624},[1480],[1482,25626,25627],{"xmlns":1484},[1487,25628,25629,25637],{},[1490,25630,25631],{},[1497,25632,25633,25635],{},[1493,25634,1501],{},[1493,25636,3633],{},[1528,25638,3862],{"encoding":1530}," alternativního zboží (ceteris paribus).",[1030,25641,25642],{},[1047,25643,25644],{},"Znaménko závisí na povaze alternativního zboží:",[1203,25646,25647,25735],{},[1206,25648,25649,25650,25653,25654,25671,25672,1656,25685,2632],{},"Je-li alternativní zboží ",[1047,25651,25652],{},"komplement",", růst ",[1035,25655,25657],{"className":25656},[1480],[1482,25658,25659],{"xmlns":1484},[1487,25660,25661,25669],{},[1490,25662,25663],{},[1497,25664,25665,25667],{},[1493,25666,1501],{},[1493,25668,3633],{},[1528,25670,3862],{"encoding":1530}," způsobí zdražení dvojice, pokles ",[1035,25673,25675],{"className":25674},[1480],[1482,25676,25677],{"xmlns":1484},[1487,25678,25679,25683],{},[1490,25680,25681],{},[1493,25682,1520],{},[1528,25684,1520],{"encoding":1530},[1035,25686,25688],{"className":25687},[1480],[1482,25689,25690],{"xmlns":1484},[1487,25691,25692,25732],{},[1490,25693,25694,25696,25698,25710,25712,25714,25716,25718,25728,25730],{},[1506,25695,2183],{},[1988,25697,1990],{},[1697,25699,25700,25702,25708],{},[1493,25701,1520],{},[1497,25703,25704,25706],{},[1493,25705,1501],{},[1493,25707,3633],{},[1506,25709,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,25711,3961],{},[1680,25713,1871],{},[1506,25715,1559],{"separator":1041},[1988,25717,1990],{},[1497,25719,25720,25722],{},[1493,25721,2711],{},[1497,25723,25724,25726],{},[1493,25725,1501],{},[1493,25727,3633],{},[1506,25729,3961],{},[1680,25731,1871],{},[1528,25733,25734],{"encoding":1530},"\\Rightarrow\\; Q'_{P_A} \u003C 0,\\; E_{P_A} \u003C 0",[1206,25736,25649,25737,25653,25739,25756,25757,25770,25771,2632],{},[1047,25738,15763],{},[1035,25740,25742],{"className":25741},[1480],[1482,25743,25744],{"xmlns":1484},[1487,25745,25746,25754],{},[1490,25747,25748],{},[1497,25749,25750,25752],{},[1493,25751,1501],{},[1493,25753,3633],{},[1528,25755,3862],{"encoding":1530}," učiní základní zboží relativně levnější, zájem se přesune, ",[1035,25758,25760],{"className":25759},[1480],[1482,25761,25762],{"xmlns":1484},[1487,25763,25764,25768],{},[1490,25765,25766],{},[1493,25767,1520],{},[1528,25769,1520],{"encoding":1530}," roste ",[1035,25772,25774],{"className":25773},[1480],[1482,25775,25776],{"xmlns":1484},[1487,25777,25778,25818],{},[1490,25779,25780,25782,25784,25796,25798,25800,25802,25804,25814,25816],{},[1506,25781,2183],{},[1988,25783,1990],{},[1697,25785,25786,25788,25794],{},[1493,25787,1520],{},[1497,25789,25790,25792],{},[1493,25791,1501],{},[1493,25793,3633],{},[1506,25795,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,25797,2796],{},[1680,25799,1871],{},[1506,25801,1559],{"separator":1041},[1988,25803,1990],{},[1497,25805,25806,25808],{},[1493,25807,2711],{},[1497,25809,25810,25812],{},[1493,25811,1501],{},[1493,25813,3633],{},[1506,25815,2796],{},[1680,25817,1871],{},[1528,25819,25820],{"encoding":1530},"\\Rightarrow\\; Q'_{P_A} > 0,\\; E_{P_A} > 0",[1035,25822,25827],{"className":25823,"title":25825,"style":25826},[25824],"katex-error","ParseError: KaTeX parse error: Expected 'EOF', got '&' at position 9: E_{P_A} &̲> 0 \\;\\;\\Leftri…","color:#cc0000","undefined",[1030,25829,25830],{},"\\boxed{;E_Y = \\frac{Y}{Q},Q'_Y;} \\tag{4.20}",[1035,25832,25827],{"className":25833,"title":25834,"style":25826},[25824],"ParseError: KaTeX parse error: Can't use function '$' in math mode at position 51: …rocentní změnu $̲Q$ při 1% změně…",[1030,25836,25837],{},"\\Delta Q% \\approx -E_P,\\Delta P%, \\qquad \\Delta Q% \\approx E_,\\Delta P_A%, \\qquad \\Delta Q% \\approx E_Y,\\Delta Y%. \\tag{4.21}",[1035,25839,25841],{"className":25840},[1480],[1482,25842,25843],{"xmlns":1484,"display":1485},[1487,25844,25845,26045],{},[1490,25846,25847,25849,25851,25854,25856,25858,25860,25862,25864,25870,25873,25875,25881,25883,25885,25888,25890,25892,25894,25896,25902,25904,25907,25909,25911,25917,25919,25921,25923,25929,25932,25934,25940,25942,25948,25951,25957,25959,25961,25963,25965,25967,25969,25971,25977,25979,25981,25987,25989,25991,25993,25995,25997,25999,26005,26007,26009,26015,26017,26019,26021,26023,26025,26027,26029,26031,26033,26039,26041,26043],{},[1493,25848,1501],{},[1493,25850,7740],{},[1493,25852,25853],{},"o",[1493,25855,7781],{},[1493,25857,25853],{},[1493,25859,7774],{},[1493,25861,6277],{},[1493,25863,7781],{},[2178,25865,25866,25868],{"accent":1041},[1493,25867,1052],{},[1506,25869,3055],{},[1493,25871,25872],{},"l",[1493,25874,7781],{},[2178,25876,25877,25879],{"accent":1041},[1493,25878,7095],{"mathvariant":1516},[1506,25880,3055],{},[1493,25882,25853],{},[1493,25884,3384],{},[1493,25886,25887],{},"h",[1493,25889,1052],{},[1493,25891,3384],{},[1493,25893,3052],{},[1493,25895,1030],{},[2178,25897,25898,25900],{"accent":1041},[1493,25899,7740],{},[1506,25901,8576],{},[1493,25903,6277],{},[1493,25905,25906],{},"s",[1493,25908,25853],{},[1493,25910,7105],{},[2178,25912,25913,25915],{"accent":1041},[1493,25914,8730],{},[1506,25916,8576],{},[1493,25918,1052],{},[1493,25920,25906],{},[1493,25922,7781],{},[2178,25924,25925,25927],{"accent":1041},[1493,25926,8584],{},[1506,25928,3055],{},[1493,25930,25931],{},"z",[1493,25933,7774],{},[2178,25935,25936,25938],{"accent":1041},[1493,25937,8584],{},[1506,25939,8576],{},[1493,25941,7781],{},[2178,25943,25944,25946],{"accent":1041},[1493,25945,8584],{},[1506,25947,8576],{},[1493,25949,25950],{},"v",[2178,25952,25953,25955],{"accent":1041},[1493,25954,25906],{},[1506,25956,8576],{},[1493,25958,8584],{},[1493,25960,8730],{},[1493,25962,25887],{},[1493,25964,1030],{},[1493,25966,7740],{},[1493,25968,25853],{},[1493,25970,7774],{},[2178,25972,25973,25975],{"accent":1041},[1493,25974,8584],{},[1506,25976,8576],{},[1493,25978,7781],{},[1493,25980,7781],{},[2178,25982,25983,25985],{"accent":1041},[1493,25984,3052],{},[1506,25986,3055],{},[1493,25988,8730],{},[1493,25990,25887],{},[1506,25992,1553],{"stretchy":1552},[1493,25994,10917],{},[1493,25996,25853],{},[1493,25998,10917],{},[2178,26000,26001,26003],{"accent":1041},[1493,26002,1052],{},[1506,26004,3055],{},[1493,26006,25872],{},[1493,26008,7781],{},[2178,26010,26011,26013],{"accent":1041},[1493,26012,7095],{"mathvariant":1516},[1506,26014,3055],{},[1493,26016,3384],{},[1493,26018,6277],{},[1493,26020,12889],{},[1493,26022,8584],{},[1493,26024,7740],{},[1493,26026,8584],{},[1493,26028,7781],{},[1493,26030,8730],{},[1493,26032,6277],{},[2178,26034,26035,26037],{"accent":1041},[1493,26036,1052],{},[1506,26038,3055],{},[1493,26040,25872],{},[1506,26042,1564],{"stretchy":1552},[1506,26044,1274],{},[1528,26046,26047],{"encoding":1530},"\nPro nominální odhady při současné změně všech proměnných (totální diferenciál):\n",[1030,26049,26050,26051,26054],{},"\\boxed{;\\Delta Q \\approx \\mathrm{d}Q = Q'",[1176,26052,26053],{"p-a":17269},"P,\\mathrm{d}P + Q'",",\\mathrm{d}P_A + Q'_Y,\\mathrm{d}Y;} \\tag{4.22}",[1035,26056,25827],{"className":26057,"title":26058,"style":25826},[25824],"ParseError: KaTeX parse error: Expected 'EOF', got '#' at position 75: ….22) vypadne.\n\n#̲## Příklad 4.8\n…",[1030,26060,26061],{},"\\Delta Q \\approx (-3)\\cdot 5 + (-2)\\cdot(-3) + 0{,}01\\cdot 100 = -15 + 6 + 1 = -8.",[1035,26063,25827],{"className":26064,"title":26065,"style":25826},[25824],"ParseError: KaTeX parse error: Expected 'EOF', got '#' at position 34: …řibližně o 8.\n\n#̲# Shrnutí kapit…",{"title":17269,"searchDepth":141,"depth":141,"links":26067},[26068,26072,26073,26081,26082,26086,26089],{"id":19311,"depth":141,"text":19312,"children":26069},[26070,26071],{"id":19340,"depth":96,"text":19341},{"id":19513,"depth":96,"text":19514},{"id":19549,"depth":141,"text":19550},{"id":19579,"depth":141,"text":19580,"children":26074},[26075,26076,26077,26078,26080],{"id":20574,"depth":96,"text":20575},{"id":20664,"depth":96,"text":20665},{"id":20995,"depth":96,"text":20996},{"id":21077,"depth":96,"text":26079},"Výpočet, je-li dáno PP jako funkce QQ",{"id":21391,"depth":96,"text":21392},{"id":21823,"depth":141,"text":21824},{"id":22421,"depth":141,"text":22422,"children":26083},[26084,26085],{"id":23132,"depth":96,"text":23133},{"id":23960,"depth":96,"text":23961},{"id":24582,"depth":141,"text":24583,"children":26087},[26088],{"id":24900,"depth":96,"text":24901},{"id":25183,"depth":141,"text":25184,"children":26090},[26091,26092],{"id":25318,"depth":96,"text":25319},{"id":25527,"depth":96,"text":25528},"2026-04-22",{},"\u002Ftopics\u002Felasticita",{"title":3809,"description":17269},[26098,26099],"raw\u002Fimek\u002Fkniha_scanned\u002F","raw\u002Fimek\u002FKS_druhy_blok.pdf","topics\u002Felasticita",[9,79,402,237,183,726],"2026-04-26","O075ZW9YEH7A_TZ6UZuaqK2U_Yowee7OIOtkQsoQEm4",{"id":26105,"title":26106,"body":26107,"course":9,"courses":17424,"created":19266,"description":27627,"extension":17426,"meta":27628,"navigation":17428,"path":27629,"seo":27630,"sources":27631,"stem":27632,"tags":27633,"type":19275,"updated":19276,"__hash__":27634},"topics\u002Ftopics\u002Ffunkce-vice-promennych.md","Kalkul funkcí více proměnných",{"type":1016,"value":26108,"toc":27612},[26109,26112,26185,26192,26196,26259,26344,26348,26375,26439,26494,26498,26525,26617,26619,26651,26822,26826,26894,26942,26946,27006,27110,27123,27127,27129,27157,27220,27222,27229,27315,27340,27538,27542,27578,27580],[1019,26110,26106],{"id":26111},"kalkul-funkcí-více-proměnných",[1030,26113,26114,26115,26118,26119,1732,26147,2632],{},"Většina ekonomických veličin závisí na ",[1047,26116,26117],{},"více faktorech"," — produkce na práci a kapitálu, užitečnost na množství různých statků, poptávka na cenách více zboží i důchodu. Kalkul jedné proměnné se proto rozšiřuje na ",[1035,26120,26122],{"className":26121},[1480],[1482,26123,26124],{"xmlns":1484},[1487,26125,26126,26144],{},[1490,26127,26128,26130,26132,26134,26136,26138,26140,26142],{},[1493,26129,25931],{},[1506,26131,1508],{},[1493,26133,12889],{},[1506,26135,1553],{"stretchy":1552},[1493,26137,17494],{},[1506,26139,1559],{"separator":1041},[1493,26141,3052],{},[1506,26143,1564],{"stretchy":1552},[1528,26145,26146],{"encoding":1530},"z = f(x, y)",[1035,26148,26150],{"className":26149},[1480],[1482,26151,26152],{"xmlns":1484},[1487,26153,26154,26182],{},[1490,26155,26156,26159,26161,26163,26165,26167,26169,26171,26173,26175,26177,26179],{},[1493,26157,26158],{},"w",[1506,26160,1508],{},[1493,26162,12889],{},[1506,26164,1553],{"stretchy":1552},[1493,26166,17494],{},[1506,26168,1559],{"separator":1041},[1493,26170,3052],{},[1506,26172,1559],{"separator":1041},[1493,26174,25931],{},[1506,26176,1564],{"stretchy":1552},[1506,26178,1559],{"separator":1041},[1506,26180,26181],{},"…",[1528,26183,26184],{"encoding":1530},"w = f(x, y, z), \\ldots",[1030,26186,26187],{},[18014,26188],{"alt":26189,"className":26190,"src":26191},"imek-funkce-2d-vrstevnice",[1055,18018],"\u002Fwiki-assets\u002Fimek-funkce-2d-vrstevnice.jpeg",[1065,26193,26195],{"id":26194},"indiferenční-izokvantové-křivky","Indiferenční \u002F izokvantové křivky",[1030,26197,2364,26198,26225,26226,26254,26255,26258],{},[1035,26199,26201],{"className":26200},[1480],[1482,26202,26203],{"xmlns":1484},[1487,26204,26205,26223],{},[1490,26206,26207,26209,26211,26213,26215,26217,26219,26221],{},[1493,26208,25931],{},[1506,26210,1508],{},[1493,26212,12889],{},[1506,26214,1553],{"stretchy":1552},[1493,26216,17494],{},[1506,26218,1559],{"separator":1041},[1493,26220,3052],{},[1506,26222,1564],{"stretchy":1552},[1528,26224,26146],{"encoding":1530}," se křivkou s předpisem ",[1035,26227,26229],{"className":26228},[1480],[1482,26230,26231],{"xmlns":1484},[1487,26232,26233,26251],{},[1490,26234,26235,26237,26239,26241,26243,26245,26247,26249],{},[1493,26236,12889],{},[1506,26238,1553],{"stretchy":1552},[1493,26240,17494],{},[1506,26242,1559],{"separator":1041},[1493,26244,3052],{},[1506,26246,1564],{"stretchy":1552},[1506,26248,1508],{},[1493,26250,8730],{},[1528,26252,26253],{"encoding":1530},"f(x, y) = c"," (konstanta) rozumí ",[1047,26256,26257],{},"vrstevnice"," funkce. V ekonomii:",[1203,26260,26261,26307],{},[1206,26262,26263,26266,26267,26303,26304,2632],{},[1047,26264,26265],{},"Indiferenční křivky"," užitečnosti ",[1035,26268,26270],{"className":26269},[1480],[1482,26271,26272],{"xmlns":1484},[1487,26273,26274,26300],{},[1490,26275,26276,26278,26280,26286,26288,26294,26296,26298],{},[1493,26277,1668],{},[1506,26279,1553],{"stretchy":1552},[1497,26281,26282,26284],{},[1493,26283,1520],{},[1680,26285,1682],{},[1506,26287,1559],{"separator":1041},[1497,26289,26290,26292],{},[1493,26291,1520],{},[1680,26293,1691],{},[1506,26295,1564],{"stretchy":1552},[1506,26297,1508],{},[1493,26299,8730],{},[1528,26301,26302],{"encoding":1530},"U(Q_1, Q_2) = c"," — viz ",[1052,26305,93],{"className":26306,"dataFsResolvedFilePath":6613,"href":6614},[1055],[1206,26308,26309,26312,26313,26303,26341,2632],{},[1047,26310,26311],{},"Izokvanty"," produkce ",[1035,26314,26316],{"className":26315},[1480],[1482,26317,26318],{"xmlns":1484},[1487,26319,26320,26338],{},[1490,26321,26322,26324,26326,26328,26330,26332,26334,26336],{},[1493,26323,1520],{},[1506,26325,1553],{"stretchy":1552},[1493,26327,1556],{},[1506,26329,1559],{"separator":1041},[1493,26331,1504],{},[1506,26333,1564],{"stretchy":1552},[1506,26335,1508],{},[1493,26337,8730],{},[1528,26339,26340],{"encoding":1530},"Q(L, K) = c",[1052,26342,287],{"className":26343,"dataFsResolvedFilePath":1572,"href":1573},[1055],[1065,26345,26347],{"id":26346},"parciální-derivace","Parciální derivace",[1030,26349,2364,26350,26374],{},[1035,26351,26353],{"className":26352},[1480],[1482,26354,26355],{"xmlns":1484},[1487,26356,26357,26371],{},[1490,26358,26359,26361,26363,26365,26367,26369],{},[1493,26360,12889],{},[1506,26362,1553],{"stretchy":1552},[1493,26364,17494],{},[1506,26366,1559],{"separator":1041},[1493,26368,3052],{},[1506,26370,1564],{"stretchy":1552},[1528,26372,26373],{"encoding":1530},"f(x, y)"," derivujeme jako kdyby druhá proměnná byla konstanta:",[1035,26376,26378],{"className":26377},[1480],[1482,26379,26380],{"xmlns":1484,"display":1485},[1487,26381,26382,26436],{},[1490,26383,26384,26392,26394,26408,26410,26412,26420,26422],{},[1697,26385,26386,26388,26390],{},[1493,26387,12889],{},[1493,26389,17494],{},[1506,26391,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,26393,1508],{},[1510,26395,26396,26402],{},[1490,26397,26398,26400],{},[1493,26399,1517],{"mathvariant":1516},[1493,26401,12889],{},[1490,26403,26404,26406],{},[1493,26405,1517],{"mathvariant":1516},[1493,26407,17494],{},[1506,26409,1559],{"separator":1041},[1912,26411],{"width":1914},[1697,26413,26414,26416,26418],{},[1493,26415,12889],{},[1493,26417,3052],{},[1506,26419,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,26421,1508],{},[1510,26423,26424,26430],{},[1490,26425,26426,26428],{},[1493,26427,1517],{"mathvariant":1516},[1493,26429,12889],{},[1490,26431,26432,26434],{},[1493,26433,1517],{"mathvariant":1516},[1493,26435,3052],{},[1528,26437,26438],{"encoding":1530},"f'_x = \\frac{\\partial f}{\\partial x}, \\qquad f'_y = \\frac{\\partial f}{\\partial y}",[1030,26440,26441,26442,2632],{},"Hodnoty v bodě: ",[1035,26443,26445],{"className":26444},[1480],[1482,26446,26447],{"xmlns":1484},[1487,26448,26449,26491],{},[1490,26450,26451,26459,26461,26463,26465,26467,26469,26471,26473,26481,26483,26485,26487,26489],{},[1697,26452,26453,26455,26457],{},[1493,26454,12889],{},[1493,26456,17494],{},[1506,26458,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,26460,1553],{"stretchy":1552},[1493,26462,1052],{},[1506,26464,1559],{"separator":1041},[1493,26466,2394],{},[1506,26468,1564],{"stretchy":1552},[1506,26470,1559],{"separator":1041},[1988,26472,10922],{},[1697,26474,26475,26477,26479],{},[1493,26476,12889],{},[1493,26478,3052],{},[1506,26480,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,26482,1553],{"stretchy":1552},[1493,26484,1052],{},[1506,26486,1559],{"separator":1041},[1493,26488,2394],{},[1506,26490,1564],{"stretchy":1552},[1528,26492,26493],{"encoding":1530},"f'_x(a, b),\\ f'_y(a, b)",[1304,26495,26497],{"id":26496},"ekonomické-značení","Ekonomické značení",[1030,26499,26500,26501,1274],{},"Pro produkční funkci ",[1035,26502,26504],{"className":26503},[1480],[1482,26505,26506],{"xmlns":1484},[1487,26507,26508,26522],{},[1490,26509,26510,26512,26514,26516,26518,26520],{},[1493,26511,1520],{},[1506,26513,1553],{"stretchy":1552},[1493,26515,1556],{},[1506,26517,1559],{"separator":1041},[1493,26519,1504],{},[1506,26521,1564],{"stretchy":1552},[1528,26523,26524],{"encoding":1530},"Q(L, K)",[1203,26526,26527,26572],{},[1206,26528,26529,17929,26549,7606,26552,1564],{},[1035,26530,26532],{"className":26531},[1480],[1482,26533,26534],{"xmlns":1484},[1487,26535,26536,26546],{},[1490,26537,26538],{},[1697,26539,26540,26542,26544],{},[1493,26541,1520],{},[1493,26543,1556],{},[1506,26545,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,26547,26548],{"encoding":1530},"Q'_L",[1047,26550,26551],{},"mezní produkt práce",[1035,26553,26555],{"className":26554},[1480],[1482,26556,26557],{"xmlns":1484},[1487,26558,26559,26569],{},[1490,26560,26561,26563],{},[1493,26562,1495],{},[1497,26564,26565,26567],{},[1493,26566,1501],{},[1493,26568,1556],{},[1528,26570,26571],{"encoding":1530},"MP_L",[1206,26573,26574,17929,26594,7606,26597,1564],{},[1035,26575,26577],{"className":26576},[1480],[1482,26578,26579],{"xmlns":1484},[1487,26580,26581,26591],{},[1490,26582,26583],{},[1697,26584,26585,26587,26589],{},[1493,26586,1520],{},[1493,26588,1504],{},[1506,26590,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,26592,26593],{"encoding":1530},"Q'_K",[1047,26595,26596],{},"mezní produkt kapitálu",[1035,26598,26600],{"className":26599},[1480],[1482,26601,26602],{"xmlns":1484},[1487,26603,26604,26614],{},[1490,26605,26606,26608],{},[1493,26607,1495],{},[1497,26609,26610,26612],{},[1493,26611,1501],{},[1493,26613,1504],{},[1528,26615,26616],{"encoding":1530},"MP_K",[1304,26618,18023],{"id":18022},[1030,26620,26621,1274],{},[1035,26622,26624],{"className":26623},[1480],[1482,26625,26626],{"xmlns":1484},[1487,26627,26628,26648],{},[1490,26629,26630,26638,26640,26642,26644,26646],{},[1697,26631,26632,26634,26636],{},[1493,26633,12889],{},[1493,26635,17494],{},[1506,26637,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,26639,1553],{"stretchy":1552},[1493,26641,1052],{},[1506,26643,1559],{"separator":1041},[1493,26645,2394],{},[1506,26647,1564],{"stretchy":1552},[1528,26649,26650],{"encoding":1530},"f'_x(a, b)",[1203,26652,26653,26711],{},[1206,26654,26655,26656,26669,26670,26683,26684,26710],{},"rychlost změny ",[1035,26657,26659],{"className":26658},[1480],[1482,26660,26661],{"xmlns":1484},[1487,26662,26663,26667],{},[1490,26664,26665],{},[1493,26666,12889],{},[1528,26668,12889],{"encoding":1530}," vůči ",[1035,26671,26673],{"className":26672},[1480],[1482,26674,26675],{"xmlns":1484},[1487,26676,26677,26681],{},[1490,26678,26679],{},[1493,26680,17494],{},[1528,26682,17494],{"encoding":1530}," při ",[1035,26685,26687],{"className":26686},[1480],[1482,26688,26689],{"xmlns":1484},[1487,26690,26691,26707],{},[1490,26692,26693,26695,26697,26699,26701,26703,26705],{},[1493,26694,17494],{},[1506,26696,1508],{},[1493,26698,1052],{},[1506,26700,1559],{"separator":1041},[1493,26702,3052],{},[1506,26704,1508],{},[1493,26706,2394],{},[1528,26708,26709],{"encoding":1530},"x = a, y = b"," (kapitál fixní),",[1206,26712,26713,26714,18111,26727,26740,26741,26759,26760,2632],{},"přibližná změna ",[1035,26715,26717],{"className":26716},[1480],[1482,26718,26719],{"xmlns":1484},[1487,26720,26721,26725],{},[1490,26722,26723],{},[1493,26724,12889],{},[1528,26726,12889],{"encoding":1530},[1035,26728,26730],{"className":26729},[1480],[1482,26731,26732],{"xmlns":1484},[1487,26733,26734,26738],{},[1490,26735,26736],{},[1493,26737,17494],{},[1528,26739,17494],{"encoding":1530}," o 1 (a pevném ",[1035,26742,26744],{"className":26743},[1480],[1482,26745,26746],{"xmlns":1484},[1487,26747,26748,26756],{},[1490,26749,26750,26752,26754],{},[1493,26751,3052],{},[1506,26753,1508],{},[1493,26755,2394],{},[1528,26757,26758],{"encoding":1530},"y = b","): ",[1035,26761,26763],{"className":26762},[1480],[1482,26764,26765],{"xmlns":1484},[1487,26766,26767,26819],{},[1490,26768,26769,26771,26773,26775,26777,26779,26781,26783,26785,26787,26789,26791,26793,26795,26797,26799,26801,26809,26811,26813,26815,26817],{},[1493,26770,12889],{},[1506,26772,1553],{"stretchy":1552},[1493,26774,1052],{},[1506,26776,2162],{},[1680,26778,1682],{},[1506,26780,1559],{"separator":1041},[1493,26782,2394],{},[1506,26784,1564],{"stretchy":1552},[1506,26786,2343],{},[1493,26788,12889],{},[1506,26790,1553],{"stretchy":1552},[1493,26792,1052],{},[1506,26794,1559],{"separator":1041},[1493,26796,2394],{},[1506,26798,1564],{"stretchy":1552},[1506,26800,2162],{},[1697,26802,26803,26805,26807],{},[1493,26804,12889],{},[1493,26806,17494],{},[1506,26808,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,26810,1553],{"stretchy":1552},[1493,26812,1052],{},[1506,26814,1559],{"separator":1041},[1493,26816,2394],{},[1506,26818,1564],{"stretchy":1552},[1528,26820,26821],{"encoding":1530},"f(a+1, b) \\approx f(a, b) + f'_x(a, b)",[1065,26823,26825],{"id":26824},"diferenciál-funkce-dvou-proměnných","Diferenciál funkce dvou proměnných",[1035,26827,26829],{"className":26828},[1480],[1482,26830,26831],{"xmlns":1484,"display":1485},[1487,26832,26833,26891],{},[1490,26834,26835,26837,26839,26841,26849,26851,26853,26855,26857,26859,26861,26863,26865,26867,26875,26877,26879,26881,26883,26885,26887,26889],{},[1493,26836,3384],{},[1493,26838,12889],{},[1506,26840,1508],{},[1697,26842,26843,26845,26847],{},[1493,26844,12889],{},[1493,26846,17494],{},[1506,26848,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,26850,1553],{"stretchy":1552},[1493,26852,17494],{},[1506,26854,1559],{"separator":1041},[1493,26856,3052],{},[1506,26858,1564],{"stretchy":1552},[1988,26860,5016],{},[1493,26862,3384],{},[1493,26864,17494],{},[1506,26866,2162],{},[1697,26868,26869,26871,26873],{},[1493,26870,12889],{},[1493,26872,3052],{},[1506,26874,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,26876,1553],{"stretchy":1552},[1493,26878,17494],{},[1506,26880,1559],{"separator":1041},[1493,26882,3052],{},[1506,26884,1564],{"stretchy":1552},[1988,26886,5016],{},[1493,26888,3384],{},[1493,26890,3052],{},[1528,26892,26893],{"encoding":1530},"df = f'_x(x, y)\\, dx + f'_y(x, y)\\, dy",[1030,26895,18432,26896,26918,26919,26941],{},[1035,26897,26899],{"className":26898},[1480],[1482,26900,26901],{"xmlns":1484},[1487,26902,26903,26915],{},[1490,26904,26905,26907,26909,26911,26913],{},[1493,26906,3384],{},[1493,26908,17494],{},[1506,26910,1559],{"separator":1041},[1493,26912,3384],{},[1493,26914,3052],{},[1528,26916,26917],{"encoding":1530},"dx, dy"," platí ",[1035,26920,26922],{"className":26921},[1480],[1482,26923,26924],{"xmlns":1484},[1487,26925,26926,26938],{},[1490,26927,26928,26930,26932,26934,26936],{},[1493,26929,2976],{"mathvariant":1516},[1493,26931,12889],{},[1506,26933,2343],{},[1493,26935,3384],{},[1493,26937,12889],{},[1528,26939,26940],{"encoding":1530},"\\Delta f \\approx df",". Linearizace přírůstku ve dvou směrech současně.",[1065,26943,26945],{"id":26944},"implicitní-funkce","Implicitní funkce",[1030,26947,26948,26949,26977,26978,26991,26992,27005],{},"Je-li vztah dán rovnicí ",[1035,26950,26952],{"className":26951},[1480],[1482,26953,26954],{"xmlns":1484},[1487,26955,26956,26974],{},[1490,26957,26958,26960,26962,26964,26966,26968,26970,26972],{},[1493,26959,10790],{},[1506,26961,1553],{"stretchy":1552},[1493,26963,17494],{},[1506,26965,1559],{"separator":1041},[1493,26967,3052],{},[1506,26969,1564],{"stretchy":1552},[1506,26971,1508],{},[1680,26973,1871],{},[1528,26975,26976],{"encoding":1530},"F(x, y) = 0"," a chceme derivaci ",[1035,26979,26981],{"className":26980},[1480],[1482,26982,26983],{"xmlns":1484},[1487,26984,26985,26989],{},[1490,26986,26987],{},[1493,26988,3052],{},[1528,26990,3052],{"encoding":1530}," podle ",[1035,26993,26995],{"className":26994},[1480],[1482,26996,26997],{"xmlns":1484},[1487,26998,26999,27003],{},[1490,27000,27001],{},[1493,27002,17494],{},[1528,27004,17494],{"encoding":1530}," (nebo naopak):",[1035,27007,27009],{"className":27008},[1480],[1482,27010,27011],{"xmlns":1484,"display":1485},[1487,27012,27013,27107],{},[1490,27014,27015,27021,27023,27037,27039,27041,27059,27061,27063,27069,27071,27085,27087,27089],{},[2315,27016,27017,27019],{},[1493,27018,3052],{},[1506,27020,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,27022,1508],{},[1510,27024,27025,27031],{},[1490,27026,27027,27029],{},[1493,27028,3384],{},[1493,27030,3052],{},[1490,27032,27033,27035],{},[1493,27034,3384],{},[1493,27036,17494],{},[1506,27038,1508],{},[1506,27040,1888],{},[1510,27042,27043,27051],{},[1697,27044,27045,27047,27049],{},[1493,27046,10790],{},[1493,27048,17494],{},[1506,27050,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1697,27052,27053,27055,27057],{},[1493,27054,10790],{},[1493,27056,3052],{},[1506,27058,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,27060,1559],{"separator":1041},[1912,27062],{"width":1914},[2315,27064,27065,27067],{},[1493,27066,17494],{},[1506,27068,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,27070,1508],{},[1510,27072,27073,27079],{},[1490,27074,27075,27077],{},[1493,27076,3384],{},[1493,27078,17494],{},[1490,27080,27081,27083],{},[1493,27082,3384],{},[1493,27084,3052],{},[1506,27086,1508],{},[1506,27088,1888],{},[1510,27090,27091,27099],{},[1697,27092,27093,27095,27097],{},[1493,27094,10790],{},[1493,27096,3052],{},[1506,27098,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1697,27100,27101,27103,27105],{},[1493,27102,10790],{},[1493,27104,17494],{},[1506,27106,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,27108,27109],{"encoding":1530},"y' = \\frac{dy}{dx} = -\\frac{F'_x}{F'_y}, \\qquad x' = \\frac{dx}{dy} = -\\frac{F'_y}{F'_x}",[1030,27111,27112,27113,27116,27117,1586,27120,2632],{},"Tato vzorec dává ",[1047,27114,27115],{},"sklon vrstevnice"," — používá se mj. pro výpočet ",[1052,27118,16555],{"className":27119,"dataFsResolvedFilePath":1572,"href":1573},[1055],[1052,27121,13960],{"className":27122,"dataFsResolvedFilePath":6613,"href":6614},[1055],[1065,27124,27126],{"id":27125},"volné-extrémy-funkce-dvou-proměnných","Volné extrémy funkce dvou proměnných",[1304,27128,18677],{"id":18676},[1030,27130,27131,27132,27156],{},"V bodě extrému ",[1035,27133,27135],{"className":27134},[1480],[1482,27136,27137],{"xmlns":1484},[1487,27138,27139,27153],{},[1490,27140,27141,27143,27145,27147,27149,27151],{},[1493,27142,3633],{},[1506,27144,14314],{"stretchy":1552},[1493,27146,1052],{},[1506,27148,1559],{"separator":1041},[1493,27150,2394],{},[1506,27152,14323],{"stretchy":1552},[1528,27154,27155],{"encoding":1530},"A[a, b]"," musí platit současně:",[1035,27158,27160],{"className":27159},[1480],[1482,27161,27162],{"xmlns":1484,"display":1485},[1487,27163,27164,27217],{},[1490,27165,27166,27174,27176,27178,27180,27182,27184,27186,27188,27190,27193,27195,27203,27205,27207,27209,27211,27213,27215],{},[1697,27167,27168,27170,27172],{},[1493,27169,12889],{},[1493,27171,17494],{},[1506,27173,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,27175,1553],{"stretchy":1552},[1493,27177,1052],{},[1506,27179,1559],{"separator":1041},[1493,27181,2394],{},[1506,27183,1564],{"stretchy":1552},[1506,27185,1508],{},[1680,27187,1871],{},[1988,27189,1990],{},[1506,27191,27192],{},"∧",[1988,27194,1990],{},[1697,27196,27197,27199,27201],{},[1493,27198,12889],{},[1493,27200,3052],{},[1506,27202,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,27204,1553],{"stretchy":1552},[1493,27206,1052],{},[1506,27208,1559],{"separator":1041},[1493,27210,2394],{},[1506,27212,1564],{"stretchy":1552},[1506,27214,1508],{},[1680,27216,1871],{},[1528,27218,27219],{"encoding":1530},"f'_x(a, b) = 0 \\;\\wedge\\; f'_y(a, b) = 0",[1304,27221,18751],{"id":18750},[1030,27223,27224,27225,27228],{},"Definujeme ",[1047,27226,27227],{},"diskriminant"," (Hessián zjednodušeně):",[1035,27230,27232],{"className":27231},[1480],[1482,27233,27234],{"xmlns":1484,"display":1485},[1487,27235,27236,27312],{},[1490,27237,27238,27240,27242,27244,27246,27248,27250,27252,27268,27270,27286,27288,27290,27306],{},[1493,27239,3712],{},[1506,27241,1553],{"stretchy":1552},[1493,27243,17494],{},[1506,27245,1559],{"separator":1041},[1493,27247,3052],{},[1506,27249,1564],{"stretchy":1552},[1506,27251,1508],{},[1697,27253,27254,27256,27262],{},[1493,27255,12889],{},[1490,27257,27258,27260],{},[1493,27259,17494],{},[1493,27261,17494],{},[1490,27263,27264,27266],{},[1506,27265,6927],{"mathvariant":1516},[1506,27267,6927],{"mathvariant":1516},[1506,27269,1714],{},[1697,27271,27272,27274,27280],{},[1493,27273,12889],{},[1490,27275,27276,27278],{},[1493,27277,3052],{},[1493,27279,3052],{},[1490,27281,27282,27284],{},[1506,27283,6927],{"mathvariant":1516},[1506,27285,6927],{"mathvariant":1516},[1506,27287,1888],{},[1506,27289,1553],{"stretchy":1552},[1697,27291,27292,27294,27300],{},[1493,27293,12889],{},[1490,27295,27296,27298],{},[1493,27297,17494],{},[1493,27299,3052],{},[1490,27301,27302,27304],{},[1506,27303,6927],{"mathvariant":1516},[1506,27305,6927],{"mathvariant":1516},[2315,27307,27308,27310],{},[1506,27309,1564],{"stretchy":1552},[1680,27311,1691],{},[1528,27313,27314],{"encoding":1530},"D(x, y) = f''_{xx} \\cdot f''_{yy} - (f''_{xy})^2",[1030,27316,27317,27318,1274],{},"V podezřelém bodě ",[1035,27319,27321],{"className":27320},[1480],[1482,27322,27323],{"xmlns":1484},[1487,27324,27325,27337],{},[1490,27326,27327,27329,27331,27333,27335],{},[1506,27328,14314],{"stretchy":1552},[1493,27330,1052],{},[1506,27332,1559],{"separator":1041},[1493,27334,2394],{},[1506,27336,14323],{"stretchy":1552},[1528,27338,27339],{"encoding":1530},"[a, b]",[1276,27341,27342,27469,27505],{},[1206,27343,27344,27374,27375],{},[1047,27345,27346,1274],{},[1035,27347,27349],{"className":27348},[1480],[1482,27350,27351],{"xmlns":1484},[1487,27352,27353,27371],{},[1490,27354,27355,27357,27359,27361,27363,27365,27367,27369],{},[1493,27356,3712],{},[1506,27358,1553],{"stretchy":1552},[1493,27360,1052],{},[1506,27362,1559],{"separator":1041},[1493,27364,2394],{},[1506,27366,1564],{"stretchy":1552},[1506,27368,2796],{},[1680,27370,1871],{},[1528,27372,27373],{"encoding":1530},"D(a, b) > 0"," je to extrém.\n",[1203,27376,27377,27423],{},[1206,27378,27379,18838,27421],{},[1035,27380,27382],{"className":27381},[1480],[1482,27383,27384],{"xmlns":1484},[1487,27385,27386,27418],{},[1490,27387,27388,27404,27406,27408,27410,27412,27414,27416],{},[1697,27389,27390,27392,27398],{},[1493,27391,12889],{},[1490,27393,27394,27396],{},[1493,27395,17494],{},[1493,27397,17494],{},[1490,27399,27400,27402],{},[1506,27401,6927],{"mathvariant":1516},[1506,27403,6927],{"mathvariant":1516},[1506,27405,1553],{"stretchy":1552},[1493,27407,1052],{},[1506,27409,1559],{"separator":1041},[1493,27411,2394],{},[1506,27413,1564],{"stretchy":1552},[1506,27415,2796],{},[1680,27417,1871],{},[1528,27419,27420],{"encoding":1530},"f''_{xx}(a, b) > 0",[1047,27422,19195],{},[1206,27424,27425,18838,27467],{},[1035,27426,27428],{"className":27427},[1480],[1482,27429,27430],{"xmlns":1484},[1487,27431,27432,27464],{},[1490,27433,27434,27450,27452,27454,27456,27458,27460,27462],{},[1697,27435,27436,27438,27444],{},[1493,27437,12889],{},[1490,27439,27440,27442],{},[1493,27441,17494],{},[1493,27443,17494],{},[1490,27445,27446,27448],{},[1506,27447,6927],{"mathvariant":1516},[1506,27449,6927],{"mathvariant":1516},[1506,27451,1553],{"stretchy":1552},[1493,27453,1052],{},[1506,27455,1559],{"separator":1041},[1493,27457,2394],{},[1506,27459,1564],{"stretchy":1552},[1506,27461,3961],{},[1680,27463,1871],{},[1528,27465,27466],{"encoding":1530},"f''_{xx}(a, b) \u003C 0",[1047,27468,9982],{},[1206,27470,27471,1656,27501,27504],{},[1047,27472,27473,1274],{},[1035,27474,27476],{"className":27475},[1480],[1482,27477,27478],{"xmlns":1484},[1487,27479,27480,27498],{},[1490,27481,27482,27484,27486,27488,27490,27492,27494,27496],{},[1493,27483,3712],{},[1506,27485,1553],{"stretchy":1552},[1493,27487,1052],{},[1506,27489,1559],{"separator":1041},[1493,27491,2394],{},[1506,27493,1564],{"stretchy":1552},[1506,27495,3961],{},[1680,27497,1871],{},[1528,27499,27500],{"encoding":1530},"D(a, b) \u003C 0",[1047,27502,27503],{},"sedlo"," (v daném bodě extrém není).",[1206,27506,27507,27537],{},[1047,27508,27509,1274],{},[1035,27510,27512],{"className":27511},[1480],[1482,27513,27514],{"xmlns":1484},[1487,27515,27516,27534],{},[1490,27517,27518,27520,27522,27524,27526,27528,27530,27532],{},[1493,27519,3712],{},[1506,27521,1553],{"stretchy":1552},[1493,27523,1052],{},[1506,27525,1559],{"separator":1041},[1493,27527,2394],{},[1506,27529,1564],{"stretchy":1552},[1506,27531,1508],{},[1680,27533,1871],{},[1528,27535,27536],{"encoding":1530},"D(a, b) = 0"," podmínka nerozhoduje.",[1065,27539,27541],{"id":27540},"vázané-extrémy","Vázané extrémy",[1030,27543,27544,27545,27574,27575,2632],{},"Pro extrémy s omezující podmínkou ",[1035,27546,27548],{"className":27547},[1480],[1482,27549,27550],{"xmlns":1484},[1487,27551,27552,27571],{},[1490,27553,27554,27557,27559,27561,27563,27565,27567,27569],{},[1493,27555,27556],{},"g",[1506,27558,1553],{"stretchy":1552},[1493,27560,17494],{},[1506,27562,1559],{"separator":1041},[1493,27564,3052],{},[1506,27566,1564],{"stretchy":1552},[1506,27568,1508],{},[1680,27570,1871],{},[1528,27572,27573],{"encoding":1530},"g(x, y) = 0"," se používá ",[1052,27576,17267],{"className":27577,"dataFsResolvedFilePath":17265,"href":17266},[1055],[1065,27579,17159],{"id":17158},[1203,27581,27582,27589,27596],{},[1206,27583,27584,1656,27586],{},[1047,27585,19217],{},[1052,27587,17258],{"className":27588,"dataFsResolvedFilePath":17256,"href":17257},[1055],[1206,27590,27591,1656,27593],{},[1047,27592,19228],{},[1052,27594,17267],{"className":27595,"dataFsResolvedFilePath":17265,"href":17266},[1055],[1206,27597,27598,1656,27600,27603,27604,27607,27608,27611],{},[1047,27599,19236],{},[1052,27601,6836],{"className":27602,"dataFsResolvedFilePath":1572,"href":1573},[1055]," (parciální derivace = mezní produkty), ",[1052,27605,6615],{"className":27606,"dataFsResolvedFilePath":6613,"href":6614},[1055]," (parciální derivace = mezní užitečnost), ",[1052,27609,17218],{"className":27610,"dataFsResolvedFilePath":3807,"href":3808},[1055]," (vícefaktorový model)",{"title":17269,"searchDepth":141,"depth":141,"links":27613},[27614,27615,27619,27620,27621,27625,27626],{"id":26194,"depth":141,"text":26195},{"id":26346,"depth":141,"text":26347,"children":27616},[27617,27618],{"id":26496,"depth":96,"text":26497},{"id":18022,"depth":96,"text":18023},{"id":26824,"depth":141,"text":26825},{"id":26944,"depth":141,"text":26945},{"id":27125,"depth":141,"text":27126,"children":27622},[27623,27624],{"id":18676,"depth":96,"text":18677},{"id":18750,"depth":96,"text":18751},{"id":27540,"depth":141,"text":27541},{"id":17158,"depth":141,"text":17159},"Většina ekonomických veličin závisí na více faktorech — produkce na práci a kapitálu, užitečnost na množství různých statků, poptávka na cenách více zboží i důchodu. Kalkul jedné proměnné se proto rozšiřuje na z=f(x,y)z = f(x, y), w=f(x,y,z),…w = f(x, y, z), \\ldots.",{},"\u002Ftopics\u002Ffunkce-vice-promennych",{"title":26106,"description":27627},[19272],"topics\u002Ffunkce-vice-promennych",[9,778,173,576,968,106],"t-U-Y83-NNLBZcf4ObkjZoaALOwcN_ZVIENjQr9qDVI",{"id":27636,"title":17258,"body":27637,"course":9,"courses":17424,"created":19266,"description":28473,"extension":17426,"meta":28474,"navigation":17428,"path":28475,"seo":28476,"sources":28477,"stem":28478,"tags":28479,"type":19275,"updated":19276,"__hash__":28480},"topics\u002Ftopics\u002Fintegral.md",{"type":1016,"value":27638,"toc":28463},[27639,27642,27653,27657,27699,27779,27783,27857,27898,27905,27909,27913,27942,27998,28044,28080,28084,28134,28184,28236,28278,28282,28284,28354,28356,28426,28432,28434],[1019,27640,17258],{"id":27641},"integrál",[1030,27643,27644,27645,27648,27649,27652],{},"Druhá polovina kalkulu jedné proměnné. Slouží k ",[1047,27646,27647],{},"rekonstrukci totální veličiny z mezní"," (TR z MR, TC z MC) a k výpočtu ",[1047,27650,27651],{},"přebytků"," (consumer\u002Fproducer surplus).",[1065,27654,27656],{"id":27655},"neurčitý-integrál","Neurčitý integrál",[1035,27658,27660],{"className":27659},[1480],[1482,27661,27662],{"xmlns":1484,"display":1485},[1487,27663,27664,27696],{},[1490,27665,27666,27668,27670,27672,27674,27676,27678,27680,27682,27684,27686,27688,27690,27692,27694],{},[1493,27667,10790],{},[1506,27669,1553],{"stretchy":1552},[1493,27671,17494],{},[1506,27673,1564],{"stretchy":1552},[1506,27675,1508],{},[1506,27677,10857],{},[1493,27679,12889],{},[1506,27681,1553],{"stretchy":1552},[1493,27683,17494],{},[1506,27685,1564],{"stretchy":1552},[1988,27687,5016],{},[1493,27689,3384],{},[1493,27691,17494],{},[1506,27693,2162],{},[1493,27695,1998],{},[1528,27697,27698],{"encoding":1530},"F(x) = \\int f(x)\\, dx + C",[1030,27700,20022,27701,18367,27735,8994,27748,27751,27752,1732,27765,27778],{},[1035,27702,27704],{"className":27703},[1480],[1482,27705,27706],{"xmlns":1484},[1487,27707,27708,27732],{},[1490,27709,27710,27716,27718,27720,27722,27724,27726,27728,27730],{},[2315,27711,27712,27714],{},[1493,27713,10790],{},[1506,27715,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,27717,1553],{"stretchy":1552},[1493,27719,17494],{},[1506,27721,1564],{"stretchy":1552},[1506,27723,1508],{},[1493,27725,12889],{},[1506,27727,1553],{"stretchy":1552},[1493,27729,17494],{},[1506,27731,1564],{"stretchy":1552},[1528,27733,27734],{"encoding":1530},"F'(x) = f(x)",[1035,27736,27738],{"className":27737},[1480],[1482,27739,27740],{"xmlns":1484},[1487,27741,27742,27746],{},[1490,27743,27744],{},[1493,27745,10790],{},[1528,27747,10790],{"encoding":1530},[1047,27749,27750],{},"primitivní funkce"," k ",[1035,27753,27755],{"className":27754},[1480],[1482,27756,27757],{"xmlns":1484},[1487,27758,27759,27763],{},[1490,27760,27761],{},[1493,27762,12889],{},[1528,27764,12889],{"encoding":1530},[1035,27766,27768],{"className":27767},[1480],[1482,27769,27770],{"xmlns":1484},[1487,27771,27772,27776],{},[1490,27773,27774],{},[1493,27775,1998],{},[1528,27777,1998],{"encoding":1530}," konstanta.",[1065,27780,27782],{"id":27781},"určitý-integrál","Určitý integrál",[1035,27784,27786],{"className":27785},[1480],[1482,27787,27788],{"xmlns":1484,"display":1485},[1487,27789,27790,27854],{},[1490,27791,27792,27800,27802,27804,27806,27808,27810,27812,27814,27816,27818,27820,27822,27824,27826,27834,27836,27838,27840,27842,27844,27846,27848,27850,27852],{},[1697,27793,27794,27796,27798],{},[1506,27795,10857],{},[1493,27797,1052],{},[1493,27799,2394],{},[1493,27801,12889],{},[1506,27803,1553],{"stretchy":1552},[1493,27805,17494],{},[1506,27807,1564],{"stretchy":1552},[1988,27809,5016],{},[1493,27811,3384],{},[1493,27813,17494],{},[1506,27815,1508],{},[1506,27817,14314],{"stretchy":1552},[1493,27819,10790],{},[1506,27821,1553],{"stretchy":1552},[1493,27823,17494],{},[1506,27825,1564],{"stretchy":1552},[1697,27827,27828,27830,27832],{},[1506,27829,14323],{"stretchy":1552},[1493,27831,1052],{},[1493,27833,2394],{},[1506,27835,1508],{},[1493,27837,10790],{},[1506,27839,1553],{"stretchy":1552},[1493,27841,2394],{},[1506,27843,1564],{"stretchy":1552},[1506,27845,1888],{},[1493,27847,10790],{},[1506,27849,1553],{"stretchy":1552},[1493,27851,1052],{},[1506,27853,1564],{"stretchy":1552},[1528,27855,27856],{"encoding":1530},"\\int_a^b f(x)\\, dx = [F(x)]_a^b = F(b) - F(a)",[1030,27858,27859,27860,1656,27863,15048,27876,27897],{},"Geometricky ",[1047,27861,27862],{},"plocha pod grafem",[1035,27864,27866],{"className":27865},[1480],[1482,27867,27868],{"xmlns":1484},[1487,27869,27870,27874],{},[1490,27871,27872],{},[1493,27873,12889],{},[1528,27875,12889],{"encoding":1530},[1035,27877,27879],{"className":27878},[1480],[1482,27880,27881],{"xmlns":1484},[1487,27882,27883,27895],{},[1490,27884,27885,27887,27889,27891,27893],{},[1506,27886,14314],{"stretchy":1552},[1493,27888,1052],{},[1506,27890,1559],{"separator":1041},[1493,27892,2394],{},[1506,27894,14323],{"stretchy":1552},[1528,27896,27339],{"encoding":1530}," (orientovaná).",[1030,27899,27900],{},[18014,27901],{"alt":27902,"className":27903,"src":27904},"imek-integral-plocha",[1055,18018],"\u002Fwiki-assets\u002Fimek-integral-plocha.jpeg",[1065,27906,27908],{"id":27907},"aplikace-v-ekonomii","Aplikace v ekonomii",[1304,27910,27912],{"id":27911},"příklad-tr-z-mr","Příklad — TR z MR",[1030,27914,27915,27916,2632],{},"Mezní příjem ",[1035,27917,27919],{"className":27918},[1480],[1482,27920,27921],{"xmlns":1484},[1487,27922,27923,27939],{},[1490,27924,27925,27927,27929,27931,27933,27935,27937],{},[1493,27926,1495],{},[1493,27928,1995],{},[1506,27930,1508],{},[1680,27932,2916],{},[1506,27934,1888],{},[1680,27936,1691],{},[1493,27938,1520],{},[1528,27940,27941],{"encoding":1530},"MR = 100 - 2Q",[1035,27943,27945],{"className":27944},[1480],[1482,27946,27947],{"xmlns":1484,"display":1485},[1487,27948,27949,27995],{},[1490,27950,27951,27953,27955,27957,27959,27961,27963,27965,27967,27969,27971,27973,27975,27977,27979,27981,27983,27985,27991,27993],{},[1493,27952,5289],{},[1493,27954,1995],{},[1506,27956,1508],{},[1506,27958,10857],{},[1506,27960,1553],{"stretchy":1552},[1680,27962,2916],{},[1506,27964,1888],{},[1680,27966,1691],{},[1493,27968,1520],{},[1506,27970,1564],{"stretchy":1552},[1988,27972,5016],{},[1493,27974,3384],{},[1493,27976,1520],{},[1506,27978,1508],{},[1680,27980,2916],{},[1493,27982,1520],{},[1506,27984,1888],{},[2315,27986,27987,27989],{},[1493,27988,1520],{},[1680,27990,1691],{},[1506,27992,2162],{},[1493,27994,8730],{},[1528,27996,27997],{"encoding":1530},"TR = \\int (100 - 2Q)\\, dQ = 100Q - Q^2 + c",[1030,27999,28000,28001,18838,28026,1274],{},"Okrajová podmínka ",[1035,28002,28004],{"className":28003},[1480],[1482,28005,28006],{"xmlns":1484},[1487,28007,28008,28024],{},[1490,28009,28010,28012,28014,28016,28018,28020,28022],{},[1493,28011,5289],{},[1493,28013,1995],{},[1506,28015,1553],{"stretchy":1552},[1680,28017,1871],{},[1506,28019,1564],{"stretchy":1552},[1506,28021,1508],{},[1680,28023,1871],{},[1528,28025,1282],{"encoding":1530},[1035,28027,28029],{"className":28028},[1480],[1482,28030,28031],{"xmlns":1484},[1487,28032,28033,28041],{},[1490,28034,28035,28037,28039],{},[1493,28036,8730],{},[1506,28038,1508],{},[1680,28040,1871],{},[1528,28042,28043],{"encoding":1530},"c = 0",[1035,28045,28047],{"className":28046},[1480],[1482,28048,28049],{"xmlns":1484,"display":1485},[1487,28050,28051,28077],{},[1490,28052,28053,28055,28057,28059,28061,28063,28065,28067,28069,28071],{},[1493,28054,5289],{},[1493,28056,1995],{},[1506,28058,1553],{"stretchy":1552},[1493,28060,1520],{},[1506,28062,1564],{"stretchy":1552},[1506,28064,1508],{},[1680,28066,2916],{},[1493,28068,1520],{},[1506,28070,1888],{},[2315,28072,28073,28075],{},[1493,28074,1520],{},[1680,28076,1691],{},[1528,28078,28079],{"encoding":1530},"TR(Q) = 100Q - Q^2",[1304,28081,28083],{"id":28082},"příklad-tc-z-mc","Příklad — TC z MC",[1030,28085,28086,28087,28113,28114,2632],{},"Mezní náklady ",[1035,28088,28090],{"className":28089},[1480],[1482,28091,28092],{"xmlns":1484},[1487,28093,28094,28110],{},[1490,28095,28096,28098,28100,28102,28104,28106,28108],{},[1493,28097,1495],{},[1493,28099,1998],{},[1506,28101,1508],{},[1680,28103,1691],{},[1506,28105,2162],{},[1680,28107,2929],{},[1493,28109,1520],{},[1528,28111,28112],{"encoding":1530},"MC = 2 + 0{,}2 Q",", fixní náklady ",[1035,28115,28117],{"className":28116},[1480],[1482,28118,28119],{"xmlns":1484},[1487,28120,28121,28131],{},[1490,28122,28123,28125,28127,28129],{},[1493,28124,10790],{},[1493,28126,1998],{},[1506,28128,1508],{},[1680,28130,2916],{},[1528,28132,28133],{"encoding":1530},"FC = 100",[1035,28135,28137],{"className":28136},[1480],[1482,28138,28139],{"xmlns":1484,"display":1485},[1487,28140,28141,28181],{},[1490,28142,28143,28145,28147,28149,28151,28153,28155,28157,28159,28161,28163,28165,28167,28169,28171,28177,28179],{},[1493,28144,5289],{},[1493,28146,1998],{},[1506,28148,1508],{},[1506,28150,10857],{},[1493,28152,1495],{},[1493,28154,1998],{},[1988,28156,5016],{},[1493,28158,3384],{},[1493,28160,1520],{},[1506,28162,1508],{},[1680,28164,1691],{},[1493,28166,1520],{},[1506,28168,2162],{},[1680,28170,13237],{},[2315,28172,28173,28175],{},[1493,28174,1520],{},[1680,28176,1691],{},[1506,28178,2162],{},[1493,28180,8730],{},[1528,28182,28183],{"encoding":1530},"TC = \\int MC\\, dQ = 2Q + 0{,}1 Q^2 + c",[1030,28185,28000,28186,18838,28218,1274],{},[1035,28187,28189],{"className":28188},[1480],[1482,28190,28191],{"xmlns":1484},[1487,28192,28193,28215],{},[1490,28194,28195,28197,28199,28201,28203,28205,28207,28209,28211,28213],{},[1493,28196,5289],{},[1493,28198,1998],{},[1506,28200,1553],{"stretchy":1552},[1680,28202,1871],{},[1506,28204,1564],{"stretchy":1552},[1506,28206,1508],{},[1493,28208,10790],{},[1493,28210,1998],{},[1506,28212,1508],{},[1680,28214,2916],{},[1528,28216,28217],{"encoding":1530},"TC(0) = FC = 100",[1035,28219,28221],{"className":28220},[1480],[1482,28222,28223],{"xmlns":1484},[1487,28224,28225,28233],{},[1490,28226,28227,28229,28231],{},[1493,28228,8730],{},[1506,28230,1508],{},[1680,28232,2916],{},[1528,28234,28235],{"encoding":1530},"c = 100",[1035,28237,28239],{"className":28238},[1480],[1482,28240,28241],{"xmlns":1484,"display":1485},[1487,28242,28243,28275],{},[1490,28244,28245,28247,28249,28251,28253,28255,28257,28259,28261,28263,28265,28267,28269],{},[1493,28246,5289],{},[1493,28248,1998],{},[1506,28250,1553],{"stretchy":1552},[1493,28252,1520],{},[1506,28254,1564],{"stretchy":1552},[1506,28256,1508],{},[1680,28258,2916],{},[1506,28260,2162],{},[1680,28262,1691],{},[1493,28264,1520],{},[1506,28266,2162],{},[1680,28268,13237],{},[2315,28270,28271,28273],{},[1493,28272,1520],{},[1680,28274,1691],{},[1528,28276,28277],{"encoding":1530},"TC(Q) = 100 + 2Q + 0{,}1 Q^2",[1304,28279,28281],{"id":28280},"přebytek-spotřebitele-a-výrobce","Přebytek spotřebitele a výrobce",[1030,28283,14766],{},[1035,28285,28287],{"className":28286},[1480],[1482,28288,28289],{"xmlns":1484,"display":1485},[1487,28290,28291,28351],{},[1490,28292,28293,28295,28297,28299,28305,28307,28309,28321,28323,28325,28327,28329,28331,28333,28335,28337,28343,28345],{},[1493,28294,1998],{},[1493,28296,2001],{},[1506,28298,1553],{"stretchy":1552},[1497,28300,28301,28303],{},[1493,28302,1520],{},[1680,28304,1871],{},[1506,28306,1564],{"stretchy":1552},[1506,28308,1508],{},[1697,28310,28311,28313,28315],{},[1506,28312,10857],{},[1680,28314,1871],{},[1497,28316,28317,28319],{},[1493,28318,1520],{},[1680,28320,1871],{},[1493,28322,3712],{},[1506,28324,1553],{"stretchy":1552},[1493,28326,1520],{},[1506,28328,1564],{"stretchy":1552},[1988,28330,5016],{},[1493,28332,3384],{},[1493,28334,1520],{},[1506,28336,1888],{},[1497,28338,28339,28341],{},[1493,28340,1501],{},[1680,28342,1871],{},[1988,28344,5016],{},[1497,28346,28347,28349],{},[1493,28348,1520],{},[1680,28350,1871],{},[1528,28352,28353],{"encoding":1530},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\, dQ - P_0\\, Q_0",[1030,28355,14883],{},[1035,28357,28359],{"className":28358},[1480],[1482,28360,28361],{"xmlns":1484,"display":1485},[1487,28362,28363,28423],{},[1490,28364,28365,28367,28369,28371,28377,28379,28381,28387,28389,28395,28397,28409,28411,28413,28415,28417,28419,28421],{},[1493,28366,1501],{},[1493,28368,2001],{},[1506,28370,1553],{"stretchy":1552},[1497,28372,28373,28375],{},[1493,28374,1520],{},[1680,28376,1871],{},[1506,28378,1564],{"stretchy":1552},[1506,28380,1508],{},[1497,28382,28383,28385],{},[1493,28384,1501],{},[1680,28386,1871],{},[1988,28388,5016],{},[1497,28390,28391,28393],{},[1493,28392,1520],{},[1680,28394,1871],{},[1506,28396,1888],{},[1697,28398,28399,28401,28403],{},[1506,28400,10857],{},[1680,28402,1871],{},[1497,28404,28405,28407],{},[1493,28406,1520],{},[1680,28408,1871],{},[1493,28410,2001],{},[1506,28412,1553],{"stretchy":1552},[1493,28414,1520],{},[1506,28416,1564],{"stretchy":1552},[1988,28418,5016],{},[1493,28420,3384],{},[1493,28422,1520],{},[1528,28424,28425],{"encoding":1530},"PS(Q_0) = P_0\\, Q_0 - \\int_0^{Q_0} S(Q)\\, dQ",[1030,28427,28428,28429,2632],{},"Detailně viz ",[1052,28430,17211],{"className":28431,"dataFsResolvedFilePath":3487,"href":3488},[1055],[1065,28433,17159],{"id":17158},[1203,28435,28436,28444,28451],{},[1206,28437,28438,1656,28440],{},[1047,28439,19217],{},[1052,28441,28443],{"className":28442,"dataFsResolvedFilePath":16621,"href":16622},[1055],"Derivace, diferenciál a extrémy 1D",[1206,28445,28446,1656,28448],{},[1047,28447,19228],{},[1052,28449,9472],{"className":28450,"dataFsResolvedFilePath":9470,"href":9471},[1055],[1206,28452,28453,1656,28455,28458,28459,28462],{},[1047,28454,19236],{},[1052,28456,1301],{"className":28457,"dataFsResolvedFilePath":1299,"href":1300},[1055]," (TR\u002FTC), ",[1052,28460,17211],{"className":28461,"dataFsResolvedFilePath":3487,"href":3488},[1055]," (přebytky CS\u002FPS)",{"title":17269,"searchDepth":141,"depth":141,"links":28464},[28465,28466,28467,28472],{"id":27655,"depth":141,"text":27656},{"id":27781,"depth":141,"text":27782},{"id":27907,"depth":141,"text":27908,"children":28468},[28469,28470,28471],{"id":27911,"depth":96,"text":27912},{"id":28082,"depth":96,"text":28083},{"id":28280,"depth":96,"text":28281},{"id":17158,"depth":141,"text":17159},"Druhá polovina kalkulu jedné proměnné. Slouží k rekonstrukci totální veličiny z mezní (TR z MR, TC z MC) a k výpočtu přebytků (consumer\u002Fproducer surplus).",{},"\u002Ftopics\u002Fintegral",{"title":17258,"description":28473},[19272],"topics\u002Fintegral",[9,110,746,946,824,930,916],"KDT9glz6LCGfpVDG7n5tikhQo4Va9sJD97Pzs9_xxow",{"id":28482,"title":28483,"body":28484,"course":9,"courses":17424,"created":26093,"description":17269,"extension":17426,"meta":32427,"navigation":17428,"path":32428,"seo":32429,"sources":32430,"stem":32432,"tags":32433,"type":19275,"updated":26102,"__hash__":32434},"topics\u002Ftopics\u002Fis-lm.md","IS-LM analýza — simultánní rovnováha trhu zboží a peněz",{"type":1016,"value":28485,"toc":32415},[28486,28489,28492,28634,28641,28645,28714,28752,28860,28864,28894,28958,29005,29008,29075,29078,29111,29147,29151,29199,29206,29250,29294,29297,29372,29469,29558,29562,29606,29634,29640,29669,29691,29738,29791,29855,29858,29922,29951,30008,30024,30109,30206,30343,30347,30503,30885,30889,30892,30950,30953,31039,31067,31103,31106,31141,31181,31213,31215,31250,31282,31376,31381,31502,31554,31633,31637,31757,31764,31875,31882,31886,32360,32362],[1019,28487,28483],{"id":28488},"is-lm-analýza-simultánní-rovnováha-trhu-zboží-a-peněz",[1065,28490,1042],{"id":28491},"tldr",[1030,28493,28494,28496,28497,7606,28500,28513,28514,28527,28528,28531,28532,1732,28535,28538,28539,1732,28542,28545,28546,1656,28549,28579,28580,28583,28584,1732,28598,28611,28612,28615,28616,16623],{},[1047,28495,16530],{}," je makroekonomický model se ",[1047,28498,28499],{},"dvěma neznámými",[1035,28501,28503],{"className":28502},[1480],[1482,28504,28505],{"xmlns":1484},[1487,28506,28507,28511],{},[1490,28508,28509],{},[1493,28510,1791],{},[1528,28512,1791],{"encoding":1530}," — národní důchod a ",[1035,28515,28517],{"className":28516},[1480],[1482,28518,28519],{"xmlns":1484},[1487,28520,28521,28525],{},[1490,28522,28523],{},[1493,28524,7740],{},[1528,28526,7740],{"encoding":1530}," — úroková míra) a ",[1047,28529,28530],{},"dvěma trhy",": trhem zboží (křivka ",[1047,28533,28534],{},"IS",[1176,28536,28537],{},"Investment = Savings",") a trhem peněz (křivka ",[1047,28540,28541],{},"LM",[1176,28543,28544],{},"Liquidity of Money","). Průsečík obou křivek určuje ",[1047,28547,28548],{},"simultánní rovnováhu",[1035,28550,28552],{"className":28551},[1480],[1482,28553,28554],{"xmlns":1484},[1487,28555,28556,28576],{},[1490,28557,28558,28560,28566,28568,28574],{},[1506,28559,1553],{"stretchy":1552},[2315,28561,28562,28564],{},[1493,28563,1791],{},[1493,28565,2711],{},[1506,28567,1559],{"separator":1041},[2315,28569,28570,28572],{},[1493,28571,7740],{},[1493,28573,2711],{},[1506,28575,1564],{"stretchy":1552},[1528,28577,28578],{"encoding":1530},"(Y^E, r^E)",", v níž jsou oba trhy vyvážené zároveň. Model je klíčovým nástrojem pro analýzu ",[1047,28581,28582],{},"fiskální politiky"," (posun IS změnou ",[1035,28585,28587],{"className":28586},[1480],[1482,28588,28589],{"xmlns":1484},[1487,28590,28591,28596],{},[1490,28592,28593],{},[1493,28594,28595],{},"G",[1528,28597,28595],{"encoding":1530},[1035,28599,28601],{"className":28600},[1480],[1482,28602,28603],{"xmlns":1484},[1487,28604,28605,28609],{},[1490,28606,28607],{},[1493,28608,5289],{},[1528,28610,5289],{"encoding":1530},") a ",[1047,28613,28614],{},"monetární politiky"," (posun LM změnou nabídky peněz ",[1035,28617,28619],{"className":28618},[1480],[1482,28620,28621],{"xmlns":1484},[1487,28622,28623,28631],{},[1490,28624,28625],{},[2315,28626,28627,28629],{},[1493,28628,1495],{},[1506,28630,2287],{},[1528,28632,28633],{"encoding":1530},"M^*",[1030,28635,28636],{},[18014,28637],{"alt":28638,"className":28639,"src":28640},"imek-is-lm-model",[1055,18018],"\u002Fwiki-assets\u002Fimek-is-lm-model.jpeg",[1065,28642,28644],{"id":28643},"motivace-proč-přejít-od-c-i-g-x-k-is-lm","Motivace — proč přejít od C-I-G-X k IS-LM",[1030,28646,28647,28648,28652,28653,7606,28656,28678,28679,28682,28683,28699,28700,28713],{},"V modelech ",[1052,28649,28651],{"className":28650,"dataFsResolvedFilePath":2622,"href":2623},[1055],"C-I, C-I-G a C-I-G-X"," byly ",[1047,28654,28655],{},"investice pokládány za konstantní",[1035,28657,28659],{"className":28658},[1480],[1482,28660,28661],{"xmlns":1484},[1487,28662,28663,28675],{},[1490,28664,28665,28667,28669],{},[1493,28666,2662],{},[1506,28668,1508],{},[2315,28670,28671,28673],{},[1493,28672,2662],{},[1506,28674,2287],{},[1528,28676,28677],{"encoding":1530},"I = I^*","). To není realistické — investice firem závisejí na ",[1047,28680,28681],{},"ceně peněz",", tedy na ",[1047,28684,28685,28686],{},"úrokové míře ",[1035,28687,28689],{"className":28688},[1480],[1482,28690,28691],{"xmlns":1484},[1487,28692,28693,28697],{},[1490,28694,28695],{},[1493,28696,7740],{},[1528,28698,7740],{"encoding":1530},": čím vyšší ",[1035,28701,28703],{"className":28702},[1480],[1482,28704,28705],{"xmlns":1484},[1487,28706,28707,28711],{},[1490,28708,28709],{},[1493,28710,7740],{},[1528,28712,7740],{"encoding":1530},", tím dražší úvěr a tím méně investic. IS-LM analýza proto zavádí:",[1203,28715,28716,28746],{},[1206,28717,28718,1656,28721,28745],{},[1047,28719,28720],{},"funkci investic",[1035,28722,28724],{"className":28723},[1480],[1482,28725,28726],{"xmlns":1484},[1487,28727,28728,28742],{},[1490,28729,28730,28732,28734,28736,28738,28740],{},[1493,28731,2662],{},[1506,28733,1508],{},[1493,28735,2662],{},[1506,28737,1553],{"stretchy":1552},[1493,28739,7740],{},[1506,28741,1564],{"stretchy":1552},[1528,28743,28744],{"encoding":1530},"I = I(r)"," jako klesající funkci úrokové míry,",[1206,28747,28748,28751],{},[1047,28749,28750],{},"trh peněz",", jehož rovnováha (poptávka = nabídka peněz) doplňuje druhou rovnici potřebnou pro určení obou neznámých.",[1023,28753,28755,28762],{"className":28754,"dataCallout":1155},[1026,1154],[1030,28756,28758,28761],{"className":28757},[1033],[1035,28759],{"className":28760,"ariaHidden":1041},[1038,1162,1040],"Pozor — dvě neznámé vyžadují dvě rovnice",[1030,28763,28647,28764,28783,28784,28811,28812,28825,28826,28855,28856,28859],{},[1035,28765,28767],{"className":28766},[1480],[1482,28768,28769],{"xmlns":1484},[1487,28770,28771,28780],{},[1490,28772,28773,28775,28778],{},[1493,28774,1998],{},[1988,28776,28777],{},"-",[1493,28779,2662],{},[1528,28781,28782],{"encoding":1530},"C\\text{-}I"," až ",[1035,28785,28787],{"className":28786},[1480],[1482,28788,28789],{"xmlns":1484},[1487,28790,28791,28808],{},[1490,28792,28793,28795,28797,28799,28801,28803,28805],{},[1493,28794,1998],{},[1988,28796,28777],{},[1493,28798,2662],{},[1988,28800,28777],{},[1493,28802,28595],{},[1988,28804,28777],{},[1493,28806,28807],{},"X",[1528,28809,28810],{"encoding":1530},"C\\text{-}I\\text{-}G\\text{-}X"," byla hlavní neznámou jen ",[1035,28813,28815],{"className":28814},[1480],[1482,28816,28817],{"xmlns":1484},[1487,28818,28819,28823],{},[1490,28820,28821],{},[1493,28822,1791],{},[1528,28824,1791],{"encoding":1530},". V IS-LM jsou ",[1047,28827,28828,28829,1586,28842],{},"dvě neznámé ",[1035,28830,28832],{"className":28831},[1480],[1482,28833,28834],{"xmlns":1484},[1487,28835,28836,28840],{},[1490,28837,28838],{},[1493,28839,1791],{},[1528,28841,1791],{"encoding":1530},[1035,28843,28845],{"className":28844},[1480],[1482,28846,28847],{"xmlns":1484},[1487,28848,28849,28853],{},[1490,28850,28851],{},[1493,28852,7740],{},[1528,28854,7740],{"encoding":1530},", a proto potřebujeme ",[1047,28857,28858],{},"dvě rovnice",": jednu z trhu zboží (křivka IS) a jednu z trhu peněz (křivka LM).",[1065,28861,28863],{"id":28862},"funkce-investic-a-funkce-spotřeby","Funkce investic a funkce spotřeby",[1030,28865,28866,28867,28880,28881,1274],{},"Lineární závislost investic ",[1035,28868,28870],{"className":28869},[1480],[1482,28871,28872],{"xmlns":1484},[1487,28873,28874,28878],{},[1490,28875,28876],{},[1493,28877,2662],{},[1528,28879,2662],{"encoding":1530}," na úrokové míře ",[1035,28882,28884],{"className":28883},[1480],[1482,28885,28886],{"xmlns":1484},[1487,28887,28888,28892],{},[1490,28889,28890],{},[1493,28891,7740],{},[1528,28893,7740],{"encoding":1530},[1035,28895,28897],{"className":28896},[1480],[1482,28898,28899],{"xmlns":1484,"display":1485},[1487,28900,28901,28955],{},[1490,28902,28903,28905,28907,28909,28911,28913,28915,28917,28919,28921,28923,28925,28927,28929,28931,28933,28935,28937,28939,28941,28943,28946,28948,28950,28953],{},[1493,28904,2662],{},[1506,28906,1508],{},[1493,28908,2662],{},[1506,28910,1553],{"stretchy":1552},[1493,28912,7740],{},[1506,28914,1564],{"stretchy":1552},[1506,28916,1508],{},[1493,28918,8730],{},[1493,28920,7740],{},[1506,28922,2162],{},[1493,28924,3384],{},[1506,28926,1559],{"separator":1041},[1912,28928],{"width":1914},[1493,28930,8730],{},[1506,28932,3961],{},[1680,28934,1871],{},[1506,28936,1559],{"separator":1041},[1988,28938,10922],{},[1493,28940,3384],{},[1506,28942,2796],{},[1680,28944,28945],{},"0.",[1912,28947],{"width":1914},[1506,28949,1553],{"stretchy":1552},[1680,28951,28952],{},"7.11",[1506,28954,1564],{"stretchy":1552},[1528,28956,28957],{"encoding":1530},"I = I(r) = cr + d, \\qquad c \u003C 0,\\ d > 0. \\qquad (7.11)",[1203,28959,28960,28981],{},[1206,28961,28962,28980],{},[1035,28963,28965],{"className":28964},[1480],[1482,28966,28967],{"xmlns":1484},[1487,28968,28969,28977],{},[1490,28970,28971,28973,28975],{},[1493,28972,3384],{},[1506,28974,2796],{},[1680,28976,1871],{},[1528,28978,28979],{"encoding":1530},"d > 0"," zřejmé,",[1206,28982,28983,29001,29002,2632],{},[1035,28984,28986],{"className":28985},[1480],[1482,28987,28988],{"xmlns":1484},[1487,28989,28990,28998],{},[1490,28991,28992,28994,28996],{},[1493,28993,8730],{},[1506,28995,3961],{},[1680,28997,1871],{},[1528,28999,29000],{"encoding":1530},"c \u003C 0",", protože růst úrokové míry tlumí investice — funkce investic je ",[1047,29003,29004],{},"klesající",[1030,29006,29007],{},"Spotřeba zůstává lineární funkcí důchodu:",[1035,29009,29011],{"className":29010},[1480],[1482,29012,29013],{"xmlns":1484,"display":1485},[1487,29014,29015,29072],{},[1490,29016,29017,29019,29021,29023,29025,29027,29029,29031,29033,29035,29037,29039,29041,29043,29045,29047,29049,29051,29053,29055,29057,29059,29061,29063,29065,29067,29070],{},[1493,29018,1998],{},[1506,29020,1508],{},[1493,29022,1998],{},[1506,29024,1553],{"stretchy":1552},[1493,29026,1791],{},[1506,29028,1564],{"stretchy":1552},[1506,29030,1508],{},[1493,29032,1052],{},[1493,29034,1791],{},[1506,29036,2162],{},[1493,29038,2394],{},[1506,29040,1559],{"separator":1041},[1912,29042],{"width":1914},[1680,29044,1871],{},[1506,29046,3961],{},[1493,29048,1052],{},[1506,29050,3961],{},[1680,29052,1682],{},[1506,29054,1559],{"separator":1041},[1988,29056,10922],{},[1493,29058,2394],{},[1506,29060,2796],{},[1680,29062,28945],{},[1912,29064],{"width":1914},[1506,29066,1553],{"stretchy":1552},[1680,29068,29069],{},"7.12",[1506,29071,1564],{"stretchy":1552},[1528,29073,29074],{"encoding":1530},"C = C(Y) = aY + b, \\qquad 0 \u003C a \u003C 1,\\ b > 0. \\qquad (7.12)",[1030,29076,29077],{},"Podmínka rovnováhy na trhu zboží:",[1035,29079,29081],{"className":29080},[1480],[1482,29082,29083],{"xmlns":1484,"display":1485},[1487,29084,29085,29108],{},[1490,29086,29087,29089,29091,29093,29095,29097,29099,29101,29103,29106],{},[1493,29088,1791],{},[1506,29090,1508],{},[1493,29092,1998],{},[1506,29094,2162],{},[1493,29096,2662],{},[1493,29098,2632],{"mathvariant":1516},[1912,29100],{"width":1914},[1506,29102,1553],{"stretchy":1552},[1680,29104,29105],{},"7.13",[1506,29107,1564],{"stretchy":1552},[1528,29109,29110],{"encoding":1530},"Y = C + I. \\qquad (7.13)",[1030,29112,29113,29114,1656,29117,29143,29144,2632],{},"To dává ",[1047,29115,29116],{},"tři rovnice o čtyřech neznámých",[1035,29118,29120],{"className":29119},[1480],[1482,29121,29122],{"xmlns":1484},[1487,29123,29124,29140],{},[1490,29125,29126,29128,29130,29132,29134,29136,29138],{},[1493,29127,1791],{},[1506,29129,1559],{"separator":1041},[1493,29131,1998],{},[1506,29133,1559],{"separator":1041},[1493,29135,2662],{},[1506,29137,1559],{"separator":1041},[1493,29139,7740],{},[1528,29141,29142],{"encoding":1530},"Y, C, I, r",". Pro jednoznačné určení rovnováhy potřebujeme čtvrtou rovnici — odvodí se z ",[1047,29145,29146],{},"rovnováhy na trhu peněz",[1065,29148,29150],{"id":29149},"křivka-is-rovnováha-na-trhu-zboží","Křivka IS — rovnováha na trhu zboží",[1030,29152,29153,29154,21333,29176,29194,29195,29198],{},"Podmínka (7.13) reprezentuje rovnováhu na trhu zboží, protože s ohledem na ",[1035,29155,29157],{"className":29156},[1480],[1482,29158,29159],{"xmlns":1484},[1487,29160,29161,29173],{},[1490,29162,29163,29165,29167,29169,29171],{},[1493,29164,1791],{},[1506,29166,1508],{},[1493,29168,1998],{},[1506,29170,2162],{},[1493,29172,2001],{},[1528,29174,29175],{"encoding":1530},"Y = C + S",[1035,29177,29179],{"className":29178},[1480],[1482,29180,29181],{"xmlns":1484},[1487,29182,29183,29191],{},[1490,29184,29185,29187,29189],{},[1493,29186,2662],{},[1506,29188,1508],{},[1493,29190,2001],{},[1528,29192,29193],{"encoding":1530},"I = S"," (plánované ",[1047,29196,29197],{},"investice = úspory","). Dosazením (7.11) a (7.12) do (7.13):",[1030,29200,29201],{},[18014,29202],{"alt":29203,"className":29204,"src":29205},"imek-odvozeni-is-4panelu",[1055,18018],"\u002Fwiki-assets\u002Fimek-odvozeni-is-4panelu.jpeg",[1035,29207,29209],{"className":29208},[1480],[1482,29210,29211],{"xmlns":1484,"display":1485},[1487,29212,29213,29247],{},[1490,29214,29215,29217,29219,29221,29223,29225,29227,29229,29231,29233,29235,29237,29239,29241,29243,29245],{},[1493,29216,1791],{},[1506,29218,1508],{},[1506,29220,1553],{"stretchy":1552},[1493,29222,1052],{},[1493,29224,1791],{},[1506,29226,2162],{},[1493,29228,2394],{},[1506,29230,1564],{"stretchy":1552},[1506,29232,2162],{},[1506,29234,1553],{"stretchy":1552},[1493,29236,8730],{},[1493,29238,7740],{},[1506,29240,2162],{},[1493,29242,3384],{},[1506,29244,1564],{"stretchy":1552},[1506,29246,1559],{"separator":1041},[1528,29248,29249],{"encoding":1530},"Y = (aY + b) + (cr + d),",[1035,29251,29253],{"className":29252},[1480],[1482,29254,29255],{"xmlns":1484,"display":1485},[1487,29256,29257,29291],{},[1490,29258,29259,29261,29263,29265,29267,29269,29271,29273,29275,29277,29279,29281,29283,29285,29287,29289],{},[1506,29260,1553],{"stretchy":1552},[1680,29262,1682],{},[1506,29264,1888],{},[1493,29266,1052],{},[1506,29268,1564],{"stretchy":1552},[1493,29270,1791],{},[1506,29272,1888],{},[1493,29274,8730],{},[1493,29276,7740],{},[1506,29278,1888],{},[1493,29280,2394],{},[1506,29282,1888],{},[1493,29284,3384],{},[1506,29286,1508],{},[1680,29288,1871],{},[1506,29290,1559],{"separator":1041},[1528,29292,29293],{"encoding":1530},"(1 - a)Y - cr - b - d = 0,",[1030,29295,29296],{},"odkud",[1035,29298,29300],{"className":29299},[1480],[1482,29301,29302],{"xmlns":1484,"display":1485},[1487,29303,29304,29369],{},[1490,29305,29306,29360,29362,29364,29367],{},[1976,29307,29308],{"notation":1978},[1869,29309,29310],{"scriptlevel":1871,"displaystyle":1552},[1869,29311,29312],{"scriptlevel":1871,"displaystyle":1552},[1869,29313,29314],{"scriptlevel":1871,"displaystyle":1041},[1490,29315,29316,29318,29320,29322,29334,29336,29338,29340,29358],{},[1988,29317,5016],{},[1493,29319,1791],{},[1506,29321,1508],{},[1510,29323,29324,29326],{},[1493,29325,8730],{},[1490,29327,29328,29330,29332],{},[1680,29329,1682],{},[1506,29331,1888],{},[1493,29333,1052],{},[1988,29335,5016],{},[1493,29337,7740],{},[1506,29339,2162],{},[1510,29341,29342,29350],{},[1490,29343,29344,29346,29348],{},[1493,29345,2394],{},[1506,29347,2162],{},[1493,29349,3384],{},[1490,29351,29352,29354,29356],{},[1680,29353,1682],{},[1506,29355,1888],{},[1493,29357,1052],{},[1988,29359,5016],{},[1912,29361],{"width":1914},[1506,29363,1553],{"stretchy":1552},[1680,29365,29366],{},"7.14",[1506,29368,1564],{"stretchy":1552},[1528,29370,29371],{"encoding":1530},"\\boxed{\\,Y = \\frac{c}{1 - a}\\,r + \\frac{b + d}{1 - a}\\,} \\qquad (7.14)",[1030,29373,29374,29375,7606,29378,29381,29382,29385,29386,29388,29389,29411,29412,29440,29441,29462,29463,29465,29466,29468],{},"Tento vztah se nazývá ",[1047,29376,29377],{},"funkce IS",[1176,29379,29380],{},"IS schedule",") a její graf ",[1047,29383,29384],{},"křivka IS",". Křivka je ",[1047,29387,29004],{}," přímka v rovině ",[1035,29390,29392],{"className":29391},[1480],[1482,29393,29394],{"xmlns":1484},[1487,29395,29396,29408],{},[1490,29397,29398,29400,29402,29404,29406],{},[1506,29399,1553],{"stretchy":1552},[1493,29401,7740],{},[1506,29403,1559],{"separator":1041},[1493,29405,1791],{},[1506,29407,1564],{"stretchy":1552},[1528,29409,29410],{"encoding":1530},"(r, Y)",", neboť ",[1035,29413,29415],{"className":29414},[1480],[1482,29416,29417],{"xmlns":1484},[1487,29418,29419,29437],{},[1490,29420,29421,29433,29435],{},[1510,29422,29423,29425],{},[1493,29424,8730],{},[1490,29426,29427,29429,29431],{},[1680,29428,1682],{},[1506,29430,1888],{},[1493,29432,1052],{},[1506,29434,3961],{},[1680,29436,1871],{},[1528,29438,29439],{"encoding":1530},"\\frac{c}{1-a} \u003C 0"," (čitatel záporný, jmenovatel kladný). Název vyjadřuje, že křivka popisuje ty kombinace ",[1035,29442,29444],{"className":29443},[1480],[1482,29445,29446],{"xmlns":1484},[1487,29447,29448,29460],{},[1490,29449,29450,29452,29454,29456,29458],{},[1506,29451,1553],{"stretchy":1552},[1493,29453,7740],{},[1506,29455,1559],{"separator":1041},[1493,29457,1791],{},[1506,29459,1564],{"stretchy":1552},[1528,29461,29410],{"encoding":1530},", pro které plánované ",[1047,29464,2662],{},"nvestment = ",[1047,29467,2001],{},"avings.",[1023,29470,29472,29479],{"className":29471,"dataCallout":582},[1026,1186],[1030,29473,29475,29478],{"className":29474},[1033],[1035,29476],{"className":29477,"ariaHidden":1041},[1038,1193,1040],"Intuice — proč IS klesá",[1030,29480,29481,29482,29495,29496,1656,29499,29512,29513,29526,29527,1586,29540,29553,29554,29557],{},"Nižší úroková míra ",[1035,29483,29485],{"className":29484},[1480],[1482,29486,29487],{"xmlns":1484},[1487,29488,29489,29493],{},[1490,29490,29491],{},[1493,29492,7740],{},[1528,29494,7740],{"encoding":1530}," → levnější úvěr → ",[1047,29497,29498],{},"více investic",[1035,29500,29502],{"className":29501},[1480],[1482,29503,29504],{"xmlns":1484},[1487,29505,29506,29510],{},[1490,29507,29508],{},[1493,29509,2662],{},[1528,29511,2662],{"encoding":1530}," → vyšší agregátní poptávka → vyšší rovnovážný důchod ",[1035,29514,29516],{"className":29515},[1480],[1482,29517,29518],{"xmlns":1484},[1487,29519,29520,29524],{},[1490,29521,29522],{},[1493,29523,1791],{},[1528,29525,1791],{"encoding":1530},". Vztah mezi ",[1035,29528,29530],{"className":29529},[1480],[1482,29531,29532],{"xmlns":1484},[1487,29533,29534,29538],{},[1490,29535,29536],{},[1493,29537,7740],{},[1528,29539,7740],{"encoding":1530},[1035,29541,29543],{"className":29542},[1480],[1482,29544,29545],{"xmlns":1484},[1487,29546,29547,29551],{},[1490,29548,29549],{},[1493,29550,1791],{},[1528,29552,1791],{"encoding":1530}," na trhu zboží je proto ",[1047,29555,29556],{},"nepřímý"," (klesající křivka).",[1065,29559,29561],{"id":29560},"křivka-lm-rovnováha-na-trhu-peněz","Křivka LM — rovnováha na trhu peněz",[1030,29563,29564,29565,29583,29584,18367,29602,29605],{},"Rovnováha na trhu peněz: poptávka po penězích ",[1035,29566,29568],{"className":29567},[1480],[1482,29569,29570],{"xmlns":1484},[1487,29571,29572,29580],{},[1490,29573,29574],{},[2315,29575,29576,29578],{},[1493,29577,1495],{},[1493,29579,3712],{},[1528,29581,29582],{"encoding":1530},"M^D"," se rovná nabídce peněz ",[1035,29585,29587],{"className":29586},[1480],[1482,29588,29589],{"xmlns":1484},[1487,29590,29591,29599],{},[1490,29592,29593],{},[2315,29594,29595,29597],{},[1493,29596,1495],{},[1493,29598,2001],{},[1528,29600,29601],{"encoding":1530},"M^S",[1047,29603,29604],{},"Nabídka"," je pod kontrolou národní banky a je pevně zadána:",[1035,29607,29609],{"className":29608},[1480],[1482,29610,29611],{"xmlns":1484,"display":1485},[1487,29612,29613,29631],{},[1490,29614,29615,29621,29623,29629],{},[2315,29616,29617,29619],{},[1493,29618,1495],{},[1493,29620,2001],{},[1506,29622,1508],{},[2315,29624,29625,29627],{},[1493,29626,1495],{},[1506,29628,2287],{},[1493,29630,2632],{"mathvariant":1516},[1528,29632,29633],{"encoding":1530},"M^S = M^*.",[1030,29635,29636,29639],{},[1047,29637,29638],{},"Poptávka"," po penězích má tři zdroje:",[1203,29641,29642,29651,29660],{},[1206,29643,29644,7606,29647,29650],{},[1047,29645,29646],{},"transakční poptávka",[1176,29648,29649],{},"transactions demand",") — peníze pro nákup zboží,",[1206,29652,29653,7606,29656,29659],{},[1047,29654,29655],{},"opatrnostní poptávka",[1176,29657,29658],{},"precautionary demand",") — peníze pro nenadálé výdaje,",[1206,29661,29662,7606,29665,29668],{},[1047,29663,29664],{},"spekulační poptávka",[1176,29666,29667],{},"speculative demand",") — peníze pro zhodnocení (akcie, obligace).",[1030,29670,29671,29672,29690],{},"Součet transakční a opatrnostní poptávky ",[1035,29673,29675],{"className":29674},[1480],[1482,29676,29677],{"xmlns":1484},[1487,29678,29679,29687],{},[1490,29680,29681],{},[1497,29682,29683,29685],{},[1493,29684,1556],{},[1680,29686,1682],{},[1528,29688,29689],{"encoding":1530},"L_1"," je úměrný důchodu:",[1035,29692,29694],{"className":29693},[1480],[1482,29695,29696],{"xmlns":1484,"display":1485},[1487,29697,29698,29735],{},[1490,29699,29700,29706,29708,29714,29716,29718,29720,29722,29724,29730,29732],{},[1497,29701,29702,29704],{},[1493,29703,1556],{},[1680,29705,1682],{},[1506,29707,1508],{},[1497,29709,29710,29712],{},[1493,29711,7100],{},[1680,29713,1682],{},[1493,29715,1791],{},[1506,29717,1559],{"separator":1041},[1912,29719],{"width":1914},[1680,29721,1871],{},[1506,29723,3961],{},[1497,29725,29726,29728],{},[1493,29727,7100],{},[1680,29729,1682],{},[1506,29731,3961],{},[1680,29733,29734],{},"1.",[1528,29736,29737],{"encoding":1530},"L_1 = k_1 Y, \\qquad 0 \u003C k_1 \u003C 1.",[1030,29739,29740,29741,29759,29760,1732,29773,29790],{},"Spekulační poptávka ",[1035,29742,29744],{"className":29743},[1480],[1482,29745,29746],{"xmlns":1484},[1487,29747,29748,29756],{},[1490,29749,29750],{},[1497,29751,29752,29754],{},[1493,29753,1556],{},[1680,29755,1691],{},[1528,29757,29758],{"encoding":1530},"L_2"," závisí na úrokové míře (roste-li ",[1035,29761,29763],{"className":29762},[1480],[1482,29764,29765],{"xmlns":1484},[1487,29766,29767,29771],{},[1490,29768,29769],{},[1493,29770,7740],{},[1528,29772,7740],{"encoding":1530},[1035,29774,29776],{"className":29775},[1480],[1482,29777,29778],{"xmlns":1484},[1487,29779,29780,29788],{},[1490,29781,29782],{},[1497,29783,29784,29786],{},[1493,29785,1556],{},[1680,29787,1691],{},[1528,29789,29758],{"encoding":1530}," klesá, protože vyšší výnos obligací snižuje atraktivitu držby peněz):",[1035,29792,29794],{"className":29793},[1480],[1482,29795,29796],{"xmlns":1484,"display":1485},[1487,29797,29798,29852],{},[1490,29799,29800,29806,29808,29814,29816,29818,29824,29826,29828,29834,29836,29838,29840,29842,29848,29850],{},[1497,29801,29802,29804],{},[1493,29803,1556],{},[1680,29805,1691],{},[1506,29807,1508],{},[1497,29809,29810,29812],{},[1493,29811,7100],{},[1680,29813,1691],{},[1493,29815,7740],{},[1506,29817,2162],{},[1497,29819,29820,29822],{},[1493,29821,7100],{},[1680,29823,3201],{},[1506,29825,1559],{"separator":1041},[1912,29827],{"width":1914},[1497,29829,29830,29832],{},[1493,29831,7100],{},[1680,29833,1691],{},[1506,29835,3961],{},[1680,29837,1871],{},[1506,29839,1559],{"separator":1041},[1988,29841,10922],{},[1497,29843,29844,29846],{},[1493,29845,7100],{},[1680,29847,3201],{},[1506,29849,2796],{},[1680,29851,28945],{},[1528,29853,29854],{"encoding":1530},"L_2 = k_2 r + k_3, \\qquad k_2 \u003C 0,\\ k_3 > 0.",[1030,29856,29857],{},"Celková poptávka po penězích:",[1035,29859,29861],{"className":29860},[1480],[1482,29862,29863],{"xmlns":1484,"display":1485},[1487,29864,29865,29919],{},[1490,29866,29867,29873,29875,29881,29883,29889,29891,29897,29899,29901,29907,29909,29911,29917],{},[2315,29868,29869,29871],{},[1493,29870,1495],{},[1493,29872,3712],{},[1506,29874,1508],{},[1497,29876,29877,29879],{},[1493,29878,1556],{},[1680,29880,1682],{},[1506,29882,2162],{},[1497,29884,29885,29887],{},[1493,29886,1556],{},[1680,29888,1691],{},[1506,29890,1508],{},[1497,29892,29893,29895],{},[1493,29894,7100],{},[1680,29896,1682],{},[1493,29898,1791],{},[1506,29900,2162],{},[1497,29902,29903,29905],{},[1493,29904,7100],{},[1680,29906,1691],{},[1493,29908,7740],{},[1506,29910,2162],{},[1497,29912,29913,29915],{},[1493,29914,7100],{},[1680,29916,3201],{},[1493,29918,2632],{"mathvariant":1516},[1528,29920,29921],{"encoding":1530},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3.",[1030,29923,29924,29925,1274],{},"Podmínka rovnováhy na trhu peněz ",[1035,29926,29928],{"className":29927},[1480],[1482,29929,29930],{"xmlns":1484},[1487,29931,29932,29948],{},[1490,29933,29934,29940,29942],{},[2315,29935,29936,29938],{},[1493,29937,1495],{},[1493,29939,3712],{},[1506,29941,1508],{},[2315,29943,29944,29946],{},[1493,29945,1495],{},[1506,29947,2287],{},[1528,29949,29950],{"encoding":1530},"M^D = M^*",[1035,29952,29954],{"className":29953},[1480],[1482,29955,29956],{"xmlns":1484,"display":1485},[1487,29957,29958,30005],{},[1490,29959,29960,29966,29968,29974,29976,29978,29984,29986,29988,29994,29996,29998,30000,30003],{},[2315,29961,29962,29964],{},[1493,29963,1495],{},[1506,29965,2287],{},[1506,29967,1508],{},[1497,29969,29970,29972],{},[1493,29971,7100],{},[1680,29973,1682],{},[1493,29975,1791],{},[1506,29977,2162],{},[1497,29979,29980,29982],{},[1493,29981,7100],{},[1680,29983,1691],{},[1493,29985,7740],{},[1506,29987,2162],{},[1497,29989,29990,29992],{},[1493,29991,7100],{},[1680,29993,3201],{},[1506,29995,1559],{"separator":1041},[1912,29997],{"width":1914},[1506,29999,1553],{"stretchy":1552},[1680,30001,30002],{},"7.15",[1506,30004,1564],{"stretchy":1552},[1528,30006,30007],{"encoding":1530},"M^* = k_1 Y + k_2 r + k_3, \\qquad (7.15)",[1030,30009,30010,30011,18579],{},"po úpravě (vyjádření ",[1035,30012,30014],{"className":30013},[1480],[1482,30015,30016],{"xmlns":1484},[1487,30017,30018,30022],{},[1490,30019,30020],{},[1493,30021,1791],{},[1528,30023,1791],{"encoding":1530},[1035,30025,30027],{"className":30026},[1480],[1482,30028,30029],{"xmlns":1484,"display":1485},[1487,30030,30031,30106],{},[1490,30032,30033,30097,30099,30101,30104],{},[1976,30034,30035],{"notation":1978},[1869,30036,30037],{"scriptlevel":1871,"displaystyle":1552},[1869,30038,30039],{"scriptlevel":1871,"displaystyle":1552},[1869,30040,30041],{"scriptlevel":1871,"displaystyle":1041},[1490,30042,30043,30045,30047,30049,30051,30065,30067,30069,30071,30095],{},[1988,30044,5016],{},[1493,30046,1791],{},[1506,30048,1508],{},[1506,30050,1888],{},[1510,30052,30053,30059],{},[1497,30054,30055,30057],{},[1493,30056,7100],{},[1680,30058,1691],{},[1497,30060,30061,30063],{},[1493,30062,7100],{},[1680,30064,1682],{},[1988,30066,5016],{},[1493,30068,7740],{},[1506,30070,2162],{},[1510,30072,30073,30089],{},[1490,30074,30075,30081,30083],{},[2315,30076,30077,30079],{},[1493,30078,1495],{},[1506,30080,2287],{},[1506,30082,1888],{},[1497,30084,30085,30087],{},[1493,30086,7100],{},[1680,30088,3201],{},[1497,30090,30091,30093],{},[1493,30092,7100],{},[1680,30094,1682],{},[1988,30096,5016],{},[1912,30098],{"width":1914},[1506,30100,1553],{"stretchy":1552},[1680,30102,30103],{},"7.16",[1506,30105,1564],{"stretchy":1552},[1528,30107,30108],{"encoding":1530},"\\boxed{\\,Y = -\\frac{k_2}{k_1}\\,r + \\frac{M^* - k_3}{k_1}\\,} \\qquad (7.16)",[1030,30110,29374,30111,7606,30114,30117,30118,29385,30121,29388,30123,29411,30144,30176,30177,30199,30200,30202,30203,30205],{},[1047,30112,30113],{},"funkce LM",[1176,30115,30116],{},"LM schedule","), její graf ",[1047,30119,30120],{},"křivka LM",[1047,30122,3482],{},[1035,30124,30126],{"className":30125},[1480],[1482,30127,30128],{"xmlns":1484},[1487,30129,30130,30142],{},[1490,30131,30132,30134,30136,30138,30140],{},[1506,30133,1553],{"stretchy":1552},[1493,30135,7740],{},[1506,30137,1559],{"separator":1041},[1493,30139,1791],{},[1506,30141,1564],{"stretchy":1552},[1528,30143,29410],{"encoding":1530},[1035,30145,30147],{"className":30146},[1480],[1482,30148,30149],{"xmlns":1484},[1487,30150,30151,30173],{},[1490,30152,30153,30155,30169,30171],{},[1506,30154,1888],{},[1510,30156,30157,30163],{},[1497,30158,30159,30161],{},[1493,30160,7100],{},[1680,30162,1691],{},[1497,30164,30165,30167],{},[1493,30166,7100],{},[1680,30168,1682],{},[1506,30170,2796],{},[1680,30172,1871],{},[1528,30174,30175],{"encoding":1530},"-\\frac{k_2}{k_1} > 0"," (čitatel kladný, protože ",[1035,30178,30180],{"className":30179},[1480],[1482,30181,30182],{"xmlns":1484},[1487,30183,30184,30196],{},[1490,30185,30186,30192,30194],{},[1497,30187,30188,30190],{},[1493,30189,7100],{},[1680,30191,1691],{},[1506,30193,3961],{},[1680,30195,1871],{},[1528,30197,30198],{"encoding":1530},"k_2 \u003C 0",", jmenovatel kladný). Název: ",[1047,30201,1556],{},"iquidity of ",[1047,30204,1495],{},"oney.",[1023,30207,30209,30216],{"className":30208,"dataCallout":582},[1026,1186],[1030,30210,30212,30215],{"className":30211},[1033],[1035,30213],{"className":30214,"ariaHidden":1041},[1038,1193,1040],"Intuice — proč LM roste",[1030,30217,30218,30219,30232,30233,30261,30262,30279,30280,30293,30294,30311,30312,1586,30325,30338,30339,30342],{},"Vyšší důchod ",[1035,30220,30222],{"className":30221},[1480],[1482,30223,30224],{"xmlns":1484},[1487,30225,30226,30230],{},[1490,30227,30228],{},[1493,30229,1791],{},[1528,30231,1791],{"encoding":1530}," → větší transakční poptávka po penězích ",[1035,30234,30236],{"className":30235},[1480],[1482,30237,30238],{"xmlns":1484},[1487,30239,30240,30258],{},[1490,30241,30242,30248,30250,30256],{},[1497,30243,30244,30246],{},[1493,30245,1556],{},[1680,30247,1682],{},[1506,30249,1508],{},[1497,30251,30252,30254],{},[1493,30253,7100],{},[1680,30255,1682],{},[1493,30257,1791],{},[1528,30259,30260],{"encoding":1530},"L_1 = k_1 Y"," → při pevné nabídce ",[1035,30263,30265],{"className":30264},[1480],[1482,30266,30267],{"xmlns":1484},[1487,30268,30269,30277],{},[1490,30270,30271],{},[2315,30272,30273,30275],{},[1493,30274,1495],{},[1506,30276,2287],{},[1528,30278,28633],{"encoding":1530}," vzniká na trhu peněz přebytek poptávky → úroková míra ",[1035,30281,30283],{"className":30282},[1480],[1482,30284,30285],{"xmlns":1484},[1487,30286,30287,30291],{},[1490,30288,30289],{},[1493,30290,7740],{},[1528,30292,7740],{"encoding":1530}," musí vzrůst, aby se spekulační poptávka ",[1035,30295,30297],{"className":30296},[1480],[1482,30298,30299],{"xmlns":1484},[1487,30300,30301,30309],{},[1490,30302,30303],{},[1497,30304,30305,30307],{},[1493,30306,1556],{},[1680,30308,1691],{},[1528,30310,29758],{"encoding":1530}," stlačila a trh se vyrovnal. Vztah mezi ",[1035,30313,30315],{"className":30314},[1480],[1482,30316,30317],{"xmlns":1484},[1487,30318,30319,30323],{},[1490,30320,30321],{},[1493,30322,1791],{},[1528,30324,1791],{"encoding":1530},[1035,30326,30328],{"className":30327},[1480],[1482,30329,30330],{"xmlns":1484},[1487,30331,30332,30336],{},[1490,30333,30334],{},[1493,30335,7740],{},[1528,30337,7740],{"encoding":1530}," na trhu peněz je proto ",[1047,30340,30341],{},"přímý"," (rostoucí křivka).",[1065,30344,30346],{"id":30345},"simultánní-rovnováha-is-lm","Simultánní rovnováha IS-LM",[1030,30348,30349,30350,30353,30354,1656,30357,1586,30374,1656,30377,30395,30396,30414,30415,30433,30434,30450,30451,1586,30466,30481,30482,2632],{},"Řešením ",[1047,30351,30352],{},"soustavy dvou lineárních rovnic"," (7.14) a (7.15) určíme ",[1047,30355,30356],{},"rovnovážný důchod",[1035,30358,30360],{"className":30359},[1480],[1482,30361,30362],{"xmlns":1484},[1487,30363,30364,30372],{},[1490,30365,30366],{},[2315,30367,30368,30370],{},[1493,30369,1791],{},[1493,30371,2711],{},[1528,30373,3419],{"encoding":1530},[1047,30375,30376],{},"rovnovážnou úrokovou míru",[1035,30378,30380],{"className":30379},[1480],[1482,30381,30382],{"xmlns":1484},[1487,30383,30384,30392],{},[1490,30385,30386],{},[2315,30387,30388,30390],{},[1493,30389,7740],{},[1493,30391,2711],{},[1528,30393,30394],{"encoding":1530},"r^E","; zpětným dosazením do (7.11) a (7.12) pak rovnovážné investice ",[1035,30397,30399],{"className":30398},[1480],[1482,30400,30401],{"xmlns":1484},[1487,30402,30403,30411],{},[1490,30404,30405],{},[2315,30406,30407,30409],{},[1493,30408,2662],{},[1493,30410,2711],{},[1528,30412,30413],{"encoding":1530},"I^E"," a rovnovážnou spotřebu ",[1035,30416,30418],{"className":30417},[1480],[1482,30419,30420],{"xmlns":1484},[1487,30421,30422,30430],{},[1490,30423,30424],{},[2315,30425,30426,30428],{},[1493,30427,1998],{},[1493,30429,2711],{},[1528,30431,30432],{"encoding":1530},"C^E",". Graficky jde o ",[1047,30435,30436,30437],{},"průsečík ",[1035,30438,30440],{"className":30439},[1480],[1482,30441,30442],{"xmlns":1484},[1487,30443,30444,30448],{},[1490,30445,30446],{},[1493,30447,2711],{},[1528,30449,2711],{"encoding":1530}," křivek ",[1035,30452,30454],{"className":30453},[1480],[1482,30455,30456],{"xmlns":1484},[1487,30457,30458,30464],{},[1490,30459,30460,30462],{},[1493,30461,2662],{},[1493,30463,2001],{},[1528,30465,28534],{"encoding":1530},[1035,30467,30469],{"className":30468},[1480],[1482,30470,30471],{"xmlns":1484},[1487,30472,30473,30479],{},[1490,30474,30475,30477],{},[1493,30476,1556],{},[1493,30478,1495],{},[1528,30480,28541],{"encoding":1530}," v rovině ",[1035,30483,30485],{"className":30484},[1480],[1482,30486,30487],{"xmlns":1484},[1487,30488,30489,30501],{},[1490,30490,30491,30493,30495,30497,30499],{},[1506,30492,1553],{"stretchy":1552},[1493,30494,7740],{},[1506,30496,1559],{"separator":1041},[1493,30498,1791],{},[1506,30500,1564],{"stretchy":1552},[1528,30502,29410],{"encoding":1530},[1023,30504,30506,30513],{"className":30505,"dataCallout":1443},[1026,1442],[1030,30507,30509,30512],{"className":30508},[1033],[1035,30510],{"className":30511,"ariaHidden":1041},[1038,1450,1040],"Postup — jak najít IS-LM rovnováhu",[1276,30514,30515,30591,30659,30716,30789],{},[1206,30516,30517,30520,30521,1586,30541,30561,30562,1586,30575,30588,30589,2632],{},[1047,30518,30519],{},"Z trhu zboží (7.13)"," dosaď funkce ",[1035,30522,30524],{"className":30523},[1480],[1482,30525,30526],{"xmlns":1484},[1487,30527,30528,30538],{},[1490,30529,30530,30532,30534,30536],{},[1493,30531,1998],{},[1506,30533,1553],{"stretchy":1552},[1493,30535,1791],{},[1506,30537,1564],{"stretchy":1552},[1528,30539,30540],{"encoding":1530},"C(Y)",[1035,30542,30544],{"className":30543},[1480],[1482,30545,30546],{"xmlns":1484},[1487,30547,30548,30558],{},[1490,30549,30550,30552,30554,30556],{},[1493,30551,2662],{},[1506,30553,1553],{"stretchy":1552},[1493,30555,7740],{},[1506,30557,1564],{"stretchy":1552},[1528,30559,30560],{"encoding":1530},"I(r)"," a vyjádři vztah mezi ",[1035,30563,30565],{"className":30564},[1480],[1482,30566,30567],{"xmlns":1484},[1487,30568,30569,30573],{},[1490,30570,30571],{},[1493,30572,1791],{},[1528,30574,1791],{"encoding":1530},[1035,30576,30578],{"className":30577},[1480],[1482,30579,30580],{"xmlns":1484},[1487,30581,30582,30586],{},[1490,30583,30584],{},[1493,30585,7740],{},[1528,30587,7740],{"encoding":1530}," — dostaneš rovnici ",[1047,30590,28534],{},[1206,30592,30593,30596,30597,1586,30614,30631,30632,30588,30657,2632],{},[1047,30594,30595],{},"Z trhu peněz (7.15)"," dosaď ",[1035,30598,30600],{"className":30599},[1480],[1482,30601,30602],{"xmlns":1484},[1487,30603,30604,30612],{},[1490,30605,30606],{},[1497,30607,30608,30610],{},[1493,30609,1556],{},[1680,30611,1682],{},[1528,30613,29689],{"encoding":1530},[1035,30615,30617],{"className":30616},[1480],[1482,30618,30619],{"xmlns":1484},[1487,30620,30621,30629],{},[1490,30622,30623],{},[1497,30624,30625,30627],{},[1493,30626,1556],{},[1680,30628,1691],{},[1528,30630,29758],{"encoding":1530}," a vztah ",[1035,30633,30635],{"className":30634},[1480],[1482,30636,30637],{"xmlns":1484},[1487,30638,30639,30655],{},[1490,30640,30641,30647,30649],{},[2315,30642,30643,30645],{},[1493,30644,1495],{},[1493,30646,3712],{},[1506,30648,1508],{},[2315,30650,30651,30653],{},[1493,30652,1495],{},[1506,30654,2287],{},[1528,30656,29950],{"encoding":1530},[1047,30658,28541],{},[1206,30660,30661,30663,30664,1586,30677,30690,30691,30715],{},[1047,30662,17100],{}," dvou lineárních rovnic o dvou neznámých ",[1035,30665,30667],{"className":30666},[1480],[1482,30668,30669],{"xmlns":1484},[1487,30670,30671,30675],{},[1490,30672,30673],{},[1493,30674,1791],{},[1528,30676,1791],{"encoding":1530},[1035,30678,30680],{"className":30679},[1480],[1482,30681,30682],{"xmlns":1484},[1487,30683,30684,30688],{},[1490,30685,30686],{},[1493,30687,7740],{},[1528,30689,7740],{"encoding":1530}," — nejsnáze substituční metodou (vyjádři z IS ",[1035,30692,30694],{"className":30693},[1480],[1482,30695,30696],{"xmlns":1484},[1487,30697,30698,30712],{},[1490,30699,30700,30702,30704,30706,30708,30710],{},[1493,30701,1791],{},[1506,30703,1508],{},[1493,30705,12889],{},[1506,30707,1553],{"stretchy":1552},[1493,30709,7740],{},[1506,30711,1564],{"stretchy":1552},[1528,30713,30714],{"encoding":1530},"Y = f(r)"," a dosaď do LM).",[1206,30717,30718,1656,30721,1586,30755,2632],{},[1047,30719,30720],{},"Zpětně dopočítej",[1035,30722,30724],{"className":30723},[1480],[1482,30725,30726],{"xmlns":1484},[1487,30727,30728,30752],{},[1490,30729,30730,30736,30738,30740,30742,30748,30750],{},[2315,30731,30732,30734],{},[1493,30733,1998],{},[1493,30735,2711],{},[1506,30737,1508],{},[1493,30739,1052],{},[1988,30741,5016],{},[2315,30743,30744,30746],{},[1493,30745,1791],{},[1493,30747,2711],{},[1506,30749,2162],{},[1493,30751,2394],{},[1528,30753,30754],{"encoding":1530},"C^E = a\\,Y^E + b",[1035,30756,30758],{"className":30757},[1480],[1482,30759,30760],{"xmlns":1484},[1487,30761,30762,30786],{},[1490,30763,30764,30770,30772,30774,30776,30782,30784],{},[2315,30765,30766,30768],{},[1493,30767,2662],{},[1493,30769,2711],{},[1506,30771,1508],{},[1493,30773,8730],{},[1988,30775,5016],{},[2315,30777,30778,30780],{},[1493,30779,7740],{},[1493,30781,2711],{},[1506,30783,2162],{},[1493,30785,3384],{},[1528,30787,30788],{"encoding":1530},"I^E = c\\,r^E + d",[1206,30790,30791,30794,30795,30829,30830,30884],{},[1047,30792,30793],{},"Ověř:"," musí platit ",[1035,30796,30798],{"className":30797},[1480],[1482,30799,30800],{"xmlns":1484},[1487,30801,30802,30826],{},[1490,30803,30804,30810,30812,30818,30820],{},[2315,30805,30806,30808],{},[1493,30807,1791],{},[1493,30809,2711],{},[1506,30811,1508],{},[2315,30813,30814,30816],{},[1493,30815,1998],{},[1493,30817,2711],{},[1506,30819,2162],{},[2315,30821,30822,30824],{},[1493,30823,2662],{},[1493,30825,2711],{},[1528,30827,30828],{"encoding":1530},"Y^E = C^E + I^E"," (rovnováha trhu zboží) i ",[1035,30831,30833],{"className":30832},[1480],[1482,30834,30835],{"xmlns":1484},[1487,30836,30837,30881],{},[1490,30838,30839,30845,30847,30853,30859,30861,30867,30873,30875],{},[2315,30840,30841,30843],{},[1493,30842,1495],{},[1506,30844,2287],{},[1506,30846,1508],{},[1497,30848,30849,30851],{},[1493,30850,7100],{},[1680,30852,1682],{},[2315,30854,30855,30857],{},[1493,30856,1791],{},[1493,30858,2711],{},[1506,30860,2162],{},[1497,30862,30863,30865],{},[1493,30864,7100],{},[1680,30866,1691],{},[2315,30868,30869,30871],{},[1493,30870,7740],{},[1493,30872,2711],{},[1506,30874,2162],{},[1497,30876,30877,30879],{},[1493,30878,7100],{},[1680,30880,3201],{},[1528,30882,30883],{"encoding":1530},"M^* = k_1 Y^E + k_2 r^E + k_3"," (rovnováha trhu peněz).",[1065,30886,30888],{"id":30887},"příklad-76-is-lm","Příklad 7.6 (IS-LM)",[1030,30890,30891],{},"Pro trh zboží jsou dány:",[1203,30893,30894,30921],{},[1206,30895,30896,30897,1559],{},"spotřeba ",[1035,30898,30900],{"className":30899},[1480],[1482,30901,30902],{"xmlns":1484},[1487,30903,30904,30918],{},[1490,30905,30906,30908,30910,30912,30914,30916],{},[1493,30907,1998],{},[1506,30909,1508],{},[1680,30911,2939],{},[1493,30913,1791],{},[1506,30915,2162],{},[1680,30917,2916],{},[1528,30919,30920],{"encoding":1530},"C = 0{,}8Y + 100",[1206,30922,30923,30924,2632],{},"investice ",[1035,30925,30927],{"className":30926},[1480],[1482,30928,30929],{"xmlns":1484},[1487,30930,30931,30947],{},[1490,30932,30933,30935,30937,30939,30941,30943,30945],{},[1493,30934,2662],{},[1506,30936,1508],{},[1506,30938,1888],{},[1680,30940,8436],{},[1493,30942,7740],{},[1506,30944,2162],{},[1680,30946,1401],{},[1528,30948,30949],{"encoding":1530},"I = -20r + 1000",[1030,30951,30952],{},"Pro trh peněz:",[1203,30954,30955,30981,31013],{},[1206,30956,30957,1559],{},[1035,30958,30960],{"className":30959},[1480],[1482,30961,30962],{"xmlns":1484},[1487,30963,30964,30978],{},[1490,30965,30966,30972,30974,30976],{},[1497,30967,30968,30970],{},[1493,30969,1556],{},[1680,30971,1682],{},[1506,30973,1508],{},[1680,30975,13237],{},[1493,30977,1791],{},[1528,30979,30980],{"encoding":1530},"L_1 = 0{,}1Y",[1206,30982,30983,1559],{},[1035,30984,30986],{"className":30985},[1480],[1482,30987,30988],{"xmlns":1484},[1487,30989,30990,31010],{},[1490,30991,30992,30998,31000,31002,31004,31006,31008],{},[1497,30993,30994,30996],{},[1493,30995,1556],{},[1680,30997,1691],{},[1506,30999,1508],{},[1506,31001,1888],{},[1680,31003,2309],{},[1493,31005,7740],{},[1506,31007,2162],{},[1680,31009,8113],{},[1528,31011,31012],{"encoding":1530},"L_2 = -25r + 2000",[1206,31014,31015,31016,2632],{},"nabídka peněz ",[1035,31017,31019],{"className":31018},[1480],[1482,31020,31021],{"xmlns":1484},[1487,31022,31023,31036],{},[1490,31024,31025,31031,31033],{},[2315,31026,31027,31029],{},[1493,31028,1495],{},[1506,31030,2287],{},[1506,31032,1508],{},[1680,31034,31035],{},"2375",[1528,31037,31038],{"encoding":1530},"M^* = 2375",[1030,31040,31041,31044,31045,1274],{},[1047,31042,31043],{},"Funkce IS"," — dosazením do (7.13) ",[1035,31046,31048],{"className":31047},[1480],[1482,31049,31050],{"xmlns":1484},[1487,31051,31052,31064],{},[1490,31053,31054,31056,31058,31060,31062],{},[1493,31055,1791],{},[1506,31057,1508],{},[1493,31059,1998],{},[1506,31061,2162],{},[1493,31063,2662],{},[1528,31065,31066],{"encoding":1530},"Y = C + I",[1035,31068,31070],{"className":31069},[1480],[1482,31071,31072],{"xmlns":1484,"display":1485},[1487,31073,31074,31100],{},[1490,31075,31076,31078,31080,31082,31084,31086,31088,31090,31092,31094,31096,31098],{},[1493,31077,1791],{},[1506,31079,1508],{},[1680,31081,2939],{},[1493,31083,1791],{},[1506,31085,2162],{},[1680,31087,2916],{},[1506,31089,1888],{},[1680,31091,8436],{},[1493,31093,7740],{},[1506,31095,2162],{},[1680,31097,1401],{},[1506,31099,1559],{"separator":1041},[1528,31101,31102],{"encoding":1530},"Y = 0{,}8Y + 100 - 20r + 1000,",[1030,31104,31105],{},"tj.",[1035,31107,31109],{"className":31108},[1480],[1482,31110,31111],{"xmlns":1484,"display":1485},[1487,31112,31113,31138],{},[1490,31114,31115,31117,31119,31121,31123,31125,31127,31130,31132,31134,31136],{},[1680,31116,2929],{},[1493,31118,1791],{},[1506,31120,2162],{},[1680,31122,8436],{},[1493,31124,7740],{},[1506,31126,1508],{},[1680,31128,31129],{},"1100.",[1912,31131],{"width":1914},[1506,31133,1553],{"stretchy":1552},[1988,31135,28534],{},[1506,31137,1564],{"stretchy":1552},[1528,31139,31140],{"encoding":1530},"0{,}2Y + 20r = 1100. \\qquad (\\text{IS})",[1030,31142,31143,31146,31147,1274],{},[1047,31144,31145],{},"Funkce LM"," — dosazením do (7.15) ",[1035,31148,31150],{"className":31149},[1480],[1482,31151,31152],{"xmlns":1484},[1487,31153,31154,31178],{},[1490,31155,31156,31162,31164,31170,31172],{},[2315,31157,31158,31160],{},[1493,31159,1495],{},[1506,31161,2287],{},[1506,31163,1508],{},[1497,31165,31166,31168],{},[1493,31167,1556],{},[1680,31169,1682],{},[1506,31171,2162],{},[1497,31173,31174,31176],{},[1493,31175,1556],{},[1680,31177,1691],{},[1528,31179,31180],{"encoding":1530},"M^* = L_1 + L_2",[1035,31182,31184],{"className":31183},[1480],[1482,31185,31186],{"xmlns":1484,"display":1485},[1487,31187,31188,31210],{},[1490,31189,31190,31192,31194,31196,31198,31200,31202,31204,31206,31208],{},[1680,31191,31035],{},[1506,31193,1508],{},[1680,31195,13237],{},[1493,31197,1791],{},[1506,31199,1888],{},[1680,31201,2309],{},[1493,31203,7740],{},[1506,31205,2162],{},[1680,31207,8113],{},[1506,31209,1559],{"separator":1041},[1528,31211,31212],{"encoding":1530},"2375 = 0{,}1Y - 25r + 2000,",[1030,31214,31105],{},[1035,31216,31218],{"className":31217},[1480],[1482,31219,31220],{"xmlns":1484,"display":1485},[1487,31221,31222,31247],{},[1490,31223,31224,31226,31228,31230,31232,31234,31236,31239,31241,31243,31245],{},[1680,31225,13237],{},[1493,31227,1791],{},[1506,31229,1888],{},[1680,31231,2309],{},[1493,31233,7740],{},[1506,31235,1508],{},[1680,31237,31238],{},"375.",[1912,31240],{"width":1914},[1506,31242,1553],{"stretchy":1552},[1988,31244,28541],{},[1506,31246,1564],{"stretchy":1552},[1528,31248,31249],{"encoding":1530},"0{,}1Y - 25r = 375. \\qquad (\\text{LM})",[1030,31251,31252,31255,31256,31281],{},[1047,31253,31254],{},"Řešení soustavy."," Z (IS) vyjádříme ",[1035,31257,31259],{"className":31258},[1480],[1482,31260,31261],{"xmlns":1484},[1487,31262,31263,31278],{},[1490,31264,31265,31267,31269,31272,31274,31276],{},[1493,31266,1791],{},[1506,31268,1508],{},[1680,31270,31271],{},"5500",[1506,31273,1888],{},[1680,31275,2916],{},[1493,31277,7740],{},[1528,31279,31280],{"encoding":1530},"Y = 5500 - 100r"," a dosadíme do (LM):",[1035,31283,31285],{"className":31284},[1480],[1482,31286,31287],{"xmlns":1484,"display":1485},[1487,31288,31289,31373],{},[1490,31290,31291,31293,31295,31297,31299,31301,31303,31305,31307,31309,31311,31313,31316,31318,31320,31322,31325,31327,31329,31331,31333,31335,31337,31339,31341,31343,31345,31347,31349,31351,31353,31356,31358,31360,31362,31368,31370],{},[1680,31292,13237],{},[1506,31294,1553],{"stretchy":1552},[1680,31296,31271],{},[1506,31298,1888],{},[1680,31300,2916],{},[1493,31302,7740],{},[1506,31304,1564],{"stretchy":1552},[1506,31306,1888],{},[1680,31308,2309],{},[1493,31310,7740],{},[1506,31312,1508],{},[1680,31314,31315],{},"375",[1988,31317,1990],{},[1506,31319,2111],{},[1988,31321,1990],{},[1680,31323,31324],{},"550",[1506,31326,1888],{},[1680,31328,1775],{},[1493,31330,7740],{},[1506,31332,1888],{},[1680,31334,2309],{},[1493,31336,7740],{},[1506,31338,1508],{},[1680,31340,31315],{},[1988,31342,1990],{},[1506,31344,2111],{},[1988,31346,1990],{},[1680,31348,5603],{},[1493,31350,7740],{},[1506,31352,1508],{},[1680,31354,31355],{},"175",[1988,31357,1990],{},[1506,31359,2111],{},[1988,31361,1990],{},[2315,31363,31364,31366],{},[1493,31365,7740],{},[1493,31367,2711],{},[1506,31369,1508],{},[1680,31371,31372],{},"5.",[1528,31374,31375],{"encoding":1530},"0{,}1(5500 - 100r) - 25r = 375 \\;\\Longrightarrow\\; 550 - 10r - 25r = 375 \\;\\Longrightarrow\\; 35r = 175 \\;\\Longrightarrow\\; r^E = 5.",[1030,31377,31378],{},[1047,31379,31380],{},"Zpětné dosazení:",[1203,31382,31383,31427,31464],{},[1206,31384,31385,1559],{},[1035,31386,31388],{"className":31387},[1480],[1482,31389,31390],{"xmlns":1484},[1487,31391,31392,31424],{},[1490,31393,31394,31400,31402,31404,31406,31408,31410,31412,31414,31416,31418,31420,31422],{},[2315,31395,31396,31398],{},[1493,31397,1791],{},[1493,31399,2711],{},[1506,31401,1508],{},[1680,31403,31271],{},[1506,31405,1888],{},[1680,31407,2916],{},[1506,31409,1714],{},[1680,31411,1752],{},[1506,31413,1508],{},[1680,31415,31271],{},[1506,31417,1888],{},[1680,31419,1796],{},[1506,31421,1508],{},[1680,31423,5296],{},[1528,31425,31426],{"encoding":1530},"Y^E = 5500 - 100 \\cdot 5 = 5500 - 500 = 5000",[1206,31428,31429,1559],{},[1035,31430,31432],{"className":31431},[1480],[1482,31433,31434],{"xmlns":1484},[1487,31435,31436,31461],{},[1490,31437,31438,31444,31446,31448,31450,31452,31454,31456,31458],{},[2315,31439,31440,31442],{},[1493,31441,1998],{},[1493,31443,2711],{},[1506,31445,1508],{},[1680,31447,2939],{},[1506,31449,1714],{},[1680,31451,5296],{},[1506,31453,2162],{},[1680,31455,2916],{},[1506,31457,1508],{},[1680,31459,31460],{},"4100",[1528,31462,31463],{"encoding":1530},"C^E = 0{,}8 \\cdot 5000 + 100 = 4100",[1206,31465,31466,2632],{},[1035,31467,31469],{"className":31468},[1480],[1482,31470,31471],{"xmlns":1484},[1487,31472,31473,31499],{},[1490,31474,31475,31481,31483,31485,31487,31489,31491,31493,31495,31497],{},[2315,31476,31477,31479],{},[1493,31478,2662],{},[1493,31480,2711],{},[1506,31482,1508],{},[1506,31484,1888],{},[1680,31486,8436],{},[1506,31488,1714],{},[1680,31490,1752],{},[1506,31492,2162],{},[1680,31494,1401],{},[1506,31496,1508],{},[1680,31498,7032],{},[1528,31500,31501],{"encoding":1530},"I^E = -20 \\cdot 5 + 1000 = 900",[1030,31503,31504,1656,31507,31553],{},[1047,31505,31506],{},"Ověření:",[1035,31508,31510],{"className":31509},[1480],[1482,31511,31512],{"xmlns":1484},[1487,31513,31514,31550],{},[1490,31515,31516,31522,31524,31530,31532,31534,31536,31538,31540,31542,31544],{},[2315,31517,31518,31520],{},[1493,31519,1998],{},[1493,31521,2711],{},[1506,31523,2162],{},[2315,31525,31526,31528],{},[1493,31527,2662],{},[1493,31529,2711],{},[1506,31531,1508],{},[1680,31533,31460],{},[1506,31535,2162],{},[1680,31537,7032],{},[1506,31539,1508],{},[1680,31541,5296],{},[1506,31543,1508],{},[2315,31545,31546,31548],{},[1493,31547,1791],{},[1493,31549,2711],{},[1528,31551,31552],{"encoding":1530},"C^E + I^E = 4100 + 900 = 5000 = Y^E",". ✓",[1035,31555,31557],{"className":31556},[1480],[1482,31558,31559],{"xmlns":1484,"display":1485},[1487,31560,31561,31630],{},[1490,31562,31563],{},[1976,31564,31565],{"notation":1978},[1869,31566,31567],{"scriptlevel":1871,"displaystyle":1552},[1869,31568,31569],{"scriptlevel":1871,"displaystyle":1552},[1869,31570,31571],{"scriptlevel":1871,"displaystyle":1041},[1490,31572,31573,31575,31581,31583,31585,31587,31589,31595,31597,31599,31601,31603,31609,31611,31613,31615,31617,31623,31625,31628],{},[1988,31574,5016],{},[2315,31576,31577,31579],{},[1493,31578,1791],{},[1493,31580,2711],{},[1506,31582,1508],{},[1680,31584,5296],{},[1506,31586,1559],{"separator":1041},[1912,31588],{"width":2108},[2315,31590,31591,31593],{},[1493,31592,7740],{},[1493,31594,2711],{},[1506,31596,1508],{},[1680,31598,1752],{},[1506,31600,1559],{"separator":1041},[1912,31602],{"width":2108},[2315,31604,31605,31607],{},[1493,31606,1998],{},[1493,31608,2711],{},[1506,31610,1508],{},[1680,31612,31460],{},[1506,31614,1559],{"separator":1041},[1912,31616],{"width":2108},[2315,31618,31619,31621],{},[1493,31620,2662],{},[1493,31622,2711],{},[1506,31624,1508],{},[1680,31626,31627],{},"900.",[1988,31629,5016],{},[1528,31631,31632],{"encoding":1530},"\\boxed{\\,Y^E = 5000, \\quad r^E = 5, \\quad C^E = 4100, \\quad I^E = 900.\\,}",[1065,31634,31636],{"id":31635},"ekonomická-interpretace-fiskální-a-monetární-politika","Ekonomická interpretace — fiskální a monetární politika",[1030,31638,31639,31642,31643,31656,31657,22970,31670,31673,31674,31692,31693,31710,31711,31728,31729,31742,31743,31756],{},[1047,31640,31641],{},"Posun křivky IS (fiskální politika)."," Expanzivní fiskální politika — zvýšení vládních výdajů ",[1035,31644,31646],{"className":31645},[1480],[1482,31647,31648],{"xmlns":1484},[1487,31649,31650,31654],{},[1490,31651,31652],{},[1493,31653,28595],{},[1528,31655,28595],{"encoding":1530}," nebo snížení daní ",[1035,31658,31660],{"className":31659},[1480],[1482,31661,31662],{"xmlns":1484},[1487,31663,31664,31668],{},[1490,31665,31666],{},[1493,31667,5289],{},[1528,31669,5289],{"encoding":1530},[1047,31671,31672],{},"posouvá IS doprava",": při dané úrokové míře vzroste rovnovážný důchod trhu zboží. Nová rovnováha ",[1035,31675,31677],{"className":31676},[1480],[1482,31678,31679],{"xmlns":1484},[1487,31680,31681,31689],{},[1490,31682,31683],{},[2315,31684,31685,31687],{},[1493,31686,2711],{},[1506,31688,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,31690,31691],{"encoding":1530},"E'"," má vyšší ",[1035,31694,31696],{"className":31695},[1480],[1482,31697,31698],{"xmlns":1484},[1487,31699,31700,31708],{},[1490,31701,31702],{},[2315,31703,31704,31706],{},[1493,31705,1791],{},[1493,31707,2711],{},[1528,31709,3419],{"encoding":1530}," i vyšší ",[1035,31712,31714],{"className":31713},[1480],[1482,31715,31716],{"xmlns":1484},[1487,31717,31718,31726],{},[1490,31719,31720],{},[2315,31721,31722,31724],{},[1493,31723,7740],{},[1493,31725,2711],{},[1528,31727,30394],{"encoding":1530}," (vyšší ",[1035,31730,31732],{"className":31731},[1480],[1482,31733,31734],{"xmlns":1484},[1487,31735,31736,31740],{},[1490,31737,31738],{},[1493,31739,1791],{},[1528,31741,1791],{"encoding":1530}," zvedá poptávku po penězích, což tlačí ",[1035,31744,31746],{"className":31745},[1480],[1482,31747,31748],{"xmlns":1484},[1487,31749,31750,31754],{},[1490,31751,31752],{},[1493,31753,7740],{},[1528,31755,7740],{"encoding":1530}," nahoru).",[1030,31758,31759],{},[18014,31760],{"alt":31761,"className":31762,"src":31763},"imek-posun-is-lm-politiky",[1055,18018],"\u002Fwiki-assets\u002Fimek-posun-is-lm-politiky.jpeg",[1030,31765,31766,31769,31770,31787,31788,31791,31792,31809,31810,31827,31828,31841,31842,31861,31862,16623],{},[1047,31767,31768],{},"Posun křivky LM (monetární politika)."," Expanzivní monetární politika — zvýšení nabídky peněz ",[1035,31771,31773],{"className":31772},[1480],[1482,31774,31775],{"xmlns":1484},[1487,31776,31777,31785],{},[1490,31778,31779],{},[2315,31780,31781,31783],{},[1493,31782,1495],{},[1506,31784,2287],{},[1528,31786,28633],{"encoding":1530}," národní bankou — ",[1047,31789,31790],{},"posouvá LM doprava\u002Fdolů",": při daném důchodu je trh peněz v rovnováze při nižší úrokové míře. Nová rovnováha má nižší ",[1035,31793,31795],{"className":31794},[1480],[1482,31796,31797],{"xmlns":1484},[1487,31798,31799,31807],{},[1490,31800,31801],{},[2315,31802,31803,31805],{},[1493,31804,7740],{},[1493,31806,2711],{},[1528,31808,30394],{"encoding":1530}," a vyšší ",[1035,31811,31813],{"className":31812},[1480],[1482,31814,31815],{"xmlns":1484},[1487,31816,31817,31825],{},[1490,31818,31819],{},[2315,31820,31821,31823],{},[1493,31822,1791],{},[1493,31824,2711],{},[1528,31826,3419],{"encoding":1530}," (nižší ",[1035,31829,31831],{"className":31830},[1480],[1482,31832,31833],{"xmlns":1484},[1487,31834,31835,31839],{},[1490,31836,31837],{},[1493,31838,7740],{},[1528,31840,7740],{"encoding":1530}," povzbuzuje investice ",[1035,31843,31845],{"className":31844},[1480],[1482,31846,31847],{"xmlns":1484},[1487,31848,31849,31859],{},[1490,31850,31851,31853,31855,31857],{},[1493,31852,2662],{},[1506,31854,1553],{"stretchy":1552},[1493,31856,7740],{},[1506,31858,1564],{"stretchy":1552},[1528,31860,30560],{"encoding":1530},", ty zvedají ",[1035,31863,31865],{"className":31864},[1480],[1482,31866,31867],{"xmlns":1484},[1487,31868,31869,31873],{},[1490,31870,31871],{},[1493,31872,1791],{},[1528,31874,1791],{"encoding":1530},[1030,31876,31877,31878,31881],{},"IS-LM tak dává jednotný rámec pro diskusi ",[1047,31879,31880],{},"dopadu obou typů politik"," na důchod a úrokovou míru současně.",[1065,31883,31885],{"id":31884},"klíčové-pojmy","Klíčové pojmy",[1203,31887,31888,31960,32006,32088,32138,32205,32262,32303,32336],{},[1206,31889,31890,22970,31923,1732,31940,16351,31957,31959],{},[1047,31891,31892,31893],{},"Funkce investic ",[1035,31894,31896],{"className":31895},[1480],[1482,31897,31898],{"xmlns":1484},[1487,31899,31900,31920],{},[1490,31901,31902,31904,31906,31908,31910,31912,31914,31916,31918],{},[1493,31903,2662],{},[1506,31905,1553],{"stretchy":1552},[1493,31907,7740],{},[1506,31909,1564],{"stretchy":1552},[1506,31911,1508],{},[1493,31913,8730],{},[1493,31915,7740],{},[1506,31917,2162],{},[1493,31919,3384],{},[1528,31921,31922],{"encoding":1530},"I(r) = cr + d",[1035,31924,31926],{"className":31925},[1480],[1482,31927,31928],{"xmlns":1484},[1487,31929,31930,31938],{},[1490,31931,31932,31934,31936],{},[1493,31933,8730],{},[1506,31935,3961],{},[1680,31937,1871],{},[1528,31939,29000],{"encoding":1530},[1035,31941,31943],{"className":31942},[1480],[1482,31944,31945],{"xmlns":1484},[1487,31946,31947,31955],{},[1490,31948,31949,31951,31953],{},[1493,31950,3384],{},[1506,31952,2796],{},[1680,31954,1871],{},[1528,31956,28979],{"encoding":1530},[1047,31958,29004],{}," funkce úrokové míry.",[1206,31961,31962,31965,31966,31987,31988,32005],{},[1047,31963,31964],{},"Trh zboží"," — rovnováha ",[1035,31967,31969],{"className":31968},[1480],[1482,31970,31971],{"xmlns":1484},[1487,31972,31973,31985],{},[1490,31974,31975,31977,31979,31981,31983],{},[1493,31976,1791],{},[1506,31978,1508],{},[1493,31980,1998],{},[1506,31982,2162],{},[1493,31984,2662],{},[1528,31986,31066],{"encoding":1530},", ekvivalentně ",[1035,31989,31991],{"className":31990},[1480],[1482,31992,31993],{"xmlns":1484},[1487,31994,31995,32003],{},[1490,31996,31997,31999,32001],{},[1493,31998,2662],{},[1506,32000,1508],{},[1493,32002,2001],{},[1528,32004,29193],{"encoding":1530}," (investice = úspory).",[1206,32007,32008,7606,32011,32013,32014,32064,32065,29388,32067,2632],{},[1047,32009,32010],{},"Křivka IS",[1176,32012,28537],{},") — ",[1035,32015,32017],{"className":32016},[1480],[1482,32018,32019],{"xmlns":1484},[1487,32020,32021,32061],{},[1490,32022,32023,32025,32027,32039,32041,32043],{},[1493,32024,1791],{},[1506,32026,1508],{},[1510,32028,32029,32031],{},[1493,32030,8730],{},[1490,32032,32033,32035,32037],{},[1680,32034,1682],{},[1506,32036,1888],{},[1493,32038,1052],{},[1493,32040,7740],{},[1506,32042,2162],{},[1510,32044,32045,32053],{},[1490,32046,32047,32049,32051],{},[1493,32048,2394],{},[1506,32050,2162],{},[1493,32052,3384],{},[1490,32054,32055,32057,32059],{},[1680,32056,1682],{},[1506,32058,1888],{},[1493,32060,1052],{},[1528,32062,32063],{"encoding":1530},"Y = \\frac{c}{1-a}r + \\frac{b+d}{1-a}"," (7.14); ",[1047,32066,29004],{},[1035,32068,32070],{"className":32069},[1480],[1482,32071,32072],{"xmlns":1484},[1487,32073,32074,32086],{},[1490,32075,32076,32078,32080,32082,32084],{},[1506,32077,1553],{"stretchy":1552},[1493,32079,7740],{},[1506,32081,1559],{"separator":1041},[1493,32083,1791],{},[1506,32085,1564],{"stretchy":1552},[1528,32087,29410],{"encoding":1530},[1206,32089,32090,31965,32093,32119,32120,2632],{},[1047,32091,32092],{},"Trh peněz",[1035,32094,32096],{"className":32095},[1480],[1482,32097,32098],{"xmlns":1484},[1487,32099,32100,32116],{},[1490,32101,32102,32108,32110],{},[2315,32103,32104,32106],{},[1493,32105,1495],{},[1493,32107,3712],{},[1506,32109,1508],{},[2315,32111,32112,32114],{},[1493,32113,1495],{},[1493,32115,2001],{},[1528,32117,32118],{"encoding":1530},"M^D = M^S"," při pevné nabídce ",[1035,32121,32123],{"className":32122},[1480],[1482,32124,32125],{"xmlns":1484},[1487,32126,32127,32135],{},[1490,32128,32129],{},[2315,32130,32131,32133],{},[1493,32132,1495],{},[1506,32134,2287],{},[1528,32136,32137],{"encoding":1530},"M^* ",[1206,32139,32140,22970,32143,2632],{},[1047,32141,32142],{},"Transakční, opatrnostní, spekulační poptávka",[1035,32144,32146],{"className":32145},[1480],[1482,32147,32148],{"xmlns":1484},[1487,32149,32150,32202],{},[1490,32151,32152,32158,32160,32166,32168,32174,32176,32182,32184,32186,32192,32194,32196],{},[2315,32153,32154,32156],{},[1493,32155,1495],{},[1493,32157,3712],{},[1506,32159,1508],{},[1497,32161,32162,32164],{},[1493,32163,1556],{},[1680,32165,1682],{},[1506,32167,2162],{},[1497,32169,32170,32172],{},[1493,32171,1556],{},[1680,32173,1691],{},[1506,32175,1508],{},[1497,32177,32178,32180],{},[1493,32179,7100],{},[1680,32181,1682],{},[1493,32183,1791],{},[1506,32185,2162],{},[1497,32187,32188,32190],{},[1493,32189,7100],{},[1680,32191,1691],{},[1493,32193,7740],{},[1506,32195,2162],{},[1497,32197,32198,32200],{},[1493,32199,7100],{},[1680,32201,3201],{},[1528,32203,32204],{"encoding":1530},"M^D = L_1 + L_2 = k_1 Y + k_2 r + k_3",[1206,32206,32207,7606,32210,32013,32212,32258,32259,32261],{},[1047,32208,32209],{},"Křivka LM",[1176,32211,28544],{},[1035,32213,32215],{"className":32214},[1480],[1482,32216,32217],{"xmlns":1484},[1487,32218,32219,32255],{},[1490,32220,32221,32227,32229,32235,32237,32239,32245,32247,32249],{},[2315,32222,32223,32225],{},[1493,32224,1495],{},[1506,32226,2287],{},[1506,32228,1508],{},[1497,32230,32231,32233],{},[1493,32232,7100],{},[1680,32234,1682],{},[1493,32236,1791],{},[1506,32238,2162],{},[1497,32240,32241,32243],{},[1493,32242,7100],{},[1680,32244,1691],{},[1493,32246,7740],{},[1506,32248,2162],{},[1497,32250,32251,32253],{},[1493,32252,7100],{},[1680,32254,3201],{},[1528,32256,32257],{"encoding":1530},"M^* = k_1 Y + k_2 r + k_3"," (7.15); ",[1047,32260,3482],{}," přímka.",[1206,32263,32264,32267,32268,32302],{},[1047,32265,32266],{},"Simultánní rovnováha"," — průsečík ",[1035,32269,32271],{"className":32270},[1480],[1482,32272,32273],{"xmlns":1484},[1487,32274,32275,32299],{},[1490,32276,32277,32279,32281,32283,32289,32291,32297],{},[1493,32278,2711],{},[1506,32280,1508],{},[1506,32282,1553],{"stretchy":1552},[2315,32284,32285,32287],{},[1493,32286,7740],{},[1493,32288,2711],{},[1506,32290,1559],{"separator":1041},[2315,32292,32293,32295],{},[1493,32294,1791],{},[1493,32296,2711],{},[1506,32298,1564],{"stretchy":1552},[1528,32300,32301],{"encoding":1530},"E = (r^E, Y^E)"," křivek IS a LM.",[1206,32304,32305,32308,32309,1732,32322,32335],{},[1047,32306,32307],{},"Fiskální politika"," — nástroje ",[1035,32310,32312],{"className":32311},[1480],[1482,32313,32314],{"xmlns":1484},[1487,32315,32316,32320],{},[1490,32317,32318],{},[1493,32319,28595],{},[1528,32321,28595],{"encoding":1530},[1035,32323,32325],{"className":32324},[1480],[1482,32326,32327],{"xmlns":1484},[1487,32328,32329,32333],{},[1490,32330,32331],{},[1493,32332,5289],{},[1528,32334,5289],{"encoding":1530}," posouvající křivku IS.",[1206,32337,32338,32341,32342,32359],{},[1047,32339,32340],{},"Monetární politika"," — nástroj ",[1035,32343,32345],{"className":32344},[1480],[1482,32346,32347],{"xmlns":1484},[1487,32348,32349,32357],{},[1490,32350,32351],{},[2315,32352,32353,32355],{},[1493,32354,1495],{},[1506,32356,2287],{},[1528,32358,28633],{"encoding":1530}," posouvající křivku LM.",[1065,32361,17159],{"id":17158},[1203,32363,32364,32371,32380,32389],{},[1206,32365,32366,1656,32368],{},[1047,32367,17176],{},[1052,32369,1058],{"className":32370,"dataFsResolvedFilePath":1056,"href":1057},[1055],[1206,32372,32373,1656,32376],{},[1047,32374,32375],{},"Přednáška:",[1052,32377,32379],{"className":32378,"dataFsResolvedFilePath":17200,"href":17201},[1055],"imek-blok-03",[1206,32381,32382,1656,32385,32388],{},[1047,32383,32384],{},"Nadřazené téma:",[1052,32386,265],{"className":32387,"dataFsResolvedFilePath":2622,"href":2623},[1055]," — makroekonomické modely C-I, C-I-G, C-I-G-X a úvod do IS-LM",[1206,32390,32391,32394],{},[1047,32392,32393],{},"Související:",[1203,32395,32396,32402,32408],{},[1206,32397,32398,32401],{},[1052,32399,132],{"className":32400,"dataFsResolvedFilePath":3487,"href":3488},[1055]," — paralela rovnovážného bodu (průsečík dvou křivek) v mikroekonomii",[1206,32403,32404,32407],{},[1052,32405,102],{"className":32406,"dataFsResolvedFilePath":16621,"href":16622},[1055]," — matematický základ pro směrnice IS a LM",[1206,32409,32410,32414],{},[1052,32411,32413],{"className":32412,"dataFsResolvedFilePath":9470,"href":9471},[1055],"funkce-vice-promennych"," — dvě neznámé a řešení lineárních soustav",{"title":17269,"searchDepth":141,"depth":141,"links":32416},[32417,32418,32419,32420,32421,32422,32423,32424,32425,32426],{"id":28491,"depth":141,"text":1042},{"id":28643,"depth":141,"text":28644},{"id":28862,"depth":141,"text":28863},{"id":29149,"depth":141,"text":29150},{"id":29560,"depth":141,"text":29561},{"id":30345,"depth":141,"text":30346},{"id":30887,"depth":141,"text":30888},{"id":31635,"depth":141,"text":31636},{"id":31884,"depth":141,"text":31885},{"id":17158,"depth":141,"text":17159},{},"\u002Ftopics\u002Fis-lm",{"title":28483,"description":17269},[26098,32431],"raw\u002Fimek\u002FKS_treti_blok.pdf","topics\u002Fis-lm",[9,112,53,938,934,948,598,265],"ZLkDw0RUM5SbYxrSxuRFrkzFpNPS26FNOXZXfijtFB4",{"id":32436,"title":32437,"body":32438,"course":17424,"courses":34020,"created":19266,"description":34021,"extension":17426,"meta":34022,"navigation":17428,"path":34023,"seo":34024,"sources":34025,"stem":34026,"tags":34027,"type":19275,"updated":19276,"__hash__":34028},"topics\u002Ftopics\u002Flagrangeova-metoda.md","Lagrangeova metoda (vázané extrémy)",{"type":1016,"value":32439,"toc":34008},[32440,32443,32539,32546,32566,32570,32575,32636,32655,32657,32660,32708,32756,32794,32796,33004,33038,33175,33179,33241,33257,33285,33289,33387,33391,33395,33448,33552,33766,33770,33813,33917,33968,33970],[1019,32441,32437],{"id":32442},"lagrangeova-metoda-vázané-extrémy",[1030,32444,32445,32446,19330,32469,32501,32502,32505,32506,32533,32534,32538],{},"Hledáme extrém funkce ",[1035,32447,32449],{"className":32448},[1480],[1482,32450,32451],{"xmlns":1484},[1487,32452,32453,32467],{},[1490,32454,32455,32457,32459,32461,32463,32465],{},[1493,32456,12889],{},[1506,32458,1553],{"stretchy":1552},[1493,32460,17494],{},[1506,32462,1559],{"separator":1041},[1493,32464,3052],{},[1506,32466,1564],{"stretchy":1552},[1528,32468,26373],{"encoding":1530},[1035,32470,32472],{"className":32471},[1480],[1482,32473,32474],{"xmlns":1484},[1487,32475,32476,32498],{},[1490,32477,32478,32480,32482,32488,32490,32496],{},[1493,32479,1668],{},[1506,32481,1553],{"stretchy":1552},[1497,32483,32484,32486],{},[1493,32485,1520],{},[1680,32487,1682],{},[1506,32489,1559],{"separator":1041},[1497,32491,32492,32494],{},[1493,32493,1520],{},[1680,32495,1691],{},[1506,32497,1564],{"stretchy":1552},[1528,32499,32500],{"encoding":1530},"U(Q_1, Q_2)"," apod.) ",[1047,32503,32504],{},"podmíněný"," rovnicí ",[1035,32507,32509],{"className":32508},[1480],[1482,32510,32511],{"xmlns":1484},[1487,32512,32513,32531],{},[1490,32514,32515,32517,32519,32521,32523,32525,32527,32529],{},[1493,32516,27556],{},[1506,32518,1553],{"stretchy":1552},[1493,32520,17494],{},[1506,32522,1559],{"separator":1041},[1493,32524,3052],{},[1506,32526,1564],{"stretchy":1552},[1506,32528,1508],{},[1680,32530,1871],{},[1528,32532,27573],{"encoding":1530},". V ",[1052,32535,32537],{"className":32536,"dataFsResolvedFilePath":1056,"href":1057},[1055],"matematické ekonomii"," se používá pro:",[1030,32540,32541],{},[18014,32542],{"alt":32543,"className":32544,"src":32545},"imek-lagrange-tecnost",[1055,18018],"\u002Fwiki-assets\u002Fimek-lagrange-tecnost.jpeg",[1203,32547,32548,32557,32563],{},[1206,32549,32550,32553,32554,1564],{},[1047,32551,32552],{},"Maximalizaci užitečnosti"," při rozpočtovém omezení (viz ",[1052,32555,93],{"className":32556,"dataFsResolvedFilePath":6613,"href":6614},[1055],[1206,32558,32559,32562],{},[1047,32560,32561],{},"Minimalizaci výdajů"," při dané úrovni užitečnosti (duální úloha)",[1206,32564,32565],{},"Optimalizaci produkce \u002F nákladů za omezení",[1065,32567,32569],{"id":32568},"princip","Princip",[1030,32571,27224,32572,1274],{},[1047,32573,32574],{},"Lagrangeovu funkci",[1035,32576,32578],{"className":32577},[1480],[1482,32579,32580],{"xmlns":1484,"display":1485},[1487,32581,32582,32633],{},[1490,32583,32584,32586,32588,32590,32592,32594,32596,32599,32601,32603,32605,32607,32609,32611,32613,32615,32617,32619,32621,32623,32625,32627,32629,32631],{},[1493,32585,1556],{},[1506,32587,1553],{"stretchy":1552},[1493,32589,17494],{},[1506,32591,1559],{"separator":1041},[1493,32593,3052],{},[1506,32595,1559],{"separator":1041},[1493,32597,32598],{},"λ",[1506,32600,1564],{"stretchy":1552},[1506,32602,1508],{},[1493,32604,12889],{},[1506,32606,1553],{"stretchy":1552},[1493,32608,17494],{},[1506,32610,1559],{"separator":1041},[1493,32612,3052],{},[1506,32614,1564],{"stretchy":1552},[1506,32616,2162],{},[1493,32618,32598],{},[1988,32620,5016],{},[1493,32622,27556],{},[1506,32624,1553],{"stretchy":1552},[1493,32626,17494],{},[1506,32628,1559],{"separator":1041},[1493,32630,3052],{},[1506,32632,1564],{"stretchy":1552},[1528,32634,32635],{"encoding":1530},"L(x, y, \\lambda) = f(x, y) + \\lambda\\, g(x, y)",[1030,32637,20022,32638,8994,32652,2632],{},[1035,32639,32641],{"className":32640},[1480],[1482,32642,32643],{"xmlns":1484},[1487,32644,32645,32649],{},[1490,32646,32647],{},[1493,32648,32598],{},[1528,32650,32651],{"encoding":1530},"\\lambda",[1047,32653,32654],{},"Lagrangeův multiplikátor",[1065,32656,18677],{"id":18676},[1030,32658,32659],{},"Řešíme soustavu:",[1035,32661,32663],{"className":32662},[1480],[1482,32664,32665],{"xmlns":1484,"display":1485},[1487,32666,32667,32705],{},[1490,32668,32669,32677,32679,32687,32689,32691,32693,32701,32703],{},[1697,32670,32671,32673,32675],{},[1493,32672,1556],{},[1493,32674,17494],{},[1506,32676,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,32678,1508],{},[1697,32680,32681,32683,32685],{},[1493,32682,12889],{},[1493,32684,17494],{},[1506,32686,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,32688,2162],{},[1493,32690,32598],{},[1988,32692,5016],{},[1697,32694,32695,32697,32699],{},[1493,32696,27556],{},[1493,32698,17494],{},[1506,32700,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,32702,1508],{},[1680,32704,1871],{},[1528,32706,32707],{"encoding":1530},"L'_x = f'_x + \\lambda\\, g'_x = 0",[1035,32709,32711],{"className":32710},[1480],[1482,32712,32713],{"xmlns":1484,"display":1485},[1487,32714,32715,32753],{},[1490,32716,32717,32725,32727,32735,32737,32739,32741,32749,32751],{},[1697,32718,32719,32721,32723],{},[1493,32720,1556],{},[1493,32722,3052],{},[1506,32724,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,32726,1508],{},[1697,32728,32729,32731,32733],{},[1493,32730,12889],{},[1493,32732,3052],{},[1506,32734,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,32736,2162],{},[1493,32738,32598],{},[1988,32740,5016],{},[1697,32742,32743,32745,32747],{},[1493,32744,27556],{},[1493,32746,3052],{},[1506,32748,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,32750,1508],{},[1680,32752,1871],{},[1528,32754,32755],{"encoding":1530},"L'_y = f'_y + \\lambda\\, g'_y = 0",[1035,32757,32759],{"className":32758},[1480],[1482,32760,32761],{"xmlns":1484,"display":1485},[1487,32762,32763,32791],{},[1490,32764,32765,32773,32775,32777,32779,32781,32783,32785,32787,32789],{},[1697,32766,32767,32769,32771],{},[1493,32768,1556],{},[1493,32770,32598],{},[1506,32772,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,32774,1508],{},[1493,32776,27556],{},[1506,32778,1553],{"stretchy":1552},[1493,32780,17494],{},[1506,32782,1559],{"separator":1041},[1493,32784,3052],{},[1506,32786,1564],{"stretchy":1552},[1506,32788,1508],{},[1680,32790,1871],{},[1528,32792,32793],{"encoding":1530},"L'_\\lambda = g(x, y) = 0",[1065,32795,18751],{"id":18750},[1035,32797,32799],{"className":32798},[1480],[1482,32800,32801],{"xmlns":1484,"display":1485},[1487,32802,32803,33001],{},[1490,32804,32805,32807,32809,32811,32813,32815,32817,32819,32821,32823,32825,32841,32843,32845,32861,32863,32865,32873,32879,32881,32883,32899,32901,32903,32919,32921,32923,32931,32937,32939,32941,32943,32959,32961,32963,32979,32981,32983,32991,32993],{},[1493,32806,3712],{},[1506,32808,1553],{"stretchy":1552},[1493,32810,17494],{},[1506,32812,1559],{"separator":1041},[1493,32814,3052],{},[1506,32816,1559],{"separator":1041},[1493,32818,32598],{},[1506,32820,1564],{"stretchy":1552},[1506,32822,1508],{},[1506,32824,1553],{"stretchy":1552},[1697,32826,32827,32829,32835],{},[1493,32828,12889],{},[1490,32830,32831,32833],{},[1493,32832,17494],{},[1493,32834,17494],{},[1490,32836,32837,32839],{},[1506,32838,6927],{"mathvariant":1516},[1506,32840,6927],{"mathvariant":1516},[1506,32842,2162],{},[1493,32844,32598],{},[1697,32846,32847,32849,32855],{},[1493,32848,27556],{},[1490,32850,32851,32853],{},[1493,32852,17494],{},[1493,32854,17494],{},[1490,32856,32857,32859],{},[1506,32858,6927],{"mathvariant":1516},[1506,32860,6927],{"mathvariant":1516},[1506,32862,1564],{"stretchy":1552},[1506,32864,1553],{"stretchy":1552},[1697,32866,32867,32869,32871],{},[1493,32868,27556],{},[1493,32870,3052],{},[1506,32872,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[2315,32874,32875,32877],{},[1506,32876,1564],{"stretchy":1552},[1680,32878,1691],{},[1506,32880,2162],{},[1506,32882,1553],{"stretchy":1552},[1697,32884,32885,32887,32893],{},[1493,32886,12889],{},[1490,32888,32889,32891],{},[1493,32890,3052],{},[1493,32892,3052],{},[1490,32894,32895,32897],{},[1506,32896,6927],{"mathvariant":1516},[1506,32898,6927],{"mathvariant":1516},[1506,32900,2162],{},[1493,32902,32598],{},[1697,32904,32905,32907,32913],{},[1493,32906,27556],{},[1490,32908,32909,32911],{},[1493,32910,3052],{},[1493,32912,3052],{},[1490,32914,32915,32917],{},[1506,32916,6927],{"mathvariant":1516},[1506,32918,6927],{"mathvariant":1516},[1506,32920,1564],{"stretchy":1552},[1506,32922,1553],{"stretchy":1552},[1697,32924,32925,32927,32929],{},[1493,32926,27556],{},[1493,32928,17494],{},[1506,32930,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[2315,32932,32933,32935],{},[1506,32934,1564],{"stretchy":1552},[1680,32936,1691],{},[1506,32938,1888],{},[1680,32940,1691],{},[1506,32942,1553],{"stretchy":1552},[1697,32944,32945,32947,32953],{},[1493,32946,12889],{},[1490,32948,32949,32951],{},[1493,32950,17494],{},[1493,32952,3052],{},[1490,32954,32955,32957],{},[1506,32956,6927],{"mathvariant":1516},[1506,32958,6927],{"mathvariant":1516},[1506,32960,2162],{},[1493,32962,32598],{},[1697,32964,32965,32967,32973],{},[1493,32966,27556],{},[1490,32968,32969,32971],{},[1493,32970,17494],{},[1493,32972,3052],{},[1490,32974,32975,32977],{},[1506,32976,6927],{"mathvariant":1516},[1506,32978,6927],{"mathvariant":1516},[1506,32980,1564],{"stretchy":1552},[1988,32982,5016],{},[1697,32984,32985,32987,32989],{},[1493,32986,27556],{},[1493,32988,17494],{},[1506,32990,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1988,32992,5016],{},[1697,32994,32995,32997,32999],{},[1493,32996,27556],{},[1493,32998,3052],{},[1506,33000,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,33002,33003],{"encoding":1530},"D(x, y, \\lambda) = (f''_{xx} + \\lambda g''_{xx})(g'_y)^2 + (f''_{yy} + \\lambda g''_{yy})(g'_x)^2 - 2(f''_{xy} + \\lambda g''_{xy})\\, g'_x\\, g'_y",[1030,33005,33006,33007,33037],{},"Je-li ",[1035,33008,33010],{"className":33009},[1480],[1482,33011,33012],{"xmlns":1484},[1487,33013,33014,33034],{},[1490,33015,33016,33018,33020,33022,33024,33026,33032],{},[1506,33017,14314],{"stretchy":1552},[1493,33019,1052],{},[1506,33021,1559],{"separator":1041},[1493,33023,2394],{},[1506,33025,1559],{"separator":1041},[1497,33027,33028,33030],{},[1493,33029,32598],{},[1680,33031,1871],{},[1506,33033,14323],{"stretchy":1552},[1528,33035,33036],{"encoding":1530},"[a, b, \\lambda_0]"," podezřelý bod:",[1203,33039,33040,33108],{},[1206,33041,33042,18838,33078,33080,33081],{},[1035,33043,33045],{"className":33044},[1480],[1482,33046,33047],{"xmlns":1484},[1487,33048,33049,33075],{},[1490,33050,33051,33053,33055,33057,33059,33061,33063,33069,33071,33073],{},[1493,33052,3712],{},[1506,33054,1553],{"stretchy":1552},[1493,33056,1052],{},[1506,33058,1559],{"separator":1041},[1493,33060,2394],{},[1506,33062,1559],{"separator":1041},[1497,33064,33065,33067],{},[1493,33066,32598],{},[1680,33068,1871],{},[1506,33070,1564],{"stretchy":1552},[1506,33072,3961],{},[1680,33074,1871],{},[1528,33076,33077],{"encoding":1530},"D(a, b, \\lambda_0) \u003C 0",[1047,33079,9982],{}," vázané podmínkou ",[1035,33082,33084],{"className":33083},[1480],[1482,33085,33086],{"xmlns":1484},[1487,33087,33088,33106],{},[1490,33089,33090,33092,33094,33096,33098,33100,33102,33104],{},[1493,33091,27556],{},[1506,33093,1553],{"stretchy":1552},[1493,33095,17494],{},[1506,33097,1559],{"separator":1041},[1493,33099,3052],{},[1506,33101,1564],{"stretchy":1552},[1506,33103,1508],{},[1680,33105,1871],{},[1528,33107,27573],{"encoding":1530},[1206,33109,33110,18838,33146,33080,33148],{},[1035,33111,33113],{"className":33112},[1480],[1482,33114,33115],{"xmlns":1484},[1487,33116,33117,33143],{},[1490,33118,33119,33121,33123,33125,33127,33129,33131,33137,33139,33141],{},[1493,33120,3712],{},[1506,33122,1553],{"stretchy":1552},[1493,33124,1052],{},[1506,33126,1559],{"separator":1041},[1493,33128,2394],{},[1506,33130,1559],{"separator":1041},[1497,33132,33133,33135],{},[1493,33134,32598],{},[1680,33136,1871],{},[1506,33138,1564],{"stretchy":1552},[1506,33140,2796],{},[1680,33142,1871],{},[1528,33144,33145],{"encoding":1530},"D(a, b, \\lambda_0) > 0",[1047,33147,19195],{},[1035,33149,33151],{"className":33150},[1480],[1482,33152,33153],{"xmlns":1484},[1487,33154,33155,33173],{},[1490,33156,33157,33159,33161,33163,33165,33167,33169,33171],{},[1493,33158,27556],{},[1506,33160,1553],{"stretchy":1552},[1493,33162,17494],{},[1506,33164,1559],{"separator":1041},[1493,33166,3052],{},[1506,33168,1564],{"stretchy":1552},[1506,33170,1508],{},[1680,33172,1871],{},[1528,33174,27573],{"encoding":1530},[1065,33176,33178],{"id":33177},"význam-multiplikátoru","Význam multiplikátoru",[1035,33180,33182],{"className":33181},[1480],[1482,33183,33184],{"xmlns":1484,"display":1485},[1487,33185,33186,33238],{},[1490,33187,33188,33190,33192,33214,33216],{},[1493,33189,32598],{},[1506,33191,1508],{},[1510,33193,33194,33202],{},[1697,33195,33196,33198,33200],{},[1493,33197,12889],{},[1493,33199,17494],{},[1506,33201,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1490,33203,33204,33206],{},[1506,33205,1888],{},[1697,33207,33208,33210,33212],{},[1493,33209,27556],{},[1493,33211,17494],{},[1506,33213,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,33215,1508],{},[1510,33217,33218,33226],{},[1697,33219,33220,33222,33224],{},[1493,33221,12889],{},[1493,33223,3052],{},[1506,33225,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1490,33227,33228,33230],{},[1506,33229,1888],{},[1697,33231,33232,33234,33236],{},[1493,33233,27556],{},[1493,33235,3052],{},[1506,33237,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,33239,33240],{"encoding":1530},"\\lambda = \\frac{f'_x}{-g'_x} = \\frac{f'_y}{-g'_y}",[1030,33242,33243,33256],{},[1035,33244,33246],{"className":33245},[1480],[1482,33247,33248],{"xmlns":1484},[1487,33249,33250,33254],{},[1490,33251,33252],{},[1493,33253,32598],{},[1528,33255,32651],{"encoding":1530}," udává:",[1203,33258,33259,33265],{},[1206,33260,33261,33262],{},"konstantní ",[1047,33263,33264],{},"poměr mezi mezním prospěchem a mezním nákladem",[1206,33266,33267,33270,33271,33284],{},[1047,33268,33269],{},"náklady příležitosti"," (opportunity cost) — o kolik vzroste optimální hodnota ",[1035,33272,33274],{"className":33273},[1480],[1482,33275,33276],{"xmlns":1484},[1487,33277,33278,33282],{},[1490,33279,33280],{},[1493,33281,12889],{},[1528,33283,12889],{"encoding":1530},", uvolní-li se omezení o jednotku",[1065,33286,33288],{"id":33287},"alternativní-postup","Alternativní postup",[1030,33290,33291,33292,33319,33320,33344,33345,33369,33370,33383,33384,2632],{},"Lze-li z ",[1035,33293,33295],{"className":33294},[1480],[1482,33296,33297],{"xmlns":1484},[1487,33298,33299,33317],{},[1490,33300,33301,33303,33305,33307,33309,33311,33313,33315],{},[1493,33302,27556],{},[1506,33304,1553],{"stretchy":1552},[1493,33306,17494],{},[1506,33308,1559],{"separator":1041},[1493,33310,3052],{},[1506,33312,1564],{"stretchy":1552},[1506,33314,1508],{},[1680,33316,1871],{},[1528,33318,27573],{"encoding":1530}," vyjádřit ",[1035,33321,33323],{"className":33322},[1480],[1482,33324,33325],{"xmlns":1484},[1487,33326,33327,33341],{},[1490,33328,33329,33331,33333,33335,33337,33339],{},[1493,33330,3052],{},[1506,33332,1508],{},[1493,33334,3052],{},[1506,33336,1553],{"stretchy":1552},[1493,33338,17494],{},[1506,33340,1564],{"stretchy":1552},[1528,33342,33343],{"encoding":1530},"y = y(x)"," (nebo ",[1035,33346,33348],{"className":33347},[1480],[1482,33349,33350],{"xmlns":1484},[1487,33351,33352,33366],{},[1490,33353,33354,33356,33358,33360,33362,33364],{},[1493,33355,17494],{},[1506,33357,1508],{},[1493,33359,17494],{},[1506,33361,1553],{"stretchy":1552},[1493,33363,3052],{},[1506,33365,1564],{"stretchy":1552},[1528,33367,33368],{"encoding":1530},"x = x(y)","), dosadíme do ",[1035,33371,33373],{"className":33372},[1480],[1482,33374,33375],{"xmlns":1484},[1487,33376,33377,33381],{},[1490,33378,33379],{},[1493,33380,12889],{},[1528,33382,12889],{"encoding":1530}," a převedeme na ",[1047,33385,33386],{},"extrém funkce jedné proměnné",[1065,33388,33390],{"id":33389},"použití-v-imek","Použití v ImeK",[1304,33392,33394],{"id":33393},"maximalizace-užitečnosti","Maximalizace užitečnosti",[1030,33396,33397,33398,2632],{},"Rozpočtové omezení: ",[1035,33399,33401],{"className":33400},[1480],[1482,33402,33403],{"xmlns":1484},[1487,33404,33405,33445],{},[1490,33406,33407,33413,33415,33423,33429,33431,33439],{},[2315,33408,33409,33411],{},[1493,33410,1791],{},[1506,33412,2287],{},[1506,33414,1508],{},[1697,33416,33417,33419,33421],{},[1493,33418,1501],{},[1680,33420,1682],{},[1506,33422,2287],{},[1497,33424,33425,33427],{},[1493,33426,1520],{},[1680,33428,1682],{},[1506,33430,2162],{},[1697,33432,33433,33435,33437],{},[1493,33434,1501],{},[1680,33436,1691],{},[1506,33438,2287],{},[1497,33440,33441,33443],{},[1493,33442,1520],{},[1680,33444,1691],{},[1528,33446,33447],{"encoding":1530},"Y^* = P_1^* Q_1 + P_2^* Q_2",[1035,33449,33451],{"className":33450},[1480],[1482,33452,33453],{"xmlns":1484,"display":1485},[1487,33454,33455,33549],{},[1490,33456,33457,33459,33461,33467,33469,33475,33477,33479,33481,33483,33485,33487,33493,33495,33501,33503,33505,33507,33509,33515,33517,33525,33531,33533,33541,33547],{},[1493,33458,1556],{},[1506,33460,1553],{"stretchy":1552},[1497,33462,33463,33465],{},[1493,33464,1520],{},[1680,33466,1682],{},[1506,33468,1559],{"separator":1041},[1497,33470,33471,33473],{},[1493,33472,1520],{},[1680,33474,1691],{},[1506,33476,1559],{"separator":1041},[1493,33478,32598],{},[1506,33480,1564],{"stretchy":1552},[1506,33482,1508],{},[1493,33484,1668],{},[1506,33486,1553],{"stretchy":1552},[1497,33488,33489,33491],{},[1493,33490,1520],{},[1680,33492,1682],{},[1506,33494,1559],{"separator":1041},[1497,33496,33497,33499],{},[1493,33498,1520],{},[1680,33500,1691],{},[1506,33502,1564],{"stretchy":1552},[1506,33504,2162],{},[1493,33506,32598],{},[1506,33508,1553],{"stretchy":1552},[2315,33510,33511,33513],{},[1493,33512,1791],{},[1506,33514,2287],{},[1506,33516,1888],{},[1697,33518,33519,33521,33523],{},[1493,33520,1501],{},[1680,33522,1682],{},[1506,33524,2287],{},[1497,33526,33527,33529],{},[1493,33528,1520],{},[1680,33530,1682],{},[1506,33532,1888],{},[1697,33534,33535,33537,33539],{},[1493,33536,1501],{},[1680,33538,1691],{},[1506,33540,2287],{},[1497,33542,33543,33545],{},[1493,33544,1520],{},[1680,33546,1691],{},[1506,33548,1564],{"stretchy":1552},[1528,33550,33551],{"encoding":1530},"L(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda (Y^* - P_1^* Q_1 - P_2^* Q_2)",[1030,33553,33554,33555,1732,33587,1732,33619,33668,33669,33723,33724,2632],{},"Soustava: ",[1035,33556,33558],{"className":33557},[1480],[1482,33559,33560],{"xmlns":1484},[1487,33561,33562,33584],{},[1490,33563,33564,33572,33574,33576],{},[1697,33565,33566,33568,33570],{},[1493,33567,1668],{},[1680,33569,1682],{},[1506,33571,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,33573,1508],{},[1493,33575,32598],{},[1697,33577,33578,33580,33582],{},[1493,33579,1501],{},[1680,33581,1682],{},[1506,33583,2287],{},[1528,33585,33586],{"encoding":1530},"U'_1 = \\lambda P_1^*",[1035,33588,33590],{"className":33589},[1480],[1482,33591,33592],{"xmlns":1484},[1487,33593,33594,33616],{},[1490,33595,33596,33604,33606,33608],{},[1697,33597,33598,33600,33602],{},[1493,33599,1668],{},[1680,33601,1691],{},[1506,33603,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,33605,1508],{},[1493,33607,32598],{},[1697,33609,33610,33612,33614],{},[1493,33611,1501],{},[1680,33613,1691],{},[1506,33615,2287],{},[1528,33617,33618],{"encoding":1530},"U'_2 = \\lambda P_2^*",[1035,33620,33622],{"className":33621},[1480],[1482,33623,33624],{"xmlns":1484},[1487,33625,33626,33666],{},[1490,33627,33628,33634,33636,33644,33650,33652,33660],{},[2315,33629,33630,33632],{},[1493,33631,1791],{},[1506,33633,2287],{},[1506,33635,1508],{},[1697,33637,33638,33640,33642],{},[1493,33639,1501],{},[1680,33641,1682],{},[1506,33643,2287],{},[1497,33645,33646,33648],{},[1493,33647,1520],{},[1680,33649,1682],{},[1506,33651,2162],{},[1697,33653,33654,33656,33658],{},[1493,33655,1501],{},[1680,33657,1691],{},[1506,33659,2287],{},[1497,33661,33662,33664],{},[1493,33663,1520],{},[1680,33665,1691],{},[1528,33667,33447],{"encoding":1530},". Z prvních dvou: ",[1035,33670,33672],{"className":33671},[1480],[1482,33673,33674],{"xmlns":1484},[1487,33675,33676,33720],{},[1490,33677,33678,33698,33700],{},[1869,33679,33680],{"scriptlevel":1871,"displaystyle":1552},[1510,33681,33682,33690],{},[1697,33683,33684,33686,33688],{},[1493,33685,1668],{},[1680,33687,1682],{},[1506,33689,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1697,33691,33692,33694,33696],{},[1493,33693,1668],{},[1680,33695,1691],{},[1506,33697,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,33699,1508],{},[1869,33701,33702],{"scriptlevel":1871,"displaystyle":1552},[1510,33703,33704,33712],{},[1697,33705,33706,33708,33710],{},[1493,33707,1501],{},[1680,33709,1682],{},[1506,33711,2287],{},[1697,33713,33714,33716,33718],{},[1493,33715,1501],{},[1680,33717,1691],{},[1506,33719,2287],{},[1528,33721,33722],{"encoding":1530},"\\tfrac{U'_1}{U'_2} = \\tfrac{P_1^*}{P_2^*}",", tj. ",[1035,33725,33727],{"className":33726},[1480],[1482,33728,33729],{"xmlns":1484},[1487,33730,33731,33763],{},[1490,33732,33733,33735,33737,33739,33741,33743],{},[1493,33734,1495],{},[1493,33736,1995],{},[1493,33738,1998],{},[1493,33740,2001],{},[1506,33742,1508],{},[1869,33744,33745],{"scriptlevel":1871,"displaystyle":1552},[1510,33746,33747,33755],{},[1697,33748,33749,33751,33753],{},[1493,33750,1501],{},[1680,33752,1682],{},[1506,33754,2287],{},[1697,33756,33757,33759,33761],{},[1493,33758,1501],{},[1680,33760,1691],{},[1506,33762,2287],{},[1528,33764,33765],{"encoding":1530},"MRCS = \\tfrac{P_1^*}{P_2^*}",[1304,33767,33769],{"id":33768},"minimalizace-výdajů","Minimalizace výdajů",[1030,33771,33772,33773,2632],{},"Podmínka dané užitečnosti ",[1035,33774,33776],{"className":33775},[1480],[1482,33777,33778],{"xmlns":1484},[1487,33779,33780,33810],{},[1490,33781,33782,33788,33790,33792,33794,33800,33802,33808],{},[2315,33783,33784,33786],{},[1493,33785,1668],{},[1506,33787,2287],{},[1506,33789,1508],{},[1493,33791,1668],{},[1506,33793,1553],{"stretchy":1552},[1497,33795,33796,33798],{},[1493,33797,1520],{},[1680,33799,1682],{},[1506,33801,1559],{"separator":1041},[1497,33803,33804,33806],{},[1493,33805,1520],{},[1680,33807,1691],{},[1506,33809,1564],{"stretchy":1552},[1528,33811,33812],{"encoding":1530},"U^* = U(Q_1, Q_2)",[1035,33814,33816],{"className":33815},[1480],[1482,33817,33818],{"xmlns":1484,"display":1485},[1487,33819,33820,33914],{},[1490,33821,33822,33824,33826,33832,33834,33840,33842,33844,33846,33848,33856,33862,33864,33872,33878,33880,33882,33884,33890,33892,33894,33896,33902,33904,33910,33912],{},[1493,33823,1556],{},[1506,33825,1553],{"stretchy":1552},[1497,33827,33828,33830],{},[1493,33829,1520],{},[1680,33831,1682],{},[1506,33833,1559],{"separator":1041},[1497,33835,33836,33838],{},[1493,33837,1520],{},[1680,33839,1691],{},[1506,33841,1559],{"separator":1041},[1493,33843,32598],{},[1506,33845,1564],{"stretchy":1552},[1506,33847,1508],{},[1697,33849,33850,33852,33854],{},[1493,33851,1501],{},[1680,33853,1682],{},[1506,33855,2287],{},[1497,33857,33858,33860],{},[1493,33859,1520],{},[1680,33861,1682],{},[1506,33863,2162],{},[1697,33865,33866,33868,33870],{},[1493,33867,1501],{},[1680,33869,1691],{},[1506,33871,2287],{},[1497,33873,33874,33876],{},[1493,33875,1520],{},[1680,33877,1691],{},[1506,33879,2162],{},[1493,33881,32598],{},[1506,33883,1553],{"stretchy":1552},[2315,33885,33886,33888],{},[1493,33887,1668],{},[1506,33889,2287],{},[1506,33891,1888],{},[1493,33893,1668],{},[1506,33895,1553],{"stretchy":1552},[1497,33897,33898,33900],{},[1493,33899,1520],{},[1680,33901,1682],{},[1506,33903,1559],{"separator":1041},[1497,33905,33906,33908],{},[1493,33907,1520],{},[1680,33909,1691],{},[1506,33911,1564],{"stretchy":1552},[1506,33913,1564],{"stretchy":1552},[1528,33915,33916],{"encoding":1530},"L(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda (U^* - U(Q_1, Q_2))",[1030,33918,33919,33920,2632],{},"Duálně dostaneme Hicksovy poptávkové funkce ",[1035,33921,33923],{"className":33922},[1480],[1482,33924,33925],{"xmlns":1484},[1487,33926,33927,33965],{},[1490,33928,33929,33935,33937,33943,33945,33951,33953,33959,33961,33963],{},[1497,33930,33931,33933],{},[1493,33932,1520],{},[1493,33934,6277],{},[1506,33936,1508],{},[1497,33938,33939,33941],{},[1493,33940,3712],{},[1493,33942,6277],{},[1506,33944,1553],{"stretchy":1552},[1497,33946,33947,33949],{},[1493,33948,1501],{},[1680,33950,1682],{},[1506,33952,1559],{"separator":1041},[1497,33954,33955,33957],{},[1493,33956,1501],{},[1680,33958,1691],{},[1506,33960,1559],{"separator":1041},[1493,33962,1668],{},[1506,33964,1564],{"stretchy":1552},[1528,33966,33967],{"encoding":1530},"Q_i = D_i(P_1, P_2, U)",[1065,33969,17159],{"id":17158},[1203,33971,33972,33979,33986,33995],{},[1206,33973,33974,1656,33976],{},[1047,33975,19217],{},[1052,33977,9472],{"className":33978,"dataFsResolvedFilePath":9470,"href":9471},[1055],[1206,33980,33981,1656,33983],{},[1047,33982,19228],{},[1052,33984,17211],{"className":33985,"dataFsResolvedFilePath":3487,"href":3488},[1055],[1206,33987,33988,1656,33991,33994],{},[1047,33989,33990],{},"Aplikace v kurzu:",[1052,33992,6615],{"className":33993,"dataFsResolvedFilePath":6613,"href":6614},[1055]," (maximalizace užitečnosti při rozpočtovém omezení), minimalizace výdajů (duální úloha), optimalizace produkce",[1206,33996,33997,1656,33999,1732,34002,34007],{},[1047,33998,19236],{},[1052,34000,2624],{"className":34001,"dataFsResolvedFilePath":2622,"href":2623},[1055],[1052,34003,1135],{"className":34004,"dataFsResolvedFilePath":34005,"href":34006},[1055],"topics\u002Foptimalizace.md","\u002Fwiki\u002Foptimalizace"," (IpmrK)",{"title":17269,"searchDepth":141,"depth":141,"links":34009},[34010,34011,34012,34013,34014,34015,34019],{"id":32568,"depth":141,"text":32569},{"id":18676,"depth":141,"text":18677},{"id":18750,"depth":141,"text":18751},{"id":33177,"depth":141,"text":33178},{"id":33287,"depth":141,"text":33288},{"id":33389,"depth":141,"text":33390,"children":34016},[34017,34018],{"id":33393,"depth":96,"text":33394},{"id":33768,"depth":96,"text":33769},{"id":17158,"depth":141,"text":17159},[9,17],"Hledáme extrém funkce f(x,y)f(x, y) (resp. U(Q1,Q2)U(Q_1, Q_2) apod.) podmíněný rovnicí g(x,y)=0g(x, y) = 0. V matematické ekonomii se používá pro:",{},"\u002Ftopics\u002Flagrangeova-metoda",{"title":32437,"description":34021},[19272,32431],"topics\u002Flagrangeova-metoda",[9,45,954,126],"tPjF8YA54Yn63DF17Ti0HGb0p393jTEIilMbA173OpA",{"id":34030,"title":2624,"body":34031,"course":9,"courses":17424,"created":26093,"description":17269,"extension":17426,"meta":43324,"navigation":17428,"path":43325,"seo":43326,"sources":43327,"stem":43328,"tags":43329,"type":19275,"updated":26102,"__hash__":43330},"topics\u002Ftopics\u002Fnarodni-duchod.md",{"type":1016,"value":34032,"toc":43286},[34033,34036,34038,34160,34299,34303,34306,34419,34423,34451,34496,34499,34565,34610,34613,34637,34668,34671,34675,34719,34761,34823,34876,34879,34883,34886,34931,35027,35033,35108,35137,35141,35169,35216,35305,35309,35335,35371,35397,35433,35495,35568,35647,35705,35769,35812,35816,35873,35920,35963,36176,36296,36302,36306,36329,36333,36340,36344,36375,36408,36412,36462,36545,36587,36608,36670,36728,36732,36803,36869,36941,36989,36993,36996,37037,37074,37097,37211,37380,37388,37413,37443,37446,37523,37674,37758,38100,38104,38227,38361,38497,38548,38551,38800,38880,38884,38887,38945,38975,38978,39025,39028,39099,39293,39297,39446,39674,39712,39763,39806,39809,39863,39911,40115,40205,40209,40225,40232,40401,40405,40476,40554,40631,40708,40860,40947,40951,41134,41265,41310,41407,41411,42150,42152,43203,43205],[1019,34034,2624],{"id":34035},"národní-důchod",[1065,34037,1042],{"id":28491},[1030,34039,34040,34041,1656,34045,34048,34049,1656,34052,34065,34066,34068,34069,34072,34073,34076,34077,34079,34080,1656,34082,34099,34100,34117,34118,34121,34122,16623],{},"Kapitola 7 ",[1052,34042,34044],{"className":34043,"dataFsResolvedFilePath":1056,"href":1057},[1055],"Matematické ekonomie",[1047,34046,34047],{},"přechází z mikroekonomie do makroekonomie",": předmětem zkoumání už není jedna firma, ale celá národní ekonomika popsaná ",[1047,34050,34051],{},"národním důchodem",[1035,34053,34055],{"className":34054},[1480],[1482,34056,34057],{"xmlns":1484},[1487,34058,34059,34063],{},[1490,34060,34061],{},[1493,34062,1791],{},[1528,34064,1791],{"encoding":1530},". Budují se postupně bohatší modely — ",[1047,34067,16500],{}," (jen spotřeba a investice) → ",[1047,34070,34071],{},"C-I-G"," (přidá vládu a zdanění) → ",[1047,34074,34075],{},"C-I-G-X"," (otevře ekonomiku o čistý export) → ",[1047,34078,16530],{}," (propojí trh zboží s trhem peněz přes úrokovou míru). V každém modelu hledáme ",[1047,34081,30356],{},[1035,34083,34085],{"className":34084},[1480],[1482,34086,34087],{"xmlns":1484},[1487,34088,34089,34097],{},[1490,34090,34091],{},[2315,34092,34093,34095],{},[1493,34094,1791],{},[1493,34096,2711],{},[1528,34098,3419],{"encoding":1530}," jako řešení soustavy lineárních rovnic; citlivost ",[1035,34101,34103],{"className":34102},[1480],[1482,34104,34105],{"xmlns":1484},[1487,34106,34107,34115],{},[1490,34108,34109],{},[2315,34110,34111,34113],{},[1493,34112,1791],{},[1493,34114,2711],{},[1528,34116,3419],{"encoding":1530}," na exogenní veličiny popisují ",[1047,34119,34120],{},"multiplikátory"," (zejména Keynesův multiplikátor investic ",[1035,34123,34125],{"className":34124},[1480],[1482,34126,34127],{"xmlns":1484},[1487,34128,34129,34157],{},[1490,34130,34131,34133,34135,34137,34139,34141,34143,34145,34147,34149,34151,34153,34155],{},[1680,34132,1682],{},[1493,34134,1709],{"mathvariant":1516},[1506,34136,1553],{"stretchy":1552},[1680,34138,1682],{},[1506,34140,1888],{},[1493,34142,1052],{},[1506,34144,1564],{"stretchy":1552},[1506,34146,1508],{},[1680,34148,1682],{},[1493,34150,1709],{"mathvariant":1516},[1493,34152,1495],{},[1493,34154,1501],{},[1493,34156,2001],{},[1528,34158,34159],{"encoding":1530},"1\u002F(1-a) = 1\u002FMPS",[1023,34161,34163,34169],{"className":34162,"dataCallout":582},[1026,1186],[1030,34164,34166,6749],{"className":34165},[1033],[1035,34167],{"className":34168,"ariaHidden":1041},[1038,1193,1040],[1030,34170,34171,34174,34175,34193,34194,34224,34225,34272,34273,34275,34276,34298],{},[1047,34172,34173],{},"Makroekonomie je zrcadlovým obrazem mikroekonomie"," na úrovni celé ekonomiky. Mezní sklon ke spotřebě ",[1035,34176,34178],{"className":34177},[1480],[1482,34179,34180],{"xmlns":1484},[1487,34181,34182,34190],{},[1490,34183,34184,34186,34188],{},[1493,34185,1495],{},[1493,34187,1501],{},[1493,34189,1998],{},[1528,34191,34192],{"encoding":1530},"MPC"," je „ta část dodatečné korunky důchodu, kterou domácnost utratí“; zbytek ",[1035,34195,34197],{"className":34196},[1480],[1482,34198,34199],{"xmlns":1484},[1487,34200,34201,34221],{},[1490,34202,34203,34205,34207,34209,34211,34213,34215,34217,34219],{},[1493,34204,1495],{},[1493,34206,1501],{},[1493,34208,2001],{},[1506,34210,1508],{},[1680,34212,1682],{},[1506,34214,1888],{},[1493,34216,1495],{},[1493,34218,1501],{},[1493,34220,1998],{},[1528,34222,34223],{"encoding":1530},"MPS = 1 - MPC"," jde na úspory. Keynesův multiplikátor vyjadřuje, že jedna koruna navíc v investicích zvedne důchod o víc než korunu — utracená koruna se stane něčím důchodem, ten z ní část utratí, atd. (geometrická řada ",[1035,34226,34228],{"className":34227},[1480],[1482,34229,34230],{"xmlns":1484},[1487,34231,34232,34269],{},[1490,34233,34234,34236,34238,34240,34242,34248,34250,34253,34255,34257,34259,34261,34263,34265,34267],{},[1680,34235,1682],{},[1506,34237,2162],{},[1493,34239,1052],{},[1506,34241,2162],{},[2315,34243,34244,34246],{},[1493,34245,1052],{},[1680,34247,1691],{},[1506,34249,2162],{},[1506,34251,34252],{},"⋯",[1506,34254,1508],{},[1680,34256,1682],{},[1493,34258,1709],{"mathvariant":1516},[1506,34260,1553],{"stretchy":1552},[1680,34262,1682],{},[1506,34264,1888],{},[1493,34266,1052],{},[1506,34268,1564],{"stretchy":1552},[1528,34270,34271],{"encoding":1530},"1 + a + a^2 + \\dots = 1\u002F(1-a)","). ",[1047,34274,16530],{}," popisuje dva trhy zároveň: IS je rovnováha na trhu zboží (investice = úspory), LM je rovnováha na trhu peněz (poptávka = nabídka); společný bod určuje, při jakém páru ",[1035,34277,34279],{"className":34278},[1480],[1482,34280,34281],{"xmlns":1484},[1487,34282,34283,34295],{},[1490,34284,34285,34287,34289,34291,34293],{},[1506,34286,1553],{"stretchy":1552},[1493,34288,1791],{},[1506,34290,1559],{"separator":1041},[1493,34292,7740],{},[1506,34294,1564],{"stretchy":1552},[1528,34296,34297],{"encoding":1530},"(Y, r)"," jsou oba trhy v rovnováze současně.",[1065,34300,34302],{"id":34301},"úvod-cílové-znalosti-kapitoly-7","Úvod — cílové znalosti kapitoly 7",[1030,34304,34305],{},"Po prostudování kapitoly by čtenář měl umět:",[1203,34307,34308,34311,34314,34317,34320,34323,34326,34416],{},[1206,34309,34310],{},"popsat zjednodušený model národní ekonomiky,",[1206,34312,34313],{},"formulovat pojmy funkcí spotřeby a úspor spolu s jejich základními vlastnostmi,",[1206,34315,34316],{},"popsat lineární model spotřeby a úspor,",[1206,34318,34319],{},"stanovit mezní sklony ke spotřebě a úsporám,",[1206,34321,34322],{},"vymezit pojem makroekonomické rovnováhy ve vztahu k agregátní poptávce a nabídce,",[1206,34324,34325],{},"vyložit pojmy křivek agregátní poptávky, agregátní nabídky a rovnovážného bodu,",[1206,34327,34328,34329,1732,34346,1732,34368,1586,34393,34415],{},"popsat modely ",[1035,34330,34332],{"className":34331},[1480],[1482,34333,34334],{"xmlns":1484},[1487,34335,34336,34344],{},[1490,34337,34338,34340,34342],{},[1493,34339,1998],{},[1988,34341,28777],{},[1493,34343,2662],{},[1528,34345,28782],{"encoding":1530},[1035,34347,34349],{"className":34348},[1480],[1482,34350,34351],{"xmlns":1484},[1487,34352,34353,34365],{},[1490,34354,34355,34357,34359,34361,34363],{},[1493,34356,1998],{},[1988,34358,28777],{},[1493,34360,2662],{},[1988,34362,28777],{},[1493,34364,28595],{},[1528,34366,34367],{"encoding":1530},"C\\text{-}I\\text{-}G",[1035,34369,34371],{"className":34370},[1480],[1482,34372,34373],{"xmlns":1484},[1487,34374,34375,34391],{},[1490,34376,34377,34379,34381,34383,34385,34387,34389],{},[1493,34378,1998],{},[1988,34380,28777],{},[1493,34382,2662],{},[1988,34384,28777],{},[1493,34386,28595],{},[1988,34388,28777],{},[1493,34390,28807],{},[1528,34392,28810],{"encoding":1530},[1035,34394,34396],{"className":34395},[1480],[1482,34397,34398],{"xmlns":1484},[1487,34399,34400,34412],{},[1490,34401,34402,34404,34406,34408,34410],{},[1493,34403,2662],{},[1493,34405,2001],{},[1988,34407,28777],{},[1493,34409,1556],{},[1493,34411,1495],{},[1528,34413,34414],{"encoding":1530},"IS\\text{-}LM"," národních ekonomik a vypočítat rovnovážné veličiny,",[1206,34417,34418],{},"formulovat a stanovit základní makroekonomické multiplikátory.",[1065,34420,34422],{"id":34421},"gnp-a-národní-důchod","GNP a národní důchod",[1030,34424,34425,1656,34428,7606,34447,34450],{},[1047,34426,34427],{},"Hrubý národní produkt",[1035,34429,34431],{"className":34430},[1480],[1482,34432,34433],{"xmlns":1484},[1487,34434,34435,34444],{},[1490,34436,34437,34439,34442],{},[1493,34438,28595],{},[1493,34440,34441],{},"N",[1493,34443,1501],{},[1528,34445,34446],{"encoding":1530},"GNP",[1176,34448,34449],{},"gross national product",") vyjadřuje hodnotu (v peněžních jednotkách) finálních statků a služeb vytvořených ekonomikou během daného období (obvykle jednoho roku). Je základním ukazatelem výkonnosti národní ekonomiky:",[1035,34452,34454],{"className":34453},[1480],[1482,34455,34456],{"xmlns":1484,"display":1485},[1487,34457,34458,34493],{},[1490,34459,34460,34462,34464,34466,34468,34470,34472,34474,34476,34478,34480,34482,34484,34486,34488,34491],{},[1493,34461,28595],{},[1493,34463,34441],{},[1493,34465,1501],{},[1506,34467,1508],{},[1493,34469,1998],{},[1506,34471,2162],{},[1493,34473,2662],{},[1506,34475,2162],{},[1493,34477,28595],{},[1506,34479,2162],{},[1493,34481,28807],{},[1506,34483,1559],{"separator":1041},[1912,34485],{"width":1914},[1506,34487,1553],{"stretchy":1552},[1680,34489,34490],{},"7.1",[1506,34492,1564],{"stretchy":1552},[1528,34494,34495],{"encoding":1530},"GNP = C + I + G + X, \\qquad (7.1)",[1030,34497,34498],{},"kde",[1203,34500,34501,34517,34533,34549],{},[1206,34502,34503,34516],{},[1035,34504,34506],{"className":34505},[1480],[1482,34507,34508],{"xmlns":1484},[1487,34509,34510,34514],{},[1490,34511,34512],{},[1493,34513,1998],{},[1528,34515,1998],{"encoding":1530}," — výdaje domácností na spotřebu,",[1206,34518,34519,34532],{},[1035,34520,34522],{"className":34521},[1480],[1482,34523,34524],{"xmlns":1484},[1487,34525,34526,34530],{},[1490,34527,34528],{},[1493,34529,2662],{},[1528,34531,2662],{"encoding":1530}," — hrubé domácí investice,",[1206,34534,34535,34548],{},[1035,34536,34538],{"className":34537},[1480],[1482,34539,34540],{"xmlns":1484},[1487,34541,34542,34546],{},[1490,34543,34544],{},[1493,34545,28595],{},[1528,34547,28595],{"encoding":1530}," — vládní výdaje,",[1206,34550,34551,34564],{},[1035,34552,34554],{"className":34553},[1480],[1482,34555,34556],{"xmlns":1484},[1487,34557,34558,34562],{},[1490,34559,34560],{},[1493,34561,28807],{},[1528,34563,28807],{"encoding":1530}," — čistý export.",[1030,34566,34567,34568,34585,34586,34589,34590,1656,34593,7606,34606,34609],{},"K měření ",[1035,34569,34571],{"className":34570},[1480],[1482,34572,34573],{"xmlns":1484},[1487,34574,34575,34583],{},[1490,34576,34577,34579,34581],{},[1493,34578,28595],{},[1493,34580,34441],{},[1493,34582,1501],{},[1528,34584,34446],{"encoding":1530}," se užívá ",[1047,34587,34588],{},"důchodová metoda",". Jejím hlavním konstrukčním prvkem je ",[1047,34591,34592],{},"národní důchod",[1035,34594,34596],{"className":34595},[1480],[1482,34597,34598],{"xmlns":1484},[1487,34599,34600,34604],{},[1490,34601,34602],{},[1493,34603,1791],{},[1528,34605,1791],{"encoding":1530},[1176,34607,34608],{},"national income",") — součet důchodů všech vrstev domácností, tj. tok důchodů od firem k domácnostem jako platba za pronájem výrobních faktorů.",[1030,34611,34612],{},"Pro tvorbu základních makroekonomických modelů se zjednodušeně ztotožňuje hrubý národní produkt s národním důchodem (rovněž s agregátní poptávkou):",[1035,34614,34616],{"className":34615},[1480],[1482,34617,34618],{"xmlns":1484,"display":1485},[1487,34619,34620,34634],{},[1490,34621,34622,34624,34626,34628,34630,34632],{},[1493,34623,28595],{},[1493,34625,34441],{},[1493,34627,1501],{},[1506,34629,2343],{},[1493,34631,1791],{},[1506,34633,1559],{"separator":1041},[1528,34635,34636],{"encoding":1530},"GNP \\approx Y,",[1030,34638,34639,34640,7606,34643,34646,34647,34660,34661,34664,34665,2632],{},"a užívá se společného názvu ",[1047,34641,34642],{},"důchod",[1176,34644,34645],{},"income",") s označením ",[1035,34648,34650],{"className":34649},[1480],[1482,34651,34652],{"xmlns":1484},[1487,34653,34654,34658],{},[1490,34655,34656],{},[1493,34657,1791],{},[1528,34659,1791],{"encoding":1530},". Domácnosti důchod použijí ke ",[1047,34662,34663],{},"spotřebě"," zboží a služeb nebo ke tvorbě ",[1047,34666,34667],{},"úspor",[1065,34669,13676],{"id":34670},"spotřeba-a-úspory",[1304,34672,34674],{"id":34673},"funkce-spotřeby-a-úspor","Funkce spotřeby a úspor",[1030,34676,34677,34678,34691,34692,34705,34706,1274],{},"Jak spotřeba ",[1035,34679,34681],{"className":34680},[1480],[1482,34682,34683],{"xmlns":1484},[1487,34684,34685,34689],{},[1490,34686,34687],{},[1493,34688,1998],{},[1528,34690,1998],{"encoding":1530},", tak úspory ",[1035,34693,34695],{"className":34694},[1480],[1482,34696,34697],{"xmlns":1484},[1487,34698,34699,34703],{},[1490,34700,34701],{},[1493,34702,2001],{},[1528,34704,2001],{"encoding":1530}," závisejí na důchodu ",[1035,34707,34709],{"className":34708},[1480],[1482,34710,34711],{"xmlns":1484},[1487,34712,34713,34717],{},[1490,34714,34715],{},[1493,34716,1791],{},[1528,34718,1791],{"encoding":1530},[1035,34720,34722],{"className":34721},[1480],[1482,34723,34724],{"xmlns":1484,"display":1485},[1487,34725,34726,34758],{},[1490,34727,34728,34730,34732,34734,34736,34738,34740,34742,34744,34746,34748,34750,34752,34754,34756],{},[1493,34729,1998],{},[1506,34731,1508],{},[1493,34733,1998],{},[1506,34735,1553],{"stretchy":1552},[1493,34737,1791],{},[1506,34739,1564],{"stretchy":1552},[1506,34741,1559],{"separator":1041},[1912,34743],{"width":1914},[1493,34745,2001],{},[1506,34747,1508],{},[1493,34749,2001],{},[1506,34751,1553],{"stretchy":1552},[1493,34753,1791],{},[1506,34755,1564],{"stretchy":1552},[1493,34757,2632],{"mathvariant":1516},[1528,34759,34760],{"encoding":1530},"C = C(Y), \\qquad S = S(Y).",[1030,34762,34763,8994,34782,7606,34785,34788,34789,8994,34809,7606,34812,34815,34816,1586,34819,34822],{},[1035,34764,34766],{"className":34765},[1480],[1482,34767,34768],{"xmlns":1484},[1487,34769,34770,34780],{},[1490,34771,34772,34774,34776,34778],{},[1493,34773,1998],{},[1506,34775,1553],{"stretchy":1552},[1493,34777,1791],{},[1506,34779,1564],{"stretchy":1552},[1528,34781,30540],{"encoding":1530},[1047,34783,34784],{},"funkce spotřeby",[1176,34786,34787],{},"consumption function","), ",[1035,34790,34792],{"className":34791},[1480],[1482,34793,34794],{"xmlns":1484},[1487,34795,34796,34806],{},[1490,34797,34798,34800,34802,34804],{},[1493,34799,2001],{},[1506,34801,1553],{"stretchy":1552},[1493,34803,1791],{},[1506,34805,1564],{"stretchy":1552},[1528,34807,34808],{"encoding":1530},"S(Y)",[1047,34810,34811],{},"funkce úspor",[1176,34813,34814],{},"savings function","); jejich grafy se nazývají ",[1047,34817,34818],{},"křivka spotřeby",[1047,34820,34821],{},"křivka úspor",". Platí základní identita",[1035,34824,34826],{"className":34825},[1480],[1482,34827,34828],{"xmlns":1484,"display":1485},[1487,34829,34830,34873],{},[1490,34831,34832,34834,34836,34838,34840,34842,34844,34846,34848,34850,34852,34854,34856,34858,34860,34862,34864,34866,34868,34871],{},[1493,34833,1791],{},[1506,34835,1508],{},[1493,34837,1998],{},[1506,34839,2162],{},[1493,34841,2001],{},[1506,34843,1508],{},[1493,34845,1998],{},[1506,34847,1553],{"stretchy":1552},[1493,34849,1791],{},[1506,34851,1564],{"stretchy":1552},[1506,34853,2162],{},[1493,34855,2001],{},[1506,34857,1553],{"stretchy":1552},[1493,34859,1791],{},[1506,34861,1564],{"stretchy":1552},[1493,34863,2632],{"mathvariant":1516},[1912,34865],{"width":1914},[1506,34867,1553],{"stretchy":1552},[1680,34869,34870],{},"7.2",[1506,34872,1564],{"stretchy":1552},[1528,34874,34875],{"encoding":1530},"Y = C + S = C(Y) + S(Y). \\qquad (7.2)",[1030,34877,34878],{},"Známe-li jednu z funkcí, je tím určena i druhá. Obě funkce jsou rostoucí (s růstem důchodu roste spotřeba i úspory).",[1304,34880,34882],{"id":34881},"lineární-model-spotřeby-a-úspor","Lineární model spotřeby a úspor",[1030,34884,34885],{},"Nejjednodušší model předpokládá lineární tvar",[1035,34887,34889],{"className":34888},[1480],[1482,34890,34891],{"xmlns":1484,"display":1485},[1487,34892,34893,34928],{},[1490,34894,34895,34897,34899,34901,34903,34905,34907,34909,34911,34913,34915,34917,34919,34921,34923,34926],{},[1493,34896,1998],{},[1506,34898,1508],{},[1493,34900,1998],{},[1506,34902,1553],{"stretchy":1552},[1493,34904,1791],{},[1506,34906,1564],{"stretchy":1552},[1506,34908,1508],{},[1493,34910,1052],{},[1493,34912,1791],{},[1506,34914,2162],{},[1493,34916,2394],{},[1506,34918,1559],{"separator":1041},[1912,34920],{"width":1914},[1506,34922,1553],{"stretchy":1552},[1680,34924,34925],{},"7.3",[1506,34927,1564],{"stretchy":1552},[1528,34929,34930],{"encoding":1530},"C = C(Y) = aY + b, \\qquad (7.3)",[1030,34932,20022,34933,1586,34951,34973,34974,35013,35014,2632],{},[1035,34934,34936],{"className":34935},[1480],[1482,34937,34938],{"xmlns":1484},[1487,34939,34940,34948],{},[1490,34941,34942,34944,34946],{},[1493,34943,2394],{},[1506,34945,2796],{},[1680,34947,1871],{},[1528,34949,34950],{"encoding":1530},"b > 0",[1035,34952,34954],{"className":34953},[1480],[1482,34955,34956],{"xmlns":1484},[1487,34957,34958,34970],{},[1490,34959,34960,34962,34964,34966,34968],{},[1680,34961,1871],{},[1506,34963,3961],{},[1493,34965,1052],{},[1506,34967,3961],{},[1680,34969,1682],{},[1528,34971,34972],{"encoding":1530},"0 \u003C a \u003C 1",". Směrnice ",[1035,34975,34977],{"className":34976},[1480],[1482,34978,34979],{"xmlns":1484},[1487,34980,34981,35010],{},[1490,34982,34983,34985,34987,34993,34995,34998,35000,35002,35004,35006,35008],{},[1493,34984,1052],{},[1506,34986,1508],{},[1490,34988,34989,34991],{},[1493,34990,10917],{"mathvariant":1516},[1493,34992,27556],{"mathvariant":1516},[1988,34994,5016],{},[1493,34996,34997],{},"α",[1506,34999,1508],{},[1493,35001,2976],{"mathvariant":1516},[1493,35003,1998],{},[1493,35005,1709],{"mathvariant":1516},[1493,35007,2976],{"mathvariant":1516},[1493,35009,1791],{},[1528,35011,35012],{"encoding":1530},"a = \\mathrm{tg}\\,\\alpha = \\Delta C \u002F \\Delta Y",": vzroste-li důchod o jednotku, spotřeba vzroste o méně než 1 (část „dodatečné jednotky“ jde na úspory). Domácnost v tomto modelu nevydává na spotřebu víc, než kolik dostala navíc — pokud by čerpala víc, musela by sáhnout do úspor; toto je reálné zejména pro malé ",[1035,35015,35017],{"className":35016},[1480],[1482,35018,35019],{"xmlns":1484},[1487,35020,35021,35025],{},[1490,35022,35023],{},[1493,35024,1791],{},[1528,35026,1791],{"encoding":1530},[1030,35028,35029,35030,1274],{},"Dosazením do (7.2) plyne ",[1047,35031,35032],{},"lineární model úspor",[1035,35034,35036],{"className":35035},[1480],[1482,35037,35038],{"xmlns":1484,"display":1485},[1487,35039,35040,35105],{},[1490,35041,35042,35044,35046,35048,35050,35052,35054,35056,35058,35060,35062,35064,35066,35068,35070,35072,35074,35076,35078,35080,35082,35084,35086,35088,35090,35092,35094,35096,35098,35100,35103],{},[1493,35043,2001],{},[1506,35045,1508],{},[1493,35047,1791],{},[1506,35049,1888],{},[1493,35051,1998],{},[1506,35053,1553],{"stretchy":1552},[1493,35055,1791],{},[1506,35057,1564],{"stretchy":1552},[1506,35059,1508],{},[1493,35061,1791],{},[1506,35063,1888],{},[1506,35065,1553],{"stretchy":1552},[1493,35067,1052],{},[1493,35069,1791],{},[1506,35071,2162],{},[1493,35073,2394],{},[1506,35075,1564],{"stretchy":1552},[1506,35077,1508],{},[1506,35079,1553],{"stretchy":1552},[1680,35081,1682],{},[1506,35083,1888],{},[1493,35085,1052],{},[1506,35087,1564],{"stretchy":1552},[1493,35089,1791],{},[1506,35091,1888],{},[1493,35093,2394],{},[1493,35095,2632],{"mathvariant":1516},[1912,35097],{"width":1914},[1506,35099,1553],{"stretchy":1552},[1680,35101,35102],{},"7.4",[1506,35104,1564],{"stretchy":1552},[1528,35106,35107],{"encoding":1530},"S = Y - C(Y) = Y - (aY + b) = (1 - a)Y - b. \\qquad (7.4)",[1030,35109,35110,35111,16623],{},"Úspory jsou také lineární a „pomalu rostoucí“ (protože ",[1035,35112,35114],{"className":35113},[1480],[1482,35115,35116],{"xmlns":1484},[1487,35117,35118,35134],{},[1490,35119,35120,35122,35124,35126,35128,35130,35132],{},[1680,35121,1871],{},[1506,35123,3961],{},[1680,35125,1682],{},[1506,35127,1888],{},[1493,35129,1052],{},[1506,35131,3961],{},[1680,35133,1682],{},[1528,35135,35136],{"encoding":1530},"0 \u003C 1 - a \u003C 1",[1304,35138,35140],{"id":35139},"příklad-71","Příklad 7.1",[1030,35142,35143,35144,35168],{},"Pro spotřebu ",[1035,35145,35147],{"className":35146},[1480],[1482,35148,35149],{"xmlns":1484},[1487,35150,35151,35165],{},[1490,35152,35153,35155,35157,35159,35161,35163],{},[1493,35154,1998],{},[1506,35156,1508],{},[1680,35158,3322],{},[1493,35160,1791],{},[1506,35162,2162],{},[1680,35164,1775],{},[1528,35166,35167],{"encoding":1530},"C = 0{,}4Y + 10"," jsou úspory",[1035,35170,35172],{"className":35171},[1480],[1482,35173,35174],{"xmlns":1484,"display":1485},[1487,35175,35176,35213],{},[1490,35177,35178,35180,35182,35184,35186,35188,35190,35192,35194,35196,35198,35200,35202,35204,35206,35208,35210],{},[1493,35179,2001],{},[1506,35181,1508],{},[1493,35183,1791],{},[1506,35185,1888],{},[1493,35187,1998],{},[1506,35189,1508],{},[1493,35191,1791],{},[1506,35193,1888],{},[1680,35195,3322],{},[1493,35197,1791],{},[1506,35199,1888],{},[1680,35201,1775],{},[1506,35203,1508],{},[1680,35205,3332],{},[1493,35207,1791],{},[1506,35209,1888],{},[1680,35211,35212],{},"10.",[1528,35214,35215],{"encoding":1530},"S = Y - C = Y - 0{,}4Y - 10 = 0{,}6Y - 10.",[1030,35217,35218,35219,8994,35237,35266,35267,7606,35270,35273,35274,8994,35298,7606,35301,35304],{},"Funkce úspor může nabývat záporných hodnot — pro ",[1035,35220,35222],{"className":35221},[1480],[1482,35223,35224],{"xmlns":1484},[1487,35225,35226,35234],{},[1490,35227,35228,35230,35232],{},[1493,35229,1791],{},[1506,35231,1508],{},[1680,35233,1871],{},[1528,35235,35236],{"encoding":1530},"Y = 0",[1035,35238,35240],{"className":35239},[1480],[1482,35241,35242],{"xmlns":1484},[1487,35243,35244,35264],{},[1490,35245,35246,35248,35250,35252,35254,35256,35258,35260,35262],{},[1493,35247,2001],{},[1506,35249,1553],{"stretchy":1552},[1680,35251,1871],{},[1506,35253,1564],{"stretchy":1552},[1506,35255,1508],{},[1506,35257,1888],{},[1493,35259,2394],{},[1506,35261,3961],{},[1680,35263,1871],{},[1528,35265,13668],{"encoding":1530},"; hovoří se o ",[1047,35268,35269],{},"autonomních úsporách",[1176,35271,35272],{},"autonomous savings","). Analogicky ",[1035,35275,35277],{"className":35276},[1480],[1482,35278,35279],{"xmlns":1484},[1487,35280,35281,35295],{},[1490,35282,35283,35285,35287,35289,35291,35293],{},[1493,35284,1998],{},[1506,35286,1553],{"stretchy":1552},[1680,35288,1871],{},[1506,35290,1564],{"stretchy":1552},[1506,35292,1508],{},[1493,35294,2394],{},[1528,35296,35297],{"encoding":1530},"C(0) = b",[1047,35299,35300],{},"autonomní spotřeba",[1176,35302,35303],{},"autonomous consumption",") — spotřeba při nulovém důchodu krytá dřívějšími úsporami.",[1065,35306,35308],{"id":35307},"mezní-sklon-ke-spotřebě-mpc-a-k-úsporám-mps","Mezní sklon ke spotřebě (MPC) a k úsporám (MPS)",[1030,35310,35311,1656,35314,7606,35331,35334],{},[1047,35312,35313],{},"Mezní sklon ke spotřebě",[1035,35315,35317],{"className":35316},[1480],[1482,35318,35319],{"xmlns":1484},[1487,35320,35321,35329],{},[1490,35322,35323,35325,35327],{},[1493,35324,1495],{},[1493,35326,1501],{},[1493,35328,1998],{},[1528,35330,34192],{"encoding":1530},[1176,35332,35333],{},"marginal propensity to consume",") je derivace spotřeby podle důchodu:",[1035,35336,35338],{"className":35337},[1480],[1482,35339,35340],{"xmlns":1484,"display":1485},[1487,35341,35342,35368],{},[1490,35343,35344,35346,35348,35350,35352,35366],{},[1493,35345,1495],{},[1493,35347,1501],{},[1493,35349,1998],{},[1506,35351,1508],{},[1510,35353,35354,35360],{},[1490,35355,35356,35358],{},[1493,35357,3384],{"mathvariant":1516},[1493,35359,1998],{},[1490,35361,35362,35364],{},[1493,35363,3384],{"mathvariant":1516},[1493,35365,1791],{},[1493,35367,2632],{"mathvariant":1516},[1528,35369,35370],{"encoding":1530},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y}.",[1030,35372,35373,1656,35376,7606,35393,35396],{},[1047,35374,35375],{},"Mezní sklon k úsporám",[1035,35377,35379],{"className":35378},[1480],[1482,35380,35381],{"xmlns":1484},[1487,35382,35383,35391],{},[1490,35384,35385,35387,35389],{},[1493,35386,1495],{},[1493,35388,1501],{},[1493,35390,2001],{},[1528,35392,13693],{"encoding":1530},[1176,35394,35395],{},"marginal propensity to save",") je derivace úspor podle důchodu:",[1035,35398,35400],{"className":35399},[1480],[1482,35401,35402],{"xmlns":1484,"display":1485},[1487,35403,35404,35430],{},[1490,35405,35406,35408,35410,35412,35414,35428],{},[1493,35407,1495],{},[1493,35409,1501],{},[1493,35411,2001],{},[1506,35413,1508],{},[1510,35415,35416,35422],{},[1490,35417,35418,35420],{},[1493,35419,3384],{"mathvariant":1516},[1493,35421,2001],{},[1490,35423,35424,35426],{},[1493,35425,3384],{"mathvariant":1516},[1493,35427,1791],{},[1493,35429,2632],{"mathvariant":1516},[1528,35431,35432],{"encoding":1530},"MPS = \\frac{\\mathrm{d}S}{\\mathrm{d}Y}.",[1030,35434,35435,35436,35494],{},"Z (7.2) plyne ",[1035,35437,35439],{"className":35438},[1480],[1482,35440,35441],{"xmlns":1484},[1487,35442,35443,35491],{},[1490,35444,35445,35459,35461,35475,35477],{},[1510,35446,35447,35453],{},[1490,35448,35449,35451],{},[1493,35450,3384],{"mathvariant":1516},[1493,35452,1791],{},[1490,35454,35455,35457],{},[1493,35456,3384],{"mathvariant":1516},[1493,35458,1791],{},[1506,35460,1508],{},[1510,35462,35463,35469],{},[1490,35464,35465,35467],{},[1493,35466,3384],{"mathvariant":1516},[1493,35468,1998],{},[1490,35470,35471,35473],{},[1493,35472,3384],{"mathvariant":1516},[1493,35474,1791],{},[1506,35476,2162],{},[1510,35478,35479,35485],{},[1490,35480,35481,35483],{},[1493,35482,3384],{"mathvariant":1516},[1493,35484,2001],{},[1490,35486,35487,35489],{},[1493,35488,3384],{"mathvariant":1516},[1493,35490,1791],{},[1528,35492,35493],{"encoding":1530},"\\frac{\\mathrm{d}Y}{\\mathrm{d}Y} = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} + \\frac{\\mathrm{d}S}{\\mathrm{d}Y}",", a tedy",[1035,35496,35498],{"className":35497},[1480],[1482,35499,35500],{"xmlns":1484,"display":1485},[1487,35501,35502,35565],{},[1490,35503,35504,35556,35558,35560,35563],{},[1976,35505,35506],{"notation":1978},[1869,35507,35508],{"scriptlevel":1871,"displaystyle":1552},[1869,35509,35510],{"scriptlevel":1871,"displaystyle":1552},[1869,35511,35512],{"scriptlevel":1871,"displaystyle":1041},[1490,35513,35514,35516,35518,35520,35522,35524,35526,35528,35530,35532,35534,35536,35538,35540,35542,35544,35546,35548,35550,35552,35554],{},[1493,35515,1495],{},[1493,35517,1501],{},[1493,35519,1998],{},[1506,35521,2162],{},[1493,35523,1495],{},[1493,35525,1501],{},[1493,35527,2001],{},[1506,35529,1508],{},[1680,35531,1682],{},[1506,35533,1559],{"separator":1041},[1912,35535],{"width":1914},[1493,35537,1495],{},[1493,35539,1501],{},[1493,35541,2001],{},[1506,35543,1508],{},[1680,35545,1682],{},[1506,35547,1888],{},[1493,35549,1495],{},[1493,35551,1501],{},[1493,35553,1998],{},[1493,35555,2632],{"mathvariant":1516},[1912,35557],{"width":1914},[1506,35559,1553],{"stretchy":1552},[1680,35561,35562],{},"7.5",[1506,35564,1564],{"stretchy":1552},[1528,35566,35567],{"encoding":1530},"\\boxed{MPC + MPS = 1, \\qquad MPS = 1 - MPC.} \\qquad (7.5)",[1030,35569,35570,1656,35573,35597,35598,1586,35620,35646],{},[1047,35571,35572],{},"Pro lineární model",[1035,35574,35576],{"className":35575},[1480],[1482,35577,35578],{"xmlns":1484},[1487,35579,35580,35594],{},[1490,35581,35582,35584,35586,35588,35590,35592],{},[1493,35583,1998],{},[1506,35585,1508],{},[1493,35587,1052],{},[1493,35589,1791],{},[1506,35591,2162],{},[1493,35593,2394],{},[1528,35595,35596],{"encoding":1530},"C = aY + b"," vychází ",[1035,35599,35601],{"className":35600},[1480],[1482,35602,35603],{"xmlns":1484},[1487,35604,35605,35617],{},[1490,35606,35607,35609,35611,35613,35615],{},[1493,35608,1495],{},[1493,35610,1501],{},[1493,35612,1998],{},[1506,35614,1508],{},[1493,35616,1052],{},[1528,35618,35619],{"encoding":1530},"MPC = a",[1035,35621,35623],{"className":35622},[1480],[1482,35624,35625],{"xmlns":1484},[1487,35626,35627,35643],{},[1490,35628,35629,35631,35633,35635,35637,35639,35641],{},[1493,35630,1495],{},[1493,35632,1501],{},[1493,35634,2001],{},[1506,35636,1508],{},[1680,35638,1682],{},[1506,35640,1888],{},[1493,35642,1052],{},[1528,35644,35645],{"encoding":1530},"MPS = 1 - a"," — tedy směrnice přímek spotřeby a úspor.",[1030,35648,35649,35652,35653,35675,35676,35704],{},[1047,35650,35651],{},"Interpretace diferenciálem."," Pro pevné ",[1035,35654,35656],{"className":35655},[1480],[1482,35657,35658],{"xmlns":1484},[1487,35659,35660,35672],{},[1490,35661,35662,35664,35666],{},[1493,35663,1791],{},[1506,35665,1508],{},[2315,35667,35668,35670],{},[1493,35669,1791],{},[1506,35671,2287],{},[1528,35673,35674],{"encoding":1530},"Y = Y^*"," udává ",[1035,35677,35679],{"className":35678},[1480],[1482,35680,35681],{"xmlns":1484},[1487,35682,35683,35701],{},[1490,35684,35685,35687,35689,35691,35693,35699],{},[1493,35686,1495],{},[1493,35688,1501],{},[1493,35690,1998],{},[1506,35692,1553],{"stretchy":1552},[2315,35694,35695,35697],{},[1493,35696,1791],{},[1506,35698,2287],{},[1506,35700,1564],{"stretchy":1552},[1528,35702,35703],{"encoding":1530},"MPC(Y^*)"," přibližnou změnu spotřeby při jednotkovém přírůstku důchodu:",[1035,35706,35708],{"className":35707},[1480],[1482,35709,35710],{"xmlns":1484,"display":1485},[1487,35711,35712,35766],{},[1490,35713,35714,35716,35718,35720,35722,35724,35726,35732,35734,35736,35738,35740,35742,35744,35746,35748,35750,35752,35754,35756,35758,35760,35762,35764],{},[1493,35715,2976],{"mathvariant":1516},[1493,35717,1998],{},[1506,35719,2343],{},[1493,35721,3384],{"mathvariant":1516},[1493,35723,1998],{},[1506,35725,1508],{},[2315,35727,35728,35730],{},[1493,35729,1998],{},[1506,35731,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,35733,1553],{"stretchy":1552},[1493,35735,1791],{},[1506,35737,1564],{"stretchy":1552},[1988,35739,5016],{},[1493,35741,3384],{"mathvariant":1516},[1493,35743,1791],{},[1506,35745,1508],{},[1493,35747,1495],{},[1493,35749,1501],{},[1493,35751,1998],{},[1506,35753,1553],{"stretchy":1552},[1493,35755,1791],{},[1506,35757,1564],{"stretchy":1552},[1988,35759,5016],{},[1493,35761,3384],{"mathvariant":1516},[1493,35763,1791],{},[1493,35765,2632],{"mathvariant":1516},[1528,35767,35768],{"encoding":1530},"\\Delta C \\approx \\mathrm{d}C = C'(Y)\\,\\mathrm{d}Y = MPC(Y)\\,\\mathrm{d}Y.",[1030,35770,35771,35772,4212,35808,35811],{},"Analogicky ",[1035,35773,35775],{"className":35774},[1480],[1482,35776,35777],{"xmlns":1484},[1487,35778,35779,35805],{},[1490,35780,35781,35783,35785,35787,35789,35791,35793,35795,35797,35799,35801,35803],{},[1493,35782,2976],{"mathvariant":1516},[1493,35784,2001],{},[1506,35786,2343],{},[1493,35788,1495],{},[1493,35790,1501],{},[1493,35792,2001],{},[1506,35794,1553],{"stretchy":1552},[1493,35796,1791],{},[1506,35798,1564],{"stretchy":1552},[1988,35800,5016],{},[1493,35802,3384],{"mathvariant":1516},[1493,35804,1791],{},[1528,35806,35807],{"encoding":1530},"\\Delta S \\approx MPS(Y)\\,\\mathrm{d}Y",[1052,35809,102],{"className":35810,"dataFsResolvedFilePath":16621,"href":16622},[1055]," a její ekonomická interpretace.",[1304,35813,35815],{"id":35814},"příklad-72","Příklad 7.2",[1030,35817,35143,35818,35853,35854,35872],{},[1035,35819,35821],{"className":35820},[1480],[1482,35822,35823],{"xmlns":1484},[1487,35824,35825,35850],{},[1490,35826,35827,35829,35831,35834,35840,35842,35844,35846,35848],{},[1493,35828,1998],{},[1506,35830,1508],{},[1680,35832,35833],{},"0,001",[2315,35835,35836,35838],{},[1493,35837,1791],{},[1680,35839,1691],{},[1506,35841,2162],{},[1680,35843,2929],{},[1493,35845,1791],{},[1506,35847,2162],{},[1680,35849,2292],{},[1528,35851,35852],{"encoding":1530},"C = 0{,}001Y^2 + 0{,}2Y + 50"," (pro ",[1035,35855,35857],{"className":35856},[1480],[1482,35858,35859],{"xmlns":1484},[1487,35860,35861,35869],{},[1490,35862,35863,35865,35867],{},[1493,35864,1791],{},[1506,35866,3961],{},[1680,35868,5765],{},[1528,35870,35871],{"encoding":1530},"Y \u003C 400",") platí",[1035,35874,35876],{"className":35875},[1480],[1482,35877,35878],{"xmlns":1484,"display":1485},[1487,35879,35880,35917],{},[1490,35881,35882,35884,35886,35888,35890,35904,35906,35909,35911,35913,35915],{},[1493,35883,1495],{},[1493,35885,1501],{},[1493,35887,1998],{},[1506,35889,1508],{},[1510,35891,35892,35898],{},[1490,35893,35894,35896],{},[1493,35895,3384],{"mathvariant":1516},[1493,35897,1998],{},[1490,35899,35900,35902],{},[1493,35901,3384],{"mathvariant":1516},[1493,35903,1791],{},[1506,35905,1508],{},[1680,35907,35908],{},"0,002",[1493,35910,1791],{},[1506,35912,2162],{},[1680,35914,2929],{},[1506,35916,1559],{"separator":1041},[1528,35918,35919],{"encoding":1530},"MPC = \\frac{\\mathrm{d}C}{\\mathrm{d}Y} = 0{,}002Y + 0{,}2,",[1035,35921,35923],{"className":35922},[1480],[1482,35924,35925],{"xmlns":1484,"display":1485},[1487,35926,35927,35960],{},[1490,35928,35929,35931,35933,35935,35937,35939,35941,35943,35945,35947,35949,35951,35953,35955,35957],{},[1493,35930,1495],{},[1493,35932,1501],{},[1493,35934,2001],{},[1506,35936,1508],{},[1680,35938,1682],{},[1506,35940,1888],{},[1493,35942,1495],{},[1493,35944,1501],{},[1493,35946,1998],{},[1506,35948,1508],{},[1506,35950,1888],{},[1680,35952,35908],{},[1493,35954,1791],{},[1506,35956,2162],{},[1680,35958,35959],{},"0,8.",[1528,35961,35962],{"encoding":1530},"MPS = 1 - MPC = -0{,}002Y + 0{,}8.",[1203,35964,35965,36045,36124],{},[1206,35966,35967,1732,35995,36023,36024,8994,36042,2632],{},[1035,35968,35970],{"className":35969},[1480],[1482,35971,35972],{"xmlns":1484},[1487,35973,35974,35992],{},[1490,35975,35976,35978,35980,35982,35984,35986,35988,35990],{},[1493,35977,1495],{},[1493,35979,1501],{},[1493,35981,1998],{},[1506,35983,1553],{"stretchy":1552},[1680,35985,2916],{},[1506,35987,1564],{"stretchy":1552},[1506,35989,1508],{},[1680,35991,3322],{},[1528,35993,35994],{"encoding":1530},"MPC(100) = 0{,}4",[1035,35996,35998],{"className":35997},[1480],[1482,35999,36000],{"xmlns":1484},[1487,36001,36002,36020],{},[1490,36003,36004,36006,36008,36010,36012,36014,36016,36018],{},[1493,36005,1495],{},[1493,36007,1501],{},[1493,36009,2001],{},[1506,36011,1553],{"stretchy":1552},[1680,36013,2916],{},[1506,36015,1564],{"stretchy":1552},[1506,36017,1508],{},[1680,36019,3332],{},[1528,36021,36022],{"encoding":1530},"MPS(100) = 0{,}6"," — při ",[1035,36025,36027],{"className":36026},[1480],[1482,36028,36029],{"xmlns":1484},[1487,36030,36031,36039],{},[1490,36032,36033,36035,36037],{},[1493,36034,1791],{},[1506,36036,1508],{},[1680,36038,2916],{},[1528,36040,36041],{"encoding":1530},"Y = 100",[1047,36043,36044],{},"větší sklon k úsporám",[1206,36046,36047,1732,36075,36023,36103,8994,36121,2632],{},[1035,36048,36050],{"className":36049},[1480],[1482,36051,36052],{"xmlns":1484},[1487,36053,36054,36072],{},[1490,36055,36056,36058,36060,36062,36064,36066,36068,36070],{},[1493,36057,1495],{},[1493,36059,1501],{},[1493,36061,1998],{},[1506,36063,1553],{"stretchy":1552},[1680,36065,5263],{},[1506,36067,1564],{"stretchy":1552},[1506,36069,1508],{},[1680,36071,3332],{},[1528,36073,36074],{"encoding":1530},"MPC(200) = 0{,}6",[1035,36076,36078],{"className":36077},[1480],[1482,36079,36080],{"xmlns":1484},[1487,36081,36082,36100],{},[1490,36083,36084,36086,36088,36090,36092,36094,36096,36098],{},[1493,36085,1495],{},[1493,36087,1501],{},[1493,36089,2001],{},[1506,36091,1553],{"stretchy":1552},[1680,36093,5263],{},[1506,36095,1564],{"stretchy":1552},[1506,36097,1508],{},[1680,36099,3322],{},[1528,36101,36102],{"encoding":1530},"MPS(200) = 0{,}4",[1035,36104,36106],{"className":36105},[1480],[1482,36107,36108],{"xmlns":1484},[1487,36109,36110,36118],{},[1490,36111,36112,36114,36116],{},[1493,36113,1791],{},[1506,36115,1508],{},[1680,36117,5263],{},[1528,36119,36120],{"encoding":1530},"Y = 200",[1047,36122,36123],{},"větší sklon ke spotřebě",[1206,36125,36126,36127,36145,36146,16623],{},"Přesně při ",[1035,36128,36130],{"className":36129},[1480],[1482,36131,36132],{"xmlns":1484},[1487,36133,36134,36142],{},[1490,36135,36136,36138,36140],{},[1493,36137,1791],{},[1506,36139,1508],{},[1680,36141,5551],{},[1528,36143,36144],{"encoding":1530},"Y = 150"," se oba sklony rovnají (",[1035,36147,36149],{"className":36148},[1480],[1482,36150,36151],{"xmlns":1484},[1487,36152,36153,36173],{},[1490,36154,36155,36157,36159,36161,36163,36165,36167,36169,36171],{},[1493,36156,1495],{},[1493,36158,1501],{},[1493,36160,1998],{},[1506,36162,1508],{},[1493,36164,1495],{},[1493,36166,1501],{},[1493,36168,2001],{},[1506,36170,1508],{},[1680,36172,3687],{},[1528,36174,36175],{"encoding":1530},"MPC = MPS = 0{,}5",[1030,36177,36178,36179,36196,36197,36211,36212,18139,36225,36239,36240,36253,36254,36295],{},"Interpretace: při ",[1035,36180,36182],{"className":36181},[1480],[1482,36183,36184],{"xmlns":1484},[1487,36185,36186,36194],{},[1490,36187,36188,36190,36192],{},[1493,36189,1791],{},[1506,36191,1508],{},[1680,36193,2916],{},[1528,36195,36041],{"encoding":1530}," se spotřeba mění ",[1035,36198,36200],{"className":36199},[1480],[1482,36201,36202],{"xmlns":1484},[1487,36203,36204,36208],{},[1490,36205,36206],{},[1680,36207,3322],{},[1528,36209,36210],{"encoding":1530},"0{,}4","-krát rychleji než důchod; změní-li se důchod ze ",[1035,36213,36215],{"className":36214},[1480],[1482,36216,36217],{"xmlns":1484},[1487,36218,36219,36223],{},[1490,36220,36221],{},[1680,36222,2916],{},[1528,36224,2916],{"encoding":1530},[1035,36226,36228],{"className":36227},[1480],[1482,36229,36230],{"xmlns":1484},[1487,36231,36232,36237],{},[1490,36233,36234],{},[1680,36235,36236],{},"101",[1528,36238,36236],{"encoding":1530},", změní se spotřeba přibližně o ",[1035,36241,36243],{"className":36242},[1480],[1482,36244,36245],{"xmlns":1484},[1487,36246,36247,36251],{},[1490,36248,36249],{},[1680,36250,3322],{},[1528,36252,36210],{"encoding":1530},". Skutečná změna ",[1035,36255,36257],{"className":36256},[1480],[1482,36258,36259],{"xmlns":1484},[1487,36260,36261,36292],{},[1490,36262,36263,36265,36267,36269,36271,36273,36275,36277,36279,36281,36283,36285,36287,36289],{},[1493,36264,2976],{"mathvariant":1516},[1493,36266,1998],{},[1506,36268,1508],{},[1493,36270,1998],{},[1506,36272,1553],{"stretchy":1552},[1680,36274,36236],{},[1506,36276,1564],{"stretchy":1552},[1506,36278,1888],{},[1493,36280,1998],{},[1506,36282,1553],{"stretchy":1552},[1680,36284,2916],{},[1506,36286,1564],{"stretchy":1552},[1506,36288,1508],{},[1680,36290,36291],{},"0,401",[1528,36293,36294],{"encoding":1530},"\\Delta C = C(101) - C(100) = 0{,}401"," — aproximace diferenciálem je přesná na setiny.",[1030,36297,36298,36299],{},"Obecný trend: ",[1047,36300,36301],{},"s růstem důchodu se sklon ke spotřebě zvětšuje.",[1065,36303,36305],{"id":36304},"makroekonomická-rovnováha","Makroekonomická rovnováha",[1030,36307,36308,36309,7606,36312,36315,36316,7606,36319,28611,36322,7606,36325,36328],{},"Při modelování národní ekonomiky hraje klíčovou roli ",[1047,36310,36311],{},"makroekonomická rovnováha",[1176,36313,36314],{},"macroeconomic equilibrium",") — stav, kdy se všechny trhy nacházejí v rovnováze: trh zboží a služeb, trh práce a ostatních výrobních faktorů, trh kapitálu a peněz. Významnou součástí je rovnost ",[1047,36317,36318],{},"agregátní poptávky",[1176,36320,36321],{},"aggregate demand",[1047,36323,36324],{},"agregátní nabídky",[1176,36326,36327],{},"aggregate supply",") — obě popisují závislost mezi cenovou hladinou a množstvím, které jsou spotřebitelé ochotni koupit (agregátními výdaji).",[1065,36330,36332],{"id":36331},"model-c-i-uzavřená-ekonomika-bez-vlády","Model C-I — uzavřená ekonomika bez vlády",[1030,36334,36335],{},[18014,36336],{"alt":36337,"className":36338,"src":36339},"imek-keynesian-kriz",[1055,18018],"\u002Fwiki-assets\u002Fimek-keynesian-kriz.jpeg",[1304,36341,36343],{"id":36342},"zadání-modelu","Zadání modelu",[1030,36345,36346,36347,36360,36361,36374],{},"Nejjednodušší model uzavřené ekonomiky bez vlády obsahuje jen spotřebu ",[1035,36348,36350],{"className":36349},[1480],[1482,36351,36352],{"xmlns":1484},[1487,36353,36354,36358],{},[1490,36355,36356],{},[1493,36357,1998],{},[1528,36359,1998],{"encoding":1530}," a investice ",[1035,36362,36364],{"className":36363},[1480],[1482,36365,36366],{"xmlns":1484},[1487,36367,36368,36372],{},[1490,36369,36370],{},[1493,36371,2662],{},[1528,36373,2662],{"encoding":1530},". Podmínka rovnováhy:",[1035,36376,36378],{"className":36377},[1480],[1482,36379,36380],{"xmlns":1484,"display":1485},[1487,36381,36382,36405],{},[1490,36383,36384,36386,36388,36390,36392,36394,36396,36398,36400,36403],{},[1493,36385,1791],{},[1506,36387,1508],{},[1493,36389,1998],{},[1506,36391,2162],{},[1493,36393,2662],{},[1493,36395,2632],{"mathvariant":1516},[1912,36397],{"width":1914},[1506,36399,1553],{"stretchy":1552},[1680,36401,36402],{},"7.6",[1506,36404,1564],{"stretchy":1552},[1528,36406,36407],{"encoding":1530},"Y = C + I. \\qquad (7.6)",[1304,36409,36411],{"id":36410},"soustava-rovnic","Soustava rovnic",[1030,36413,36414,36415,36436,36437,36461],{},"Pro pevně zadané (plánované) investice ",[1035,36416,36418],{"className":36417},[1480],[1482,36419,36420],{"xmlns":1484},[1487,36421,36422,36434],{},[1490,36423,36424,36426,36428],{},[1493,36425,2662],{},[1506,36427,1508],{},[2315,36429,36430,36432],{},[1493,36431,2662],{},[1506,36433,2287],{},[1528,36435,28677],{"encoding":1530}," a funkci spotřeby ",[1035,36438,36440],{"className":36439},[1480],[1482,36441,36442],{"xmlns":1484},[1487,36443,36444,36458],{},[1490,36445,36446,36448,36450,36452,36454,36456],{},[1493,36447,1998],{},[1506,36449,1508],{},[1493,36451,1998],{},[1506,36453,1553],{"stretchy":1552},[1493,36455,1791],{},[1506,36457,1564],{"stretchy":1552},[1528,36459,36460],{"encoding":1530},"C = C(Y)"," dostáváme soustavu",[1035,36463,36465],{"className":36464},[1480],[1482,36466,36467],{"xmlns":1484,"display":1485},[1487,36468,36469,36542],{},[1490,36470,36471,36533,36535,36537,36540],{},[19617,36472,36475,36505],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},"0.25em","right left",[19621,36476,36477,36483],{},[19624,36478,36479],{},[1869,36480,36481],{"scriptlevel":1871,"displaystyle":1041},[1493,36482,1791],{},[19624,36484,36485],{},[1869,36486,36487],{"scriptlevel":1871,"displaystyle":1041},[1490,36488,36489,36491,36493,36495,36497,36503],{},[1490,36490],{},[1506,36492,1508],{},[1493,36494,1998],{},[1506,36496,2162],{},[2315,36498,36499,36501],{},[1493,36500,2662],{},[1506,36502,2287],{},[1506,36504,1559],{"separator":1041},[19621,36506,36507,36513],{},[19624,36508,36509],{},[1869,36510,36511],{"scriptlevel":1871,"displaystyle":1041},[1493,36512,1998],{},[19624,36514,36515],{},[1869,36516,36517],{"scriptlevel":1871,"displaystyle":1041},[1490,36518,36519,36521,36523,36525,36527,36529,36531],{},[1490,36520],{},[1506,36522,1508],{},[1493,36524,1998],{},[1506,36526,1553],{"stretchy":1552},[1493,36528,1791],{},[1506,36530,1564],{"stretchy":1552},[1506,36532,1559],{"separator":1041},[1912,36534],{"width":1914},[1506,36536,1553],{"stretchy":1552},[1680,36538,36539],{},"7.7",[1506,36541,1564],{"stretchy":1552},[1528,36543,36544],{"encoding":1530},"\\begin{aligned} Y &= C + I^*, \\\\ C &= C(Y), \\end{aligned} \\qquad (7.7)",[1030,36546,36547,36548,1656,36550,1586,36567,1656,36570,2632],{},"jejímž řešením jsou ",[1047,36549,30356],{},[1035,36551,36553],{"className":36552},[1480],[1482,36554,36555],{"xmlns":1484},[1487,36556,36557,36565],{},[1490,36558,36559],{},[2315,36560,36561,36563],{},[1493,36562,1791],{},[1493,36564,2711],{},[1528,36566,3419],{"encoding":1530},[1047,36568,36569],{},"rovnovážná spotřeba",[1035,36571,36573],{"className":36572},[1480],[1482,36574,36575],{"xmlns":1484},[1487,36576,36577,36585],{},[1490,36578,36579],{},[2315,36580,36581,36583],{},[1493,36582,1998],{},[1493,36584,2711],{},[1528,36586,30432],{"encoding":1530},[1304,36588,36590,36591],{"id":36589},"výpočet-yeye","Výpočet ",[1035,36592,36594],{"className":36593},[1480],[1482,36595,36596],{"xmlns":1484},[1487,36597,36598,36606],{},[1490,36599,36600],{},[2315,36601,36602,36604],{},[1493,36603,1791],{},[1493,36605,2711],{},[1528,36607,3419],{"encoding":1530},[1030,36609,36610,36611,36634,36635,23638,36667],{},"Pro lineární spotřebu ",[1035,36612,36614],{"className":36613},[1480],[1482,36615,36616],{"xmlns":1484},[1487,36617,36618,36632],{},[1490,36619,36620,36622,36624,36626,36628,36630],{},[1493,36621,1998],{},[1506,36623,1508],{},[1493,36625,1052],{},[1493,36627,1791],{},[1506,36629,2162],{},[1493,36631,2394],{},[1528,36633,35596],{"encoding":1530}," plyne z (7.7) rovnice ",[1035,36636,36638],{"className":36637},[1480],[1482,36639,36640],{"xmlns":1484},[1487,36641,36642,36664],{},[1490,36643,36644,36646,36648,36650,36652,36654,36656,36658],{},[1493,36645,1791],{},[1506,36647,1508],{},[1493,36649,1052],{},[1493,36651,1791],{},[1506,36653,2162],{},[1493,36655,2394],{},[1506,36657,2162],{},[2315,36659,36660,36662],{},[1493,36661,2662],{},[1506,36663,2287],{},[1528,36665,36666],{"encoding":1530},"Y = aY + b + I^*",[1047,36668,36669],{},"redukovaný tvar",[1035,36671,36673],{"className":36672},[1480],[1482,36674,36675],{"xmlns":1484,"display":1485},[1487,36676,36677,36725],{},[1490,36678,36679],{},[1976,36680,36681],{"notation":1978},[1869,36682,36683],{"scriptlevel":1871,"displaystyle":1552},[1869,36684,36685],{"scriptlevel":1871,"displaystyle":1552},[1869,36686,36687],{"scriptlevel":1871,"displaystyle":1041},[1490,36688,36689,36691,36697,36699,36721,36723],{},[1988,36690,5016],{},[2315,36692,36693,36695],{},[1493,36694,1791],{},[1493,36696,2711],{},[1506,36698,1508],{},[1510,36700,36701,36713],{},[1490,36702,36703,36705,36707],{},[1493,36704,2394],{},[1506,36706,2162],{},[2315,36708,36709,36711],{},[1493,36710,2662],{},[1506,36712,2287],{},[1490,36714,36715,36717,36719],{},[1680,36716,1682],{},[1506,36718,1888],{},[1493,36720,1052],{},[1493,36722,2632],{"mathvariant":1516},[1988,36724,5016],{},[1528,36726,36727],{"encoding":1530},"\\boxed{\\,Y^E = \\frac{b + I^*}{1 - a}.\\,}",[1304,36729,36731],{"id":36730},"příklad-73","Příklad 7.3",[1030,36733,36734,36735,8994,36752,1586,36776,36802],{},"V modelu ",[1035,36736,36738],{"className":36737},[1480],[1482,36739,36740],{"xmlns":1484},[1487,36741,36742,36750],{},[1490,36743,36744,36746,36748],{},[1493,36745,1998],{},[1988,36747,28777],{},[1493,36749,2662],{},[1528,36751,28782],{"encoding":1530},[1035,36753,36755],{"className":36754},[1480],[1482,36756,36757],{"xmlns":1484},[1487,36758,36759,36773],{},[1490,36760,36761,36763,36765,36767,36769,36771],{},[1493,36762,1998],{},[1506,36764,1508],{},[1680,36766,3332],{},[1493,36768,1791],{},[1506,36770,2162],{},[1680,36772,1775],{},[1528,36774,36775],{"encoding":1530},"C = 0{,}6Y + 10",[1035,36777,36779],{"className":36778},[1480],[1482,36780,36781],{"xmlns":1484},[1487,36782,36783,36799],{},[1490,36784,36785,36787,36789,36791,36793],{},[1493,36786,2662],{},[1506,36788,1508],{},[1680,36790,6797],{},[1506,36792,1508],{},[2315,36794,36795,36797],{},[1493,36796,2662],{},[1506,36798,2287],{},[1528,36800,36801],{"encoding":1530},"I = 12 = I^*",". Soustava",[1035,36804,36806],{"className":36805},[1480],[1482,36807,36808],{"xmlns":1484,"display":1485},[1487,36809,36810,36866],{},[19617,36811,36812,36838],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,36813,36814,36820],{},[19624,36815,36816],{},[1869,36817,36818],{"scriptlevel":1871,"displaystyle":1041},[1493,36819,1791],{},[19624,36821,36822],{},[1869,36823,36824],{"scriptlevel":1871,"displaystyle":1041},[1490,36825,36826,36828,36830,36832,36834,36836],{},[1490,36827],{},[1506,36829,1508],{},[1493,36831,1998],{},[1506,36833,2162],{},[1680,36835,6797],{},[1506,36837,1559],{"separator":1041},[19621,36839,36840,36846],{},[19624,36841,36842],{},[1869,36843,36844],{"scriptlevel":1871,"displaystyle":1041},[1493,36845,1998],{},[19624,36847,36848],{},[1869,36849,36850],{"scriptlevel":1871,"displaystyle":1041},[1490,36851,36852,36854,36856,36858,36860,36862,36864],{},[1490,36853],{},[1506,36855,1508],{},[1680,36857,3332],{},[1493,36859,1791],{},[1506,36861,2162],{},[1680,36863,1775],{},[1506,36865,1559],{"separator":1041},[1528,36867,36868],{"encoding":1530},"\\begin{aligned} Y &= C + 12, \\\\ C &= 0{,}6Y + 10, \\end{aligned}",[1030,36870,36871,36872,1732,36895,36918,36919,16623],{},"má řešení ",[1035,36873,36875],{"className":36874},[1480],[1482,36876,36877],{"xmlns":1484},[1487,36878,36879,36892],{},[1490,36880,36881,36887,36889],{},[2315,36882,36883,36885],{},[1493,36884,1791],{},[1493,36886,2711],{},[1506,36888,1508],{},[1680,36890,36891],{},"55",[1528,36893,36894],{"encoding":1530},"Y^E = 55",[1035,36896,36898],{"className":36897},[1480],[1482,36899,36900],{"xmlns":1484},[1487,36901,36902,36915],{},[1490,36903,36904,36910,36912],{},[2315,36905,36906,36908],{},[1493,36907,1998],{},[1493,36909,2711],{},[1506,36911,1508],{},[1680,36913,36914],{},"43",[1528,36916,36917],{"encoding":1530},"C^E = 43"," (a ",[1035,36920,36922],{"className":36921},[1480],[1482,36923,36924],{"xmlns":1484},[1487,36925,36926,36938],{},[1490,36927,36928,36934,36936],{},[2315,36929,36930,36932],{},[1493,36931,2001],{},[1493,36933,2711],{},[1506,36935,1508],{},[1680,36937,6797],{},[1528,36939,36940],{"encoding":1530},"S^E = 12",[1030,36942,36943,36946,36947,36964,36965,2632],{},[1047,36944,36945],{},"Komentář k přechodu."," Model ",[1035,36948,36950],{"className":36949},[1480],[1482,36951,36952],{"xmlns":1484},[1487,36953,36954,36962],{},[1490,36955,36956,36958,36960],{},[1493,36957,1998],{},[1988,36959,28777],{},[1493,36961,2662],{},[1528,36963,28782],{"encoding":1530}," ignoruje stát. V praxi však stát vybírá daně a provádí vlastní výdaje, což ovlivňuje jak disponibilní důchod domácností, tak celkovou poptávku — přidáním vládního sektoru dostaneme ",[1047,36966,36967,36968],{},"model ",[1035,36969,36971],{"className":36970},[1480],[1482,36972,36973],{"xmlns":1484},[1487,36974,36975,36987],{},[1490,36976,36977,36979,36981,36983,36985],{},[1493,36978,1998],{},[1988,36980,28777],{},[1493,36982,2662],{},[1988,36984,28777],{},[1493,36986,28595],{},[1528,36988,34367],{"encoding":1530},[1065,36990,36992],{"id":36991},"model-c-i-g-s-vládním-sektorem","Model C-I-G — s vládním sektorem",[1304,36994,36343],{"id":36995},"zadání-modelu-1",[1030,36997,36998,36999,37016,37017,1656,37020,7606,37033,37036],{},"Rozšíření modelu ",[1035,37000,37002],{"className":37001},[1480],[1482,37003,37004],{"xmlns":1484},[1487,37005,37006,37014],{},[1490,37007,37008,37010,37012],{},[1493,37009,1998],{},[1988,37011,28777],{},[1493,37013,2662],{},[1528,37015,28782],{"encoding":1530}," o ",[1047,37018,37019],{},"vládní výdaje",[1035,37021,37023],{"className":37022},[1480],[1482,37024,37025],{"xmlns":1484},[1487,37026,37027,37031],{},[1490,37028,37029],{},[1493,37030,28595],{},[1528,37032,28595],{"encoding":1530},[1176,37034,37035],{},"government expenditure","). Podmínka rovnováhy:",[1035,37038,37040],{"className":37039},[1480],[1482,37041,37042],{"xmlns":1484,"display":1485},[1487,37043,37044,37071],{},[1490,37045,37046,37048,37050,37052,37054,37056,37058,37060,37062,37064,37066,37069],{},[1493,37047,1791],{},[1506,37049,1508],{},[1493,37051,1998],{},[1506,37053,2162],{},[1493,37055,2662],{},[1506,37057,2162],{},[1493,37059,28595],{},[1493,37061,2632],{"mathvariant":1516},[1912,37063],{"width":1914},[1506,37065,1553],{"stretchy":1552},[1680,37067,37068],{},"7.8",[1506,37070,1564],{"stretchy":1552},[1528,37072,37073],{"encoding":1530},"Y = C + I + G. \\qquad (7.8)",[1030,37075,37076,37077,1656,37080,7606,37093,37096],{},"Stát se stává spotřebitelem, jehož „důchod“ získává ",[1047,37078,37079],{},"zdaněním domácností",[1035,37081,37083],{"className":37082},[1480],[1482,37084,37085],{"xmlns":1484},[1487,37086,37087,37091],{},[1490,37088,37089],{},[1493,37090,5289],{},[1528,37092,5289],{"encoding":1530},[1176,37094,37095],{},"taxation","). Zdanění bývá:",[1203,37098,37099,37132,37157],{},[1206,37100,37101,37102,1559],{},"úměrné důchodu: ",[1035,37103,37105],{"className":37104},[1480],[1482,37106,37107],{"xmlns":1484},[1487,37108,37109,37129],{},[1490,37110,37111,37113,37115,37117,37119,37121,37123,37125,37127],{},[1493,37112,5289],{},[1506,37114,1508],{},[1493,37116,5289],{},[1506,37118,1553],{"stretchy":1552},[1493,37120,1791],{},[1506,37122,1564],{"stretchy":1552},[1506,37124,1508],{},[1493,37126,10917],{},[1493,37128,1791],{},[1528,37130,37131],{"encoding":1530},"T = T(Y) = tY",[1206,37133,37134,37135,1559],{},"fixní: ",[1035,37136,37138],{"className":37137},[1480],[1482,37139,37140],{"xmlns":1484},[1487,37141,37142,37154],{},[1490,37143,37144,37146,37148],{},[1493,37145,5289],{},[1506,37147,1508],{},[2315,37149,37150,37152],{},[1493,37151,5289],{},[1506,37153,2287],{},[1528,37155,37156],{"encoding":1530},"T = T^*",[1206,37158,37159,37160,37188,37189,2632],{},"kombinované: ",[1035,37161,37163],{"className":37162},[1480],[1482,37164,37165],{"xmlns":1484},[1487,37166,37167,37185],{},[1490,37168,37169,37171,37173,37179,37181,37183],{},[1493,37170,5289],{},[1506,37172,1508],{},[2315,37174,37175,37177],{},[1493,37176,5289],{},[1506,37178,2287],{},[1506,37180,2162],{},[1493,37182,10917],{},[1493,37184,1791],{},[1528,37186,37187],{"encoding":1530},"T = T^* + tY",", kde ",[1035,37190,37192],{"className":37191},[1480],[1482,37193,37194],{"xmlns":1484},[1487,37195,37196,37208],{},[1490,37197,37198,37200,37202,37204,37206],{},[1680,37199,1871],{},[1506,37201,23632],{},[1493,37203,10917],{},[1506,37205,3961],{},[1680,37207,1682],{},[1528,37209,37210],{"encoding":1530},"0 \\le t \u003C 1",[1023,37212,37214,37221],{"className":37213,"dataCallout":1155},[1026,1154],[1030,37215,37217,37220],{"className":37216},[1033],[1035,37218],{"className":37219,"ariaHidden":1041},[1038,1162,1040],"Pozor na disponibilní důchod",[1030,37222,36734,37223,37244,37245,37248,37249,37262,37263,28611,37289,1656,37292,37318,37319,37347,37348,1586,37361,37379],{},[1035,37224,37226],{"className":37225},[1480],[1482,37227,37228],{"xmlns":1484},[1487,37229,37230,37242],{},[1490,37231,37232,37234,37236,37238,37240],{},[1493,37233,1998],{},[1988,37235,28777],{},[1493,37237,2662],{},[1988,37239,28777],{},[1493,37241,28595],{},[1528,37243,34367],{"encoding":1530}," je nutné ",[1047,37246,37247],{},"důsledně rozlišovat dva důchody",": celkový národní důchod ",[1035,37250,37252],{"className":37251},[1480],[1482,37253,37254],{"xmlns":1484},[1487,37255,37256,37260],{},[1490,37257,37258],{},[1493,37259,1791],{},[1528,37261,1791],{"encoding":1530}," (vstupuje do podmínky rovnováhy ",[1035,37264,37266],{"className":37265},[1480],[1482,37267,37268],{"xmlns":1484},[1487,37269,37270,37286],{},[1490,37271,37272,37274,37276,37278,37280,37282,37284],{},[1493,37273,1791],{},[1506,37275,1508],{},[1493,37277,1998],{},[1506,37279,2162],{},[1493,37281,2662],{},[1506,37283,2162],{},[1493,37285,28595],{},[1528,37287,37288],{"encoding":1530},"Y = C + I + G",[1047,37290,37291],{},"disponibilní důchod",[1035,37293,37295],{"className":37294},[1480],[1482,37296,37297],{"xmlns":1484},[1487,37298,37299,37315],{},[1490,37300,37301,37307,37309,37311,37313],{},[1497,37302,37303,37305],{},[1493,37304,1791],{},[1493,37306,3712],{},[1506,37308,1508],{},[1493,37310,1791],{},[1506,37312,1888],{},[1493,37314,5289],{},[1528,37316,37317],{"encoding":1530},"Y_D = Y - T"," (na něm závisí spotřeba domácností, ",[1035,37320,37322],{"className":37321},[1480],[1482,37323,37324],{"xmlns":1484},[1487,37325,37326,37344],{},[1490,37327,37328,37330,37332,37334,37336,37342],{},[1493,37329,1998],{},[1506,37331,1508],{},[1493,37333,1998],{},[1506,37335,1553],{"stretchy":1552},[1497,37337,37338,37340],{},[1493,37339,1791],{},[1493,37341,3712],{},[1506,37343,1564],{"stretchy":1552},[1528,37345,37346],{"encoding":1530},"C = C(Y_D)","). Záměna ",[1035,37349,37351],{"className":37350},[1480],[1482,37352,37353],{"xmlns":1484},[1487,37354,37355,37359],{},[1490,37356,37357],{},[1493,37358,1791],{},[1528,37360,1791],{"encoding":1530},[1035,37362,37364],{"className":37363},[1480],[1482,37365,37366],{"xmlns":1484},[1487,37367,37368,37376],{},[1490,37369,37370],{},[1497,37371,37372,37374],{},[1493,37373,1791],{},[1493,37375,3712],{},[1528,37377,37378],{"encoding":1530},"Y_D"," ve funkci spotřeby je nejčastější zdroj chyb.",[1030,37381,37382,7606,37385,1564],{},[1047,37383,37384],{},"Disponibilní důchod",[1176,37386,37387],{},"disposable income",[1035,37389,37391],{"className":37390},[1480],[1482,37392,37393],{"xmlns":1484,"display":1485},[1487,37394,37395,37411],{},[1490,37396,37397,37403,37405,37407,37409],{},[1497,37398,37399,37401],{},[1493,37400,1791],{},[1493,37402,3712],{},[1506,37404,1508],{},[1493,37406,1791],{},[1506,37408,1888],{},[1493,37410,5289],{},[1528,37412,37317],{"encoding":1530},[1030,37414,37415,37416,2632],{},"je to, co zbývá domácnostem po zdanění. Spotřeba je pak funkcí disponibilního důchodu: ",[1035,37417,37419],{"className":37418},[1480],[1482,37420,37421],{"xmlns":1484},[1487,37422,37423,37441],{},[1490,37424,37425,37427,37429,37431,37433,37439],{},[1493,37426,1998],{},[1506,37428,1508],{},[1493,37430,1998],{},[1506,37432,1553],{"stretchy":1552},[1497,37434,37435,37437],{},[1493,37436,1791],{},[1493,37438,3712],{},[1506,37440,1564],{"stretchy":1552},[1528,37442,37346],{"encoding":1530},[1304,37444,36411],{"id":37445},"soustava-rovnic-1",[1030,37447,37448,37449,1732,37470,37492,37493,1274],{},"Pro pevně zadané ",[1035,37450,37452],{"className":37451},[1480],[1482,37453,37454],{"xmlns":1484},[1487,37455,37456,37468],{},[1490,37457,37458,37460,37462],{},[1493,37459,2662],{},[1506,37461,1508],{},[2315,37463,37464,37466],{},[1493,37465,2662],{},[1506,37467,2287],{},[1528,37469,28677],{"encoding":1530},[1035,37471,37473],{"className":37472},[1480],[1482,37474,37475],{"xmlns":1484},[1487,37476,37477,37489],{},[1490,37478,37479,37481,37483],{},[1493,37480,28595],{},[1506,37482,1508],{},[2315,37484,37485,37487],{},[1493,37486,28595],{},[1506,37488,2287],{},[1528,37490,37491],{"encoding":1530},"G = G^*"," dostáváme soustavu 4 rovnic o 4 neznámých ",[1035,37494,37496],{"className":37495},[1480],[1482,37497,37498],{"xmlns":1484},[1487,37499,37500,37520],{},[1490,37501,37502,37504,37506,37508,37510,37516,37518],{},[1493,37503,1791],{},[1506,37505,1559],{"separator":1041},[1493,37507,1998],{},[1506,37509,1559],{"separator":1041},[1497,37511,37512,37514],{},[1493,37513,1791],{},[1493,37515,3712],{},[1506,37517,1559],{"separator":1041},[1493,37519,5289],{},[1528,37521,37522],{"encoding":1530},"Y, C, Y_D, T",[1035,37524,37526],{"className":37525},[1480],[1482,37527,37528],{"xmlns":1484,"display":1485},[1487,37529,37530,37671],{},[1490,37531,37532,37662,37664,37666,37669],{},[19617,37533,37534,37572,37600,37632],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,37535,37536,37542],{},[19624,37537,37538],{},[1869,37539,37540],{"scriptlevel":1871,"displaystyle":1041},[1493,37541,1791],{},[19624,37543,37544],{},[1869,37545,37546],{"scriptlevel":1871,"displaystyle":1041},[1490,37547,37548,37550,37552,37554,37556,37562,37564,37570],{},[1490,37549],{},[1506,37551,1508],{},[1493,37553,1998],{},[1506,37555,2162],{},[2315,37557,37558,37560],{},[1493,37559,2662],{},[1506,37561,2287],{},[1506,37563,2162],{},[2315,37565,37566,37568],{},[1493,37567,28595],{},[1506,37569,2287],{},[1506,37571,1559],{"separator":1041},[19621,37573,37574,37580],{},[19624,37575,37576],{},[1869,37577,37578],{"scriptlevel":1871,"displaystyle":1041},[1493,37579,5289],{},[19624,37581,37582],{},[1869,37583,37584],{"scriptlevel":1871,"displaystyle":1041},[1490,37585,37586,37588,37590,37592,37594,37596,37598],{},[1490,37587],{},[1506,37589,1508],{},[1493,37591,5289],{},[1506,37593,1553],{"stretchy":1552},[1493,37595,1791],{},[1506,37597,1564],{"stretchy":1552},[1506,37599,1559],{"separator":1041},[19621,37601,37602,37608],{},[19624,37603,37604],{},[1869,37605,37606],{"scriptlevel":1871,"displaystyle":1041},[1493,37607,1998],{},[19624,37609,37610],{},[1869,37611,37612],{"scriptlevel":1871,"displaystyle":1041},[1490,37613,37614,37616,37618,37620,37622,37628,37630],{},[1490,37615],{},[1506,37617,1508],{},[1493,37619,1998],{},[1506,37621,1553],{"stretchy":1552},[1497,37623,37624,37626],{},[1493,37625,1791],{},[1493,37627,3712],{},[1506,37629,1564],{"stretchy":1552},[1506,37631,1559],{"separator":1041},[19621,37633,37634,37644],{},[19624,37635,37636],{},[1869,37637,37638],{"scriptlevel":1871,"displaystyle":1041},[1497,37639,37640,37642],{},[1493,37641,1791],{},[1493,37643,3712],{},[19624,37645,37646],{},[1869,37647,37648],{"scriptlevel":1871,"displaystyle":1041},[1490,37649,37650,37652,37654,37656,37658,37660],{},[1490,37651],{},[1506,37653,1508],{},[1493,37655,1791],{},[1506,37657,1888],{},[1493,37659,5289],{},[1506,37661,1559],{"separator":1041},[1912,37663],{"width":1914},[1506,37665,1553],{"stretchy":1552},[1680,37667,37668],{},"7.9",[1506,37670,1564],{"stretchy":1552},[1528,37672,37673],{"encoding":1530},"\\begin{aligned} Y &= C + I^* + G^*, \\\\ T &= T(Y), \\\\ C &= C(Y_D), \\\\ Y_D &= Y - T, \\end{aligned} \\qquad (7.9)",[1030,37675,37676,37677,37721,37722,2632],{},"s řešeními ",[1035,37678,37680],{"className":37679},[1480],[1482,37681,37682],{"xmlns":1484},[1487,37683,37684,37718],{},[1490,37685,37686,37692,37694,37700,37702,37708,37710],{},[2315,37687,37688,37690],{},[1493,37689,1791],{},[1493,37691,2711],{},[1506,37693,1559],{"separator":1041},[2315,37695,37696,37698],{},[1493,37697,1998],{},[1493,37699,2711],{},[1506,37701,1559],{"separator":1041},[2315,37703,37704,37706],{},[1493,37705,5289],{},[1493,37707,2711],{},[1506,37709,1559],{"separator":1041},[1697,37711,37712,37714,37716],{},[1493,37713,1791],{},[1493,37715,3712],{},[1493,37717,2711],{},[1528,37719,37720],{"encoding":1530},"Y^E, C^E, T^E, Y_D^E",", případně rovnovážnými úsporami domácností ",[1035,37723,37725],{"className":37724},[1480],[1482,37726,37727],{"xmlns":1484},[1487,37728,37729,37755],{},[1490,37730,37731,37737,37739,37747,37749],{},[2315,37732,37733,37735],{},[1493,37734,2001],{},[1493,37736,2711],{},[1506,37738,1508],{},[1697,37740,37741,37743,37745],{},[1493,37742,1791],{},[1493,37744,3712],{},[1493,37746,2711],{},[1506,37748,1888],{},[2315,37750,37751,37753],{},[1493,37752,1998],{},[1493,37754,2711],{},[1528,37756,37757],{"encoding":1530},"S^E = Y_D^E - C^E",[1023,37759,37761,37768],{"className":37760,"dataCallout":1443},[1026,1442],[1030,37762,37764,37767],{"className":37763},[1033],[1035,37765],{"className":37766,"ariaHidden":1041},[1038,1450,1040],"Postup — jak sestavit a vyřešit soustavu C-I-G",[1276,37769,37770,37793,37876,37931,38021],{},[1206,37771,37772,37775,37776,2632],{},[1047,37773,37774],{},"Zapiš všechny 4 rovnice"," ze zadání: podmínku rovnováhy, daňovou funkci, funkci spotřeby, definici ",[1035,37777,37779],{"className":37778},[1480],[1482,37780,37781],{"xmlns":1484},[1487,37782,37783,37791],{},[1490,37784,37785],{},[1497,37786,37787,37789],{},[1493,37788,1791],{},[1493,37790,3712],{},[1528,37792,37378],{"encoding":1530},[1206,37794,37795,37844,37845,37862,37863,2632],{},[1047,37796,37797,37798,37818,37819],{},"Dosaď ",[1035,37799,37801],{"className":37800},[1480],[1482,37802,37803],{"xmlns":1484},[1487,37804,37805,37815],{},[1490,37806,37807,37809,37811,37813],{},[1493,37808,5289],{},[1506,37810,1553],{"stretchy":1552},[1493,37812,1791],{},[1506,37814,1564],{"stretchy":1552},[1528,37816,37817],{"encoding":1530},"T(Y)"," do ",[1035,37820,37822],{"className":37821},[1480],[1482,37823,37824],{"xmlns":1484},[1487,37825,37826,37842],{},[1490,37827,37828,37834,37836,37838,37840],{},[1497,37829,37830,37832],{},[1493,37831,1791],{},[1493,37833,3712],{},[1506,37835,1508],{},[1493,37837,1791],{},[1506,37839,1888],{},[1493,37841,5289],{},[1528,37843,37317],{"encoding":1530}," — dostaneš ",[1035,37846,37848],{"className":37847},[1480],[1482,37849,37850],{"xmlns":1484},[1487,37851,37852,37860],{},[1490,37853,37854],{},[1497,37855,37856,37858],{},[1493,37857,1791],{},[1493,37859,3712],{},[1528,37861,37378],{"encoding":1530}," jako lineární funkci ",[1035,37864,37866],{"className":37865},[1480],[1482,37867,37868],{"xmlns":1484},[1487,37869,37870,37874],{},[1490,37871,37872],{},[1493,37873,1791],{},[1528,37875,1791],{"encoding":1530},[1206,37877,37878,37844,37905,37862,37918,2632],{},[1047,37879,37797,37880,37904],{},[1035,37881,37883],{"className":37882},[1480],[1482,37884,37885],{"xmlns":1484},[1487,37886,37887,37901],{},[1490,37888,37889,37895,37897,37899],{},[1497,37890,37891,37893],{},[1493,37892,1791],{},[1493,37894,3712],{},[1506,37896,1553],{"stretchy":1552},[1493,37898,1791],{},[1506,37900,1564],{"stretchy":1552},[1528,37902,37903],{"encoding":1530},"Y_D(Y)"," do funkce spotřeby",[1035,37906,37908],{"className":37907},[1480],[1482,37909,37910],{"xmlns":1484},[1487,37911,37912,37916],{},[1490,37913,37914],{},[1493,37915,1998],{},[1528,37917,1998],{"encoding":1530},[1035,37919,37921],{"className":37920},[1480],[1482,37922,37923],{"xmlns":1484},[1487,37924,37925,37929],{},[1490,37926,37927],{},[1493,37928,1791],{},[1528,37930,1791],{"encoding":1530},[1206,37932,37933,1656,37955,37989,37990,38003,38004,2632],{},[1047,37934,37797,37935,37954],{},[1035,37936,37938],{"className":37937},[1480],[1482,37939,37940],{"xmlns":1484},[1487,37941,37942,37952],{},[1490,37943,37944,37946,37948,37950],{},[1493,37945,1998],{},[1506,37947,1553],{"stretchy":1552},[1493,37949,1791],{},[1506,37951,1564],{"stretchy":1552},[1528,37953,30540],{"encoding":1530}," do podmínky rovnováhy",[1035,37956,37958],{"className":37957},[1480],[1482,37959,37960],{"xmlns":1484},[1487,37961,37962,37986],{},[1490,37963,37964,37966,37968,37970,37972,37978,37980],{},[1493,37965,1791],{},[1506,37967,1508],{},[1493,37969,1998],{},[1506,37971,2162],{},[2315,37973,37974,37976],{},[1493,37975,2662],{},[1506,37977,2287],{},[1506,37979,2162],{},[2315,37981,37982,37984],{},[1493,37983,28595],{},[1506,37985,2287],{},[1528,37987,37988],{"encoding":1530},"Y = C + I^* + G^*"," — zbývá jediná rovnice o jedné neznámé ",[1035,37991,37993],{"className":37992},[1480],[1482,37994,37995],{"xmlns":1484},[1487,37996,37997,38001],{},[1490,37998,37999],{},[1493,38000,1791],{},[1528,38002,1791],{"encoding":1530},", odtud ",[1035,38005,38007],{"className":38006},[1480],[1482,38008,38009],{"xmlns":1484},[1487,38010,38011,38019],{},[1490,38012,38013],{},[2315,38014,38015,38017],{},[1493,38016,1791],{},[1493,38018,2711],{},[1528,38020,3419],{"encoding":1530},[1206,38022,38023,38026,38027,1732,38045,1732,38065,1732,38082,2632],{},[1047,38024,38025],{},"Zpětným dosazením"," dopočítej ",[1035,38028,38030],{"className":38029},[1480],[1482,38031,38032],{"xmlns":1484},[1487,38033,38034,38042],{},[1490,38035,38036],{},[2315,38037,38038,38040],{},[1493,38039,5289],{},[1493,38041,2711],{},[1528,38043,38044],{"encoding":1530},"T^E",[1035,38046,38048],{"className":38047},[1480],[1482,38049,38050],{"xmlns":1484},[1487,38051,38052,38062],{},[1490,38053,38054],{},[1697,38055,38056,38058,38060],{},[1493,38057,1791],{},[1493,38059,3712],{},[1493,38061,2711],{},[1528,38063,38064],{"encoding":1530},"Y_D^E",[1035,38066,38068],{"className":38067},[1480],[1482,38069,38070],{"xmlns":1484},[1487,38071,38072,38080],{},[1490,38073,38074],{},[2315,38075,38076,38078],{},[1493,38077,1998],{},[1493,38079,2711],{},[1528,38081,30432],{"encoding":1530},[1035,38083,38085],{"className":38084},[1480],[1482,38086,38087],{"xmlns":1484},[1487,38088,38089,38097],{},[1490,38090,38091],{},[2315,38092,38093,38095],{},[1493,38094,2001],{},[1493,38096,2711],{},[1528,38098,38099],{"encoding":1530},"S^E",[1304,38101,38103],{"id":38102},"příklad-74","Příklad 7.4",[1030,38105,36734,38106,38127,38128,1732,38158,1732,38182,1732,38204,38226],{},[1035,38107,38109],{"className":38108},[1480],[1482,38110,38111],{"xmlns":1484},[1487,38112,38113,38125],{},[1490,38114,38115,38117,38119,38121,38123],{},[1493,38116,1998],{},[1988,38118,28777],{},[1493,38120,2662],{},[1988,38122,28777],{},[1493,38124,28595],{},[1528,38126,34367],{"encoding":1530}," jsou dány ",[1035,38129,38131],{"className":38130},[1480],[1482,38132,38133],{"xmlns":1484},[1487,38134,38135,38155],{},[1490,38136,38137,38139,38141,38143,38145,38151,38153],{},[1493,38138,1998],{},[1506,38140,1508],{},[1680,38142,13364],{},[1988,38144,5016],{},[1497,38146,38147,38149],{},[1493,38148,1791],{},[1493,38150,3712],{},[1506,38152,2162],{},[1680,38154,21768],{},[1528,38156,38157],{"encoding":1530},"C = 0{,}9\\,Y_D + 70",[1035,38159,38161],{"className":38160},[1480],[1482,38162,38163],{"xmlns":1484},[1487,38164,38165,38179],{},[1490,38166,38167,38169,38171,38173,38175,38177],{},[1493,38168,5289],{},[1506,38170,1508],{},[1680,38172,2929],{},[1493,38174,1791],{},[1506,38176,2162],{},[1680,38178,2309],{},[1528,38180,38181],{"encoding":1530},"T = 0{,}2Y + 25",[1035,38183,38185],{"className":38184},[1480],[1482,38186,38187],{"xmlns":1484},[1487,38188,38189,38201],{},[1490,38190,38191,38197,38199],{},[2315,38192,38193,38195],{},[1493,38194,2662],{},[1506,38196,2287],{},[1506,38198,1508],{},[1680,38200,5603],{},[1528,38202,38203],{"encoding":1530},"I^* = 35",[1035,38205,38207],{"className":38206},[1480],[1482,38208,38209],{"xmlns":1484},[1487,38210,38211,38223],{},[1490,38212,38213,38219,38221],{},[2315,38214,38215,38217],{},[1493,38216,28595],{},[1506,38218,2287],{},[1506,38220,1508],{},[1680,38222,8436],{},[1528,38224,38225],{"encoding":1530},"G^* = 20",". Soustava (7.9):",[1035,38228,38230],{"className":38229},[1480],[1482,38231,38232],{"xmlns":1484,"display":1485},[1487,38233,38234,38358],{},[19617,38235,38236,38266,38294,38328],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,38237,38238,38244],{},[19624,38239,38240],{},[1869,38241,38242],{"scriptlevel":1871,"displaystyle":1041},[1493,38243,1791],{},[19624,38245,38246],{},[1869,38247,38248],{"scriptlevel":1871,"displaystyle":1041},[1490,38249,38250,38252,38254,38256,38258,38260,38262,38264],{},[1490,38251],{},[1506,38253,1508],{},[1493,38255,1998],{},[1506,38257,2162],{},[1680,38259,5603],{},[1506,38261,2162],{},[1680,38263,8436],{},[1506,38265,1559],{"separator":1041},[19621,38267,38268,38274],{},[19624,38269,38270],{},[1869,38271,38272],{"scriptlevel":1871,"displaystyle":1041},[1493,38273,5289],{},[19624,38275,38276],{},[1869,38277,38278],{"scriptlevel":1871,"displaystyle":1041},[1490,38279,38280,38282,38284,38286,38288,38290,38292],{},[1490,38281],{},[1506,38283,1508],{},[1680,38285,2929],{},[1493,38287,1791],{},[1506,38289,2162],{},[1680,38291,2309],{},[1506,38293,1559],{"separator":1041},[19621,38295,38296,38302],{},[19624,38297,38298],{},[1869,38299,38300],{"scriptlevel":1871,"displaystyle":1041},[1493,38301,1998],{},[19624,38303,38304],{},[1869,38305,38306],{"scriptlevel":1871,"displaystyle":1041},[1490,38307,38308,38310,38312,38314,38316,38322,38324,38326],{},[1490,38309],{},[1506,38311,1508],{},[1680,38313,13364],{},[1988,38315,5016],{},[1497,38317,38318,38320],{},[1493,38319,1791],{},[1493,38321,3712],{},[1506,38323,2162],{},[1680,38325,21768],{},[1506,38327,1559],{"separator":1041},[19621,38329,38330,38340],{},[19624,38331,38332],{},[1869,38333,38334],{"scriptlevel":1871,"displaystyle":1041},[1497,38335,38336,38338],{},[1493,38337,1791],{},[1493,38339,3712],{},[19624,38341,38342],{},[1869,38343,38344],{"scriptlevel":1871,"displaystyle":1041},[1490,38345,38346,38348,38350,38352,38354,38356],{},[1490,38347],{},[1506,38349,1508],{},[1493,38351,1791],{},[1506,38353,1888],{},[1493,38355,5289],{},[1493,38357,2632],{"mathvariant":1516},[1528,38359,38360],{"encoding":1530},"\\begin{aligned} Y &= C + 35 + 20, \\\\ T &= 0{,}2Y + 25, \\\\ C &= 0{,}9\\,Y_D + 70, \\\\ Y_D &= Y - T. \\end{aligned}",[1030,38362,38363,38366,38367,38421,38422,38468,38469,1274],{},[1047,38364,38365],{},"Řešení."," Z definice ",[1035,38368,38370],{"className":38369},[1480],[1482,38371,38372],{"xmlns":1484},[1487,38373,38374,38418],{},[1490,38375,38376,38382,38384,38386,38388,38390,38392,38394,38396,38398,38400,38402,38404,38406,38408,38410,38412,38414,38416],{},[1497,38377,38378,38380],{},[1493,38379,1791],{},[1493,38381,3712],{},[1506,38383,1508],{},[1493,38385,1791],{},[1506,38387,1888],{},[1493,38389,5289],{},[1506,38391,1508],{},[1493,38393,1791],{},[1506,38395,1888],{},[1506,38397,1553],{"stretchy":1552},[1680,38399,2929],{},[1493,38401,1791],{},[1506,38403,2162],{},[1680,38405,2309],{},[1506,38407,1564],{"stretchy":1552},[1506,38409,1508],{},[1680,38411,2939],{},[1493,38413,1791],{},[1506,38415,1888],{},[1680,38417,2309],{},[1528,38419,38420],{"encoding":1530},"Y_D = Y - T = Y - (0{,}2Y + 25) = 0{,}8Y - 25",". Dosazením do spotřeby: ",[1035,38423,38425],{"className":38424},[1480],[1482,38426,38427],{"xmlns":1484},[1487,38428,38429,38465],{},[1490,38430,38431,38433,38435,38437,38439,38441,38443,38445,38447,38449,38451,38453,38455,38458,38460,38462],{},[1493,38432,1998],{},[1506,38434,1508],{},[1680,38436,13364],{},[1506,38438,1553],{"stretchy":1552},[1680,38440,2939],{},[1493,38442,1791],{},[1506,38444,1888],{},[1680,38446,2309],{},[1506,38448,1564],{"stretchy":1552},[1506,38450,2162],{},[1680,38452,21768],{},[1506,38454,1508],{},[1680,38456,38457],{},"0,72",[1493,38459,1791],{},[1506,38461,2162],{},[1680,38463,38464],{},"47,5",[1528,38466,38467],{"encoding":1530},"C = 0{,}9(0{,}8Y - 25) + 70 = 0{,}72Y + 47{,}5",". Dosazením do rovnovážné rovnice ",[1035,38470,38472],{"className":38471},[1480],[1482,38473,38474],{"xmlns":1484},[1487,38475,38476,38494],{},[1490,38477,38478,38480,38482,38484,38486,38488,38490,38492],{},[1493,38479,1791],{},[1506,38481,1508],{},[1680,38483,38457],{},[1493,38485,1791],{},[1506,38487,2162],{},[1680,38489,38464],{},[1506,38491,2162],{},[1680,38493,36891],{},[1528,38495,38496],{"encoding":1530},"Y = 0{,}72Y + 47{,}5 + 55",[1035,38498,38500],{"className":38499},[1480],[1482,38501,38502],{"xmlns":1484,"display":1485},[1487,38503,38504,38545],{},[1490,38505,38506,38509,38511,38513,38516,38518,38520,38522,38528,38530,38540,38542],{},[1680,38507,38508],{},"0,28",[1493,38510,1791],{},[1506,38512,1508],{},[1680,38514,38515],{},"102,5",[1988,38517,1990],{},[1506,38519,2111],{},[1988,38521,1990],{},[2315,38523,38524,38526],{},[1493,38525,1791],{},[1493,38527,2711],{},[1506,38529,1508],{},[1869,38531,38532],{"scriptlevel":1871,"displaystyle":1552},[1510,38533,38534,38537],{},[1680,38535,38536],{},"5125",[1680,38538,38539],{},"14",[1506,38541,21771],{},[1680,38543,38544],{},"366,071.",[1528,38546,38547],{"encoding":1530},"0{,}28Y = 102{,}5 \\;\\Longrightarrow\\; Y^E = \\tfrac{5125}{14} \\doteq 366{,}071.",[1030,38549,38550],{},"Rovnovážné veličiny:",[1203,38552,38553,38588,38639,38693,38741],{},[1206,38554,38555,1559],{},[1035,38556,38558],{"className":38557},[1480],[1482,38559,38560],{"xmlns":1484},[1487,38561,38562,38585],{},[1490,38563,38564,38570,38572,38580,38582],{},[2315,38565,38566,38568],{},[1493,38567,1791],{},[1493,38569,2711],{},[1506,38571,1508],{},[1869,38573,38574],{"scriptlevel":1871,"displaystyle":1552},[1510,38575,38576,38578],{},[1680,38577,38536],{},[1680,38579,38539],{},[1506,38581,21771],{},[1680,38583,38584],{},"366,071",[1528,38586,38587],{"encoding":1530},"Y^E = \\tfrac{5125}{14} \\doteq 366{,}071",[1206,38589,38590,1559],{},[1035,38591,38593],{"className":38592},[1480],[1482,38594,38595],{"xmlns":1484},[1487,38596,38597,38636],{},[1490,38598,38599,38605,38607,38609,38611,38617,38619,38621,38623,38631,38633],{},[2315,38600,38601,38603],{},[1493,38602,5289],{},[1493,38604,2711],{},[1506,38606,1508],{},[1680,38608,2929],{},[1988,38610,5016],{},[2315,38612,38613,38615],{},[1493,38614,1791],{},[1493,38616,2711],{},[1506,38618,2162],{},[1680,38620,2309],{},[1506,38622,1508],{},[1869,38624,38625],{"scriptlevel":1871,"displaystyle":1552},[1510,38626,38627,38629],{},[1680,38628,2952],{},[1680,38630,38539],{},[1506,38632,21771],{},[1680,38634,38635],{},"98,214",[1528,38637,38638],{"encoding":1530},"T^E = 0{,}2\\,Y^E + 25 = \\tfrac{1375}{14} \\doteq 98{,}214",[1206,38640,38641,1559],{},[1035,38642,38644],{"className":38643},[1480],[1482,38645,38646],{"xmlns":1484},[1487,38647,38648,38690],{},[1490,38649,38650,38658,38660,38666,38668,38674,38676,38685,38687],{},[1697,38651,38652,38654,38656],{},[1493,38653,1791],{},[1493,38655,3712],{},[1493,38657,2711],{},[1506,38659,1508],{},[2315,38661,38662,38664],{},[1493,38663,1791],{},[1493,38665,2711],{},[1506,38667,1888],{},[2315,38669,38670,38672],{},[1493,38671,5289],{},[1493,38673,2711],{},[1506,38675,1508],{},[1869,38677,38678],{"scriptlevel":1871,"displaystyle":1552},[1510,38679,38680,38683],{},[1680,38681,38682],{},"3750",[1680,38684,38539],{},[1506,38686,21771],{},[1680,38688,38689],{},"267,857",[1528,38691,38692],{"encoding":1530},"Y_D^E = Y^E - T^E = \\tfrac{3750}{14} \\doteq 267{,}857",[1206,38694,38695,1559],{},[1035,38696,38698],{"className":38697},[1480],[1482,38699,38700],{"xmlns":1484},[1487,38701,38702,38738],{},[1490,38703,38704,38710,38712,38718,38720,38722,38724,38733,38735],{},[2315,38705,38706,38708],{},[1493,38707,1998],{},[1493,38709,2711],{},[1506,38711,1508],{},[2315,38713,38714,38716],{},[1493,38715,1791],{},[1493,38717,2711],{},[1506,38719,1888],{},[1680,38721,36891],{},[1506,38723,1508],{},[1869,38725,38726],{"scriptlevel":1871,"displaystyle":1552},[1510,38727,38728,38731],{},[1680,38729,38730],{},"4355",[1680,38732,38539],{},[1506,38734,21771],{},[1680,38736,38737],{},"311,071",[1528,38739,38740],{"encoding":1530},"C^E = Y^E - 55 = \\tfrac{4355}{14} \\doteq 311{,}071",[1206,38742,38743,38799],{},[1035,38744,38746],{"className":38745},[1480],[1482,38747,38748],{"xmlns":1484},[1487,38749,38750,38796],{},[1490,38751,38752,38758,38760,38768,38770,38776,38778,38780,38789,38791,38793],{},[2315,38753,38754,38756],{},[1493,38755,2001],{},[1493,38757,2711],{},[1506,38759,1508],{},[1697,38761,38762,38764,38766],{},[1493,38763,1791],{},[1493,38765,3712],{},[1493,38767,2711],{},[1506,38769,1888],{},[2315,38771,38772,38774],{},[1493,38773,1998],{},[1493,38775,2711],{},[1506,38777,1508],{},[1506,38779,1888],{},[1869,38781,38782],{"scriptlevel":1871,"displaystyle":1552},[1510,38783,38784,38787],{},[1680,38785,38786],{},"605",[1680,38788,38539],{},[1506,38790,21771],{},[1506,38792,1888],{},[1680,38794,38795],{},"43,214",[1528,38797,38798],{"encoding":1530},"S^E = Y_D^E - C^E = -\\tfrac{605}{14} \\doteq -43{,}214"," (záporné — domácnosti při této kalibraci čerpají úspory).",[1030,38801,38802,36946,38804,38825,38826,38829,38830,38852,38853,2632],{},[1047,38803,36945],{},[1035,38805,38807],{"className":38806},[1480],[1482,38808,38809],{"xmlns":1484},[1487,38810,38811,38823],{},[1490,38812,38813,38815,38817,38819,38821],{},[1493,38814,1998],{},[1988,38816,28777],{},[1493,38818,2662],{},[1988,38820,28777],{},[1493,38822,28595],{},[1528,38824,34367],{"encoding":1530}," stále uvažuje ",[1047,38827,38828],{},"uzavřenou"," ekonomiku. Reálné ekonomiky dovážejí a vyvážejí zboží — otevření ekonomiky o čistý export ",[1035,38831,38833],{"className":38832},[1480],[1482,38834,38835],{"xmlns":1484},[1487,38836,38837,38849],{},[1490,38838,38839,38841,38843,38845,38847],{},[1493,38840,28807],{},[1506,38842,1508],{},[1493,38844,11353],{},[1506,38846,1888],{},[1493,38848,1495],{},[1528,38850,38851],{"encoding":1530},"X = B - M"," dává ",[1047,38854,36967,38855],{},[1035,38856,38858],{"className":38857},[1480],[1482,38859,38860],{"xmlns":1484},[1487,38861,38862,38878],{},[1490,38863,38864,38866,38868,38870,38872,38874,38876],{},[1493,38865,1998],{},[1988,38867,28777],{},[1493,38869,2662],{},[1988,38871,28777],{},[1493,38873,28595],{},[1988,38875,28777],{},[1493,38877,28807],{},[1528,38879,28810],{"encoding":1530},[1065,38881,38883],{"id":38882},"model-c-i-g-x-otevřená-ekonomika","Model C-I-G-X — otevřená ekonomika",[1304,38885,36343],{"id":38886},"zadání-modelu-2",[1030,38888,38889,38890,1656,38893,37188,38914,38927,38928,28611,38931,38944],{},"Rozšíření o ",[1047,38891,38892],{},"čistý export",[1035,38894,38896],{"className":38895},[1480],[1482,38897,38898],{"xmlns":1484},[1487,38899,38900,38912],{},[1490,38901,38902,38904,38906,38908,38910],{},[1493,38903,28807],{},[1506,38905,1508],{},[1493,38907,11353],{},[1506,38909,1888],{},[1493,38911,1495],{},[1528,38913,38851],{"encoding":1530},[1035,38915,38917],{"className":38916},[1480],[1482,38918,38919],{"xmlns":1484},[1487,38920,38921,38925],{},[1490,38922,38923],{},[1493,38924,11353],{},[1528,38926,11353],{"encoding":1530}," je hrubý export (",[1176,38929,38930],{},"brutto export",[1035,38932,38934],{"className":38933},[1480],[1482,38935,38936],{"xmlns":1484},[1487,38937,38938,38942],{},[1490,38939,38940],{},[1493,38941,1495],{},[1528,38943,1495],{"encoding":1530}," import. Obvyklá konstrukce: import závisí (nejčastěji je úměrný) disponibilnímu důchodu:",[1035,38946,38948],{"className":38947},[1480],[1482,38949,38950],{"xmlns":1484,"display":1485},[1487,38951,38952,38972],{},[1490,38953,38954,38956,38958,38960,38962,38968,38970],{},[1493,38955,1495],{},[1506,38957,1508],{},[1493,38959,1495],{},[1506,38961,1553],{"stretchy":1552},[1497,38963,38964,38966],{},[1493,38965,1791],{},[1493,38967,3712],{},[1506,38969,1564],{"stretchy":1552},[1493,38971,2632],{"mathvariant":1516},[1528,38973,38974],{"encoding":1530},"M = M(Y_D).",[1030,38976,38977],{},"Podmínka rovnováhy:",[1035,38979,38981],{"className":38980},[1480],[1482,38982,38983],{"xmlns":1484,"display":1485},[1487,38984,38985,39022],{},[1490,38986,38987,38989,38991,38993,38995,38997,38999,39001,39003,39005,39007,39009,39011,39013,39015,39018,39020],{},[1493,38988,1791],{},[1506,38990,1508],{},[1493,38992,1998],{},[1506,38994,2162],{},[1493,38996,2662],{},[1506,38998,2162],{},[1493,39000,28595],{},[1506,39002,2162],{},[1493,39004,11353],{},[1506,39006,1888],{},[1493,39008,1495],{},[1493,39010,2632],{"mathvariant":1516},[1912,39012],{"width":1914},[1506,39014,1553],{"stretchy":1552},[1680,39016,39017],{},"7.10",[1988,39019,1052],{},[1506,39021,1564],{"stretchy":1552},[1528,39023,39024],{"encoding":1530},"Y = C + I + G + B - M. \\qquad (7.10\\text{a})",[1304,39026,36411],{"id":39027},"soustava-rovnic-2",[1030,39029,37448,39030,39064,39065,1274],{},[1035,39031,39033],{"className":39032},[1480],[1482,39034,39035],{"xmlns":1484},[1487,39036,39037,39061],{},[1490,39038,39039,39045,39047,39053,39055],{},[2315,39040,39041,39043],{},[1493,39042,2662],{},[1506,39044,2287],{},[1506,39046,1559],{"separator":1041},[2315,39048,39049,39051],{},[1493,39050,28595],{},[1506,39052,2287],{},[1506,39054,1559],{"separator":1041},[2315,39056,39057,39059],{},[1493,39058,11353],{},[1506,39060,2287],{},[1528,39062,39063],{"encoding":1530},"I^*, G^*, B^*"," dostáváme soustavu 5 rovnic o 5 neznámých ",[1035,39066,39068],{"className":39067},[1480],[1482,39069,39070],{"xmlns":1484},[1487,39071,39072,39096],{},[1490,39073,39074,39076,39078,39080,39082,39084,39086,39092,39094],{},[1493,39075,1791],{},[1506,39077,1559],{"separator":1041},[1493,39079,1998],{},[1506,39081,1559],{"separator":1041},[1493,39083,5289],{},[1506,39085,1559],{"separator":1041},[1497,39087,39088,39090],{},[1493,39089,1791],{},[1493,39091,3712],{},[1506,39093,1559],{"separator":1041},[1493,39095,1495],{},[1528,39097,39098],{"encoding":1530},"Y, C, T, Y_D, M",[1035,39100,39102],{"className":39101},[1480],[1482,39103,39104],{"xmlns":1484,"display":1485},[1487,39105,39106,39290],{},[1490,39107,39108,39282,39284,39286,39288],{},[19617,39109,39110,39142,39172,39200,39232],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,39111,39112,39118],{},[19624,39113,39114],{},[1869,39115,39116],{"scriptlevel":1871,"displaystyle":1041},[1493,39117,1998],{},[19624,39119,39120],{},[1869,39121,39122],{"scriptlevel":1871,"displaystyle":1041},[1490,39123,39124,39126,39128,39130,39132,39138,39140],{},[1490,39125],{},[1506,39127,1508],{},[1493,39129,1998],{},[1506,39131,1553],{"stretchy":1552},[1497,39133,39134,39136],{},[1493,39135,1791],{},[1493,39137,3712],{},[1506,39139,1564],{"stretchy":1552},[1506,39141,1559],{"separator":1041},[19621,39143,39144,39154],{},[19624,39145,39146],{},[1869,39147,39148],{"scriptlevel":1871,"displaystyle":1041},[1497,39149,39150,39152],{},[1493,39151,1791],{},[1493,39153,3712],{},[19624,39155,39156],{},[1869,39157,39158],{"scriptlevel":1871,"displaystyle":1041},[1490,39159,39160,39162,39164,39166,39168,39170],{},[1490,39161],{},[1506,39163,1508],{},[1493,39165,1791],{},[1506,39167,1888],{},[1493,39169,5289],{},[1506,39171,1559],{"separator":1041},[19621,39173,39174,39180],{},[19624,39175,39176],{},[1869,39177,39178],{"scriptlevel":1871,"displaystyle":1041},[1493,39179,5289],{},[19624,39181,39182],{},[1869,39183,39184],{"scriptlevel":1871,"displaystyle":1041},[1490,39185,39186,39188,39190,39192,39194,39196,39198],{},[1490,39187],{},[1506,39189,1508],{},[1493,39191,5289],{},[1506,39193,1553],{"stretchy":1552},[1493,39195,1791],{},[1506,39197,1564],{"stretchy":1552},[1506,39199,1559],{"separator":1041},[19621,39201,39202,39208],{},[19624,39203,39204],{},[1869,39205,39206],{"scriptlevel":1871,"displaystyle":1041},[1493,39207,1495],{},[19624,39209,39210],{},[1869,39211,39212],{"scriptlevel":1871,"displaystyle":1041},[1490,39213,39214,39216,39218,39220,39222,39228,39230],{},[1490,39215],{},[1506,39217,1508],{},[1493,39219,1495],{},[1506,39221,1553],{"stretchy":1552},[1497,39223,39224,39226],{},[1493,39225,1791],{},[1493,39227,3712],{},[1506,39229,1564],{"stretchy":1552},[1506,39231,1559],{"separator":1041},[19621,39233,39234,39240],{},[19624,39235,39236],{},[1869,39237,39238],{"scriptlevel":1871,"displaystyle":1041},[1493,39239,1791],{},[19624,39241,39242],{},[1869,39243,39244],{"scriptlevel":1871,"displaystyle":1041},[1490,39245,39246,39248,39250,39252,39254,39260,39262,39268,39270,39276,39278,39280],{},[1490,39247],{},[1506,39249,1508],{},[1493,39251,1998],{},[1506,39253,2162],{},[2315,39255,39256,39258],{},[1493,39257,2662],{},[1506,39259,2287],{},[1506,39261,2162],{},[2315,39263,39264,39266],{},[1493,39265,28595],{},[1506,39267,2287],{},[1506,39269,2162],{},[2315,39271,39272,39274],{},[1493,39273,11353],{},[1506,39275,2287],{},[1506,39277,1888],{},[1493,39279,1495],{},[1493,39281,2632],{"mathvariant":1516},[1912,39283],{"width":1914},[1506,39285,1553],{"stretchy":1552},[1680,39287,39017],{},[1506,39289,1564],{"stretchy":1552},[1528,39291,39292],{"encoding":1530},"\\begin{aligned} C &= C(Y_D), \\\\ Y_D &= Y - T, \\\\ T &= T(Y), \\\\ M &= M(Y_D), \\\\ Y &= C + I^* + G^* + B^* - M. \\end{aligned} \\qquad (7.10)",[1304,39294,39296],{"id":39295},"příklad-75","Příklad 7.5",[1030,39298,39299,39300,1732,39332,1732,39359,1732,39379,1732,39401,1732,39423,39445],{},"Dáno: ",[1035,39301,39303],{"className":39302},[1480],[1482,39304,39305],{"xmlns":1484},[1487,39306,39307,39329],{},[1490,39308,39309,39311,39313,39316,39318,39324,39326],{},[1493,39310,1998],{},[1506,39312,1508],{},[1680,39314,39315],{},"0,75",[1988,39317,5016],{},[1497,39319,39320,39322],{},[1493,39321,1791],{},[1493,39323,3712],{},[1506,39325,2162],{},[1680,39327,39328],{},"750",[1528,39330,39331],{"encoding":1530},"C = 0{,}75\\,Y_D + 750",[1035,39333,39335],{"className":39334},[1480],[1482,39336,39337],{"xmlns":1484},[1487,39338,39339,39356],{},[1490,39340,39341,39343,39345,39348,39350],{},[1493,39342,1495],{},[1506,39344,1508],{},[1680,39346,39347],{},"0,15",[1988,39349,5016],{},[1497,39351,39352,39354],{},[1493,39353,1791],{},[1493,39355,3712],{},[1528,39357,39358],{"encoding":1530},"M = 0{,}15\\,Y_D",[1035,39360,39362],{"className":39361},[1480],[1482,39363,39364],{"xmlns":1484},[1487,39365,39366,39376],{},[1490,39367,39368,39370,39372,39374],{},[1493,39369,5289],{},[1506,39371,1508],{},[1680,39373,5051],{},[1493,39375,1791],{},[1528,39377,39378],{"encoding":1530},"T = 0{,}25Y",[1035,39380,39382],{"className":39381},[1480],[1482,39383,39384],{"xmlns":1484},[1487,39385,39386,39398],{},[1490,39387,39388,39394,39396],{},[2315,39389,39390,39392],{},[1493,39391,2662],{},[1506,39393,2287],{},[1506,39395,1508],{},[1680,39397,1796],{},[1528,39399,39400],{"encoding":1530},"I^* = 500",[1035,39402,39404],{"className":39403},[1480],[1482,39405,39406],{"xmlns":1484},[1487,39407,39408,39420],{},[1490,39409,39410,39416,39418],{},[2315,39411,39412,39414],{},[1493,39413,28595],{},[1506,39415,2287],{},[1506,39417,1508],{},[1680,39419,5551],{},[1528,39421,39422],{"encoding":1530},"G^* = 150",[1035,39424,39426],{"className":39425},[1480],[1482,39427,39428],{"xmlns":1484},[1487,39429,39430,39442],{},[1490,39431,39432,39438,39440],{},[2315,39433,39434,39436],{},[1493,39435,11353],{},[1506,39437,2287],{},[1506,39439,1508],{},[1680,39441,7494],{},[1528,39443,39444],{"encoding":1530},"B^* = 800",". Soustava:",[1035,39447,39449],{"className":39448},[1480],[1482,39450,39451],{"xmlns":1484,"display":1485},[1487,39452,39453,39671],{},[19617,39454,39455,39501,39543,39579,39621],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,39456,39457,39473],{},[19624,39458,39459],{},[1869,39460,39461],{"scriptlevel":1871,"displaystyle":1041},[1490,39462,39463,39465,39467,39469,39471],{},[1506,39464,1553],{"stretchy":1552},[1493,39466,7740],{},[1680,39468,1682],{},[1506,39470,1564],{"stretchy":1552},[1988,39472,10922],{},[19624,39474,39475],{},[1869,39476,39477],{"scriptlevel":1871,"displaystyle":1041},[1490,39478,39479,39481,39483,39485,39487,39489,39495,39497,39499],{},[1490,39480],{},[1493,39482,1998],{},[1506,39484,1508],{},[1680,39486,39315],{},[1988,39488,5016],{},[1497,39490,39491,39493],{},[1493,39492,1791],{},[1493,39494,3712],{},[1506,39496,2162],{},[1680,39498,39328],{},[1506,39500,1559],{"separator":1041},[19621,39502,39503,39519],{},[19624,39504,39505],{},[1869,39506,39507],{"scriptlevel":1871,"displaystyle":1041},[1490,39508,39509,39511,39513,39515,39517],{},[1506,39510,1553],{"stretchy":1552},[1493,39512,7740],{},[1680,39514,1691],{},[1506,39516,1564],{"stretchy":1552},[1988,39518,10922],{},[19624,39520,39521],{},[1869,39522,39523],{"scriptlevel":1871,"displaystyle":1041},[1490,39524,39525,39527,39533,39535,39537,39539,39541],{},[1490,39526],{},[1497,39528,39529,39531],{},[1493,39530,1791],{},[1493,39532,3712],{},[1506,39534,1508],{},[1493,39536,1791],{},[1506,39538,1888],{},[1493,39540,5289],{},[1506,39542,1559],{"separator":1041},[19621,39544,39545,39561],{},[19624,39546,39547],{},[1869,39548,39549],{"scriptlevel":1871,"displaystyle":1041},[1490,39550,39551,39553,39555,39557,39559],{},[1506,39552,1553],{"stretchy":1552},[1493,39554,7740],{},[1680,39556,3201],{},[1506,39558,1564],{"stretchy":1552},[1988,39560,10922],{},[19624,39562,39563],{},[1869,39564,39565],{"scriptlevel":1871,"displaystyle":1041},[1490,39566,39567,39569,39571,39573,39575,39577],{},[1490,39568],{},[1493,39570,5289],{},[1506,39572,1508],{},[1680,39574,5051],{},[1493,39576,1791],{},[1506,39578,1559],{"separator":1041},[19621,39580,39581,39597],{},[19624,39582,39583],{},[1869,39584,39585],{"scriptlevel":1871,"displaystyle":1041},[1490,39586,39587,39589,39591,39593,39595],{},[1506,39588,1553],{"stretchy":1552},[1493,39590,7740],{},[1680,39592,4007],{},[1506,39594,1564],{"stretchy":1552},[1988,39596,10922],{},[19624,39598,39599],{},[1869,39600,39601],{"scriptlevel":1871,"displaystyle":1041},[1490,39602,39603,39605,39607,39609,39611,39613,39619],{},[1490,39604],{},[1493,39606,1495],{},[1506,39608,1508],{},[1680,39610,39347],{},[1988,39612,5016],{},[1497,39614,39615,39617],{},[1493,39616,1791],{},[1493,39618,3712],{},[1506,39620,1559],{"separator":1041},[19621,39622,39623,39639],{},[19624,39624,39625],{},[1869,39626,39627],{"scriptlevel":1871,"displaystyle":1041},[1490,39628,39629,39631,39633,39635,39637],{},[1506,39630,1553],{"stretchy":1552},[1493,39632,7740],{},[1680,39634,1752],{},[1506,39636,1564],{"stretchy":1552},[1988,39638,10922],{},[19624,39640,39641],{},[1869,39642,39643],{"scriptlevel":1871,"displaystyle":1041},[1490,39644,39645,39647,39649,39651,39653,39655,39657,39659,39661,39663,39665,39667,39669],{},[1490,39646],{},[1493,39648,1791],{},[1506,39650,1508],{},[1493,39652,1998],{},[1506,39654,2162],{},[1680,39656,1796],{},[1506,39658,2162],{},[1680,39660,5551],{},[1506,39662,2162],{},[1680,39664,7494],{},[1506,39666,1888],{},[1493,39668,1495],{},[1493,39670,2632],{"mathvariant":1516},[1528,39672,39673],{"encoding":1530},"\\begin{aligned} (r1)\\ & C = 0{,}75\\,Y_D + 750, \\\\ (r2)\\ & Y_D = Y - T, \\\\ (r3)\\ & T = 0{,}25Y, \\\\ (r4)\\ & M = 0{,}15\\,Y_D, \\\\ (r5)\\ & Y = C + 500 + 150 + 800 - M. \\end{aligned}",[1030,39675,39676,39677,39711],{},"Postupná substituce — z (r3) do (r2): ",[1035,39678,39680],{"className":39679},[1480],[1482,39681,39682],{"xmlns":1484},[1487,39683,39684,39708],{},[1490,39685,39686,39692,39694,39696,39698,39700,39702,39704,39706],{},[1497,39687,39688,39690],{},[1493,39689,1791],{},[1493,39691,3712],{},[1506,39693,1508],{},[1493,39695,1791],{},[1506,39697,1888],{},[1680,39699,5051],{},[1493,39701,1791],{},[1506,39703,1508],{},[1680,39705,39315],{},[1493,39707,1791],{},[1528,39709,39710],{"encoding":1530},"Y_D = Y - 0{,}25Y = 0{,}75Y",". Dosazením do (r1) a (r4):",[1035,39713,39715],{"className":39714},[1480],[1482,39716,39717],{"xmlns":1484,"display":1485},[1487,39718,39719,39760],{},[1490,39720,39721,39723,39725,39727,39729,39731,39733,39735,39737,39739,39741,39743,39745,39747,39749,39752,39754,39756,39758],{},[1506,39722,1553],{"stretchy":1552},[1493,39724,7740],{},[1680,39726,7508],{},[1506,39728,1564],{"stretchy":1552},[1988,39730,10922],{},[1493,39732,1998],{},[1506,39734,1508],{},[1680,39736,39315],{},[1506,39738,1714],{},[1680,39740,39315],{},[1493,39742,1791],{},[1506,39744,2162],{},[1680,39746,39328],{},[1506,39748,1508],{},[1680,39750,39751],{},"0,5625",[1493,39753,1791],{},[1506,39755,2162],{},[1680,39757,39328],{},[1506,39759,1559],{"separator":1041},[1528,39761,39762],{"encoding":1530},"(r6)\\ C = 0{,}75 \\cdot 0{,}75Y + 750 = 0{,}5625Y + 750,",[1035,39764,39766],{"className":39765},[1480],[1482,39767,39768],{"xmlns":1484,"display":1485},[1487,39769,39770,39803],{},[1490,39771,39772,39774,39776,39778,39780,39782,39784,39786,39788,39790,39792,39794,39796,39799,39801],{},[1506,39773,1553],{"stretchy":1552},[1493,39775,7740],{},[1680,39777,16580],{},[1506,39779,1564],{"stretchy":1552},[1988,39781,10922],{},[1493,39783,1495],{},[1506,39785,1508],{},[1680,39787,39347],{},[1506,39789,1714],{},[1680,39791,39315],{},[1493,39793,1791],{},[1506,39795,1508],{},[1680,39797,39798],{},"0,1125",[1493,39800,1791],{},[1493,39802,2632],{"mathvariant":1516},[1528,39804,39805],{"encoding":1530},"(r7)\\ M = 0{,}15 \\cdot 0{,}75Y = 0{,}1125Y.",[1030,39807,39808],{},"Dosazením do (r5):",[1035,39810,39812],{"className":39811},[1480],[1482,39813,39814],{"xmlns":1484,"display":1485},[1487,39815,39816,39860],{},[1490,39817,39818,39820,39822,39824,39826,39828,39830,39832,39834,39836,39838,39840,39842,39844,39846,39848,39850,39853,39855,39857],{},[1493,39819,1791],{},[1506,39821,1508],{},[1680,39823,39751],{},[1493,39825,1791],{},[1506,39827,2162],{},[1680,39829,39328],{},[1506,39831,2162],{},[1680,39833,1796],{},[1506,39835,2162],{},[1680,39837,5551],{},[1506,39839,2162],{},[1680,39841,7494],{},[1506,39843,1888],{},[1680,39845,39798],{},[1493,39847,1791],{},[1506,39849,1508],{},[1680,39851,39852],{},"0,45",[1493,39854,1791],{},[1506,39856,2162],{},[1680,39858,39859],{},"2200.",[1528,39861,39862],{"encoding":1530},"Y = 0{,}5625Y + 750 + 500 + 150 + 800 - 0{,}1125Y = 0{,}45Y + 2200.",[1030,39864,39865,39866,21352,39888,39910],{},"Odtud ",[1035,39867,39869],{"className":39868},[1480],[1482,39870,39871],{"xmlns":1484},[1487,39872,39873,39885],{},[1490,39874,39875,39878,39880,39882],{},[1680,39876,39877],{},"0,55",[1493,39879,1791],{},[1506,39881,1508],{},[1680,39883,39884],{},"2200",[1528,39886,39887],{"encoding":1530},"0{,}55Y = 2200",[1035,39889,39891],{"className":39890},[1480],[1482,39892,39893],{"xmlns":1484},[1487,39894,39895,39907],{},[1490,39896,39897,39903,39905],{},[2315,39898,39899,39901],{},[1493,39900,1791],{},[1493,39902,2711],{},[1506,39904,1508],{},[1680,39906,15351],{},[1528,39908,39909],{"encoding":1530},"Y^E = 4000",". Rovnovážné veličiny:",[1203,39912,39913,39936,39968,40003,40036,40072],{},[1206,39914,39915,1559],{},[1035,39916,39918],{"className":39917},[1480],[1482,39919,39920],{"xmlns":1484},[1487,39921,39922,39934],{},[1490,39923,39924,39930,39932],{},[2315,39925,39926,39928],{},[1493,39927,1791],{},[1493,39929,2711],{},[1506,39931,1508],{},[1680,39933,15351],{},[1528,39935,39909],{"encoding":1530},[1206,39937,39938,1559],{},[1035,39939,39941],{"className":39940},[1480],[1482,39942,39943],{"xmlns":1484},[1487,39944,39945,39965],{},[1490,39946,39947,39953,39955,39957,39959,39961,39963],{},[2315,39948,39949,39951],{},[1493,39950,5289],{},[1493,39952,2711],{},[1506,39954,1508],{},[1680,39956,5051],{},[1506,39958,1714],{},[1680,39960,15351],{},[1506,39962,1508],{},[1680,39964,1401],{},[1528,39966,39967],{"encoding":1530},"T^E = 0{,}25 \\cdot 4000 = 1000",[1206,39969,39970,1559],{},[1035,39971,39973],{"className":39972},[1480],[1482,39974,39975],{"xmlns":1484},[1487,39976,39977,40000],{},[1490,39978,39979,39987,39989,39991,39993,39995,39997],{},[1697,39980,39981,39983,39985],{},[1493,39982,1791],{},[1493,39984,3712],{},[1493,39986,2711],{},[1506,39988,1508],{},[1680,39990,39315],{},[1506,39992,1714],{},[1680,39994,15351],{},[1506,39996,1508],{},[1680,39998,39999],{},"3000",[1528,40001,40002],{"encoding":1530},"Y_D^E = 0{,}75 \\cdot 4000 = 3000",[1206,40004,40005,1559],{},[1035,40006,40008],{"className":40007},[1480],[1482,40009,40010],{"xmlns":1484},[1487,40011,40012,40033],{},[1490,40013,40014,40020,40022,40024,40026,40028,40030],{},[2315,40015,40016,40018],{},[1493,40017,1495],{},[1493,40019,2711],{},[1506,40021,1508],{},[1680,40023,39347],{},[1506,40025,1714],{},[1680,40027,39999],{},[1506,40029,1508],{},[1680,40031,40032],{},"450",[1528,40034,40035],{"encoding":1530},"M^E = 0{,}15 \\cdot 3000 = 450",[1206,40037,40038,1559],{},[1035,40039,40041],{"className":40040},[1480],[1482,40042,40043],{"xmlns":1484},[1487,40044,40045,40069],{},[1490,40046,40047,40053,40055,40057,40059,40061,40063,40065,40067],{},[2315,40048,40049,40051],{},[1493,40050,1998],{},[1493,40052,2711],{},[1506,40054,1508],{},[1680,40056,39315],{},[1506,40058,1714],{},[1680,40060,39999],{},[1506,40062,2162],{},[1680,40064,39328],{},[1506,40066,1508],{},[1680,40068,39999],{},[1528,40070,40071],{"encoding":1530},"C^E = 0{,}75 \\cdot 3000 + 750 = 3000",[1206,40073,40074,40114],{},[1035,40075,40077],{"className":40076},[1480],[1482,40078,40079],{"xmlns":1484},[1487,40080,40081,40111],{},[1490,40082,40083,40089,40091,40099,40101,40107,40109],{},[2315,40084,40085,40087],{},[1493,40086,2001],{},[1493,40088,2711],{},[1506,40090,1508],{},[1697,40092,40093,40095,40097],{},[1493,40094,1791],{},[1493,40096,3712],{},[1493,40098,2711],{},[1506,40100,1888],{},[2315,40102,40103,40105],{},[1493,40104,1998],{},[1493,40106,2711],{},[1506,40108,1508],{},[1680,40110,1871],{},[1528,40112,40113],{"encoding":1530},"S^E = Y_D^E - C^E = 0"," (při této kalibraci domácnosti celý disponibilní důchod spotřebují).",[1030,40116,40117,40119,40120,1732,40137,1586,40158,40183,40184,40187,40188,40201,40202,2632],{},[1047,40118,36945],{}," Modely ",[1035,40121,40123],{"className":40122},[1480],[1482,40124,40125],{"xmlns":1484},[1487,40126,40127,40135],{},[1490,40128,40129,40131,40133],{},[1493,40130,1998],{},[1988,40132,28777],{},[1493,40134,2662],{},[1528,40136,28782],{"encoding":1530},[1035,40138,40140],{"className":40139},[1480],[1482,40141,40142],{"xmlns":1484},[1487,40143,40144,40156],{},[1490,40145,40146,40148,40150,40152,40154],{},[1493,40147,1998],{},[1988,40149,28777],{},[1493,40151,2662],{},[1988,40153,28777],{},[1493,40155,28595],{},[1528,40157,34367],{"encoding":1530},[1035,40159,40161],{"className":40160},[1480],[1482,40162,40163],{"xmlns":1484},[1487,40164,40165,40181],{},[1490,40166,40167,40169,40171,40173,40175,40177,40179],{},[1493,40168,1998],{},[1988,40170,28777],{},[1493,40172,2662],{},[1988,40174,28777],{},[1493,40176,28595],{},[1988,40178,28777],{},[1493,40180,28807],{},[1528,40182,28810],{"encoding":1530}," pokládají investice za ",[1047,40185,40186],{},"konstantní",". To není realistické — investice závisejí na úrokové míře ",[1035,40189,40191],{"className":40190},[1480],[1482,40192,40193],{"xmlns":1484},[1487,40194,40195,40199],{},[1490,40196,40197],{},[1493,40198,7740],{},[1528,40200,7740],{"encoding":1530},". Přidáním trhu peněz a úrokové míry vzniká ",[1047,40203,40204],{},"model IS-LM",[1065,40206,40208],{"id":40207},"_74-multiplikátory-pro-makroekonomické-proměnné","7.4 Multiplikátory pro makroekonomické proměnné",[1030,40210,40211,40212,40216,40217,40220,40221,40224],{},"V článku ",[1052,40213,40215],{"className":40214,"dataFsResolvedFilePath":1299,"href":1300},[1055],"2.4"," (mikroekonomie) byly zavedeny multiplikátory pro mikroekonomické proměnné. ",[1047,40218,40219],{},"Analogické úvahy dovedou k multiplikátorům pro modely makroekonomického typu","; role multiplikátorů jako nástrojů pro postižení kvalitativních a kvantitativních charakteristik chování modelů je v makroekonomických analýzách ještě ",[1047,40222,40223],{},"výraznější"," než v mikroekonomických modelech.",[1030,40226,40227],{},[18014,40228],{"alt":40229,"className":40230,"src":40231},"imek-multiplikatorovy-efekt-chain",[1055,18018],"\u002Fwiki-assets\u002Fimek-multiplikatorovy-efekt-chain.jpeg",[1030,40233,28647,40234,1732,40251,1732,40272,40297,40298,40301,40302,40320,40321,40339,40340,40358,40359,40362,40363,1732,40380,40397,40398,40400],{},[1035,40235,40237],{"className":40236},[1480],[1482,40238,40239],{"xmlns":1484},[1487,40240,40241,40249],{},[1490,40242,40243,40245,40247],{},[1493,40244,1998],{},[1988,40246,28777],{},[1493,40248,2662],{},[1528,40250,28782],{"encoding":1530},[1035,40252,40254],{"className":40253},[1480],[1482,40255,40256],{"xmlns":1484},[1487,40257,40258,40270],{},[1490,40259,40260,40262,40264,40266,40268],{},[1493,40261,1998],{},[1988,40263,28777],{},[1493,40265,2662],{},[1988,40267,28777],{},[1493,40269,28595],{},[1528,40271,34367],{"encoding":1530},[1035,40273,40275],{"className":40274},[1480],[1482,40276,40277],{"xmlns":1484},[1487,40278,40279,40295],{},[1490,40280,40281,40283,40285,40287,40289,40291,40293],{},[1493,40282,1998],{},[1988,40284,28777],{},[1493,40286,2662],{},[1988,40288,28777],{},[1493,40290,28595],{},[1988,40292,28777],{},[1493,40294,28807],{},[1528,40296,28810],{"encoding":1530}," se vyšetřuje vliv změn ",[1047,40299,40300],{},"exogenních"," veličin (plánovaných investic ",[1035,40303,40305],{"className":40304},[1480],[1482,40306,40307],{"xmlns":1484},[1487,40308,40309,40317],{},[1490,40310,40311],{},[2315,40312,40313,40315],{},[1493,40314,2662],{},[1506,40316,2287],{},[1528,40318,40319],{"encoding":1530},"I^*",", vládních výdajů ",[1035,40322,40324],{"className":40323},[1480],[1482,40325,40326],{"xmlns":1484},[1487,40327,40328,40336],{},[1490,40329,40330],{},[2315,40331,40332,40334],{},[1493,40333,28595],{},[1506,40335,2287],{},[1528,40337,40338],{"encoding":1530},"G^*",", exportu ",[1035,40341,40343],{"className":40342},[1480],[1482,40344,40345],{"xmlns":1484},[1487,40346,40347,40355],{},[1490,40348,40349],{},[2315,40350,40351,40353],{},[1493,40352,11353],{},[1506,40354,2287],{},[1528,40356,40357],{"encoding":1530},"B^*",") na změny ",[1047,40360,40361],{},"endogenních"," rovnovážných veličin (",[1035,40364,40366],{"className":40365},[1480],[1482,40367,40368],{"xmlns":1484},[1487,40369,40370,40378],{},[1490,40371,40372],{},[2315,40373,40374,40376],{},[1493,40375,1791],{},[1493,40377,2711],{},[1528,40379,3419],{"encoding":1530},[1035,40381,40383],{"className":40382},[1480],[1482,40384,40385],{"xmlns":1484},[1487,40386,40387,40395],{},[1490,40388,40389],{},[2315,40390,40391,40393],{},[1493,40392,1998],{},[1493,40394,2711],{},[1528,40396,30432],{"encoding":1530}," atd.). Tyto citlivosti se vyjadřují ",[1047,40399,34120],{}," — parciálními derivacemi rovnovážných veličin podle exogenních veličin.",[1304,40402,40404],{"id":40403},"multiplikátory-v-modelu-c-i","Multiplikátory v modelu C-I",[1030,40406,36610,40407,40430,40431,40475],{},[1035,40408,40410],{"className":40409},[1480],[1482,40411,40412],{"xmlns":1484},[1487,40413,40414,40428],{},[1490,40415,40416,40418,40420,40422,40424,40426],{},[1493,40417,1998],{},[1506,40419,1508],{},[1493,40421,1052],{},[1493,40423,1791],{},[1506,40425,2162],{},[1493,40427,2394],{},[1528,40429,35596],{"encoding":1530}," dává (7.7) redukovaný tvar ",[1035,40432,40434],{"className":40433},[1480],[1482,40435,40436],{"xmlns":1484},[1487,40437,40438,40472],{},[1490,40439,40440,40446,40448],{},[2315,40441,40442,40444],{},[1493,40443,1791],{},[1493,40445,2711],{},[1506,40447,1508],{},[1869,40449,40450],{"scriptlevel":1871,"displaystyle":1041},[1510,40451,40452,40464],{},[1490,40453,40454,40456,40458],{},[1493,40455,2394],{},[1506,40457,2162],{},[2315,40459,40460,40462],{},[1493,40461,2662],{},[1506,40463,2287],{},[1490,40465,40466,40468,40470],{},[1680,40467,1682],{},[1506,40469,1888],{},[1493,40471,1052],{},[1528,40473,40474],{"encoding":1530},"Y^E = \\dfrac{b + I^*}{1 - a}",". Parciální derivace:",[1035,40477,40479],{"className":40478},[1480],[1482,40480,40481],{"xmlns":1484,"display":1485},[1487,40482,40483,40551],{},[1490,40484,40485,40503,40505,40535,40537],{},[1510,40486,40487,40497],{},[1490,40488,40489,40491],{},[1493,40490,1517],{"mathvariant":1516},[2315,40492,40493,40495],{},[1493,40494,1791],{},[1493,40496,2711],{},[1490,40498,40499,40501],{},[1493,40500,1517],{"mathvariant":1516},[1493,40502,1052],{},[1506,40504,1508],{},[1510,40506,40507,40519],{},[1490,40508,40509,40511,40513],{},[1493,40510,2394],{},[1506,40512,2162],{},[2315,40514,40515,40517],{},[1493,40516,2662],{},[1506,40518,2287],{},[1490,40520,40521,40523,40525,40527,40529],{},[1506,40522,1553],{"stretchy":1552},[1680,40524,1682],{},[1506,40526,1888],{},[1493,40528,1052],{},[2315,40530,40531,40533],{},[1506,40532,1564],{"stretchy":1552},[1680,40534,1691],{},[1912,40536],{"width":1914},[1490,40538,40539,40542,40548],{},[1988,40540,40541],{},"(multiplik",[2178,40543,40544,40546],{"accent":1041},[1988,40545,1052],{},[1506,40547,3055],{},[1988,40549,40550],{},"tor MPC)",[1528,40552,40553],{"encoding":1530},"\\frac{\\partial Y^E}{\\partial a} = \\frac{b + I^*}{(1 - a)^2} \\qquad \\text{(multiplikátor MPC)}",[1035,40555,40557],{"className":40556},[1480],[1482,40558,40559],{"xmlns":1484,"display":1485},[1487,40560,40561,40628],{},[1490,40562,40563,40581,40583,40595,40597],{},[1510,40564,40565,40575],{},[1490,40566,40567,40569],{},[1493,40568,1517],{"mathvariant":1516},[2315,40570,40571,40573],{},[1493,40572,1791],{},[1493,40574,2711],{},[1490,40576,40577,40579],{},[1493,40578,1517],{"mathvariant":1516},[1493,40580,2394],{},[1506,40582,1508],{},[1510,40584,40585,40587],{},[1680,40586,1682],{},[1490,40588,40589,40591,40593],{},[1680,40590,1682],{},[1506,40592,1888],{},[1493,40594,1052],{},[1912,40596],{"width":1914},[1490,40598,40599,40601,40607,40610,40616,40619,40625],{},[1988,40600,40541],{},[2178,40602,40603,40605],{"accent":1041},[1988,40604,1052],{},[1506,40606,3055],{},[1988,40608,40609],{},"tor autonomn",[2178,40611,40612,40614],{"accent":1041},[1988,40613,7095],{},[1506,40615,3055],{},[1988,40617,40618],{}," spot",[2178,40620,40621,40623],{"accent":1041},[1988,40622,7740],{},[1506,40624,8576],{},[1988,40626,40627],{},"eby)",[1528,40629,40630],{"encoding":1530},"\\frac{\\partial Y^E}{\\partial b} = \\frac{1}{1 - a} \\qquad \\text{(multiplikátor autonomní spotřeby)}",[1035,40632,40634],{"className":40633},[1480],[1482,40635,40636],{"xmlns":1484,"display":1485},[1487,40637,40638,40705],{},[1490,40639,40640,40662,40664,40676,40678,40690,40692],{},[1510,40641,40642,40652],{},[1490,40643,40644,40646],{},[1493,40645,1517],{"mathvariant":1516},[2315,40647,40648,40650],{},[1493,40649,1791],{},[1493,40651,2711],{},[1490,40653,40654,40656],{},[1493,40655,1517],{"mathvariant":1516},[2315,40657,40658,40660],{},[1493,40659,2662],{},[1506,40661,2287],{},[1506,40663,1508],{},[1510,40665,40666,40668],{},[1680,40667,1682],{},[1490,40669,40670,40672,40674],{},[1680,40671,1682],{},[1506,40673,1888],{},[1493,40675,1052],{},[1506,40677,1508],{},[1510,40679,40680,40682],{},[1680,40681,1682],{},[1490,40683,40684,40686,40688],{},[1493,40685,1495],{},[1493,40687,1501],{},[1493,40689,2001],{},[1912,40691],{"width":1914},[1490,40693,40694,40696,40702],{},[1988,40695,40541],{},[2178,40697,40698,40700],{"accent":1041},[1988,40699,1052],{},[1506,40701,3055],{},[1988,40703,40704],{},"tor investic)",[1528,40706,40707],{"encoding":1530},"\\frac{\\partial Y^E}{\\partial I^*} = \\frac{1}{1 - a} = \\frac{1}{MPS} \\qquad \\text{(multiplikátor investic)}",[1023,40709,40711,40718],{"className":40710,"dataCallout":582},[1026,1186],[1030,40712,40714,40717],{"className":40713},[1033],[1035,40715],{"className":40716,"ariaHidden":1041},[1038,1193,1040],"Intuice — proč Keynesův multiplikátor funguje",[1030,40719,40720,40721,40724,40725,40738,40739,40756,40757,40775,40776,40820,40821,37016,40838,40841,40842,40859],{},"Investice o 1 Kč se stanou něčím ",[1047,40722,40723],{},"důchodem","; z něj se utratí ",[1035,40726,40728],{"className":40727},[1480],[1482,40729,40730],{"xmlns":1484},[1487,40731,40732,40736],{},[1490,40733,40734],{},[1493,40735,1052],{},[1528,40737,1052],{"encoding":1530}," Kč (= ",[1035,40740,40742],{"className":40741},[1480],[1482,40743,40744],{"xmlns":1484},[1487,40745,40746,40754],{},[1490,40747,40748,40750,40752],{},[1493,40749,1495],{},[1493,40751,1501],{},[1493,40753,1998],{},[1528,40755,34192],{"encoding":1530},"), to je zase něčí důchod, z něj ",[1035,40758,40760],{"className":40759},[1480],[1482,40761,40762],{"xmlns":1484},[1487,40763,40764,40772],{},[1490,40765,40766],{},[2315,40767,40768,40770],{},[1493,40769,1052],{},[1680,40771,1691],{},[1528,40773,40774],{"encoding":1530},"a^2"," Kč… Součet geometrické řady ",[1035,40777,40779],{"className":40778},[1480],[1482,40780,40781],{"xmlns":1484},[1487,40782,40783,40817],{},[1490,40784,40785,40787,40789,40791,40793,40799,40801,40803,40805],{},[1680,40786,1682],{},[1506,40788,2162],{},[1493,40790,1052],{},[1506,40792,2162],{},[2315,40794,40795,40797],{},[1493,40796,1052],{},[1680,40798,1691],{},[1506,40800,2162],{},[1506,40802,34252],{},[1506,40804,1508],{},[1510,40806,40807,40809],{},[1680,40808,1682],{},[1490,40810,40811,40813,40815],{},[1680,40812,1682],{},[1506,40814,1888],{},[1493,40816,1052],{},[1528,40818,40819],{"encoding":1530},"1 + a + a^2 + \\dots = \\frac{1}{1-a}",". Proto jedna koruna investic navíc zvedne ",[1035,40822,40824],{"className":40823},[1480],[1482,40825,40826],{"xmlns":1484},[1487,40827,40828,40836],{},[1490,40829,40830],{},[2315,40831,40832,40834],{},[1493,40833,1791],{},[1493,40835,2711],{},[1528,40837,3419],{"encoding":1530},[1047,40839,40840],{},"více"," než korunu — čím vyšší ",[1035,40843,40845],{"className":40844},[1480],[1482,40846,40847],{"xmlns":1484},[1487,40848,40849,40857],{},[1490,40850,40851,40853,40855],{},[1493,40852,1495],{},[1493,40854,1501],{},[1493,40856,1998],{},[1528,40858,34192],{"encoding":1530},", tím silnější multiplikační efekt.",[1030,40861,40862,40865,40866,40892,40893,40895,40896,1586,40917,40942,40943,2632],{},[1047,40863,40864],{},"Multiplikátor autonomní spotřeby se rovná multiplikátoru investic"," — oba činí ",[1035,40867,40869],{"className":40868},[1480],[1482,40870,40871],{"xmlns":1484},[1487,40872,40873,40889],{},[1490,40874,40875],{},[1869,40876,40877],{"scriptlevel":1871,"displaystyle":1552},[1510,40878,40879,40881],{},[1680,40880,1682],{},[1490,40882,40883,40885,40887],{},[1680,40884,1682],{},[1506,40886,1888],{},[1493,40888,1052],{},[1528,40890,40891],{"encoding":1530},"\\tfrac{1}{1-a}",", což je standardní ",[1047,40894,16647],{},". Analogicky se v modelech ",[1035,40897,40899],{"className":40898},[1480],[1482,40900,40901],{"xmlns":1484},[1487,40902,40903,40915],{},[1490,40904,40905,40907,40909,40911,40913],{},[1493,40906,1998],{},[1988,40908,28777],{},[1493,40910,2662],{},[1988,40912,28777],{},[1493,40914,28595],{},[1528,40916,34367],{"encoding":1530},[1035,40918,40920],{"className":40919},[1480],[1482,40921,40922],{"xmlns":1484},[1487,40923,40924,40940],{},[1490,40925,40926,40928,40930,40932,40934,40936,40938],{},[1493,40927,1998],{},[1988,40929,28777],{},[1493,40931,2662],{},[1988,40933,28777],{},[1493,40935,28595],{},[1988,40937,28777],{},[1493,40939,28807],{},[1528,40941,28810],{"encoding":1530}," zavádějí multiplikátory vládních výdajů, zdanění a exportu. Paralela k mikroekonomickým multiplikátorům viz ",[1052,40944,40946],{"className":40945,"dataFsResolvedFilePath":3487,"href":3488},[1055],"poptávka a nabídka",[1065,40948,40950],{"id":40949},"is-lm-analýza-stručný-přehled","IS-LM analýza (stručný přehled)",[1030,40952,28647,40953,1732,40970,1586,40991,28652,41016,7606,41019,41040,41041,1656,41044,41057,41058,21432,41087,41104,41105,41108,41109,41111,41112,41133],{},[1035,40954,40956],{"className":40955},[1480],[1482,40957,40958],{"xmlns":1484},[1487,40959,40960,40968],{},[1490,40961,40962,40964,40966],{},[1493,40963,1998],{},[1988,40965,28777],{},[1493,40967,2662],{},[1528,40969,28782],{"encoding":1530},[1035,40971,40973],{"className":40972},[1480],[1482,40974,40975],{"xmlns":1484},[1487,40976,40977,40989],{},[1490,40978,40979,40981,40983,40985,40987],{},[1493,40980,1998],{},[1988,40982,28777],{},[1493,40984,2662],{},[1988,40986,28777],{},[1493,40988,28595],{},[1528,40990,34367],{"encoding":1530},[1035,40992,40994],{"className":40993},[1480],[1482,40995,40996],{"xmlns":1484},[1487,40997,40998,41014],{},[1490,40999,41000,41002,41004,41006,41008,41010,41012],{},[1493,41001,1998],{},[1988,41003,28777],{},[1493,41005,2662],{},[1988,41007,28777],{},[1493,41009,28595],{},[1988,41011,28777],{},[1493,41013,28807],{},[1528,41015,28810],{"encoding":1530},[1047,41017,41018],{},"investice konstantní",[1035,41020,41022],{"className":41021},[1480],[1482,41023,41024],{"xmlns":1484},[1487,41025,41026,41038],{},[1490,41027,41028,41030,41032],{},[1493,41029,2662],{},[1506,41031,1508],{},[2315,41033,41034,41036],{},[1493,41035,2662],{},[1506,41037,2287],{},[1528,41039,28677],{"encoding":1530},"). Reálnější je předpoklad, že ",[1047,41042,41043],{},"investice závisejí na úrokové míře",[1035,41045,41047],{"className":41046},[1480],[1482,41048,41049],{"xmlns":1484},[1487,41050,41051,41055],{},[1490,41052,41053],{},[1493,41054,7740],{},[1528,41056,7740],{"encoding":1530}," — klesající funkce ",[1035,41059,41061],{"className":41060},[1480],[1482,41062,41063],{"xmlns":1484},[1487,41064,41065,41085],{},[1490,41066,41067,41069,41071,41073,41075,41077,41079,41081,41083],{},[1493,41068,2662],{},[1506,41070,1553],{"stretchy":1552},[1493,41072,7740],{},[1506,41074,1564],{"stretchy":1552},[1506,41076,1508],{},[1493,41078,8730],{},[1493,41080,7740],{},[1506,41082,2162],{},[1493,41084,3384],{},[1528,41086,31922],{"encoding":1530},[1035,41088,41090],{"className":41089},[1480],[1482,41091,41092],{"xmlns":1484},[1487,41093,41094,41102],{},[1490,41095,41096,41098,41100],{},[1493,41097,8730],{},[1506,41099,3961],{},[1680,41101,1871],{},[1528,41103,29000],{"encoding":1530},". Přidáním ",[1047,41106,41107],{},"trhu peněz"," k trhu zboží vzniká model ",[1047,41110,16530],{}," se dvěma neznámými ",[1035,41113,41115],{"className":41114},[1480],[1482,41116,41117],{"xmlns":1484},[1487,41118,41119,41131],{},[1490,41120,41121,41123,41125,41127,41129],{},[1506,41122,1553],{"stretchy":1552},[1493,41124,1791],{},[1506,41126,1559],{"separator":1041},[1493,41128,7740],{},[1506,41130,1564],{"stretchy":1552},[1528,41132,34297],{"encoding":1530}," a dvěma rovnicemi:",[1203,41135,41136,41186],{},[1206,41137,41138,7606,41140,41142,41143,41164,41165,2632],{},[1047,41139,32010],{},[1176,41141,28537],{},") — klesající přímka v rovině ",[1035,41144,41146],{"className":41145},[1480],[1482,41147,41148],{"xmlns":1484},[1487,41149,41150,41162],{},[1490,41151,41152,41154,41156,41158,41160],{},[1506,41153,1553],{"stretchy":1552},[1493,41155,7740],{},[1506,41157,1559],{"separator":1041},[1493,41159,1791],{},[1506,41161,1564],{"stretchy":1552},[1528,41163,29410],{"encoding":1530},", odvozená z rovnováhy trhu zboží ",[1035,41166,41168],{"className":41167},[1480],[1482,41169,41170],{"xmlns":1484},[1487,41171,41172,41184],{},[1490,41173,41174,41176,41178,41180,41182],{},[1493,41175,1791],{},[1506,41177,1508],{},[1493,41179,1998],{},[1506,41181,2162],{},[1493,41183,2662],{},[1528,41185,31066],{"encoding":1530},[1206,41187,41188,7606,41190,41192,41193,37188,41218,41264],{},[1047,41189,32209],{},[1176,41191,28544],{},") — rostoucí přímka, odvozená z rovnováhy trhu peněz ",[1035,41194,41196],{"className":41195},[1480],[1482,41197,41198],{"xmlns":1484},[1487,41199,41200,41216],{},[1490,41201,41202,41208,41210],{},[2315,41203,41204,41206],{},[1493,41205,1495],{},[1493,41207,3712],{},[1506,41209,1508],{},[2315,41211,41212,41214],{},[1493,41213,1495],{},[1506,41215,2287],{},[1528,41217,29950],{"encoding":1530},[1035,41219,41221],{"className":41220},[1480],[1482,41222,41223],{"xmlns":1484},[1487,41224,41225,41261],{},[1490,41226,41227,41233,41235,41241,41243,41245,41251,41253,41255],{},[2315,41228,41229,41231],{},[1493,41230,1495],{},[1493,41232,3712],{},[1506,41234,1508],{},[1497,41236,41237,41239],{},[1493,41238,7100],{},[1680,41240,1682],{},[1493,41242,1791],{},[1506,41244,2162],{},[1497,41246,41247,41249],{},[1493,41248,7100],{},[1680,41250,1691],{},[1493,41252,7740],{},[1506,41254,2162],{},[1497,41256,41257,41259],{},[1493,41258,7100],{},[1680,41260,3201],{},[1528,41262,41263],{"encoding":1530},"M^D = k_1 Y + k_2 r + k_3"," (transakční, opatrnostní a spekulační poptávka).",[1030,41266,41267,1656,41270,41303,41304,41306,41307,41309],{},[1047,41268,41269],{},"Simultánní rovnovážný bod",[1035,41271,41273],{"className":41272},[1480],[1482,41274,41275],{"xmlns":1484},[1487,41276,41277,41301],{},[1490,41278,41279,41281,41283,41285,41291,41293,41299],{},[1493,41280,2711],{},[1506,41282,1508],{},[1506,41284,1553],{"stretchy":1552},[2315,41286,41287,41289],{},[1493,41288,7740],{},[1493,41290,2711],{},[1506,41292,1559],{"separator":1041},[2315,41294,41295,41297],{},[1493,41296,1791],{},[1493,41298,2711],{},[1506,41300,1564],{"stretchy":1552},[1528,41302,32301],{"encoding":1530}," je průsečík křivek IS a LM; určuje současně rovnovážný důchod a rovnovážnou úrokovou míru. Model slouží jako rámec pro analýzu ",[1047,41305,28582],{}," (posun IS) a ",[1047,41308,28614],{}," (posun LM).",[1030,41311,41312],{},[1047,41313,41314,41315,1732,41337,1732,41359,1732,41381,41403,41404,2632],{},"Pro detailní odvození obou křivek, řešení Příkladu 7.6 (",[1035,41316,41318],{"className":41317},[1480],[1482,41319,41320],{"xmlns":1484},[1487,41321,41322,41334],{},[1490,41323,41324,41330,41332],{},[2315,41325,41326,41328],{},[1493,41327,1791],{},[1493,41329,2711],{},[1506,41331,1508],{},[1680,41333,5296],{},[1528,41335,41336],{"encoding":1530},"Y^E = 5000",[1035,41338,41340],{"className":41339},[1480],[1482,41341,41342],{"xmlns":1484},[1487,41343,41344,41356],{},[1490,41345,41346,41352,41354],{},[2315,41347,41348,41350],{},[1493,41349,7740],{},[1493,41351,2711],{},[1506,41353,1508],{},[1680,41355,1752],{},[1528,41357,41358],{"encoding":1530},"r^E = 5",[1035,41360,41362],{"className":41361},[1480],[1482,41363,41364],{"xmlns":1484},[1487,41365,41366,41378],{},[1490,41367,41368,41374,41376],{},[2315,41369,41370,41372],{},[1493,41371,1998],{},[1493,41373,2711],{},[1506,41375,1508],{},[1680,41377,31460],{},[1528,41379,41380],{"encoding":1530},"C^E = 4100",[1035,41382,41384],{"className":41383},[1480],[1482,41385,41386],{"xmlns":1484},[1487,41387,41388,41400],{},[1490,41389,41390,41396,41398],{},[2315,41391,41392,41394],{},[1493,41393,2662],{},[1493,41395,2711],{},[1506,41397,1508],{},[1680,41399,7032],{},[1528,41401,41402],{"encoding":1530},"I^E = 900",") a ekonomickou interpretaci posunů viz ",[1052,41405,7756],{"className":41406,"dataFsResolvedFilePath":7754,"href":7755},[1055],[1065,41408,41410],{"id":41409},"shrnutí-kapitoly-7","Shrnutí kapitoly 7",[1276,41412,41413,41477,41590,41733,41974,42041],{},[1206,41414,41415,41418,41419,41441,41442,41476],{},[1047,41416,41417],{},"Zjednodušený makroekonomický model"," ztotožňuje ",[1035,41420,41422],{"className":41421},[1480],[1482,41423,41424],{"xmlns":1484},[1487,41425,41426,41438],{},[1490,41427,41428,41430,41432,41434,41436],{},[1493,41429,28595],{},[1493,41431,34441],{},[1493,41433,1501],{},[1506,41435,2343],{},[1493,41437,1791],{},[1528,41439,41440],{"encoding":1530},"GNP \\approx Y"," (národní důchod). Základ: ",[1035,41443,41445],{"className":41444},[1480],[1482,41446,41447],{"xmlns":1484},[1487,41448,41449,41473],{},[1490,41450,41451,41453,41455,41457,41459,41461,41463,41465,41467,41469,41471],{},[1493,41452,28595],{},[1493,41454,34441],{},[1493,41456,1501],{},[1506,41458,1508],{},[1493,41460,1998],{},[1506,41462,2162],{},[1493,41464,2662],{},[1506,41466,2162],{},[1493,41468,28595],{},[1506,41470,2162],{},[1493,41472,28807],{},[1528,41474,41475],{"encoding":1530},"GNP = C + I + G + X"," (7.1).",[1206,41478,41479,41481,41482,41503,41504,1732,41527,41559,41560,41573,41574,2632],{},[1047,41480,13676],{}," splňují ",[1035,41483,41485],{"className":41484},[1480],[1482,41486,41487],{"xmlns":1484},[1487,41488,41489,41501],{},[1490,41490,41491,41493,41495,41497,41499],{},[1493,41492,1791],{},[1506,41494,1508],{},[1493,41496,1998],{},[1506,41498,2162],{},[1493,41500,2001],{},[1528,41502,29175],{"encoding":1530}," (7.2); lineární model ",[1035,41505,41507],{"className":41506},[1480],[1482,41508,41509],{"xmlns":1484},[1487,41510,41511,41525],{},[1490,41512,41513,41515,41517,41519,41521,41523],{},[1493,41514,1998],{},[1506,41516,1508],{},[1493,41518,1052],{},[1493,41520,1791],{},[1506,41522,2162],{},[1493,41524,2394],{},[1528,41526,35596],{"encoding":1530},[1035,41528,41530],{"className":41529},[1480],[1482,41531,41532],{"xmlns":1484},[1487,41533,41534,41556],{},[1490,41535,41536,41538,41540,41542,41544,41546,41548,41550,41552,41554],{},[1493,41537,2001],{},[1506,41539,1508],{},[1506,41541,1553],{"stretchy":1552},[1680,41543,1682],{},[1506,41545,1888],{},[1493,41547,1052],{},[1506,41549,1564],{"stretchy":1552},[1493,41551,1791],{},[1506,41553,1888],{},[1493,41555,2394],{},[1528,41557,41558],{"encoding":1530},"S = (1-a)Y - b"," s autonomní spotřebou ",[1035,41561,41563],{"className":41562},[1480],[1482,41564,41565],{"xmlns":1484},[1487,41566,41567,41571],{},[1490,41568,41569],{},[1493,41570,2394],{},[1528,41572,2394],{"encoding":1530}," a autonomními úsporami ",[1035,41575,41577],{"className":41576},[1480],[1482,41578,41579],{"xmlns":1484},[1487,41580,41581,41587],{},[1490,41582,41583,41585],{},[1506,41584,1888],{},[1493,41586,2394],{},[1528,41588,41589],{"encoding":1530},"-b",[1206,41591,41592,1656,41595,1732,41625,41655,41656,41686,41687,1732,41708,2632],{},[1047,41593,41594],{},"Mezní sklony",[1035,41596,41598],{"className":41597},[1480],[1482,41599,41600],{"xmlns":1484},[1487,41601,41602,41622],{},[1490,41603,41604,41606,41608,41610,41612,41614,41616,41618,41620],{},[1493,41605,1495],{},[1493,41607,1501],{},[1493,41609,1998],{},[1506,41611,1508],{},[1493,41613,3384],{"mathvariant":1516},[1493,41615,1998],{},[1493,41617,1709],{"mathvariant":1516},[1493,41619,3384],{"mathvariant":1516},[1493,41621,1791],{},[1528,41623,41624],{"encoding":1530},"MPC = \\mathrm{d}C\u002F\\mathrm{d}Y",[1035,41626,41628],{"className":41627},[1480],[1482,41629,41630],{"xmlns":1484},[1487,41631,41632,41652],{},[1490,41633,41634,41636,41638,41640,41642,41644,41646,41648,41650],{},[1493,41635,1495],{},[1493,41637,1501],{},[1493,41639,2001],{},[1506,41641,1508],{},[1493,41643,3384],{"mathvariant":1516},[1493,41645,2001],{},[1493,41647,1709],{"mathvariant":1516},[1493,41649,3384],{"mathvariant":1516},[1493,41651,1791],{},[1528,41653,41654],{"encoding":1530},"MPS = \\mathrm{d}S\u002F\\mathrm{d}Y",", vazba ",[1035,41657,41659],{"className":41658},[1480],[1482,41660,41661],{"xmlns":1484},[1487,41662,41663,41683],{},[1490,41664,41665,41667,41669,41671,41673,41675,41677,41679,41681],{},[1493,41666,1495],{},[1493,41668,1501],{},[1493,41670,1998],{},[1506,41672,2162],{},[1493,41674,1495],{},[1493,41676,1501],{},[1493,41678,2001],{},[1506,41680,1508],{},[1680,41682,1682],{},[1528,41684,41685],{"encoding":1530},"MPC + MPS = 1"," (7.5). V lineárním modelu ",[1035,41688,41690],{"className":41689},[1480],[1482,41691,41692],{"xmlns":1484},[1487,41693,41694,41706],{},[1490,41695,41696,41698,41700,41702,41704],{},[1493,41697,1495],{},[1493,41699,1501],{},[1493,41701,1998],{},[1506,41703,1508],{},[1493,41705,1052],{},[1528,41707,35619],{"encoding":1530},[1035,41709,41711],{"className":41710},[1480],[1482,41712,41713],{"xmlns":1484},[1487,41714,41715,41731],{},[1490,41716,41717,41719,41721,41723,41725,41727,41729],{},[1493,41718,1495],{},[1493,41720,1501],{},[1493,41722,2001],{},[1506,41724,1508],{},[1680,41726,1682],{},[1506,41728,1888],{},[1493,41730,1052],{},[1528,41732,35645],{"encoding":1530},[1206,41734,41735,41738,41739],{},[1047,41736,41737],{},"Modely národní ekonomiky"," postupně bohatnou:\n",[1203,41740,41741,41828,41897],{},[1206,41742,41743,11074,41760,41781,41782,1559],{},[1035,41744,41746],{"className":41745},[1480],[1482,41747,41748],{"xmlns":1484},[1487,41749,41750,41758],{},[1490,41751,41752,41754,41756],{},[1493,41753,1998],{},[1988,41755,28777],{},[1493,41757,2662],{},[1528,41759,28782],{"encoding":1530},[1035,41761,41763],{"className":41762},[1480],[1482,41764,41765],{"xmlns":1484},[1487,41766,41767,41779],{},[1490,41768,41769,41771,41773,41775,41777],{},[1493,41770,1791],{},[1506,41772,1508],{},[1493,41774,1998],{},[1506,41776,2162],{},[1493,41778,2662],{},[1528,41780,31066],{"encoding":1530}," (uzavřená ekonomika bez vlády), ",[1035,41783,41785],{"className":41784},[1480],[1482,41786,41787],{"xmlns":1484},[1487,41788,41789,41825],{},[1490,41790,41791,41797,41799,41801,41803,41805,41811,41813,41815,41817,41819,41821,41823],{},[2315,41792,41793,41795],{},[1493,41794,1791],{},[1493,41796,2711],{},[1506,41798,1508],{},[1506,41800,1553],{"stretchy":1552},[1493,41802,2394],{},[1506,41804,2162],{},[2315,41806,41807,41809],{},[1493,41808,2662],{},[1506,41810,2287],{},[1506,41812,1564],{"stretchy":1552},[1493,41814,1709],{"mathvariant":1516},[1506,41816,1553],{"stretchy":1552},[1680,41818,1682],{},[1506,41820,1888],{},[1493,41822,1052],{},[1506,41824,1564],{"stretchy":1552},[1528,41826,41827],{"encoding":1530},"Y^E = (b + I^*)\u002F(1-a)",[1206,41829,41830,41851,41852,41871,41872,1559],{},[1035,41831,41833],{"className":41832},[1480],[1482,41834,41835],{"xmlns":1484},[1487,41836,41837,41849],{},[1490,41838,41839,41841,41843,41845,41847],{},[1493,41840,1998],{},[1988,41842,28777],{},[1493,41844,2662],{},[1988,41846,28777],{},[1493,41848,28595],{},[1528,41850,34367],{"encoding":1530},": přidává vládu, zdanění ",[1035,41853,41855],{"className":41854},[1480],[1482,41856,41857],{"xmlns":1484},[1487,41858,41859,41869],{},[1490,41860,41861,41863,41865,41867],{},[1493,41862,5289],{},[1506,41864,1553],{"stretchy":1552},[1493,41866,1791],{},[1506,41868,1564],{"stretchy":1552},[1528,41870,37817],{"encoding":1530}," a disponibilní důchod ",[1035,41873,41875],{"className":41874},[1480],[1482,41876,41877],{"xmlns":1484},[1487,41878,41879,41895],{},[1490,41880,41881,41887,41889,41891,41893],{},[1497,41882,41883,41885],{},[1493,41884,1791],{},[1493,41886,3712],{},[1506,41888,1508],{},[1493,41890,1791],{},[1506,41892,1888],{},[1493,41894,5289],{},[1528,41896,37317],{"encoding":1530},[1206,41898,41899,41924,41925,37188,41946,2632],{},[1035,41900,41902],{"className":41901},[1480],[1482,41903,41904],{"xmlns":1484},[1487,41905,41906,41922],{},[1490,41907,41908,41910,41912,41914,41916,41918,41920],{},[1493,41909,1998],{},[1988,41911,28777],{},[1493,41913,2662],{},[1988,41915,28777],{},[1493,41917,28595],{},[1988,41919,28777],{},[1493,41921,28807],{},[1528,41923,28810],{"encoding":1530},": otevírá ekonomiku čistým exportem ",[1035,41926,41928],{"className":41927},[1480],[1482,41929,41930],{"xmlns":1484},[1487,41931,41932,41944],{},[1490,41933,41934,41936,41938,41940,41942],{},[1493,41935,28807],{},[1506,41937,1508],{},[1493,41939,11353],{},[1506,41941,1888],{},[1493,41943,1495],{},[1528,41945,38851],{"encoding":1530},[1035,41947,41949],{"className":41948},[1480],[1482,41950,41951],{"xmlns":1484},[1487,41952,41953,41971],{},[1490,41954,41955,41957,41959,41961,41963,41969],{},[1493,41956,1495],{},[1506,41958,1508],{},[1493,41960,1495],{},[1506,41962,1553],{"stretchy":1552},[1497,41964,41965,41967],{},[1493,41966,1791],{},[1493,41968,3712],{},[1506,41970,1564],{"stretchy":1552},[1528,41972,41973],{"encoding":1530},"M = M(Y_D)",[1206,41975,41976,41978,41979,1656,41982,42040],{},[1047,41977,17142],{}," (parciální derivace rovnovážných veličin podle exogenních) — klíčový ",[1047,41980,41981],{},"multiplikátor investic",[1035,41983,41985],{"className":41984},[1480],[1482,41986,41987],{"xmlns":1484},[1487,41988,41989,42037],{},[1490,41990,41991,41993,41999,42001,42003,42009,42011,42013,42015,42017,42019,42021,42023,42025,42027,42029,42031,42033,42035],{},[1493,41992,1517],{"mathvariant":1516},[2315,41994,41995,41997],{},[1493,41996,1791],{},[1493,41998,2711],{},[1493,42000,1709],{"mathvariant":1516},[1493,42002,1517],{"mathvariant":1516},[2315,42004,42005,42007],{},[1493,42006,2662],{},[1506,42008,2287],{},[1506,42010,1508],{},[1680,42012,1682],{},[1493,42014,1709],{"mathvariant":1516},[1506,42016,1553],{"stretchy":1552},[1680,42018,1682],{},[1506,42020,1888],{},[1493,42022,1052],{},[1506,42024,1564],{"stretchy":1552},[1506,42026,1508],{},[1680,42028,1682],{},[1493,42030,1709],{"mathvariant":1516},[1493,42032,1495],{},[1493,42034,1501],{},[1493,42036,2001],{},[1528,42038,42039],{"encoding":1530},"\\partial Y^E\u002F\\partial I^* = 1\u002F(1-a) = 1\u002FMPS"," (Keynesův multiplikátor).",[1206,42042,42043,42045,42046,42061,42062,34788,42079,42094,42095,42120,42121,2632],{},[1047,42044,7756],{}," doplňuje obraz o trh peněz: investice závisejí na úrokové míře, ",[1035,42047,42049],{"className":42048},[1480],[1482,42050,42051],{"xmlns":1484},[1487,42052,42053,42059],{},[1490,42054,42055,42057],{},[1493,42056,2662],{},[1493,42058,2001],{},[1528,42060,28534],{"encoding":1530}," popisuje rovnováhu trhu zboží (",[1035,42063,42065],{"className":42064},[1480],[1482,42066,42067],{"xmlns":1484},[1487,42068,42069,42077],{},[1490,42070,42071,42073,42075],{},[1493,42072,2662],{},[1506,42074,1508],{},[1493,42076,2001],{},[1528,42078,29193],{"encoding":1530},[1035,42080,42082],{"className":42081},[1480],[1482,42083,42084],{"xmlns":1484},[1487,42085,42086,42092],{},[1490,42087,42088,42090],{},[1493,42089,1556],{},[1493,42091,1495],{},[1528,42093,28541],{"encoding":1530}," rovnováhu trhu peněz (",[1035,42096,42098],{"className":42097},[1480],[1482,42099,42100],{"xmlns":1484},[1487,42101,42102,42118],{},[1490,42103,42104,42110,42112],{},[2315,42105,42106,42108],{},[1493,42107,1495],{},[1493,42109,3712],{},[1506,42111,1508],{},[2315,42113,42114,42116],{},[1493,42115,1495],{},[1506,42117,2287],{},[1528,42119,29950],{"encoding":1530},"); průsečík dává ",[1035,42122,42124],{"className":42123},[1480],[1482,42125,42126],{"xmlns":1484},[1487,42127,42128,42148],{},[1490,42129,42130,42132,42138,42140,42146],{},[1506,42131,1553],{"stretchy":1552},[2315,42133,42134,42136],{},[1493,42135,1791],{},[1493,42137,2711],{},[1506,42139,1559],{"separator":1041},[2315,42141,42142,42144],{},[1493,42143,7740],{},[1493,42145,2711],{},[1506,42147,1564],{"stretchy":1552},[1528,42149,28578],{"encoding":1530},[1065,42151,31885],{"id":31884},[1203,42153,42154,42192,42232,42322,42404,42458,42514,42573,42608,42613,42685,42760,42846,42908,42976,43034,43087,43126],{},[1206,42155,42156,22970,42159,41476],{},[1047,42157,42158],{},"Hrubý národní produkt (GNP)",[1035,42160,42162],{"className":42161},[1480],[1482,42163,42164],{"xmlns":1484},[1487,42165,42166,42190],{},[1490,42167,42168,42170,42172,42174,42176,42178,42180,42182,42184,42186,42188],{},[1493,42169,28595],{},[1493,42171,34441],{},[1493,42173,1501],{},[1506,42175,1508],{},[1493,42177,1998],{},[1506,42179,2162],{},[1493,42181,2662],{},[1506,42183,2162],{},[1493,42185,28595],{},[1506,42187,2162],{},[1493,42189,28807],{},[1528,42191,41475],{"encoding":1530},[1206,42193,42194,42210,42211,2632],{},[1047,42195,42196,42197],{},"Národní důchod ",[1035,42198,42200],{"className":42199},[1480],[1482,42201,42202],{"xmlns":1484},[1487,42203,42204,42208],{},[1490,42205,42206],{},[1493,42207,1791],{},[1528,42209,1791],{"encoding":1530}," — součet důchodů domácností; v modelech ",[1035,42212,42214],{"className":42213},[1480],[1482,42215,42216],{"xmlns":1484},[1487,42217,42218,42230],{},[1490,42219,42220,42222,42224,42226,42228],{},[1493,42221,28595],{},[1493,42223,34441],{},[1493,42225,1501],{},[1506,42227,2343],{},[1493,42229,1791],{},[1528,42231,41440],{"encoding":1530},[1206,42233,42234,42260,42261,1732,42284,1732,42305,2632],{},[1047,42235,42236,42237],{},"Funkce spotřeby ",[1035,42238,42240],{"className":42239},[1480],[1482,42241,42242],{"xmlns":1484},[1487,42243,42244,42258],{},[1490,42245,42246,42248,42250,42252,42254,42256],{},[1493,42247,1998],{},[1506,42249,1508],{},[1493,42251,1998],{},[1506,42253,1553],{"stretchy":1552},[1493,42255,1791],{},[1506,42257,1564],{"stretchy":1552},[1528,42259,36460],{"encoding":1530}," — lineární model ",[1035,42262,42264],{"className":42263},[1480],[1482,42265,42266],{"xmlns":1484},[1487,42267,42268,42282],{},[1490,42269,42270,42272,42274,42276,42278,42280],{},[1493,42271,1998],{},[1506,42273,1508],{},[1493,42275,1052],{},[1493,42277,1791],{},[1506,42279,2162],{},[1493,42281,2394],{},[1528,42283,35596],{"encoding":1530},[1035,42285,42287],{"className":42286},[1480],[1482,42288,42289],{"xmlns":1484},[1487,42290,42291,42303],{},[1490,42292,42293,42295,42297,42299,42301],{},[1680,42294,1871],{},[1506,42296,3961],{},[1493,42298,1052],{},[1506,42300,3961],{},[1680,42302,1682],{},[1528,42304,34972],{"encoding":1530},[1035,42306,42308],{"className":42307},[1480],[1482,42309,42310],{"xmlns":1484},[1487,42311,42312,42320],{},[1490,42313,42314,42316,42318],{},[1493,42315,2394],{},[1506,42317,2796],{},[1680,42319,1871],{},[1528,42321,34950],{"encoding":1530},[1206,42323,42324,22970,42351,42372,42373,2632],{},[1047,42325,42326,42327],{},"Funkce úspor ",[1035,42328,42330],{"className":42329},[1480],[1482,42331,42332],{"xmlns":1484},[1487,42333,42334,42348],{},[1490,42335,42336,42338,42340,42342,42344,42346],{},[1493,42337,2001],{},[1506,42339,1508],{},[1493,42341,2001],{},[1506,42343,1553],{"stretchy":1552},[1493,42345,1791],{},[1506,42347,1564],{"stretchy":1552},[1528,42349,42350],{"encoding":1530},"S = S(Y)",[1035,42352,42354],{"className":42353},[1480],[1482,42355,42356],{"xmlns":1484},[1487,42357,42358,42370],{},[1490,42359,42360,42362,42364,42366,42368],{},[1493,42361,1791],{},[1506,42363,1508],{},[1493,42365,1998],{},[1506,42367,2162],{},[1493,42369,2001],{},[1528,42371,29175],{"encoding":1530},"; lineární ",[1035,42374,42376],{"className":42375},[1480],[1482,42377,42378],{"xmlns":1484},[1487,42379,42380,42402],{},[1490,42381,42382,42384,42386,42388,42390,42392,42394,42396,42398,42400],{},[1493,42383,2001],{},[1506,42385,1508],{},[1506,42387,1553],{"stretchy":1552},[1680,42389,1682],{},[1506,42391,1888],{},[1493,42393,1052],{},[1506,42395,1564],{"stretchy":1552},[1493,42397,1791],{},[1506,42399,1888],{},[1493,42401,2394],{},[1528,42403,41558],{"encoding":1530},[1206,42405,42406,22970,42409,1732,42432,2632],{},[1047,42407,42408],{},"Autonomní spotřeba\u002Fúspory",[1035,42410,42412],{"className":42411},[1480],[1482,42413,42414],{"xmlns":1484},[1487,42415,42416,42430],{},[1490,42417,42418,42420,42422,42424,42426,42428],{},[1493,42419,1998],{},[1506,42421,1553],{"stretchy":1552},[1680,42423,1871],{},[1506,42425,1564],{"stretchy":1552},[1506,42427,1508],{},[1493,42429,2394],{},[1528,42431,35297],{"encoding":1530},[1035,42433,42435],{"className":42434},[1480],[1482,42436,42437],{"xmlns":1484},[1487,42438,42439,42455],{},[1490,42440,42441,42443,42445,42447,42449,42451,42453],{},[1493,42442,2001],{},[1506,42444,1553],{"stretchy":1552},[1680,42446,1871],{},[1506,42448,1564],{"stretchy":1552},[1506,42450,1508],{},[1506,42452,1888],{},[1493,42454,2394],{},[1528,42456,42457],{"encoding":1530},"S(0) = -b",[1206,42459,42460,42492,42493,16623],{},[1047,42461,42462,42463],{},"Mezní sklon ke spotřebě ",[1035,42464,42466],{"className":42465},[1480],[1482,42467,42468],{"xmlns":1484},[1487,42469,42470,42490],{},[1490,42471,42472,42474,42476,42478,42480,42482,42484,42486,42488],{},[1493,42473,1495],{},[1493,42475,1501],{},[1493,42477,1998],{},[1506,42479,1508],{},[1493,42481,3384],{"mathvariant":1516},[1493,42483,1998],{},[1493,42485,1709],{"mathvariant":1516},[1493,42487,3384],{"mathvariant":1516},[1493,42489,1791],{},[1528,42491,41624],{"encoding":1530}," (v lineárním modelu ",[1035,42494,42496],{"className":42495},[1480],[1482,42497,42498],{"xmlns":1484},[1487,42499,42500,42512],{},[1490,42501,42502,42504,42506,42508,42510],{},[1493,42503,1495],{},[1493,42505,1501],{},[1493,42507,1998],{},[1506,42509,1508],{},[1493,42511,1052],{},[1528,42513,35619],{"encoding":1530},[1206,42515,42516,42492,42548,16623],{},[1047,42517,42518,42519],{},"Mezní sklon k úsporám ",[1035,42520,42522],{"className":42521},[1480],[1482,42523,42524],{"xmlns":1484},[1487,42525,42526,42546],{},[1490,42527,42528,42530,42532,42534,42536,42538,42540,42542,42544],{},[1493,42529,1495],{},[1493,42531,1501],{},[1493,42533,2001],{},[1506,42535,1508],{},[1493,42537,3384],{"mathvariant":1516},[1493,42539,2001],{},[1493,42541,1709],{"mathvariant":1516},[1493,42543,3384],{"mathvariant":1516},[1493,42545,1791],{},[1528,42547,41654],{"encoding":1530},[1035,42549,42551],{"className":42550},[1480],[1482,42552,42553],{"xmlns":1484},[1487,42554,42555,42571],{},[1490,42556,42557,42559,42561,42563,42565,42567,42569],{},[1493,42558,1495],{},[1493,42560,1501],{},[1493,42562,2001],{},[1506,42564,1508],{},[1680,42566,1682],{},[1506,42568,1888],{},[1493,42570,1052],{},[1528,42572,35645],{"encoding":1530},[1206,42574,42575,1656,42578,42607],{},[1047,42576,42577],{},"Vztah",[1035,42579,42581],{"className":42580},[1480],[1482,42582,42583],{"xmlns":1484},[1487,42584,42585,42605],{},[1490,42586,42587,42589,42591,42593,42595,42597,42599,42601,42603],{},[1493,42588,1495],{},[1493,42590,1501],{},[1493,42592,1998],{},[1506,42594,2162],{},[1493,42596,1495],{},[1493,42598,1501],{},[1493,42600,2001],{},[1506,42602,1508],{},[1680,42604,1682],{},[1528,42606,41685],{"encoding":1530}," (7.5).",[1206,42609,42610,42612],{},[1047,42611,36305],{}," — rovnováha agregátní poptávky a nabídky.",[1206,42614,42615,42618,42619,16351,42640,2632],{},[1047,42616,42617],{},"Model C-I"," — uzavřená ekonomika bez vlády; ",[1035,42620,42622],{"className":42621},[1480],[1482,42623,42624],{"xmlns":1484},[1487,42625,42626,42638],{},[1490,42627,42628,42630,42632,42634,42636],{},[1493,42629,1791],{},[1506,42631,1508],{},[1493,42633,1998],{},[1506,42635,2162],{},[1493,42637,2662],{},[1528,42639,31066],{"encoding":1530},[1035,42641,42643],{"className":42642},[1480],[1482,42644,42645],{"xmlns":1484},[1487,42646,42647,42683],{},[1490,42648,42649,42655,42657,42659,42661,42663,42669,42671,42673,42675,42677,42679,42681],{},[2315,42650,42651,42653],{},[1493,42652,1791],{},[1493,42654,2711],{},[1506,42656,1508],{},[1506,42658,1553],{"stretchy":1552},[1493,42660,2394],{},[1506,42662,2162],{},[2315,42664,42665,42667],{},[1493,42666,2662],{},[1506,42668,2287],{},[1506,42670,1564],{"stretchy":1552},[1493,42672,1709],{"mathvariant":1516},[1506,42674,1553],{"stretchy":1552},[1680,42676,1682],{},[1506,42678,1888],{},[1493,42680,1052],{},[1506,42682,1564],{"stretchy":1552},[1528,42684,41827],{"encoding":1530},[1206,42686,42687,42690,42691,1732,42710,16351,42735,2632],{},[1047,42688,42689],{},"Model C-I-G"," — ekonomika s vládou, zdaněním ",[1035,42692,42694],{"className":42693},[1480],[1482,42695,42696],{"xmlns":1484},[1487,42697,42698,42708],{},[1490,42699,42700,42702,42704,42706],{},[1493,42701,5289],{},[1506,42703,1553],{"stretchy":1552},[1493,42705,1791],{},[1506,42707,1564],{"stretchy":1552},[1528,42709,37817],{"encoding":1530},[1035,42711,42713],{"className":42712},[1480],[1482,42714,42715],{"xmlns":1484},[1487,42716,42717,42733],{},[1490,42718,42719,42725,42727,42729,42731],{},[1497,42720,42721,42723],{},[1493,42722,1791],{},[1493,42724,3712],{},[1506,42726,1508],{},[1493,42728,1791],{},[1506,42730,1888],{},[1493,42732,5289],{},[1528,42734,37317],{"encoding":1530},[1035,42736,42738],{"className":42737},[1480],[1482,42739,42740],{"xmlns":1484},[1487,42741,42742,42758],{},[1490,42743,42744,42746,42748,42750,42752,42754,42756],{},[1493,42745,1791],{},[1506,42747,1508],{},[1493,42749,1998],{},[1506,42751,2162],{},[1493,42753,2662],{},[1506,42755,2162],{},[1493,42757,28595],{},[1528,42759,37288],{"encoding":1530},[1206,42761,42762,42765,42766,42787,42788,16351,42812,2632],{},[1047,42763,42764],{},"Model C-I-G-X"," — otevřená ekonomika s čistým exportem ",[1035,42767,42769],{"className":42768},[1480],[1482,42770,42771],{"xmlns":1484},[1487,42772,42773,42785],{},[1490,42774,42775,42777,42779,42781,42783],{},[1493,42776,28807],{},[1506,42778,1508],{},[1493,42780,11353],{},[1506,42782,1888],{},[1493,42784,1495],{},[1528,42786,38851],{"encoding":1530},", importem ",[1035,42789,42791],{"className":42790},[1480],[1482,42792,42793],{"xmlns":1484},[1487,42794,42795,42809],{},[1490,42796,42797,42799,42801,42807],{},[1493,42798,1495],{},[1506,42800,1553],{"stretchy":1552},[1497,42802,42803,42805],{},[1493,42804,1791],{},[1493,42806,3712],{},[1506,42808,1564],{"stretchy":1552},[1528,42810,42811],{"encoding":1530},"M(Y_D)",[1035,42813,42815],{"className":42814},[1480],[1482,42816,42817],{"xmlns":1484},[1487,42818,42819,42843],{},[1490,42820,42821,42823,42825,42827,42829,42831,42833,42835,42837,42839,42841],{},[1493,42822,1791],{},[1506,42824,1508],{},[1493,42826,1998],{},[1506,42828,2162],{},[1493,42830,2662],{},[1506,42832,2162],{},[1493,42834,28595],{},[1506,42836,2162],{},[1493,42838,11353],{},[1506,42840,1888],{},[1493,42842,1495],{},[1528,42844,42845],{"encoding":1530},"Y = C + I + G + B - M",[1206,42847,42848,22970,42851,42040],{},[1047,42849,42850],{},"Multiplikátor investic",[1035,42852,42854],{"className":42853},[1480],[1482,42855,42856],{"xmlns":1484},[1487,42857,42858,42906],{},[1490,42859,42860,42862,42868,42870,42872,42878,42880,42882,42884,42886,42888,42890,42892,42894,42896,42898,42900,42902,42904],{},[1493,42861,1517],{"mathvariant":1516},[2315,42863,42864,42866],{},[1493,42865,1791],{},[1493,42867,2711],{},[1493,42869,1709],{"mathvariant":1516},[1493,42871,1517],{"mathvariant":1516},[2315,42873,42874,42876],{},[1493,42875,2662],{},[1506,42877,2287],{},[1506,42879,1508],{},[1680,42881,1682],{},[1493,42883,1709],{"mathvariant":1516},[1506,42885,1553],{"stretchy":1552},[1680,42887,1682],{},[1506,42889,1888],{},[1493,42891,1052],{},[1506,42893,1564],{"stretchy":1552},[1506,42895,1508],{},[1680,42897,1682],{},[1493,42899,1709],{"mathvariant":1516},[1493,42901,1495],{},[1493,42903,1501],{},[1493,42905,2001],{},[1528,42907,42039],{"encoding":1530},[1206,42909,42910,22970,42941,1732,42958,42975],{},[1047,42911,31892,42912],{},[1035,42913,42915],{"className":42914},[1480],[1482,42916,42917],{"xmlns":1484},[1487,42918,42919,42939],{},[1490,42920,42921,42923,42925,42927,42929,42931,42933,42935,42937],{},[1493,42922,2662],{},[1506,42924,1553],{"stretchy":1552},[1493,42926,7740],{},[1506,42928,1564],{"stretchy":1552},[1506,42930,1508],{},[1493,42932,8730],{},[1493,42934,7740],{},[1506,42936,2162],{},[1493,42938,3384],{},[1528,42940,31922],{"encoding":1530},[1035,42942,42944],{"className":42943},[1480],[1482,42945,42946],{"xmlns":1484},[1487,42947,42948,42956],{},[1490,42949,42950,42952,42954],{},[1493,42951,8730],{},[1506,42953,3961],{},[1680,42955,1871],{},[1528,42957,29000],{"encoding":1530},[1035,42959,42961],{"className":42960},[1480],[1482,42962,42963],{"xmlns":1484},[1487,42964,42965,42973],{},[1490,42966,42967,42969,42971],{},[1493,42968,3384],{},[1506,42970,2796],{},[1680,42972,1871],{},[1528,42974,28979],{"encoding":1530},"; klesající.",[1206,42977,42978,42980,42981,42983,42984,43033],{},[1047,42979,32010],{}," — rovnováha na trhu zboží (",[1176,42982,28537],{},"); ",[1035,42985,42987],{"className":42986},[1480],[1482,42988,42989],{"xmlns":1484},[1487,42990,42991,43031],{},[1490,42992,42993,42995,42997,43009,43011,43013],{},[1493,42994,1791],{},[1506,42996,1508],{},[1510,42998,42999,43001],{},[1493,43000,8730],{},[1490,43002,43003,43005,43007],{},[1680,43004,1682],{},[1506,43006,1888],{},[1493,43008,1052],{},[1493,43010,7740],{},[1506,43012,2162],{},[1510,43014,43015,43023],{},[1490,43016,43017,43019,43021],{},[1493,43018,2394],{},[1506,43020,2162],{},[1493,43022,3384],{},[1490,43024,43025,43027,43029],{},[1680,43026,1682],{},[1506,43028,1888],{},[1493,43030,1052],{},[1528,43032,32063],{"encoding":1530}," (7.14); klesající.",[1206,43035,43036,43038,43039,42983,43041,43086],{},[1047,43037,32209],{}," — rovnováha na trhu peněz (",[1176,43040,28544],{},[1035,43042,43044],{"className":43043},[1480],[1482,43045,43046],{"xmlns":1484},[1487,43047,43048,43084],{},[1490,43049,43050,43056,43058,43064,43066,43068,43074,43076,43078],{},[2315,43051,43052,43054],{},[1493,43053,1495],{},[1506,43055,2287],{},[1506,43057,1508],{},[1497,43059,43060,43062],{},[1493,43061,7100],{},[1680,43063,1682],{},[1493,43065,1791],{},[1506,43067,2162],{},[1497,43069,43070,43072],{},[1493,43071,7100],{},[1680,43073,1691],{},[1493,43075,7740],{},[1506,43077,2162],{},[1497,43079,43080,43082],{},[1493,43081,7100],{},[1680,43083,3201],{},[1528,43085,32257],{"encoding":1530}," (7.15); rostoucí.",[1206,43088,43089,22970,43092,2632],{},[1047,43090,43091],{},"Transakční, opatrnostní a spekulační poptávka po penězích",[1035,43093,43095],{"className":43094},[1480],[1482,43096,43097],{"xmlns":1484},[1487,43098,43099,43123],{},[1490,43100,43101,43107,43109,43115,43117],{},[2315,43102,43103,43105],{},[1493,43104,1495],{},[1493,43106,3712],{},[1506,43108,1508],{},[1497,43110,43111,43113],{},[1493,43112,1556],{},[1680,43114,1682],{},[1506,43116,2162],{},[1497,43118,43119,43121],{},[1493,43120,1556],{},[1680,43122,1691],{},[1528,43124,43125],{"encoding":1530},"M^D = L_1 + L_2",[1206,43127,43128,32267,43130,30450,43143,1586,43158,43173,43174,2632],{},[1047,43129,7756],{},[1035,43131,43133],{"className":43132},[1480],[1482,43134,43135],{"xmlns":1484},[1487,43136,43137,43141],{},[1490,43138,43139],{},[1493,43140,2711],{},[1528,43142,2711],{"encoding":1530},[1035,43144,43146],{"className":43145},[1480],[1482,43147,43148],{"xmlns":1484},[1487,43149,43150,43156],{},[1490,43151,43152,43154],{},[1493,43153,2662],{},[1493,43155,2001],{},[1528,43157,28534],{"encoding":1530},[1035,43159,43161],{"className":43160},[1480],[1482,43162,43163],{"xmlns":1484},[1487,43164,43165,43171],{},[1490,43166,43167,43169],{},[1493,43168,1556],{},[1493,43170,1495],{},[1528,43172,28541],{"encoding":1530}," určuje ",[1035,43175,43177],{"className":43176},[1480],[1482,43178,43179],{"xmlns":1484},[1487,43180,43181,43201],{},[1490,43182,43183,43185,43191,43193,43199],{},[1506,43184,1553],{"stretchy":1552},[2315,43186,43187,43189],{},[1493,43188,1791],{},[1493,43190,2711],{},[1506,43192,1559],{"separator":1041},[2315,43194,43195,43197],{},[1493,43196,7740],{},[1493,43198,2711],{},[1506,43200,1564],{"stretchy":1552},[1528,43202,28578],{"encoding":1530},[1065,43204,17159],{"id":17158},[1203,43206,43207,43214,43221],{},[1206,43208,43209,1656,43211],{},[1047,43210,17176],{},[1052,43212,1058],{"className":43213,"dataFsResolvedFilePath":1056,"href":1057},[1055],[1206,43215,43216,1656,43218],{},[1047,43217,32375],{},[1052,43219,32379],{"className":43220,"dataFsResolvedFilePath":17200,"href":17201},[1055],[1206,43222,43223,43225],{},[1047,43224,32393],{},[1203,43226,43227,43233,43239,43245],{},[1206,43228,43229,43232],{},[1052,43230,112],{"className":43231,"dataFsResolvedFilePath":7754,"href":7755},[1055]," — detailní IS-LM analýza (odvození křivek, Příklad 7.6, fiskální vs monetární politika)",[1206,43234,43235,43238],{},[1052,43236,132],{"className":43237,"dataFsResolvedFilePath":3487,"href":3488},[1055]," — paralela mikroekonomických multiplikátorů (multiplikátory rovnovážné ceny a množství)",[1206,43240,43241,43244],{},[1052,43242,820],{"className":43243,"dataFsResolvedFilePath":1299,"href":1300},[1055]," — mikroekonomické analogie, článek 2.4 o multiplikátorech",[1206,43246,43247,43250,43251,1732,43268,43285],{},[1052,43248,102],{"className":43249,"dataFsResolvedFilePath":16621,"href":16622},[1055]," — matematický základ pro ",[1035,43252,43254],{"className":43253},[1480],[1482,43255,43256],{"xmlns":1484},[1487,43257,43258,43266],{},[1490,43259,43260,43262,43264],{},[1493,43261,1495],{},[1493,43263,1501],{},[1493,43265,1998],{},[1528,43267,34192],{"encoding":1530},[1035,43269,43271],{"className":43270},[1480],[1482,43272,43273],{"xmlns":1484},[1487,43274,43275,43283],{},[1490,43276,43277,43279,43281],{},[1493,43278,1495],{},[1493,43280,1501],{},[1493,43282,2001],{},[1528,43284,13693],{"encoding":1530}," a interpretaci změn diferenciálem",{"title":17269,"searchDepth":141,"depth":141,"links":43287},[43288,43289,43290,43291,43296,43299,43300,43307,43312,43317,43320,43321,43322,43323],{"id":28491,"depth":141,"text":1042},{"id":34301,"depth":141,"text":34302},{"id":34421,"depth":141,"text":34422},{"id":34670,"depth":141,"text":13676,"children":43292},[43293,43294,43295],{"id":34673,"depth":96,"text":34674},{"id":34881,"depth":96,"text":34882},{"id":35139,"depth":96,"text":35140},{"id":35307,"depth":141,"text":35308,"children":43297},[43298],{"id":35814,"depth":96,"text":35815},{"id":36304,"depth":141,"text":36305},{"id":36331,"depth":141,"text":36332,"children":43301},[43302,43303,43304,43306],{"id":36342,"depth":96,"text":36343},{"id":36410,"depth":96,"text":36411},{"id":36589,"depth":96,"text":43305},"Výpočet YEY^E",{"id":36730,"depth":96,"text":36731},{"id":36991,"depth":141,"text":36992,"children":43308},[43309,43310,43311],{"id":36995,"depth":96,"text":36343},{"id":37445,"depth":96,"text":36411},{"id":38102,"depth":96,"text":38103},{"id":38882,"depth":141,"text":38883,"children":43313},[43314,43315,43316],{"id":38886,"depth":96,"text":36343},{"id":39027,"depth":96,"text":36411},{"id":39295,"depth":96,"text":39296},{"id":40207,"depth":141,"text":40208,"children":43318},[43319],{"id":40403,"depth":96,"text":40404},{"id":40949,"depth":141,"text":40950},{"id":41409,"depth":141,"text":41410},{"id":31884,"depth":141,"text":31885},{"id":17158,"depth":141,"text":17159},{},"\u002Ftopics\u002Fnarodni-duchod",{"title":2624,"description":17269},[26098,32431],"topics\u002Fnarodni-duchod",[9,265,53,205,720,724,112,126],"YAyw5Y_UKRld8SY5h_I-D60TzJvIIjkjhugmWeoz22w",{"id":43332,"title":43333,"body":43334,"course":9,"courses":17424,"created":26093,"description":17269,"extension":17426,"meta":51844,"navigation":17428,"path":51845,"seo":51846,"sources":51847,"stem":51848,"tags":51849,"type":19275,"updated":26102,"__hash__":51850},"topics\u002Ftopics\u002Foptimalizace-spotrebitele.md","Optimalizace spotřebitele — Lagrange, poptávka, minimalizace výdajů",{"type":1016,"value":43335,"toc":51813},[43336,43339,43341,43569,43573,43625,43692,43804,43968,43972,44088,44092,44095,44217,44220,44413,44437,44505,44673,44690,44756,45137,45141,45148,45203,45207,45272,45388,45519,45551,45671,45753,45756,45878,46070,46074,46114,46219,46276,46376,46553,46683,46736,46739,46826,46830,47006,47010,47013,47098,47101,47158,47263,47267,47388,47391,47574,47577,47684,47893,48216,48263,48336,48410,48412,48636,48871,49139,49143,49146,49251,49308,49342,49389,49422,49506,49508,49740,49873,49950,50072,50227,50231,50372,50379,50602,50613,50617,50621,50724,50866,50975,51074,51078,51236,51345,51347,51740,51742],[1019,43337,43333],{"id":43338},"optimalizace-spotřebitele-lagrange-poptávka-minimalizace-výdajů",[1065,43340,1042],{"id":28491},[1030,43342,43343,43345,43346,43380,43381,43384,43385,43416,43417,43463,43464,43467,43468,43509,43510,43528,43529,43533,43534,43564,43565,43568],{},[1047,43344,1843],{}," řeší, jaký svazek zboží ",[1035,43347,43349],{"className":43348},[1480],[1482,43350,43351],{"xmlns":1484},[1487,43352,43353,43377],{},[1490,43354,43355,43357,43365,43367,43375],{},[1506,43356,14314],{"stretchy":1552},[1697,43358,43359,43361,43363],{},[1493,43360,1520],{},[1680,43362,1682],{},[1506,43364,2287],{},[1506,43366,1559],{"separator":1041},[1697,43368,43369,43371,43373],{},[1493,43370,1520],{},[1680,43372,1691],{},[1506,43374,2287],{},[1506,43376,14323],{"stretchy":1552},[1528,43378,43379],{"encoding":1530},"[Q_1^*, Q_2^*]"," zvolit při známých cenách a důchodu. Existují dvě ekvivalentní formulace: ",[1047,43382,43383],{},"primární úloha"," — maximalizace užitečnosti ",[1035,43386,43388],{"className":43387},[1480],[1482,43389,43390],{"xmlns":1484},[1487,43391,43392,43414],{},[1490,43393,43394,43396,43398,43404,43406,43412],{},[1493,43395,1668],{},[1506,43397,1553],{"stretchy":1552},[1497,43399,43400,43402],{},[1493,43401,1520],{},[1680,43403,1682],{},[1506,43405,1559],{"separator":1041},[1497,43407,43408,43410],{},[1493,43409,1520],{},[1680,43411,1691],{},[1506,43413,1564],{"stretchy":1552},[1528,43415,32500],{"encoding":1530}," při rozpočtovém omezení ",[1035,43418,43420],{"className":43419},[1480],[1482,43421,43422],{"xmlns":1484},[1487,43423,43424,43460],{},[1490,43425,43426,43432,43434,43440,43446,43448,43454],{},[2315,43427,43428,43430],{},[1493,43429,1791],{},[1506,43431,2287],{},[1506,43433,1508],{},[1497,43435,43436,43438],{},[1493,43437,1501],{},[1680,43439,1682],{},[1497,43441,43442,43444],{},[1493,43443,1520],{},[1680,43445,1682],{},[1506,43447,2162],{},[1497,43449,43450,43452],{},[1493,43451,1501],{},[1680,43453,1691],{},[1497,43455,43456,43458],{},[1493,43457,1520],{},[1680,43459,1691],{},[1528,43461,43462],{"encoding":1530},"Y^* = P_1 Q_1 + P_2 Q_2",", a ",[1047,43465,43466],{},"duální úloha"," — minimalizace výdajů ",[1035,43469,43471],{"className":43470},[1480],[1482,43472,43473],{"xmlns":1484},[1487,43474,43475,43507],{},[1490,43476,43477,43479,43481,43487,43493,43495,43501],{},[1493,43478,2711],{},[1506,43480,1508],{},[1497,43482,43483,43485],{},[1493,43484,1501],{},[1680,43486,1682],{},[1497,43488,43489,43491],{},[1493,43490,1520],{},[1680,43492,1682],{},[1506,43494,2162],{},[1497,43496,43497,43499],{},[1493,43498,1501],{},[1680,43500,1691],{},[1497,43502,43503,43505],{},[1493,43504,1520],{},[1680,43506,1691],{},[1528,43508,4208],{"encoding":1530}," při zadané hladině užitečnosti ",[1035,43511,43513],{"className":43512},[1480],[1482,43514,43515],{"xmlns":1484},[1487,43516,43517,43525],{},[1490,43518,43519],{},[2315,43520,43521,43523],{},[1493,43522,1668],{},[1506,43524,2287],{},[1528,43526,43527],{"encoding":1530},"U^*",". Obě úlohy se řeší ",[1052,43530,43532],{"className":43531,"dataFsResolvedFilePath":17265,"href":17266},[1055],"metodou Lagrangeových multiplikátorů"," a vedou na tentýž bod dotyku indiferenční křivky a rozpočtové přímky, v němž platí ",[1035,43535,43537],{"className":43536},[1480],[1482,43538,43539],{"xmlns":1484},[1487,43540,43541,43561],{},[1490,43542,43543,43545,43547,43553,43555],{},[1988,43544,13960],{},[1506,43546,1508],{},[1497,43548,43549,43551],{},[1493,43550,1501],{},[1680,43552,1682],{},[1493,43554,1709],{"mathvariant":1516},[1497,43556,43557,43559],{},[1493,43558,1501],{},[1680,43560,1691],{},[1528,43562,43563],{"encoding":1530},"\\text{MRCS} = P_1\u002FP_2",". Výstupem jsou ",[1047,43566,43567],{},"funkce poptávky"," — Marshallova (závislá na důchodu) a Hicksova (závislá na hladině užitečnosti).",[1065,43570,43572],{"id":43571},"úvod-proč-optimalizovat","Úvod — proč optimalizovat",[1030,43574,43575,43576,43594,43595,43624],{},"Racionální spotřebitel má omezený důchod a musí se rozhodnout, jak jej rozdělit mezi spotřebovávané zboží. V modelu pro dvě zboží je k dispozici částka ",[1035,43577,43579],{"className":43578},[1480],[1482,43580,43581],{"xmlns":1484},[1487,43582,43583,43591],{},[1490,43584,43585],{},[2315,43586,43587,43589],{},[1493,43588,1791],{},[1506,43590,2287],{},[1528,43592,43593],{"encoding":1530},"Y^*"," a ceny ",[1035,43596,43598],{"className":43597},[1480],[1482,43599,43600],{"xmlns":1484},[1487,43601,43602,43622],{},[1490,43603,43604,43612,43614],{},[1697,43605,43606,43608,43610],{},[1493,43607,1501],{},[1680,43609,1682],{},[1506,43611,2287],{},[1506,43613,1559],{"separator":1041},[1697,43615,43616,43618,43620],{},[1493,43617,1501],{},[1680,43619,1691],{},[1506,43621,2287],{},[1528,43623,9219],{"encoding":1530},", rozpočtové omezení má tvar",[1035,43626,43628],{"className":43627},[1480],[1482,43629,43630],{"xmlns":1484,"display":1485},[1487,43631,43632,43689],{},[19617,43633,43634],{"width":19619},[19621,43635,43636,43638,43682,43684],{},[19624,43637],{"width":19626},[19624,43639,43640],{},[1490,43641,43642,43648,43650,43658,43664,43666,43674,43680],{},[2315,43643,43644,43646],{},[1493,43645,1791],{},[1506,43647,2287],{},[1506,43649,1508],{},[1697,43651,43652,43654,43656],{},[1493,43653,1501],{},[1680,43655,1682],{},[1506,43657,2287],{},[1497,43659,43660,43662],{},[1493,43661,1520],{},[1680,43663,1682],{},[1506,43665,2162],{},[1697,43667,43668,43670,43672],{},[1493,43669,1501],{},[1680,43671,1691],{},[1506,43673,2287],{},[1497,43675,43676,43678],{},[1493,43677,1520],{},[1680,43679,1691],{},[1506,43681,1559],{"separator":1041},[19624,43683],{"width":19626},[19624,43685,43686],{},[1988,43687,43688],{},"(6.12)",[1528,43690,43691],{"encoding":1530},"Y^* = P_1^* Q_1 + P_2^* Q_2, \\tag{6.12}",[1030,43693,43694,43695,43698,43699,1586,43735,43771,43772,43785,43786,43800,43801,2632],{},"geometricky ",[1047,43696,43697],{},"rozpočtová přímka (budget line)"," procházející body ",[1035,43700,43702],{"className":43701},[1480],[1482,43703,43704],{"xmlns":1484},[1487,43705,43706,43732],{},[1490,43707,43708,43710,43716,43718,43726,43728,43730],{},[1506,43709,14314],{"stretchy":1552},[2315,43711,43712,43714],{},[1493,43713,1791],{},[1506,43715,2287],{},[1493,43717,1709],{"mathvariant":1516},[1697,43719,43720,43722,43724],{},[1493,43721,1501],{},[1680,43723,1682],{},[1506,43725,2287],{},[1506,43727,1559],{"separator":1041},[1680,43729,1871],{},[1506,43731,14323],{"stretchy":1552},[1528,43733,43734],{"encoding":1530},"[Y^*\u002FP_1^*, 0]",[1035,43736,43738],{"className":43737},[1480],[1482,43739,43740],{"xmlns":1484},[1487,43741,43742,43768],{},[1490,43743,43744,43746,43748,43750,43756,43758,43766],{},[1506,43745,14314],{"stretchy":1552},[1680,43747,1871],{},[1506,43749,1559],{"separator":1041},[2315,43751,43752,43754],{},[1493,43753,1791],{},[1506,43755,2287],{},[1493,43757,1709],{"mathvariant":1516},[1697,43759,43760,43762,43764],{},[1493,43761,1501],{},[1680,43763,1691],{},[1506,43765,2287],{},[1506,43767,14323],{"stretchy":1552},[1528,43769,43770],{"encoding":1530},"[0, Y^*\u002FP_2^*]",". Spotřebitel chce v rámci této přímky (a pod ní) najít svazek s nejvyšší dostupnou užitečností. Teorie před optimalizací — tvar funkce ",[1035,43773,43775],{"className":43774},[1480],[1482,43776,43777],{"xmlns":1484},[1487,43778,43779,43783],{},[1490,43780,43781],{},[1493,43782,1668],{},[1528,43784,1668],{"encoding":1530},", indiferenční křivky a ",[1035,43787,43789],{"className":43788},[1480],[1482,43790,43791],{"xmlns":1484},[1487,43792,43793,43797],{},[1490,43794,43795],{},[1988,43796,13960],{},[1528,43798,43799],{"encoding":1530},"\\text{MRCS}"," — je shrnuta v ",[1052,43802,6615],{"className":43803,"dataFsResolvedFilePath":6613,"href":6614},[1055],[1023,43805,43807,43814],{"className":43806,"dataCallout":1155},[1026,1154],[1030,43808,43810,43813],{"className":43809},[1033],[1035,43811],{"className":43812,"ariaHidden":1041},[1038,1162,1040],"Pozor — dvě úlohy, totéž řešení",[1030,43815,43816,43819,43820,43833,43834,43836,43837,43850,43851,1656,43854,43894,43895,43912,43913,43930,43931,43948,43949,43967],{},[1047,43817,43818],{},"Primární úloha"," (max ",[1035,43821,43823],{"className":43822},[1480],[1482,43824,43825],{"xmlns":1484},[1487,43826,43827,43831],{},[1490,43828,43829],{},[1493,43830,1668],{},[1528,43832,1668],{"encoding":1530}," při pevném rozpočtu) a ",[1047,43835,43466],{}," (min ",[1035,43838,43840],{"className":43839},[1480],[1482,43841,43842],{"xmlns":1484},[1487,43843,43844,43848],{},[1490,43845,43846],{},[1493,43847,2711],{},[1528,43849,2711],{"encoding":1530}," při pevné užitečnosti) vedou na ",[1047,43852,43853],{},"tentýž bod",[1035,43855,43857],{"className":43856},[1480],[1482,43858,43859],{"xmlns":1484},[1487,43860,43861,43891],{},[1490,43862,43863,43869,43871,43879,43881,43889],{},[2315,43864,43865,43867],{},[1493,43866,1520],{},[1506,43868,2287],{},[1506,43870,14314],{"stretchy":1552},[1697,43872,43873,43875,43877],{},[1493,43874,1520],{},[1680,43876,1682],{},[1506,43878,2287],{},[1506,43880,1559],{"separator":1041},[1697,43882,43883,43885,43887],{},[1493,43884,1520],{},[1680,43886,1691],{},[1506,43888,2287],{},[1506,43890,14323],{"stretchy":1552},[1528,43892,43893],{"encoding":1530},"Q^*[Q_1^*, Q_2^*]",". Rozdíl je v tom, co je „vstup\" a co „výstup\": u primární úlohy je zadán důchod ",[1035,43896,43898],{"className":43897},[1480],[1482,43899,43900],{"xmlns":1484},[1487,43901,43902,43910],{},[1490,43903,43904],{},[2315,43905,43906,43908],{},[1493,43907,1791],{},[1506,43909,2287],{},[1528,43911,43593],{"encoding":1530}," a hledáme maximální ",[1035,43914,43916],{"className":43915},[1480],[1482,43917,43918],{"xmlns":1484},[1487,43919,43920,43928],{},[1490,43921,43922],{},[2315,43923,43924,43926],{},[1493,43925,1668],{},[1506,43927,2287],{},[1528,43929,43527],{"encoding":1530},"; u duální úlohy je zadána hladina ",[1035,43932,43934],{"className":43933},[1480],[1482,43935,43936],{"xmlns":1484},[1487,43937,43938,43946],{},[1490,43939,43940],{},[2315,43941,43942,43944],{},[1493,43943,1668],{},[1506,43945,2287],{},[1528,43947,43527],{"encoding":1530}," a hledáme minimální ",[1035,43950,43952],{"className":43951},[1480],[1482,43953,43954],{"xmlns":1484},[1487,43955,43956,43964],{},[1490,43957,43958],{},[2315,43959,43960,43962],{},[1493,43961,2711],{},[1506,43963,2287],{},[1528,43965,43966],{"encoding":1530},"E^*",". Z pozorování je přirozenější minimalizace výdajů (výdaje lze měřit).",[1065,43969,43971],{"id":43970},"maximalizace-užitečnosti-za-rozpočtového-omezení","Maximalizace užitečnosti za rozpočtového omezení",[1030,43973,43974,43975,44006,44007,44083,44084,2632],{},"Úlohou je najít maximum ",[1035,43976,43978],{"className":43977},[1480],[1482,43979,43980],{"xmlns":1484},[1487,43981,43982,44004],{},[1490,43983,43984,43986,43988,43994,43996,44002],{},[1493,43985,1668],{},[1506,43987,1553],{"stretchy":1552},[1497,43989,43990,43992],{},[1493,43991,1520],{},[1680,43993,1682],{},[1506,43995,1559],{"separator":1041},[1497,43997,43998,44000],{},[1493,43999,1520],{},[1680,44001,1691],{},[1506,44003,1564],{"stretchy":1552},[1528,44005,32500],{"encoding":1530}," vázané podmínkou (6.12) ve tvaru ",[1035,44008,44010],{"className":44009},[1480],[1482,44011,44012],{"xmlns":1484},[1487,44013,44014,44080],{},[1490,44015,44016,44018,44020,44026,44028,44034,44036,44038,44044,44046,44054,44060,44062,44070,44076,44078],{},[1493,44017,27556],{},[1506,44019,1553],{"stretchy":1552},[1497,44021,44022,44024],{},[1493,44023,1520],{},[1680,44025,1682],{},[1506,44027,1559],{"separator":1041},[1497,44029,44030,44032],{},[1493,44031,1520],{},[1680,44033,1691],{},[1506,44035,1564],{"stretchy":1552},[1506,44037,1508],{},[2315,44039,44040,44042],{},[1493,44041,1791],{},[1506,44043,2287],{},[1506,44045,1888],{},[1697,44047,44048,44050,44052],{},[1493,44049,1501],{},[1680,44051,1682],{},[1506,44053,2287],{},[1497,44055,44056,44058],{},[1493,44057,1520],{},[1680,44059,1682],{},[1506,44061,1888],{},[1697,44063,44064,44066,44068],{},[1493,44065,1501],{},[1680,44067,1691],{},[1506,44069,2287],{},[1497,44071,44072,44074],{},[1493,44073,1520],{},[1680,44075,1691],{},[1506,44077,1508],{},[1680,44079,1871],{},[1528,44081,44082],{"encoding":1530},"g(Q_1, Q_2) = Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",". Použijeme ",[1052,44085,44087],{"className":44086,"dataFsResolvedFilePath":17265,"href":17266},[1055],"metodu Lagrangeových multiplikátorů",[1304,44089,44091],{"id":44090},"lagrangeova-funkce-a-podmínky-optimality","Lagrangeova funkce a podmínky optimality",[1030,44093,44094],{},"Sestavíme",[1035,44096,44098],{"className":44097},[1480],[1482,44099,44100],{"xmlns":1484,"display":1485},[1487,44101,44102,44214],{},[19617,44103,44104],{"width":19619},[19621,44105,44106,44108,44207,44209],{},[19624,44107],{"width":19626},[19624,44109,44110],{},[1490,44111,44112,44115,44117,44123,44125,44131,44133,44135,44137,44139,44141,44143,44149,44151,44157,44159,44161,44163,44165,44171,44173,44181,44187,44189,44197,44203,44205],{},[1493,44113,1556],{"mathvariant":44114},"script",[1506,44116,1553],{"stretchy":1552},[1497,44118,44119,44121],{},[1493,44120,1520],{},[1680,44122,1682],{},[1506,44124,1559],{"separator":1041},[1497,44126,44127,44129],{},[1493,44128,1520],{},[1680,44130,1691],{},[1506,44132,1559],{"separator":1041},[1493,44134,32598],{},[1506,44136,1564],{"stretchy":1552},[1506,44138,1508],{},[1493,44140,1668],{},[1506,44142,1553],{"stretchy":1552},[1497,44144,44145,44147],{},[1493,44146,1520],{},[1680,44148,1682],{},[1506,44150,1559],{"separator":1041},[1497,44152,44153,44155],{},[1493,44154,1520],{},[1680,44156,1691],{},[1506,44158,1564],{"stretchy":1552},[1506,44160,2162],{},[1493,44162,32598],{},[1506,44164,1553],{"stretchy":1552},[2315,44166,44167,44169],{},[1493,44168,1791],{},[1506,44170,2287],{},[1506,44172,1888],{},[1697,44174,44175,44177,44179],{},[1493,44176,1501],{},[1680,44178,1682],{},[1506,44180,2287],{},[1497,44182,44183,44185],{},[1493,44184,1520],{},[1680,44186,1682],{},[1506,44188,1888],{},[1697,44190,44191,44193,44195],{},[1493,44192,1501],{},[1680,44194,1691],{},[1506,44196,2287],{},[1497,44198,44199,44201],{},[1493,44200,1520],{},[1680,44202,1691],{},[1506,44204,1564],{"stretchy":1552},[1493,44206,2632],{"mathvariant":1516},[19624,44208],{"width":19626},[19624,44210,44211],{},[1988,44212,44213],{},"(6.13)",[1528,44215,44216],{"encoding":1530},"\\mathcal{L}(Q_1, Q_2, \\lambda) = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2). \\tag{6.13}",[1030,44218,44219],{},"Soustava prvního řádu:",[1035,44221,44223],{"className":44222},[1480],[1482,44224,44225],{"xmlns":1484,"display":1485},[1487,44226,44227,44410],{},[19617,44228,44229],{"width":19619},[19621,44230,44231,44233,44403,44405],{},[19624,44232],{"width":19626},[19624,44234,44235],{},[19617,44236,44237,44287,44337],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,44238,44239,44251],{},[19624,44240,44241],{},[1869,44242,44243],{"scriptlevel":1871,"displaystyle":1041},[1697,44244,44245,44247,44249],{},[1493,44246,1556],{"mathvariant":44114},[1680,44248,1682],{},[1506,44250,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,44252,44253],{},[1869,44254,44255],{"scriptlevel":1871,"displaystyle":1041},[1490,44256,44257,44259,44261,44269,44271,44273,44281,44283,44285],{},[1490,44258],{},[1506,44260,1508],{},[1697,44262,44263,44265,44267],{},[1493,44264,1668],{},[1680,44266,1682],{},[1506,44268,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,44270,1888],{},[1493,44272,32598],{},[1697,44274,44275,44277,44279],{},[1493,44276,1501],{},[1680,44278,1682],{},[1506,44280,2287],{},[1506,44282,1508],{},[1680,44284,1871],{},[1506,44286,1559],{"separator":1041},[19621,44288,44289,44301],{},[19624,44290,44291],{},[1869,44292,44293],{"scriptlevel":1871,"displaystyle":1041},[1697,44294,44295,44297,44299],{},[1493,44296,1556],{"mathvariant":44114},[1680,44298,1691],{},[1506,44300,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,44302,44303],{},[1869,44304,44305],{"scriptlevel":1871,"displaystyle":1041},[1490,44306,44307,44309,44311,44319,44321,44323,44331,44333,44335],{},[1490,44308],{},[1506,44310,1508],{},[1697,44312,44313,44315,44317],{},[1493,44314,1668],{},[1680,44316,1691],{},[1506,44318,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,44320,1888],{},[1493,44322,32598],{},[1697,44324,44325,44327,44329],{},[1493,44326,1501],{},[1680,44328,1691],{},[1506,44330,2287],{},[1506,44332,1508],{},[1680,44334,1871],{},[1506,44336,1559],{"separator":1041},[19621,44338,44339,44351],{},[19624,44340,44341],{},[1869,44342,44343],{"scriptlevel":1871,"displaystyle":1041},[1697,44344,44345,44347,44349],{},[1493,44346,1556],{"mathvariant":44114},[1493,44348,32598],{},[1506,44350,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,44352,44353],{},[1869,44354,44355],{"scriptlevel":1871,"displaystyle":1041},[1490,44356,44357,44359,44361,44367,44369,44377,44383,44385,44393,44399,44401],{},[1490,44358],{},[1506,44360,1508],{},[2315,44362,44363,44365],{},[1493,44364,1791],{},[1506,44366,2287],{},[1506,44368,1888],{},[1697,44370,44371,44373,44375],{},[1493,44372,1501],{},[1680,44374,1682],{},[1506,44376,2287],{},[1497,44378,44379,44381],{},[1493,44380,1520],{},[1680,44382,1682],{},[1506,44384,1888],{},[1697,44386,44387,44389,44391],{},[1493,44388,1501],{},[1680,44390,1691],{},[1506,44392,2287],{},[1497,44394,44395,44397],{},[1493,44396,1520],{},[1680,44398,1691],{},[1506,44400,1508],{},[1680,44402,28945],{},[19624,44404],{"width":19626},[19624,44406,44407],{},[1988,44408,44409],{},"(6.14)",[1528,44411,44412],{"encoding":1530},"\\begin{aligned}\n\\mathcal{L}'_1 &= U'_1 - \\lambda P_1^* = 0, \\\\\n\\mathcal{L}'_2 &= U'_2 - \\lambda P_2^* = 0, \\\\\n\\mathcal{L}'_\\lambda &= Y^* - P_1^* Q_1 - P_2^* Q_2 = 0.\n\\end{aligned}\n\\tag{6.14}",[1030,44414,44415,44416,44419,44420,44433,44434,1274],{},"Díky konvexitě indiferenčních křivek je řešení ",[1047,44417,44418],{},"vázaným maximem",". Z prvních dvou rovnic po vyloučení ",[1035,44421,44423],{"className":44422},[1480],[1482,44424,44425],{"xmlns":1484},[1487,44426,44427,44431],{},[1490,44428,44429],{},[1493,44430,32598],{},[1528,44432,32651],{"encoding":1530}," dostáváme ",[1047,44435,44436],{},"podmínku optimality",[1035,44438,44440],{"className":44439},[1480],[1482,44441,44442],{"xmlns":1484,"display":1485},[1487,44443,44444,44502],{},[1490,44445,44446],{},[1976,44447,44448],{"notation":1978},[1869,44449,44450],{"scriptlevel":1871,"displaystyle":1552},[1869,44451,44452],{"scriptlevel":1871,"displaystyle":1552},[1869,44453,44454],{"scriptlevel":1871,"displaystyle":1041},[1490,44455,44456,44458,44460,44462,44480,44482,44500],{},[1988,44457,1990],{},[1988,44459,13960],{},[1506,44461,1508],{},[1510,44463,44464,44472],{},[1697,44465,44466,44468,44470],{},[1493,44467,1668],{},[1680,44469,1682],{},[1506,44471,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1697,44473,44474,44476,44478],{},[1493,44475,1668],{},[1680,44477,1691],{},[1506,44479,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,44481,1508],{},[1510,44483,44484,44492],{},[1697,44485,44486,44488,44490],{},[1493,44487,1501],{},[1680,44489,1682],{},[1506,44491,2287],{},[1697,44493,44494,44496,44498],{},[1493,44495,1501],{},[1680,44497,1691],{},[1506,44499,2287],{},[1988,44501,1990],{},[1528,44503,44504],{"encoding":1530},"\\boxed{\\; \\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*} \\;}",[1023,44506,44508,44515],{"className":44507,"dataCallout":582},[1026,1186],[1030,44509,44511,44514],{"className":44510},[1033],[1035,44512],{"className":44513,"ariaHidden":1041},[1038,1193,1040],"Intuice — mezní poměr užitečnosti = mezní poměr cen",[1030,44516,44517,44518,44552,44553,44556,44557,44574,44575,44592,44593,44623,44624,44641,44642,44672],{},"Podmínka ",[1035,44519,44521],{"className":44520},[1480],[1482,44522,44523],{"xmlns":1484},[1487,44524,44525,44549],{},[1490,44526,44527,44529,44531,44539,44541],{},[1988,44528,13960],{},[1506,44530,1508],{},[1697,44532,44533,44535,44537],{},[1493,44534,1501],{},[1680,44536,1682],{},[1506,44538,2287],{},[1493,44540,1709],{"mathvariant":1516},[1697,44542,44543,44545,44547],{},[1493,44544,1501],{},[1680,44546,1691],{},[1506,44548,2287],{},[1528,44550,44551],{"encoding":1530},"\\text{MRCS} = P_1^*\u002FP_2^*"," říká, že v optimu je ",[1047,44554,44555],{},"sklon indiferenční křivky roven sklonu rozpočtové přímky",". Ekonomicky: spotřebitel je ochoten vyměnit ",[1035,44558,44560],{"className":44559},[1480],[1482,44561,44562],{"xmlns":1484},[1487,44563,44564,44572],{},[1490,44565,44566],{},[1497,44567,44568,44570],{},[1493,44569,1520],{},[1680,44571,1682],{},[1528,44573,6702],{"encoding":1530}," za ",[1035,44576,44578],{"className":44577},[1480],[1482,44579,44580],{"xmlns":1484},[1487,44581,44582,44590],{},[1490,44583,44584],{},[1497,44585,44586,44588],{},[1493,44587,1520],{},[1680,44589,1691],{},[1528,44591,6683],{"encoding":1530}," v přesně tom poměru, v jakém je trh (ceny) umožňuje vyměňovat. Kdyby ",[1035,44594,44596],{"className":44595},[1480],[1482,44597,44598],{"xmlns":1484},[1487,44599,44600,44620],{},[1490,44601,44602,44604,44606,44612,44614],{},[1988,44603,13960],{},[1506,44605,2796],{},[1497,44607,44608,44610],{},[1493,44609,1501],{},[1680,44611,1682],{},[1493,44613,1709],{"mathvariant":1516},[1497,44615,44616,44618],{},[1493,44617,1501],{},[1680,44619,1691],{},[1528,44621,44622],{"encoding":1530},"\\text{MRCS} > P_1\u002FP_2",", vyplatilo by se nakupovat více ",[1035,44625,44627],{"className":44626},[1480],[1482,44628,44629],{"xmlns":1484},[1487,44630,44631,44639],{},[1490,44632,44633],{},[1497,44634,44635,44637],{},[1493,44636,1520],{},[1680,44638,1682],{},[1528,44640,6702],{"encoding":1530}," (subjektivní ocenění převažuje nad tržním); kdyby ",[1035,44643,44645],{"className":44644},[1480],[1482,44646,44647],{"xmlns":1484},[1487,44648,44649,44669],{},[1490,44650,44651,44653,44655,44661,44663],{},[1988,44652,13960],{},[1506,44654,3961],{},[1497,44656,44657,44659],{},[1493,44658,1501],{},[1680,44660,1682],{},[1493,44662,1709],{"mathvariant":1516},[1497,44664,44665,44667],{},[1493,44666,1501],{},[1680,44668,1691],{},[1528,44670,44671],{"encoding":1530},"\\text{MRCS} \u003C P_1\u002FP_2",", vyplatil by se opak.",[1304,44674,3814,44676,44689],{"id":44675},"interpretace-λlambda-mezní-užitečnost-důchodu",[1035,44677,44679],{"className":44678},[1480],[1482,44680,44681],{"xmlns":1484},[1487,44682,44683,44687],{},[1490,44684,44685],{},[1493,44686,32598],{},[1528,44688,32651],{"encoding":1530}," — mezní užitečnost důchodu",[1030,44691,44692,44693,44711,44712,44715,44716,44733,44734,44751,44752,44755],{},"Lagrangeův multiplikátor ",[1035,44694,44696],{"className":44695},[1480],[1482,44697,44698],{"xmlns":1484},[1487,44699,44700,44708],{},[1490,44701,44702],{},[2315,44703,44704,44706],{},[1493,44705,32598],{},[1506,44707,2287],{},[1528,44709,44710],{"encoding":1530},"\\lambda^*"," představuje ",[1047,44713,44714],{},"mezní užitečnost důchodu"," — přibližnou změnu maximální užitečnosti ",[1035,44717,44719],{"className":44718},[1480],[1482,44720,44721],{"xmlns":1484},[1487,44722,44723,44731],{},[1490,44724,44725],{},[2315,44726,44727,44729],{},[1493,44728,1668],{},[1506,44730,2287],{},[1528,44732,43527],{"encoding":1530}," při jednotkové změně důchodu ",[1035,44735,44737],{"className":44736},[1480],[1482,44738,44739],{"xmlns":1484},[1487,44740,44741,44749],{},[1490,44742,44743],{},[2315,44744,44745,44747],{},[1493,44746,1791],{},[1506,44748,2287],{},[1528,44750,43593],{"encoding":1530},". Je to ",[1047,44753,44754],{},"stínová cena"," rozpočtového omezení.",[1023,44757,44759,44766],{"className":44758,"dataCallout":1443},[1026,1442],[1030,44760,44762,44765],{"className":44761},[1033],[1035,44763],{"className":44764,"ariaHidden":1041},[1038,1450,1040],"Postup — maximalizace užitečnosti Lagrangeovou metodou",[1276,44767,44768,44828,44915,44951,45038],{},[1206,44769,44770,44773,44774,2632],{},[1047,44771,44772],{},"Zapiš rozpočtové omezení"," ve tvaru ",[1035,44775,44777],{"className":44776},[1480],[1482,44778,44779],{"xmlns":1484},[1487,44780,44781,44825],{},[1490,44782,44783,44789,44791,44799,44805,44807,44815,44821,44823],{},[2315,44784,44785,44787],{},[1493,44786,1791],{},[1506,44788,2287],{},[1506,44790,1888],{},[1697,44792,44793,44795,44797],{},[1493,44794,1501],{},[1680,44796,1682],{},[1506,44798,2287],{},[1497,44800,44801,44803],{},[1493,44802,1520],{},[1680,44804,1682],{},[1506,44806,1888],{},[1697,44808,44809,44811,44813],{},[1493,44810,1501],{},[1680,44812,1691],{},[1506,44814,2287],{},[1497,44816,44817,44819],{},[1493,44818,1520],{},[1680,44820,1691],{},[1506,44822,1508],{},[1680,44824,1871],{},[1528,44826,44827],{"encoding":1530},"Y^* - P_1^* Q_1 - P_2^* Q_2 = 0",[1206,44829,44830,1656,44833,2632],{},[1047,44831,44832],{},"Sestav Lagrangeovu funkci",[1035,44834,44836],{"className":44835},[1480],[1482,44837,44838],{"xmlns":1484},[1487,44839,44840,44912],{},[1490,44841,44842,44844,44846,44848,44850,44856,44858,44864,44866,44868,44870,44872,44878,44880,44888,44894,44896,44904,44910],{},[1493,44843,1556],{"mathvariant":44114},[1506,44845,1508],{},[1493,44847,1668],{},[1506,44849,1553],{"stretchy":1552},[1497,44851,44852,44854],{},[1493,44853,1520],{},[1680,44855,1682],{},[1506,44857,1559],{"separator":1041},[1497,44859,44860,44862],{},[1493,44861,1520],{},[1680,44863,1691],{},[1506,44865,1564],{"stretchy":1552},[1506,44867,2162],{},[1493,44869,32598],{},[1506,44871,1553],{"stretchy":1552},[2315,44873,44874,44876],{},[1493,44875,1791],{},[1506,44877,2287],{},[1506,44879,1888],{},[1697,44881,44882,44884,44886],{},[1493,44883,1501],{},[1680,44885,1682],{},[1506,44887,2287],{},[1497,44889,44890,44892],{},[1493,44891,1520],{},[1680,44893,1682],{},[1506,44895,1888],{},[1697,44897,44898,44900,44902],{},[1493,44899,1501],{},[1680,44901,1691],{},[1506,44903,2287],{},[1497,44905,44906,44908],{},[1493,44907,1520],{},[1680,44909,1691],{},[1506,44911,1564],{"stretchy":1552},[1528,44913,44914],{"encoding":1530},"\\mathcal{L} = U(Q_1, Q_2) + \\lambda(Y^* - P_1^* Q_1 - P_2^* Q_2)",[1206,44916,44917,26991,44920,44950],{},[1047,44918,44919],{},"Spočítej parciální derivace",[1035,44921,44923],{"className":44922},[1480],[1482,44924,44925],{"xmlns":1484},[1487,44926,44927,44947],{},[1490,44928,44929,44935,44937,44943,44945],{},[1497,44930,44931,44933],{},[1493,44932,1520],{},[1680,44934,1682],{},[1506,44936,1559],{"separator":1041},[1497,44938,44939,44941],{},[1493,44940,1520],{},[1680,44942,1691],{},[1506,44944,1559],{"separator":1041},[1493,44946,32598],{},[1528,44948,44949],{"encoding":1530},"Q_1, Q_2, \\lambda"," a polož je rovny nule.",[1206,44952,44953,44969,44970,45003,45004,1586,45021,2632],{},[1047,44954,44955,44956],{},"Vyluč ",[1035,44957,44959],{"className":44958},[1480],[1482,44960,44961],{"xmlns":1484},[1487,44962,44963,44967],{},[1490,44964,44965],{},[1493,44966,32598],{},[1528,44968,32651],{"encoding":1530}," dělením prvních dvou rovnic — dostaneš podmínku ",[1035,44971,44973],{"className":44972},[1480],[1482,44974,44975],{"xmlns":1484},[1487,44976,44977,45001],{},[1490,44978,44979,44981,44983,44991,44993],{},[1988,44980,13960],{},[1506,44982,1508],{},[1697,44984,44985,44987,44989],{},[1493,44986,1501],{},[1680,44988,1682],{},[1506,44990,2287],{},[1493,44992,1709],{"mathvariant":1516},[1697,44994,44995,44997,44999],{},[1493,44996,1501],{},[1680,44998,1691],{},[1506,45000,2287],{},[1528,45002,44551],{"encoding":1530},", která dá vztah mezi ",[1035,45005,45007],{"className":45006},[1480],[1482,45008,45009],{"xmlns":1484},[1487,45010,45011,45019],{},[1490,45012,45013],{},[1497,45014,45015,45017],{},[1493,45016,1520],{},[1680,45018,1682],{},[1528,45020,6702],{"encoding":1530},[1035,45022,45024],{"className":45023},[1480],[1482,45025,45026],{"xmlns":1484},[1487,45027,45028,45036],{},[1490,45029,45030],{},[1497,45031,45032,45034],{},[1493,45033,1520],{},[1680,45035,1691],{},[1528,45037,6683],{"encoding":1530},[1206,45039,45040,45043,45044,45074,45075,45092,45093,2632],{},[1047,45041,45042],{},"Dosaď do rozpočtového omezení"," a vypočítej ",[1035,45045,45047],{"className":45046},[1480],[1482,45048,45049],{"xmlns":1484},[1487,45050,45051,45071],{},[1490,45052,45053,45061,45063],{},[1697,45054,45055,45057,45059],{},[1493,45056,1520],{},[1680,45058,1682],{},[1506,45060,2287],{},[1506,45062,1559],{"separator":1041},[1697,45064,45065,45067,45069],{},[1493,45066,1520],{},[1680,45068,1691],{},[1506,45070,2287],{},[1528,45072,45073],{"encoding":1530},"Q_1^*, Q_2^*",", případně ",[1035,45076,45078],{"className":45077},[1480],[1482,45079,45080],{"xmlns":1484},[1487,45081,45082,45090],{},[1490,45083,45084],{},[2315,45085,45086,45088],{},[1493,45087,32598],{},[1506,45089,2287],{},[1528,45091,44710],{"encoding":1530}," a maximální užitečnost ",[1035,45094,45096],{"className":45095},[1480],[1482,45097,45098],{"xmlns":1484},[1487,45099,45100,45134],{},[1490,45101,45102,45108,45110,45112,45114,45122,45124,45132],{},[2315,45103,45104,45106],{},[1493,45105,1668],{},[1506,45107,2287],{},[1506,45109,1508],{},[1493,45111,1668],{},[1506,45113,1553],{"stretchy":1552},[1697,45115,45116,45118,45120],{},[1493,45117,1520],{},[1680,45119,1682],{},[1506,45121,2287],{},[1506,45123,1559],{"separator":1041},[1697,45125,45126,45128,45130],{},[1493,45127,1520],{},[1680,45129,1691],{},[1506,45131,2287],{},[1506,45133,1564],{"stretchy":1552},[1528,45135,45136],{"encoding":1530},"U^* = U(Q_1^*, Q_2^*)",[1065,45138,45140],{"id":45139},"geometrie-optima-tečnost-ic-a-rozpočtové-přímky","Geometrie optima — tečnost IC a rozpočtové přímky",[1030,45142,45143],{},[18014,45144],{"alt":45145,"className":45146,"src":45147},"imek-uzitecnost-optimum",[1055,18018],"\u002Fwiki-assets\u002Fimek-uzitecnost-optimum.jpeg",[1030,45149,45150,45151,45154,45155,45172,45173,45202],{},"Geometrie je jádrem intuice: přímka (rozpočet) a křivka (užitečnost) se v optimu ",[1047,45152,45153],{},"dotýkají",", tj. mají v bodě ",[1035,45156,45158],{"className":45157},[1480],[1482,45159,45160],{"xmlns":1484},[1487,45161,45162,45170],{},[1490,45163,45164],{},[2315,45165,45166,45168],{},[1493,45167,1520],{},[1506,45169,2287],{},[1528,45171,14097],{"encoding":1530}," společnou tečnu. To přímo převádí podmínku ",[1035,45174,45176],{"className":45175},[1480],[1482,45177,45178],{"xmlns":1484},[1487,45179,45180,45200],{},[1490,45181,45182,45184,45186,45192,45194],{},[1988,45183,13960],{},[1506,45185,1508],{},[1497,45187,45188,45190],{},[1493,45189,1501],{},[1680,45191,1682],{},[1493,45193,1709],{"mathvariant":1516},[1497,45195,45196,45198],{},[1493,45197,1501],{},[1680,45199,1691],{},[1528,45201,43563],{"encoding":1530}," — poměr mezních užitečností (sklon IC) = poměr cen (sklon přímky).",[1065,45204,45206],{"id":45205},"příklad-65-mrcs-pro-cobb-douglasovu-užitečnost","Příklad 6.5 — MRCS pro Cobb-Douglasovu užitečnost",[1030,45208,2364,45209,45271],{},[1035,45210,45212],{"className":45211},[1480],[1482,45213,45214],{"xmlns":1484},[1487,45215,45216,45268],{},[1490,45217,45218,45220,45222,45228,45230,45236,45238,45240,45254],{},[1493,45219,1668],{},[1506,45221,1553],{"stretchy":1552},[1497,45223,45224,45226],{},[1493,45225,1520],{},[1680,45227,1682],{},[1506,45229,1559],{"separator":1041},[1497,45231,45232,45234],{},[1493,45233,1520],{},[1680,45235,1691],{},[1506,45237,1564],{"stretchy":1552},[1506,45239,1508],{},[1697,45241,45242,45244,45246],{},[1493,45243,1520],{},[1680,45245,1682],{},[1490,45247,45248,45250,45252],{},[1680,45249,1682],{},[1493,45251,1709],{"mathvariant":1516},[1680,45253,1691],{},[1697,45255,45256,45258,45260],{},[1493,45257,1520],{},[1680,45259,1691],{},[1490,45261,45262,45264,45266],{},[1680,45263,1682],{},[1493,45265,1709],{"mathvariant":1516},[1680,45267,1691],{},[1528,45269,45270],{"encoding":1530},"U(Q_1, Q_2) = Q_1^{1\u002F2} Q_2^{1\u002F2}"," platí",[1035,45273,45275],{"className":45274},[1480],[1482,45276,45277],{"xmlns":1484,"display":1485},[1487,45278,45279,45385],{},[1490,45280,45281,45283,45285,45367,45369,45383],{},[1988,45282,13960],{},[1506,45284,1508],{},[1510,45286,45287,45327],{},[1490,45288,45289,45297,45313],{},[1869,45290,45291],{"scriptlevel":1871,"displaystyle":1552},[1510,45292,45293,45295],{},[1680,45294,1682],{},[1680,45296,1691],{},[1697,45298,45299,45301,45303],{},[1493,45300,1520],{},[1680,45302,1682],{},[1490,45304,45305,45307,45309,45311],{},[1506,45306,1888],{},[1680,45308,1682],{},[1493,45310,1709],{"mathvariant":1516},[1680,45312,1691],{},[1697,45314,45315,45317,45319],{},[1493,45316,1520],{},[1680,45318,1691],{},[1490,45320,45321,45323,45325],{},[1680,45322,1682],{},[1493,45324,1709],{"mathvariant":1516},[1680,45326,1691],{},[1490,45328,45329,45337,45351],{},[1869,45330,45331],{"scriptlevel":1871,"displaystyle":1552},[1510,45332,45333,45335],{},[1680,45334,1682],{},[1680,45336,1691],{},[1697,45338,45339,45341,45343],{},[1493,45340,1520],{},[1680,45342,1682],{},[1490,45344,45345,45347,45349],{},[1680,45346,1682],{},[1493,45348,1709],{"mathvariant":1516},[1680,45350,1691],{},[1697,45352,45353,45355,45357],{},[1493,45354,1520],{},[1680,45356,1691],{},[1490,45358,45359,45361,45363,45365],{},[1506,45360,1888],{},[1680,45362,1682],{},[1493,45364,1709],{"mathvariant":1516},[1680,45366,1691],{},[1506,45368,1508],{},[1510,45370,45371,45377],{},[1497,45372,45373,45375],{},[1493,45374,1520],{},[1680,45376,1691],{},[1497,45378,45379,45381],{},[1493,45380,1520],{},[1680,45382,1682],{},[1493,45384,2632],{"mathvariant":1516},[1528,45386,45387],{"encoding":1530},"\\text{MRCS} = \\frac{\\tfrac{1}{2} Q_1^{-1\u002F2} Q_2^{1\u002F2}}{\\tfrac{1}{2} Q_1^{1\u002F2} Q_2^{-1\u002F2}} = \\frac{Q_2}{Q_1}.",[1030,45389,45390,45391,18367,45435,45437,45438,45458,45459,45489,45490,2632],{},"Tedy ",[1035,45392,45394],{"className":45393},[1480],[1482,45395,45396],{"xmlns":1484},[1487,45397,45398,45432],{},[1490,45399,45400,45402,45404,45406,45408,45410,45412,45414,45422,45424],{},[1988,45401,13960],{},[1506,45403,1553],{"stretchy":1552},[1680,45405,5231],{},[1506,45407,1559],{"separator":1041},[1680,45409,1796],{},[1506,45411,1564],{"stretchy":1552},[1506,45413,1508],{},[1869,45415,45416],{"scriptlevel":1871,"displaystyle":1552},[1510,45417,45418,45420],{},[1680,45419,1796],{},[1680,45421,5231],{},[1506,45423,1508],{},[1869,45425,45426],{"scriptlevel":1871,"displaystyle":1552},[1510,45427,45428,45430],{},[1680,45429,1752],{},[1680,45431,3201],{},[1528,45433,45434],{"encoding":1530},"\\text{MRCS}(300, 500) = \\tfrac{500}{300} = \\tfrac{5}{3}",[1176,45436,12171],{}," zvýší-li spotřebitel nákup prvního zboží o 1 jednotku, musí snížit nákup druhého zboží přibližně o ",[1035,45439,45441],{"className":45440},[1480],[1482,45442,45443],{"xmlns":1484},[1487,45444,45445,45455],{},[1490,45446,45447],{},[1869,45448,45449],{"scriptlevel":1871,"displaystyle":1552},[1510,45450,45451,45453],{},[1680,45452,1752],{},[1680,45454,3201],{},[1528,45456,45457],{"encoding":1530},"\\tfrac{5}{3}"," jednotky, aby se užitečnost zachovala. Tato forma ",[1035,45460,45462],{"className":45461},[1480],[1482,45463,45464],{"xmlns":1484},[1487,45465,45466,45486],{},[1490,45467,45468,45470,45472,45478,45480],{},[1988,45469,13960],{},[1506,45471,1508],{},[1497,45473,45474,45476],{},[1493,45475,1520],{},[1680,45477,1691],{},[1493,45479,1709],{"mathvariant":1516},[1497,45481,45482,45484],{},[1493,45483,1520],{},[1680,45485,1682],{},[1528,45487,45488],{"encoding":1530},"\\text{MRCS} = Q_2\u002FQ_1"," je typická pro symetrické Cobb-Douglasovy preference a vstupuje do optimalizace skrze podmínku ",[1035,45491,45493],{"className":45492},[1480],[1482,45494,45495],{"xmlns":1484},[1487,45496,45497,45517],{},[1490,45498,45499,45501,45503,45509,45511],{},[1988,45500,13960],{},[1506,45502,1508],{},[1497,45504,45505,45507],{},[1493,45506,1501],{},[1680,45508,1682],{},[1493,45510,1709],{"mathvariant":1516},[1497,45512,45513,45515],{},[1493,45514,1501],{},[1680,45516,1691],{},[1528,45518,43563],{"encoding":1530},[1065,45520,45522,45523],{"id":45521},"příklad-66-maximalizace-užitečnosti-pro-uq1q2u-q_1-q_2","Příklad 6.6 — maximalizace užitečnosti pro ",[1035,45524,45526],{"className":45525},[1480],[1482,45527,45528],{"xmlns":1484},[1487,45529,45530,45548],{},[1490,45531,45532,45534,45536,45542],{},[1493,45533,1668],{},[1506,45535,1508],{},[1497,45537,45538,45540],{},[1493,45539,1520],{},[1680,45541,1682],{},[1497,45543,45544,45546],{},[1493,45545,1520],{},[1680,45547,1691],{},[1528,45549,45550],{"encoding":1530},"U = Q_1 Q_2",[1030,45552,45553,45554,1732,45600,1732,45624,1732,45648,45670],{},"Je dána ",[1035,45555,45557],{"className":45556},[1480],[1482,45558,45559],{"xmlns":1484},[1487,45560,45561,45597],{},[1490,45562,45563,45565,45567,45573,45575,45581,45583,45585,45591],{},[1493,45564,1668],{},[1506,45566,1553],{"stretchy":1552},[1497,45568,45569,45571],{},[1493,45570,1520],{},[1680,45572,1682],{},[1506,45574,1559],{"separator":1041},[1497,45576,45577,45579],{},[1493,45578,1520],{},[1680,45580,1691],{},[1506,45582,1564],{"stretchy":1552},[1506,45584,1508],{},[1497,45586,45587,45589],{},[1493,45588,1520],{},[1680,45590,1682],{},[1497,45592,45593,45595],{},[1493,45594,1520],{},[1680,45596,1691],{},[1528,45598,45599],{"encoding":1530},"U(Q_1, Q_2) = Q_1 Q_2",[1035,45601,45603],{"className":45602},[1480],[1482,45604,45605],{"xmlns":1484},[1487,45606,45607,45621],{},[1490,45608,45609,45617,45619],{},[1697,45610,45611,45613,45615],{},[1493,45612,1501],{},[1680,45614,1682],{},[1506,45616,2287],{},[1506,45618,1508],{},[1680,45620,1691],{},[1528,45622,45623],{"encoding":1530},"P_1^* = 2",[1035,45625,45627],{"className":45626},[1480],[1482,45628,45629],{"xmlns":1484},[1487,45630,45631,45645],{},[1490,45632,45633,45641,45643],{},[1697,45634,45635,45637,45639],{},[1493,45636,1501],{},[1680,45638,1691],{},[1506,45640,2287],{},[1506,45642,1508],{},[1680,45644,1752],{},[1528,45646,45647],{"encoding":1530},"P_2^* = 5",[1035,45649,45651],{"className":45650},[1480],[1482,45652,45653],{"xmlns":1484},[1487,45654,45655,45667],{},[1490,45656,45657,45663,45665],{},[2315,45658,45659,45661],{},[1493,45660,1791],{},[1506,45662,2287],{},[1506,45664,1508],{},[1680,45666,2916],{},[1528,45668,45669],{"encoding":1530},"Y^* = 100",". Lagrangeova funkce:",[1035,45672,45674],{"className":45673},[1480],[1482,45675,45676],{"xmlns":1484,"display":1485},[1487,45677,45678,45750],{},[1490,45679,45680,45682,45684,45690,45692,45698,45700,45702,45704,45706,45712,45718,45720,45722,45724,45726,45728,45730,45736,45738,45740,45746,45748],{},[1493,45681,1556],{"mathvariant":44114},[1506,45683,1553],{"stretchy":1552},[1497,45685,45686,45688],{},[1493,45687,1520],{},[1680,45689,1682],{},[1506,45691,1559],{"separator":1041},[1497,45693,45694,45696],{},[1493,45695,1520],{},[1680,45697,1691],{},[1506,45699,1559],{"separator":1041},[1493,45701,32598],{},[1506,45703,1564],{"stretchy":1552},[1506,45705,1508],{},[1497,45707,45708,45710],{},[1493,45709,1520],{},[1680,45711,1682],{},[1497,45713,45714,45716],{},[1493,45715,1520],{},[1680,45717,1691],{},[1506,45719,2162],{},[1493,45721,32598],{},[1506,45723,1553],{"stretchy":1552},[1680,45725,2916],{},[1506,45727,1888],{},[1680,45729,1691],{},[1497,45731,45732,45734],{},[1493,45733,1520],{},[1680,45735,1682],{},[1506,45737,1888],{},[1680,45739,1752],{},[1497,45741,45742,45744],{},[1493,45743,1520],{},[1680,45745,1691],{},[1506,45747,1564],{"stretchy":1552},[1493,45749,2632],{"mathvariant":1516},[1528,45751,45752],{"encoding":1530},"\\mathcal{L}(Q_1, Q_2, \\lambda) = Q_1 Q_2 + \\lambda(100 - 2 Q_1 - 5 Q_2).",[1030,45754,45755],{},"Soustava:",[1035,45757,45759],{"className":45758},[1480],[1482,45760,45761],{"xmlns":1484,"display":1485},[1487,45762,45763,45875],{},[19617,45764,45765,45799,45833],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,45766,45767,45785],{},[19624,45768,45769],{},[1869,45770,45771],{"scriptlevel":1871,"displaystyle":1041},[1490,45772,45773,45779,45781,45783],{},[1497,45774,45775,45777],{},[1493,45776,1520],{},[1680,45778,1691],{},[1506,45780,1888],{},[1680,45782,1691],{},[1493,45784,32598],{},[19624,45786,45787],{},[1869,45788,45789],{"scriptlevel":1871,"displaystyle":1041},[1490,45790,45791,45793,45795,45797],{},[1490,45792],{},[1506,45794,1508],{},[1680,45796,1871],{},[1506,45798,1559],{"separator":1041},[19621,45800,45801,45819],{},[19624,45802,45803],{},[1869,45804,45805],{"scriptlevel":1871,"displaystyle":1041},[1490,45806,45807,45813,45815,45817],{},[1497,45808,45809,45811],{},[1493,45810,1520],{},[1680,45812,1682],{},[1506,45814,1888],{},[1680,45816,1752],{},[1493,45818,32598],{},[19624,45820,45821],{},[1869,45822,45823],{"scriptlevel":1871,"displaystyle":1041},[1490,45824,45825,45827,45829,45831],{},[1490,45826],{},[1506,45828,1508],{},[1680,45830,1871],{},[1506,45832,1559],{"separator":1041},[19621,45834,45835,45863],{},[19624,45836,45837],{},[1869,45838,45839],{"scriptlevel":1871,"displaystyle":1041},[1490,45840,45841,45843,45845,45847,45853,45855,45857],{},[1680,45842,2916],{},[1506,45844,1888],{},[1680,45846,1691],{},[1497,45848,45849,45851],{},[1493,45850,1520],{},[1680,45852,1682],{},[1506,45854,1888],{},[1680,45856,1752],{},[1497,45858,45859,45861],{},[1493,45860,1520],{},[1680,45862,1691],{},[19624,45864,45865],{},[1869,45866,45867],{"scriptlevel":1871,"displaystyle":1041},[1490,45868,45869,45871,45873],{},[1490,45870],{},[1506,45872,1508],{},[1680,45874,28945],{},[1528,45876,45877],{"encoding":1530},"\\begin{aligned}\nQ_2 - 2 \\lambda &= 0, \\\\\nQ_1 - 5 \\lambda &= 0, \\\\\n100 - 2 Q_1 - 5 Q_2 &= 0.\n\\end{aligned}",[1030,45879,45880,45881,1732,45905,45929,45930,21352,45970,45988,45989,46039,46040,2632],{},"Z prvních dvou rovnic ",[1035,45882,45884],{"className":45883},[1480],[1482,45885,45886],{"xmlns":1484},[1487,45887,45888,45902],{},[1490,45889,45890,45896,45898,45900],{},[1497,45891,45892,45894],{},[1493,45893,1520],{},[1680,45895,1691],{},[1506,45897,1508],{},[1680,45899,1691],{},[1493,45901,32598],{},[1528,45903,45904],{"encoding":1530},"Q_2 = 2\\lambda",[1035,45906,45908],{"className":45907},[1480],[1482,45909,45910],{"xmlns":1484},[1487,45911,45912,45926],{},[1490,45913,45914,45920,45922,45924],{},[1497,45915,45916,45918],{},[1493,45917,1520],{},[1680,45919,1682],{},[1506,45921,1508],{},[1680,45923,1752],{},[1493,45925,32598],{},[1528,45927,45928],{"encoding":1530},"Q_1 = 5\\lambda","; dosazením do třetí ",[1035,45931,45933],{"className":45932},[1480],[1482,45934,45935],{"xmlns":1484},[1487,45936,45937,45967],{},[1490,45938,45939,45941,45943,45945,45947,45949,45951,45953,45955,45957,45959,45961,45963,45965],{},[1680,45940,2916],{},[1506,45942,1508],{},[1680,45944,1691],{},[1506,45946,1714],{},[1680,45948,1752],{},[1493,45950,32598],{},[1506,45952,2162],{},[1680,45954,1752],{},[1506,45956,1714],{},[1680,45958,1691],{},[1493,45960,32598],{},[1506,45962,1508],{},[1680,45964,8436],{},[1493,45966,32598],{},[1528,45968,45969],{"encoding":1530},"100 = 2 \\cdot 5\\lambda + 5 \\cdot 2\\lambda = 20\\lambda",[1035,45971,45973],{"className":45972},[1480],[1482,45974,45975],{"xmlns":1484},[1487,45976,45977,45985],{},[1490,45978,45979,45981,45983],{},[1493,45980,32598],{},[1506,45982,1508],{},[1680,45984,1752],{},[1528,45986,45987],{"encoding":1530},"\\lambda = 5",". Odtud ",[1047,45990,45991,1732,46015],{},[1035,45992,45994],{"className":45993},[1480],[1482,45995,45996],{"xmlns":1484},[1487,45997,45998,46012],{},[1490,45999,46000,46008,46010],{},[1697,46001,46002,46004,46006],{},[1493,46003,1520],{},[1680,46005,1682],{},[1506,46007,2287],{},[1506,46009,1508],{},[1680,46011,2309],{},[1528,46013,46014],{"encoding":1530},"Q_1^* = 25",[1035,46016,46018],{"className":46017},[1480],[1482,46019,46020],{"xmlns":1484},[1487,46021,46022,46036],{},[1490,46023,46024,46032,46034],{},[1697,46025,46026,46028,46030],{},[1493,46027,1520],{},[1680,46029,1691],{},[1506,46031,2287],{},[1506,46033,1508],{},[1680,46035,1775],{},[1528,46037,46038],{"encoding":1530},"Q_2^* = 10",", maximální užitečnost ",[1035,46041,46043],{"className":46042},[1480],[1482,46044,46045],{"xmlns":1484},[1487,46046,46047,46067],{},[1490,46048,46049,46055,46057,46059,46061,46063,46065],{},[2315,46050,46051,46053],{},[1493,46052,1668],{},[1506,46054,2287],{},[1506,46056,1508],{},[1680,46058,2309],{},[1506,46060,1714],{},[1680,46062,1775],{},[1506,46064,1508],{},[1680,46066,8140],{},[1528,46068,46069],{"encoding":1530},"U^* = 25 \\cdot 10 = 250",[1065,46071,46073],{"id":46072},"funkce-poptávky-spotřebitele-marshallova","Funkce poptávky spotřebitele (Marshallova)",[1030,46075,46076,46077,44574,46107,46110,46111,1274],{},"Považujeme-li v úloze ",[1035,46078,46080],{"className":46079},[1480],[1482,46081,46082],{"xmlns":1484},[1487,46083,46084,46104],{},[1490,46085,46086,46092,46094,46100,46102],{},[1497,46087,46088,46090],{},[1493,46089,1501],{},[1680,46091,1682],{},[1506,46093,1559],{"separator":1041},[1497,46095,46096,46098],{},[1493,46097,1501],{},[1680,46099,1691],{},[1506,46101,1559],{"separator":1041},[1493,46103,1791],{},[1528,46105,46106],{"encoding":1530},"P_1, P_2, Y",[1047,46108,46109],{},"parametry"," (nikoli čísla), dostáváme z první řádové podmínky ",[1047,46112,46113],{},"Marshallovy poptávkové funkce",[1035,46115,46117],{"className":46116},[1480],[1482,46118,46119],{"xmlns":1484,"display":1485},[1487,46120,46121,46216],{},[19617,46122,46123],{"width":19619},[19621,46124,46125,46127,46209,46211],{},[19624,46126],{"width":19626},[19624,46128,46129],{},[1490,46130,46131,46137,46139,46145,46147,46153,46155,46161,46163,46165,46167,46169,46171,46177,46179,46185,46187,46193,46195,46201,46203,46205,46207],{},[1497,46132,46133,46135],{},[1493,46134,1520],{},[1680,46136,1682],{},[1506,46138,1508],{},[1497,46140,46141,46143],{},[1493,46142,3712],{},[1680,46144,1682],{},[1506,46146,1553],{"stretchy":1552},[1497,46148,46149,46151],{},[1493,46150,1501],{},[1680,46152,1682],{},[1506,46154,1559],{"separator":1041},[1497,46156,46157,46159],{},[1493,46158,1501],{},[1680,46160,1691],{},[1506,46162,1559],{"separator":1041},[1493,46164,1791],{},[1506,46166,1564],{"stretchy":1552},[1506,46168,1559],{"separator":1041},[1912,46170],{"width":2108},[1497,46172,46173,46175],{},[1493,46174,1520],{},[1680,46176,1691],{},[1506,46178,1508],{},[1497,46180,46181,46183],{},[1493,46182,3712],{},[1680,46184,1691],{},[1506,46186,1553],{"stretchy":1552},[1497,46188,46189,46191],{},[1493,46190,1501],{},[1680,46192,1682],{},[1506,46194,1559],{"separator":1041},[1497,46196,46197,46199],{},[1493,46198,1501],{},[1680,46200,1691],{},[1506,46202,1559],{"separator":1041},[1493,46204,1791],{},[1506,46206,1564],{"stretchy":1552},[1506,46208,1559],{"separator":1041},[19624,46210],{"width":19626},[19624,46212,46213],{},[1988,46214,46215],{},"(6.15)",[1528,46217,46218],{"encoding":1530},"Q_1 = D_1(P_1, P_2, Y), \\quad Q_2 = D_2(P_1, P_2, Y), \\tag{6.15}",[1035,46220,46222],{"className":46221},[1480],[1482,46223,46224],{"xmlns":1484,"display":1485},[1487,46225,46226,46273],{},[19617,46227,46228],{"width":19619},[19621,46229,46230,46232,46266,46268],{},[19624,46231],{"width":19626},[19624,46233,46234],{},[1490,46235,46236,46238,46240,46242,46244,46250,46252,46258,46260,46262,46264],{},[1493,46237,32598],{},[1506,46239,1508],{},[1493,46241,32598],{},[1506,46243,1553],{"stretchy":1552},[1497,46245,46246,46248],{},[1493,46247,1501],{},[1680,46249,1682],{},[1506,46251,1559],{"separator":1041},[1497,46253,46254,46256],{},[1493,46255,1501],{},[1680,46257,1691],{},[1506,46259,1559],{"separator":1041},[1493,46261,1791],{},[1506,46263,1564],{"stretchy":1552},[1493,46265,2632],{"mathvariant":1516},[19624,46267],{"width":19626},[19624,46269,46270],{},[1988,46271,46272],{},"(6.16)",[1528,46274,46275],{"encoding":1530},"\\lambda = \\lambda(P_1, P_2, Y). \\tag{6.16}",[1030,46277,46278,46308,46309,46375],{},[1047,46279,46280,46281,2632],{},"Odvození pro ",[1035,46282,46284],{"className":46283},[1480],[1482,46285,46286],{"xmlns":1484},[1487,46287,46288,46306],{},[1490,46289,46290,46292,46294,46300],{},[1493,46291,1668],{},[1506,46293,1508],{},[1497,46295,46296,46298],{},[1493,46297,1520],{},[1680,46299,1682],{},[1497,46301,46302,46304],{},[1493,46303,1520],{},[1680,46305,1691],{},[1528,46307,45550],{"encoding":1530}," Lagrangeova funkce ",[1035,46310,46312],{"className":46311},[1480],[1482,46313,46314],{"xmlns":1484},[1487,46315,46316,46372],{},[1490,46317,46318,46320,46322,46328,46334,46336,46338,46340,46342,46344,46350,46356,46358,46364,46370],{},[1493,46319,1556],{"mathvariant":44114},[1506,46321,1508],{},[1497,46323,46324,46326],{},[1493,46325,1520],{},[1680,46327,1682],{},[1497,46329,46330,46332],{},[1493,46331,1520],{},[1680,46333,1691],{},[1506,46335,2162],{},[1493,46337,32598],{},[1506,46339,1553],{"stretchy":1552},[1493,46341,1791],{},[1506,46343,1888],{},[1497,46345,46346,46348],{},[1493,46347,1501],{},[1680,46349,1682],{},[1497,46351,46352,46354],{},[1493,46353,1520],{},[1680,46355,1682],{},[1506,46357,1888],{},[1497,46359,46360,46362],{},[1493,46361,1501],{},[1680,46363,1691],{},[1497,46365,46366,46368],{},[1493,46367,1520],{},[1680,46369,1691],{},[1506,46371,1564],{"stretchy":1552},[1528,46373,46374],{"encoding":1530},"\\mathcal{L} = Q_1 Q_2 + \\lambda(Y - P_1 Q_1 - P_2 Q_2)"," dává soustavu",[1035,46377,46379],{"className":46378},[1480],[1482,46380,46381],{"xmlns":1484,"display":1485},[1487,46382,46383,46550],{},[19617,46384,46385],{"width":19619},[19621,46386,46387,46389,46543,46545],{},[19624,46388],{"width":19626},[19624,46390,46391],{},[19617,46392,46393,46439,46485],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,46394,46395,46407],{},[19624,46396,46397],{},[1869,46398,46399],{"scriptlevel":1871,"displaystyle":1041},[1697,46400,46401,46403,46405],{},[1493,46402,1556],{"mathvariant":44114},[1680,46404,1682],{},[1506,46406,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,46408,46409],{},[1869,46410,46411],{"scriptlevel":1871,"displaystyle":1041},[1490,46412,46413,46415,46417,46423,46425,46427,46433,46435,46437],{},[1490,46414],{},[1506,46416,1508],{},[1497,46418,46419,46421],{},[1493,46420,1520],{},[1680,46422,1691],{},[1506,46424,1888],{},[1493,46426,32598],{},[1497,46428,46429,46431],{},[1493,46430,1501],{},[1680,46432,1682],{},[1506,46434,1508],{},[1680,46436,1871],{},[1506,46438,1559],{"separator":1041},[19621,46440,46441,46453],{},[19624,46442,46443],{},[1869,46444,46445],{"scriptlevel":1871,"displaystyle":1041},[1697,46446,46447,46449,46451],{},[1493,46448,1556],{"mathvariant":44114},[1680,46450,1691],{},[1506,46452,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,46454,46455],{},[1869,46456,46457],{"scriptlevel":1871,"displaystyle":1041},[1490,46458,46459,46461,46463,46469,46471,46473,46479,46481,46483],{},[1490,46460],{},[1506,46462,1508],{},[1497,46464,46465,46467],{},[1493,46466,1520],{},[1680,46468,1682],{},[1506,46470,1888],{},[1493,46472,32598],{},[1497,46474,46475,46477],{},[1493,46476,1501],{},[1680,46478,1691],{},[1506,46480,1508],{},[1680,46482,1871],{},[1506,46484,1559],{"separator":1041},[19621,46486,46487,46499],{},[19624,46488,46489],{},[1869,46490,46491],{"scriptlevel":1871,"displaystyle":1041},[1697,46492,46493,46495,46497],{},[1493,46494,1556],{"mathvariant":44114},[1493,46496,32598],{},[1506,46498,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,46500,46501],{},[1869,46502,46503],{"scriptlevel":1871,"displaystyle":1041},[1490,46504,46505,46507,46509,46511,46513,46519,46525,46527,46533,46539,46541],{},[1490,46506],{},[1506,46508,1508],{},[1493,46510,1791],{},[1506,46512,1888],{},[1497,46514,46515,46517],{},[1493,46516,1501],{},[1680,46518,1682],{},[1497,46520,46521,46523],{},[1493,46522,1520],{},[1680,46524,1682],{},[1506,46526,1888],{},[1497,46528,46529,46531],{},[1493,46530,1501],{},[1680,46532,1691],{},[1497,46534,46535,46537],{},[1493,46536,1520],{},[1680,46538,1691],{},[1506,46540,1508],{},[1680,46542,28945],{},[19624,46544],{"width":19626},[19624,46546,46547],{},[1988,46548,46549],{},"(6.17)",[1528,46551,46552],{"encoding":1530},"\\begin{aligned}\n\\mathcal{L}'_1 &= Q_2 - \\lambda P_1 = 0, \\\\\n\\mathcal{L}'_2 &= Q_1 - \\lambda P_2 = 0, \\\\\n\\mathcal{L}'_\\lambda &= Y - P_1 Q_1 - P_2 Q_2 = 0.\n\\end{aligned}\n\\tag{6.17}",[1030,46554,46555,46556,46584,46585,46613,46614,46682],{},"Z prvních dvou: ",[1035,46557,46559],{"className":46558},[1480],[1482,46560,46561],{"xmlns":1484},[1487,46562,46563,46581],{},[1490,46564,46565,46571,46573,46579],{},[1497,46566,46567,46569],{},[1493,46568,1520],{},[1680,46570,1691],{},[1506,46572,1508],{},[1497,46574,46575,46577],{},[1493,46576,1501],{},[1680,46578,1682],{},[1493,46580,32598],{},[1528,46582,46583],{"encoding":1530},"Q_2 = P_1 \\lambda"," (6.18), ",[1035,46586,46588],{"className":46587},[1480],[1482,46589,46590],{"xmlns":1484},[1487,46591,46592,46610],{},[1490,46593,46594,46600,46602,46608],{},[1497,46595,46596,46598],{},[1493,46597,1520],{},[1680,46599,1682],{},[1506,46601,1508],{},[1497,46603,46604,46606],{},[1493,46605,1501],{},[1680,46607,1691],{},[1493,46609,32598],{},[1528,46611,46612],{"encoding":1530},"Q_1 = P_2 \\lambda"," (6.19). Dosazením do třetí ",[1035,46615,46617],{"className":46616},[1480],[1482,46618,46619],{"xmlns":1484},[1487,46620,46621,46679],{},[1490,46622,46623,46625,46627,46633,46635,46641,46643,46645,46651,46653,46659,46661,46663,46665,46671,46677],{},[1493,46624,1791],{},[1506,46626,1508],{},[1497,46628,46629,46631],{},[1493,46630,1501],{},[1680,46632,1682],{},[1506,46634,1714],{},[1497,46636,46637,46639],{},[1493,46638,1501],{},[1680,46640,1691],{},[1493,46642,32598],{},[1506,46644,2162],{},[1497,46646,46647,46649],{},[1493,46648,1501],{},[1680,46650,1691],{},[1506,46652,1714],{},[1497,46654,46655,46657],{},[1493,46656,1501],{},[1680,46658,1682],{},[1493,46660,32598],{},[1506,46662,1508],{},[1680,46664,1691],{},[1497,46666,46667,46669],{},[1493,46668,1501],{},[1680,46670,1682],{},[1497,46672,46673,46675],{},[1493,46674,1501],{},[1680,46676,1691],{},[1493,46678,32598],{},[1528,46680,46681],{"encoding":1530},"Y = P_1 \\cdot P_2 \\lambda + P_2 \\cdot P_1 \\lambda = 2 P_1 P_2 \\lambda",", odtud",[1035,46684,46686],{"className":46685},[1480],[1482,46687,46688],{"xmlns":1484,"display":1485},[1487,46689,46690,46733],{},[19617,46691,46692],{"width":19619},[19621,46693,46694,46696,46726,46728],{},[19624,46695],{"width":19626},[19624,46697,46698],{},[1490,46699,46700,46702,46704,46724],{},[1493,46701,32598],{},[1506,46703,1508],{},[1510,46705,46706,46708],{},[1493,46707,1791],{},[1490,46709,46710,46712,46718],{},[1680,46711,1691],{},[1497,46713,46714,46716],{},[1493,46715,1501],{},[1680,46717,1682],{},[1497,46719,46720,46722],{},[1493,46721,1501],{},[1680,46723,1691],{},[1493,46725,2632],{"mathvariant":1516},[19624,46727],{"width":19626},[19624,46729,46730],{},[1988,46731,46732],{},"(6.20)",[1528,46734,46735],{"encoding":1530},"\\lambda = \\frac{Y}{2 P_1 P_2}. \\tag{6.20}",[1030,46737,46738],{},"Zpětně:",[1035,46740,46742],{"className":46741},[1480],[1482,46743,46744],{"xmlns":1484,"display":1485},[1487,46745,46746,46823],{},[19617,46747,46748],{"width":19619},[19621,46749,46750,46752,46816,46818],{},[19624,46751],{"width":19626},[19624,46753,46754],{},[1976,46755,46756],{"notation":1978},[1869,46757,46758],{"scriptlevel":1871,"displaystyle":1552},[1869,46759,46760],{"scriptlevel":1871,"displaystyle":1552},[1869,46761,46762],{"scriptlevel":1871,"displaystyle":1041},[1490,46763,46764,46766,46772,46774,46788,46790,46792,46798,46800,46814],{},[1988,46765,1990],{},[1497,46767,46768,46770],{},[1493,46769,1520],{},[1680,46771,1682],{},[1506,46773,1508],{},[1510,46775,46776,46778],{},[1493,46777,1791],{},[1490,46779,46780,46782],{},[1680,46781,1691],{},[1497,46783,46784,46786],{},[1493,46785,1501],{},[1680,46787,1682],{},[1506,46789,1559],{"separator":1041},[1912,46791],{"width":2108},[1497,46793,46794,46796],{},[1493,46795,1520],{},[1680,46797,1691],{},[1506,46799,1508],{},[1510,46801,46802,46804],{},[1493,46803,1791],{},[1490,46805,46806,46808],{},[1680,46807,1691],{},[1497,46809,46810,46812],{},[1493,46811,1501],{},[1680,46813,1691],{},[1988,46815,1990],{},[19624,46817],{"width":19626},[19624,46819,46820],{},[1988,46821,46822],{},"(6.21)",[1528,46824,46825],{"encoding":1530},"\\boxed{\\; Q_1 = \\frac{Y}{2 P_1}, \\quad Q_2 = \\frac{Y}{2 P_2} \\;} \\tag{6.21}",[1304,46827,46829],{"id":46828},"engelova-funkce","Engelova funkce",[1030,46831,2364,46832,46835,46836,46839,46840,35597,46857,1732,46887,46917,46918,46952,46953,1732,46979,47005],{},[1047,46833,46834],{},"pevné ceny"," a proměnný důchod se Marshallova poptávka stává ",[1047,46837,46838],{},"Engelovou funkcí",": pro ",[1035,46841,46843],{"className":46842},[1480],[1482,46844,46845],{"xmlns":1484},[1487,46846,46847,46855],{},[1490,46848,46849,46851,46853],{},[1493,46850,1791],{},[1506,46852,1508],{},[1680,46854,2916],{},[1528,46856,36041],{"encoding":1530},[1035,46858,46860],{"className":46859},[1480],[1482,46861,46862],{"xmlns":1484},[1487,46863,46864,46884],{},[1490,46865,46866,46872,46874,46876,46878],{},[1497,46867,46868,46870],{},[1493,46869,1520],{},[1680,46871,1682],{},[1506,46873,1508],{},[1680,46875,2292],{},[1493,46877,1709],{"mathvariant":1516},[1497,46879,46880,46882],{},[1493,46881,1501],{},[1680,46883,1682],{},[1528,46885,46886],{"encoding":1530},"Q_1 = 50\u002FP_1",[1035,46888,46890],{"className":46889},[1480],[1482,46891,46892],{"xmlns":1484},[1487,46893,46894,46914],{},[1490,46895,46896,46902,46904,46906,46908],{},[1497,46897,46898,46900],{},[1493,46899,1520],{},[1680,46901,1691],{},[1506,46903,1508],{},[1680,46905,2292],{},[1493,46907,1709],{"mathvariant":1516},[1497,46909,46910,46912],{},[1493,46911,1501],{},[1680,46913,1691],{},[1528,46915,46916],{"encoding":1530},"Q_2 = 50\u002FP_2",". Pro pevné ceny ",[1035,46919,46921],{"className":46920},[1480],[1482,46922,46923],{"xmlns":1484},[1487,46924,46925,46949],{},[1490,46926,46927,46933,46935,46937,46939,46945,46947],{},[1497,46928,46929,46931],{},[1493,46930,1501],{},[1680,46932,1682],{},[1506,46934,1508],{},[1680,46936,1775],{},[1506,46938,1559],{"separator":1041},[1497,46940,46941,46943],{},[1493,46942,1501],{},[1680,46944,1691],{},[1506,46946,1508],{},[1680,46948,8436],{},[1528,46950,46951],{"encoding":1530},"P_1 = 10, P_2 = 20"," dostáváme Engelovy funkce ",[1035,46954,46956],{"className":46955},[1480],[1482,46957,46958],{"xmlns":1484},[1487,46959,46960,46976],{},[1490,46961,46962,46968,46970,46972,46974],{},[1497,46963,46964,46966],{},[1493,46965,1520],{},[1680,46967,1682],{},[1506,46969,1508],{},[1493,46971,1791],{},[1493,46973,1709],{"mathvariant":1516},[1680,46975,8436],{},[1528,46977,46978],{"encoding":1530},"Q_1 = Y\u002F20",[1035,46980,46982],{"className":46981},[1480],[1482,46983,46984],{"xmlns":1484},[1487,46985,46986,47002],{},[1490,46987,46988,46994,46996,46998,47000],{},[1497,46989,46990,46992],{},[1493,46991,1520],{},[1680,46993,1691],{},[1506,46995,1508],{},[1493,46997,1791],{},[1493,46999,1709],{"mathvariant":1516},[1680,47001,7380],{},[1528,47003,47004],{"encoding":1530},"Q_2 = Y\u002F40"," — lineární závislost spotřebovaného množství na důchodu.",[1065,47007,47009],{"id":47008},"duální-úloha-minimalizace-výdajů","Duální úloha — minimalizace výdajů",[1030,47011,47012],{},"Výdaje spotřebitele jsou",[1035,47014,47016],{"className":47015},[1480],[1482,47017,47018],{"xmlns":1484,"display":1485},[1487,47019,47020,47095],{},[19617,47021,47022],{"width":19619},[19621,47023,47024,47026,47088,47090],{},[19624,47025],{"width":19626},[19624,47027,47028],{},[1490,47029,47030,47032,47034,47036,47038,47044,47046,47052,47054,47056,47064,47070,47072,47080,47086],{},[1493,47031,2711],{},[1506,47033,1508],{},[1493,47035,2711],{},[1506,47037,1553],{"stretchy":1552},[1497,47039,47040,47042],{},[1493,47041,1520],{},[1680,47043,1682],{},[1506,47045,1559],{"separator":1041},[1497,47047,47048,47050],{},[1493,47049,1520],{},[1680,47051,1691],{},[1506,47053,1564],{"stretchy":1552},[1506,47055,1508],{},[1697,47057,47058,47060,47062],{},[1493,47059,1501],{},[1680,47061,1682],{},[1506,47063,2287],{},[1497,47065,47066,47068],{},[1493,47067,1520],{},[1680,47069,1682],{},[1506,47071,2162],{},[1697,47073,47074,47076,47078],{},[1493,47075,1501],{},[1680,47077,1691],{},[1506,47079,2287],{},[1497,47081,47082,47084],{},[1493,47083,1520],{},[1680,47085,1691],{},[1506,47087,1559],{"separator":1041},[19624,47089],{"width":19626},[19624,47091,47092],{},[1988,47093,47094],{},"(6.22)",[1528,47096,47097],{"encoding":1530},"E = E(Q_1, Q_2) = P_1^* Q_1 + P_2^* Q_2, \\tag{6.22}",[1030,47099,47100],{},"a je pevně zadána hladina užitečnosti",[1035,47102,47104],{"className":47103},[1480],[1482,47105,47106],{"xmlns":1484,"display":1485},[1487,47107,47108,47155],{},[19617,47109,47110],{"width":19619},[19621,47111,47112,47114,47148,47150],{},[19624,47113],{"width":19626},[19624,47115,47116],{},[1490,47117,47118,47124,47126,47128,47130,47136,47138,47144,47146],{},[2315,47119,47120,47122],{},[1493,47121,1668],{},[1506,47123,2287],{},[1506,47125,1508],{},[1493,47127,1668],{},[1506,47129,1553],{"stretchy":1552},[1497,47131,47132,47134],{},[1493,47133,1520],{},[1680,47135,1682],{},[1506,47137,1559],{"separator":1041},[1497,47139,47140,47142],{},[1493,47141,1520],{},[1680,47143,1691],{},[1506,47145,1564],{"stretchy":1552},[1493,47147,2632],{"mathvariant":1516},[19624,47149],{"width":19626},[19624,47151,47152],{},[1988,47153,47154],{},"(6.23)",[1528,47156,47157],{"encoding":1530},"U^* = U(Q_1, Q_2). \\tag{6.23}",[1030,47159,47160,47163,47164,47196,47197,2632],{},[1047,47161,47162],{},"Úlohou o minimalizaci výdajů"," je najít minimum ",[1035,47165,47167],{"className":47166},[1480],[1482,47168,47169],{"xmlns":1484},[1487,47170,47171,47193],{},[1490,47172,47173,47175,47177,47183,47185,47191],{},[1493,47174,2711],{},[1506,47176,1553],{"stretchy":1552},[1497,47178,47179,47181],{},[1493,47180,1520],{},[1680,47182,1682],{},[1506,47184,1559],{"separator":1041},[1497,47186,47187,47189],{},[1493,47188,1520],{},[1680,47190,1691],{},[1506,47192,1564],{"stretchy":1552},[1528,47194,47195],{"encoding":1530},"E(Q_1, Q_2)"," vázané podmínkou (6.23) ve tvaru ",[1035,47198,47200],{"className":47199},[1480],[1482,47201,47202],{"xmlns":1484},[1487,47203,47204,47260],{},[1490,47205,47206,47208,47210,47216,47218,47224,47226,47228,47234,47236,47238,47240,47246,47248,47254,47256,47258],{},[1493,47207,27556],{},[1506,47209,1553],{"stretchy":1552},[1497,47211,47212,47214],{},[1493,47213,1520],{},[1680,47215,1682],{},[1506,47217,1559],{"separator":1041},[1497,47219,47220,47222],{},[1493,47221,1520],{},[1680,47223,1691],{},[1506,47225,1564],{"stretchy":1552},[1506,47227,1508],{},[2315,47229,47230,47232],{},[1493,47231,1668],{},[1506,47233,2287],{},[1506,47235,1888],{},[1493,47237,1668],{},[1506,47239,1553],{"stretchy":1552},[1497,47241,47242,47244],{},[1493,47243,1520],{},[1680,47245,1682],{},[1506,47247,1559],{"separator":1041},[1497,47249,47250,47252],{},[1493,47251,1520],{},[1680,47253,1691],{},[1506,47255,1564],{"stretchy":1552},[1506,47257,1508],{},[1680,47259,1871],{},[1528,47261,47262],{"encoding":1530},"g(Q_1, Q_2) = U^* - U(Q_1, Q_2) = 0",[1304,47264,47266],{"id":47265},"lagrangeova-funkce","Lagrangeova funkce",[1035,47268,47270],{"className":47269},[1480],[1482,47271,47272],{"xmlns":1484,"display":1485},[1487,47273,47274,47385],{},[19617,47275,47276],{"width":19619},[19621,47277,47278,47280,47378,47380],{},[19624,47279],{"width":19626},[19624,47281,47282],{},[1490,47283,47284,47286,47288,47294,47296,47302,47304,47306,47308,47310,47318,47324,47326,47334,47340,47342,47344,47346,47352,47354,47356,47358,47364,47366,47372,47374,47376],{},[1493,47285,1556],{"mathvariant":44114},[1506,47287,1553],{"stretchy":1552},[1497,47289,47290,47292],{},[1493,47291,1520],{},[1680,47293,1682],{},[1506,47295,1559],{"separator":1041},[1497,47297,47298,47300],{},[1493,47299,1520],{},[1680,47301,1691],{},[1506,47303,1559],{"separator":1041},[1493,47305,32598],{},[1506,47307,1564],{"stretchy":1552},[1506,47309,1508],{},[1697,47311,47312,47314,47316],{},[1493,47313,1501],{},[1680,47315,1682],{},[1506,47317,2287],{},[1497,47319,47320,47322],{},[1493,47321,1520],{},[1680,47323,1682],{},[1506,47325,2162],{},[1697,47327,47328,47330,47332],{},[1493,47329,1501],{},[1680,47331,1691],{},[1506,47333,2287],{},[1497,47335,47336,47338],{},[1493,47337,1520],{},[1680,47339,1691],{},[1506,47341,2162],{},[1493,47343,32598],{},[1506,47345,1553],{"stretchy":1552},[2315,47347,47348,47350],{},[1493,47349,1668],{},[1506,47351,2287],{},[1506,47353,1888],{},[1493,47355,1668],{},[1506,47357,1553],{"stretchy":1552},[1497,47359,47360,47362],{},[1493,47361,1520],{},[1680,47363,1682],{},[1506,47365,1559],{"separator":1041},[1497,47367,47368,47370],{},[1493,47369,1520],{},[1680,47371,1691],{},[1506,47373,1564],{"stretchy":1552},[1506,47375,1564],{"stretchy":1552},[1493,47377,2632],{"mathvariant":1516},[19624,47379],{"width":19626},[19624,47381,47382],{},[1988,47383,47384],{},"(6.24)",[1528,47386,47387],{"encoding":1530},"\\mathcal{L}(Q_1, Q_2, \\lambda) = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2)). \\tag{6.24}",[1030,47389,47390],{},"Soustava podmínek prvního řádu:",[1035,47392,47394],{"className":47393},[1480],[1482,47395,47396],{"xmlns":1484,"display":1485},[1487,47397,47398,47571],{},[19617,47399,47400],{"width":19619},[19621,47401,47402,47404,47564,47566],{},[19624,47403],{"width":19626},[19624,47405,47406],{},[19617,47407,47408,47458,47508],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,47409,47410,47422],{},[19624,47411,47412],{},[1869,47413,47414],{"scriptlevel":1871,"displaystyle":1041},[1697,47415,47416,47418,47420],{},[1493,47417,1556],{"mathvariant":44114},[1680,47419,1682],{},[1506,47421,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,47423,47424],{},[1869,47425,47426],{"scriptlevel":1871,"displaystyle":1041},[1490,47427,47428,47430,47432,47440,47442,47444,47452,47454,47456],{},[1490,47429],{},[1506,47431,1508],{},[1697,47433,47434,47436,47438],{},[1493,47435,1501],{},[1680,47437,1682],{},[1506,47439,2287],{},[1506,47441,1888],{},[1493,47443,32598],{},[1697,47445,47446,47448,47450],{},[1493,47447,1668],{},[1680,47449,1682],{},[1506,47451,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,47453,1508],{},[1680,47455,1871],{},[1506,47457,1559],{"separator":1041},[19621,47459,47460,47472],{},[19624,47461,47462],{},[1869,47463,47464],{"scriptlevel":1871,"displaystyle":1041},[1697,47465,47466,47468,47470],{},[1493,47467,1556],{"mathvariant":44114},[1680,47469,1691],{},[1506,47471,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,47473,47474],{},[1869,47475,47476],{"scriptlevel":1871,"displaystyle":1041},[1490,47477,47478,47480,47482,47490,47492,47494,47502,47504,47506],{},[1490,47479],{},[1506,47481,1508],{},[1697,47483,47484,47486,47488],{},[1493,47485,1501],{},[1680,47487,1691],{},[1506,47489,2287],{},[1506,47491,1888],{},[1493,47493,32598],{},[1697,47495,47496,47498,47500],{},[1493,47497,1668],{},[1680,47499,1691],{},[1506,47501,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,47503,1508],{},[1680,47505,1871],{},[1506,47507,1559],{"separator":1041},[19621,47509,47510,47522],{},[19624,47511,47512],{},[1869,47513,47514],{"scriptlevel":1871,"displaystyle":1041},[1697,47515,47516,47518,47520],{},[1493,47517,1556],{"mathvariant":44114},[1493,47519,32598],{},[1506,47521,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,47523,47524],{},[1869,47525,47526],{"scriptlevel":1871,"displaystyle":1041},[1490,47527,47528,47530,47532,47538,47540,47542,47544,47550,47552,47558,47560,47562],{},[1490,47529],{},[1506,47531,1508],{},[2315,47533,47534,47536],{},[1493,47535,1668],{},[1506,47537,2287],{},[1506,47539,1888],{},[1493,47541,1668],{},[1506,47543,1553],{"stretchy":1552},[1497,47545,47546,47548],{},[1493,47547,1520],{},[1680,47549,1682],{},[1506,47551,1559],{"separator":1041},[1497,47553,47554,47556],{},[1493,47555,1520],{},[1680,47557,1691],{},[1506,47559,1564],{"stretchy":1552},[1506,47561,1508],{},[1680,47563,28945],{},[19624,47565],{"width":19626},[19624,47567,47568],{},[1988,47569,47570],{},"(6.25)",[1528,47572,47573],{"encoding":1530},"\\begin{aligned}\n\\mathcal{L}'_1 &= P_1^* - \\lambda U'_1 = 0, \\\\\n\\mathcal{L}'_2 &= P_2^* - \\lambda U'_2 = 0, \\\\\n\\mathcal{L}'_\\lambda &= U^* - U(Q_1, Q_2) = 0.\n\\end{aligned}\n\\tag{6.25}",[1030,47575,47576],{},"Postačující podmínka pro minimum (vzhledem k linearitě funkce výdajů) má tvar",[1035,47578,47580],{"className":47579},[1480],[1482,47581,47582],{"xmlns":1484,"display":1485},[1487,47583,47584,47681],{},[19617,47585,47586],{"width":19619},[19621,47587,47588,47590,47674,47676],{},[19624,47589],{"width":19626},[19624,47591,47592],{},[1490,47593,47594,47596,47598,47604,47606,47612,47614,47616,47618,47620,47622,47624,47672],{},[1493,47595,3712],{},[1506,47597,1553],{"stretchy":1552},[1497,47599,47600,47602],{},[1493,47601,1520],{},[1680,47603,1682],{},[1506,47605,1559],{"separator":1041},[1497,47607,47608,47610],{},[1493,47609,1520],{},[1680,47611,1691],{},[1506,47613,1559],{"separator":1041},[1493,47615,32598],{},[1506,47617,1564],{"stretchy":1552},[1506,47619,1508],{},[1506,47621,1888],{},[1493,47623,32598],{},[1490,47625,47626,47628,47640,47642,47654,47656,47658,47670],{},[1506,47627,1553],{"fence":1041},[1697,47629,47630,47632,47634],{},[1493,47631,1668],{},[1680,47633,8542],{},[1490,47635,47636,47638],{},[1506,47637,6927],{"mathvariant":1516},[1506,47639,6927],{"mathvariant":1516},[1506,47641,2162],{},[1697,47643,47644,47646,47648],{},[1493,47645,1668],{},[1680,47647,9923],{},[1490,47649,47650,47652],{},[1506,47651,6927],{"mathvariant":1516},[1506,47653,6927],{"mathvariant":1516},[1506,47655,2162],{},[1680,47657,1691],{},[1697,47659,47660,47662,47664],{},[1493,47661,1668],{},[1680,47663,6797],{},[1490,47665,47666,47668],{},[1506,47667,6927],{"mathvariant":1516},[1506,47669,6927],{"mathvariant":1516},[1506,47671,1564],{"fence":1041},[1493,47673,2632],{"mathvariant":1516},[19624,47675],{"width":19626},[19624,47677,47678],{},[1988,47679,47680],{},"(6.26)",[1528,47682,47683],{"encoding":1530},"D(Q_1, Q_2, \\lambda) = -\\lambda \\left(U''_{11} + U''_{22} + 2 U''_{12}\\right). \\tag{6.26}",[1030,47685,47686,47689,47690,47729,47730,47769,47770,47820,47821,47847,47848,47865,47866,47892],{},[1047,47687,47688],{},"Geometrie."," Řešením je bod ",[1035,47691,47693],{"className":47692},[1480],[1482,47694,47695],{"xmlns":1484},[1487,47696,47697,47727],{},[1490,47698,47699,47705,47707,47715,47717,47725],{},[2315,47700,47701,47703],{},[1493,47702,1520],{},[1506,47704,2287],{},[1506,47706,14314],{"stretchy":1552},[1697,47708,47709,47711,47713],{},[1493,47710,1520],{},[1680,47712,1682],{},[1506,47714,2287],{},[1506,47716,1559],{"separator":1041},[1697,47718,47719,47721,47723],{},[1493,47720,1520],{},[1680,47722,1691],{},[1506,47724,2287],{},[1506,47726,14323],{"stretchy":1552},[1528,47728,43893],{"encoding":1530}," dotyku křivky užitečnosti ",[1035,47731,47733],{"className":47732},[1480],[1482,47734,47735],{"xmlns":1484},[1487,47736,47737,47767],{},[1490,47738,47739,47745,47747,47749,47751,47757,47759,47765],{},[2315,47740,47741,47743],{},[1493,47742,1668],{},[1506,47744,2287],{},[1506,47746,1508],{},[1493,47748,1668],{},[1506,47750,1553],{"stretchy":1552},[1497,47752,47753,47755],{},[1493,47754,1520],{},[1680,47756,1682],{},[1506,47758,1559],{"separator":1041},[1497,47760,47761,47763],{},[1493,47762,1520],{},[1680,47764,1691],{},[1506,47766,1564],{"stretchy":1552},[1528,47768,33812],{"encoding":1530}," s přímkou výdajů ",[1035,47771,47773],{"className":47772},[1480],[1482,47774,47775],{"xmlns":1484},[1487,47776,47777,47817],{},[1490,47778,47779,47785,47787,47795,47801,47803,47811],{},[2315,47780,47781,47783],{},[1493,47782,2711],{},[1506,47784,2287],{},[1506,47786,1508],{},[1697,47788,47789,47791,47793],{},[1493,47790,1501],{},[1680,47792,1682],{},[1506,47794,2287],{},[1497,47796,47797,47799],{},[1493,47798,1520],{},[1680,47800,1682],{},[1506,47802,2162],{},[1697,47804,47805,47807,47809],{},[1493,47806,1501],{},[1680,47808,1691],{},[1506,47810,2287],{},[1497,47812,47813,47815],{},[1493,47814,1520],{},[1680,47816,1691],{},[1528,47818,47819],{"encoding":1530},"E^* = P_1^* Q_1 + P_2^* Q_2",". Hladina ",[1035,47822,47824],{"className":47823},[1480],[1482,47825,47826],{"xmlns":1484},[1487,47827,47828,47844],{},[1490,47829,47830,47836,47838],{},[1497,47831,47832,47834],{},[1493,47833,2711],{},[1680,47835,1871],{},[1506,47837,3961],{},[2315,47839,47840,47842],{},[1493,47841,2711],{},[1506,47843,2287],{},[1528,47845,47846],{"encoding":1530},"E_0 \u003C E^*"," nestačí k dosažení ",[1035,47849,47851],{"className":47850},[1480],[1482,47852,47853],{"xmlns":1484},[1487,47854,47855,47863],{},[1490,47856,47857],{},[2315,47858,47859,47861],{},[1493,47860,1668],{},[1506,47862,2287],{},[1528,47864,43527],{"encoding":1530},", hladina ",[1035,47867,47869],{"className":47868},[1480],[1482,47870,47871],{"xmlns":1484},[1487,47872,47873,47889],{},[1490,47874,47875,47881,47883],{},[1497,47876,47877,47879],{},[1493,47878,2711],{},[1680,47880,1682],{},[1506,47882,2796],{},[2315,47884,47885,47887],{},[1493,47886,2711],{},[1506,47888,2287],{},[1528,47890,47891],{"encoding":1530},"E_1 > E^*"," je nadbytečná.",[1023,47894,47896,47903],{"className":47895,"dataCallout":1443},[1026,1442],[1030,47897,47899,47902],{"className":47898},[1033],[1035,47900],{"className":47901,"ariaHidden":1041},[1038,1450,1040],"Postup — duální úloha (minimalizace výdajů)",[1276,47904,47905,47955,48041,48081,48156],{},[1206,47906,47907,1656,47910,47954],{},[1047,47908,47909],{},"Zapiš vazbu",[1035,47911,47913],{"className":47912},[1480],[1482,47914,47915],{"xmlns":1484},[1487,47916,47917,47951],{},[1490,47918,47919,47925,47927,47929,47931,47937,47939,47945,47947,47949],{},[2315,47920,47921,47923],{},[1493,47922,1668],{},[1506,47924,2287],{},[1506,47926,1888],{},[1493,47928,1668],{},[1506,47930,1553],{"stretchy":1552},[1497,47932,47933,47935],{},[1493,47934,1520],{},[1680,47936,1682],{},[1506,47938,1559],{"separator":1041},[1497,47940,47941,47943],{},[1493,47942,1520],{},[1680,47944,1691],{},[1506,47946,1564],{"stretchy":1552},[1506,47948,1508],{},[1680,47950,1871],{},[1528,47952,47953],{"encoding":1530},"U^* - U(Q_1, Q_2) = 0"," (zadaná hladina užitečnosti).",[1206,47956,47957,1656,47959,2632],{},[1047,47958,44832],{},[1035,47960,47962],{"className":47961},[1480],[1482,47963,47964],{"xmlns":1484},[1487,47965,47966,48038],{},[1490,47967,47968,47970,47972,47980,47986,47988,47996,48002,48004,48006,48008,48014,48016,48018,48020,48026,48028,48034,48036],{},[1493,47969,1556],{"mathvariant":44114},[1506,47971,1508],{},[1697,47973,47974,47976,47978],{},[1493,47975,1501],{},[1680,47977,1682],{},[1506,47979,2287],{},[1497,47981,47982,47984],{},[1493,47983,1520],{},[1680,47985,1682],{},[1506,47987,2162],{},[1697,47989,47990,47992,47994],{},[1493,47991,1501],{},[1680,47993,1691],{},[1506,47995,2287],{},[1497,47997,47998,48000],{},[1493,47999,1520],{},[1680,48001,1691],{},[1506,48003,2162],{},[1493,48005,32598],{},[1506,48007,1553],{"stretchy":1552},[2315,48009,48010,48012],{},[1493,48011,1668],{},[1506,48013,2287],{},[1506,48015,1888],{},[1493,48017,1668],{},[1506,48019,1553],{"stretchy":1552},[1497,48021,48022,48024],{},[1493,48023,1520],{},[1680,48025,1682],{},[1506,48027,1559],{"separator":1041},[1497,48029,48030,48032],{},[1493,48031,1520],{},[1680,48033,1691],{},[1506,48035,1564],{"stretchy":1552},[1506,48037,1564],{"stretchy":1552},[1528,48039,48040],{"encoding":1530},"\\mathcal{L} = P_1^* Q_1 + P_2^* Q_2 + \\lambda(U^* - U(Q_1, Q_2))",[1206,48042,48043,48046,48047,48080],{},[1047,48044,48045],{},"Derivace rovny nule",", z prvních dvou rovnic podílem dostaneš podmínku ",[1035,48048,48050],{"className":48049},[1480],[1482,48051,48052],{"xmlns":1484},[1487,48053,48054,48078],{},[1490,48055,48056,48058,48060,48068,48070],{},[1988,48057,13960],{},[1506,48059,1508],{},[1697,48061,48062,48064,48066],{},[1493,48063,1501],{},[1680,48065,1682],{},[1506,48067,2287],{},[1493,48069,1709],{"mathvariant":1516},[1697,48071,48072,48074,48076],{},[1493,48073,1501],{},[1680,48075,1691],{},[1506,48077,2287],{},[1528,48079,44551],{"encoding":1530}," (stejná jako u maximalizace!).",[1206,48082,48083,1656,48086,48126,48127,2632],{},[1047,48084,48085],{},"Dosaď do vazby",[1035,48087,48089],{"className":48088},[1480],[1482,48090,48091],{"xmlns":1484},[1487,48092,48093,48123],{},[1490,48094,48095,48097,48099,48105,48107,48113,48115,48117],{},[1493,48096,1668],{},[1506,48098,1553],{"stretchy":1552},[1497,48100,48101,48103],{},[1493,48102,1520],{},[1680,48104,1682],{},[1506,48106,1559],{"separator":1041},[1497,48108,48109,48111],{},[1493,48110,1520],{},[1680,48112,1691],{},[1506,48114,1564],{"stretchy":1552},[1506,48116,1508],{},[2315,48118,48119,48121],{},[1493,48120,1668],{},[1506,48122,2287],{},[1528,48124,48125],{"encoding":1530},"U(Q_1, Q_2) = U^*"," a vyřeš pro ",[1035,48128,48130],{"className":48129},[1480],[1482,48131,48132],{"xmlns":1484},[1487,48133,48134,48154],{},[1490,48135,48136,48144,48146],{},[1697,48137,48138,48140,48142],{},[1493,48139,1520],{},[1680,48141,1682],{},[1506,48143,2287],{},[1506,48145,1559],{"separator":1041},[1697,48147,48148,48150,48152],{},[1493,48149,1520],{},[1680,48151,1691],{},[1506,48153,2287],{},[1528,48155,45073],{"encoding":1530},[1206,48157,48158,1656,48161,48215],{},[1047,48159,48160],{},"Vypočítej minimální výdaje",[1035,48162,48164],{"className":48163},[1480],[1482,48165,48166],{"xmlns":1484},[1487,48167,48168,48212],{},[1490,48169,48170,48176,48178,48186,48194,48196,48204],{},[2315,48171,48172,48174],{},[1493,48173,2711],{},[1506,48175,2287],{},[1506,48177,1508],{},[1697,48179,48180,48182,48184],{},[1493,48181,1501],{},[1680,48183,1682],{},[1506,48185,2287],{},[1697,48187,48188,48190,48192],{},[1493,48189,1520],{},[1680,48191,1682],{},[1506,48193,2287],{},[1506,48195,2162],{},[1697,48197,48198,48200,48202],{},[1493,48199,1501],{},[1680,48201,1691],{},[1506,48203,2287],{},[1697,48205,48206,48208,48210],{},[1493,48207,1520],{},[1680,48209,1691],{},[1506,48211,2287],{},[1528,48213,48214],{"encoding":1530},"E^* = P_1^* Q_1^* + P_2^* Q_2^*"," a případně ověř druhou podmínku (6.26).",[1065,48217,48219,48220],{"id":48218},"příklad-67-minimalizace-výdajů-pro-uq112q212u-q_112-q_212","Příklad 6.7 — minimalizace výdajů pro ",[1035,48221,48223],{"className":48222},[1480],[1482,48224,48225],{"xmlns":1484},[1487,48226,48227,48261],{},[1490,48228,48229,48231,48233,48247],{},[1493,48230,1668],{},[1506,48232,1508],{},[1697,48234,48235,48237,48239],{},[1493,48236,1520],{},[1680,48238,1682],{},[1490,48240,48241,48243,48245],{},[1680,48242,1682],{},[1493,48244,1709],{"mathvariant":1516},[1680,48246,1691],{},[1697,48248,48249,48251,48253],{},[1493,48250,1520],{},[1680,48252,1691],{},[1490,48254,48255,48257,48259],{},[1680,48256,1682],{},[1493,48258,1709],{"mathvariant":1516},[1680,48260,1691],{},[1528,48262,5197],{"encoding":1530},[1030,48264,48265,48266,1732,48288,1732,48312,45670],{},"Dáno ",[1035,48267,48269],{"className":48268},[1480],[1482,48270,48271],{"xmlns":1484},[1487,48272,48273,48285],{},[1490,48274,48275,48281,48283],{},[2315,48276,48277,48279],{},[1493,48278,1668],{},[1506,48280,2287],{},[1506,48282,1508],{},[1680,48284,1691],{},[1528,48286,48287],{"encoding":1530},"U^* = 2",[1035,48289,48291],{"className":48290},[1480],[1482,48292,48293],{"xmlns":1484},[1487,48294,48295,48309],{},[1490,48296,48297,48305,48307],{},[1697,48298,48299,48301,48303],{},[1493,48300,1501],{},[1680,48302,1682],{},[1506,48304,2287],{},[1506,48306,1508],{},[1680,48308,5051],{},[1528,48310,48311],{"encoding":1530},"P_1^* = 0{,}25",[1035,48313,48315],{"className":48314},[1480],[1482,48316,48317],{"xmlns":1484},[1487,48318,48319,48333],{},[1490,48320,48321,48329,48331],{},[1697,48322,48323,48325,48327],{},[1493,48324,1501],{},[1680,48326,1691],{},[1506,48328,2287],{},[1506,48330,1508],{},[1680,48332,1682],{},[1528,48334,48335],{"encoding":1530},"P_2^* = 1",[1035,48337,48339],{"className":48338},[1480],[1482,48340,48341],{"xmlns":1484,"display":1485},[1487,48342,48343,48407],{},[1490,48344,48345,48347,48349,48351,48357,48359,48365,48367,48369,48371,48373,48375,48389,48403,48405],{},[1493,48346,1556],{"mathvariant":44114},[1506,48348,1508],{},[1680,48350,5051],{},[1497,48352,48353,48355],{},[1493,48354,1520],{},[1680,48356,1682],{},[1506,48358,2162],{},[1497,48360,48361,48363],{},[1493,48362,1520],{},[1680,48364,1691],{},[1506,48366,2162],{},[1493,48368,32598],{},[1506,48370,1553],{"stretchy":1552},[1680,48372,1691],{},[1506,48374,1888],{},[1697,48376,48377,48379,48381],{},[1493,48378,1520],{},[1680,48380,1682],{},[1490,48382,48383,48385,48387],{},[1680,48384,1682],{},[1493,48386,1709],{"mathvariant":1516},[1680,48388,1691],{},[1697,48390,48391,48393,48395],{},[1493,48392,1520],{},[1680,48394,1691],{},[1490,48396,48397,48399,48401],{},[1680,48398,1682],{},[1493,48400,1709],{"mathvariant":1516},[1680,48402,1691],{},[1506,48404,1564],{"stretchy":1552},[1493,48406,2632],{"mathvariant":1516},[1528,48408,48409],{"encoding":1530},"\\mathcal{L} = 0{,}25 Q_1 + Q_2 + \\lambda(2 - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[1030,48411,45755],{},[1035,48413,48415],{"className":48414},[1480],[1482,48416,48417],{"xmlns":1484,"display":1485},[1487,48418,48419,48633],{},[19617,48420,48421,48497,48573],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,48422,48423,48435],{},[19624,48424,48425],{},[1869,48426,48427],{"scriptlevel":1871,"displaystyle":1041},[1697,48428,48429,48431,48433],{},[1493,48430,1556],{"mathvariant":44114},[1680,48432,1682],{},[1506,48434,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,48436,48437],{},[1869,48438,48439],{"scriptlevel":1871,"displaystyle":1041},[1490,48440,48441,48443,48445,48447,48449,48451,48453,48461,48477,48491,48493,48495],{},[1490,48442],{},[1506,48444,1508],{},[1680,48446,5051],{},[1506,48448,1888],{},[1493,48450,32598],{},[1506,48452,1714],{},[1869,48454,48455],{"scriptlevel":1871,"displaystyle":1552},[1510,48456,48457,48459],{},[1680,48458,1682],{},[1680,48460,1691],{},[1697,48462,48463,48465,48467],{},[1493,48464,1520],{},[1680,48466,1682],{},[1490,48468,48469,48471,48473,48475],{},[1506,48470,1888],{},[1680,48472,1682],{},[1493,48474,1709],{"mathvariant":1516},[1680,48476,1691],{},[1697,48478,48479,48481,48483],{},[1493,48480,1520],{},[1680,48482,1691],{},[1490,48484,48485,48487,48489],{},[1680,48486,1682],{},[1493,48488,1709],{"mathvariant":1516},[1680,48490,1691],{},[1506,48492,1508],{},[1680,48494,1871],{},[1506,48496,1559],{"separator":1041},[19621,48498,48499,48511],{},[19624,48500,48501],{},[1869,48502,48503],{"scriptlevel":1871,"displaystyle":1041},[1697,48504,48505,48507,48509],{},[1493,48506,1556],{"mathvariant":44114},[1680,48508,1691],{},[1506,48510,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,48512,48513],{},[1869,48514,48515],{"scriptlevel":1871,"displaystyle":1041},[1490,48516,48517,48519,48521,48523,48525,48527,48529,48537,48551,48567,48569,48571],{},[1490,48518],{},[1506,48520,1508],{},[1680,48522,1682],{},[1506,48524,1888],{},[1493,48526,32598],{},[1506,48528,1714],{},[1869,48530,48531],{"scriptlevel":1871,"displaystyle":1552},[1510,48532,48533,48535],{},[1680,48534,1682],{},[1680,48536,1691],{},[1697,48538,48539,48541,48543],{},[1493,48540,1520],{},[1680,48542,1682],{},[1490,48544,48545,48547,48549],{},[1680,48546,1682],{},[1493,48548,1709],{"mathvariant":1516},[1680,48550,1691],{},[1697,48552,48553,48555,48557],{},[1493,48554,1520],{},[1680,48556,1691],{},[1490,48558,48559,48561,48563,48565],{},[1506,48560,1888],{},[1680,48562,1682],{},[1493,48564,1709],{"mathvariant":1516},[1680,48566,1691],{},[1506,48568,1508],{},[1680,48570,1871],{},[1506,48572,1559],{"separator":1041},[19621,48574,48575,48587],{},[19624,48576,48577],{},[1869,48578,48579],{"scriptlevel":1871,"displaystyle":1041},[1697,48580,48581,48583,48585],{},[1493,48582,1556],{"mathvariant":44114},[1493,48584,32598],{},[1506,48586,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,48588,48589],{},[1869,48590,48591],{"scriptlevel":1871,"displaystyle":1041},[1490,48592,48593,48595,48597,48599,48601,48615,48629,48631],{},[1490,48594],{},[1506,48596,1508],{},[1680,48598,1691],{},[1506,48600,1888],{},[1697,48602,48603,48605,48607],{},[1493,48604,1520],{},[1680,48606,1682],{},[1490,48608,48609,48611,48613],{},[1680,48610,1682],{},[1493,48612,1709],{"mathvariant":1516},[1680,48614,1691],{},[1697,48616,48617,48619,48621],{},[1493,48618,1520],{},[1680,48620,1691],{},[1490,48622,48623,48625,48627],{},[1680,48624,1682],{},[1493,48626,1709],{"mathvariant":1516},[1680,48628,1691],{},[1506,48630,1508],{},[1680,48632,28945],{},[1528,48634,48635],{"encoding":1530},"\\begin{aligned}\n\\mathcal{L}'_1 &= 0{,}25 - \\lambda \\cdot \\tfrac{1}{2} Q_1^{-1\u002F2} Q_2^{1\u002F2} = 0, \\\\\n\\mathcal{L}'_2 &= 1 - \\lambda \\cdot \\tfrac{1}{2} Q_1^{1\u002F2} Q_2^{-1\u002F2} = 0, \\\\\n\\mathcal{L}'_\\lambda &= 2 - Q_1^{1\u002F2} Q_2^{1\u002F2} = 0.\n\\end{aligned}",[1030,48637,48638,48639,33723,48669,48697,48698,21352,48760,1732,48810,48832,48833,2632],{},"Podílem prvních dvou rovnic: ",[1035,48640,48642],{"className":48641},[1480],[1482,48643,48644],{"xmlns":1484},[1487,48645,48646,48666],{},[1490,48647,48648,48650,48652,48658,48660],{},[1680,48649,5051],{},[1506,48651,1508],{},[1497,48653,48654,48656],{},[1493,48655,1520],{},[1680,48657,1691],{},[1493,48659,1709],{"mathvariant":1516},[1497,48661,48662,48664],{},[1493,48663,1520],{},[1680,48665,1682],{},[1528,48667,48668],{"encoding":1530},"0{,}25 = Q_2 \u002F Q_1",[1035,48670,48672],{"className":48671},[1480],[1482,48673,48674],{"xmlns":1484},[1487,48675,48676,48694],{},[1490,48677,48678,48684,48686,48688],{},[1497,48679,48680,48682],{},[1493,48681,1520],{},[1680,48683,1691],{},[1506,48685,1508],{},[1680,48687,5051],{},[1497,48689,48690,48692],{},[1493,48691,1520],{},[1680,48693,1682],{},[1528,48695,48696],{"encoding":1530},"Q_2 = 0{,}25 Q_1",". Dosazením do třetí: ",[1035,48699,48701],{"className":48700},[1480],[1482,48702,48703],{"xmlns":1484},[1487,48704,48705,48757],{},[1490,48706,48707,48721,48723,48725,48731,48743,48745,48747,48753,48755],{},[1697,48708,48709,48711,48713],{},[1493,48710,1520],{},[1680,48712,1682],{},[1490,48714,48715,48717,48719],{},[1680,48716,1682],{},[1493,48718,1709],{"mathvariant":1516},[1680,48720,1691],{},[1506,48722,1553],{"stretchy":1552},[1680,48724,5051],{},[1497,48726,48727,48729],{},[1493,48728,1520],{},[1680,48730,1682],{},[2315,48732,48733,48735],{},[1506,48734,1564],{"stretchy":1552},[1490,48736,48737,48739,48741],{},[1680,48738,1682],{},[1493,48740,1709],{"mathvariant":1516},[1680,48742,1691],{},[1506,48744,1508],{},[1680,48746,3687],{},[1497,48748,48749,48751],{},[1493,48750,1520],{},[1680,48752,1682],{},[1506,48754,1508],{},[1680,48756,1691],{},[1528,48758,48759],{"encoding":1530},"Q_1^{1\u002F2} (0{,}25 Q_1)^{1\u002F2} = 0{,}5 Q_1 = 2",[1047,48761,48762,1732,48786],{},[1035,48763,48765],{"className":48764},[1480],[1482,48766,48767],{"xmlns":1484},[1487,48768,48769,48783],{},[1490,48770,48771,48779,48781],{},[1697,48772,48773,48775,48777],{},[1493,48774,1520],{},[1680,48776,1682],{},[1506,48778,2287],{},[1506,48780,1508],{},[1680,48782,4007],{},[1528,48784,48785],{"encoding":1530},"Q_1^* = 4",[1035,48787,48789],{"className":48788},[1480],[1482,48790,48791],{"xmlns":1484},[1487,48792,48793,48807],{},[1490,48794,48795,48803,48805],{},[1697,48796,48797,48799,48801],{},[1493,48798,1520],{},[1680,48800,1691],{},[1506,48802,2287],{},[1506,48804,1508],{},[1680,48806,1682],{},[1528,48808,48809],{"encoding":1530},"Q_2^* = 1",[1035,48811,48813],{"className":48812},[1480],[1482,48814,48815],{"xmlns":1484},[1487,48816,48817,48829],{},[1490,48818,48819,48825,48827],{},[2315,48820,48821,48823],{},[1493,48822,32598],{},[1506,48824,2287],{},[1506,48826,1508],{},[1680,48828,1682],{},[1528,48830,48831],{"encoding":1530},"\\lambda^* = 1",". Minimální výdaje: ",[1035,48834,48836],{"className":48835},[1480],[1482,48837,48838],{"xmlns":1484},[1487,48839,48840,48868],{},[1490,48841,48842,48848,48850,48852,48854,48856,48858,48860,48862,48864,48866],{},[2315,48843,48844,48846],{},[1493,48845,2711],{},[1506,48847,2287],{},[1506,48849,1508],{},[1680,48851,5051],{},[1506,48853,1714],{},[1680,48855,4007],{},[1506,48857,2162],{},[1680,48859,1682],{},[1506,48861,1714],{},[1680,48863,1682],{},[1506,48865,1508],{},[1680,48867,1691],{},[1528,48869,48870],{"encoding":1530},"E^* = 0{,}25 \\cdot 4 + 1 \\cdot 1 = 2",[1030,48872,48873,48876,48877,1732,48943,1732,49009,49075,49076,49113,49114,49136,49137,2632],{},[1176,48874,48875],{},"Ověření postačující podmínky"," (6.26): ",[1035,48878,48880],{"className":48879},[1480],[1482,48881,48882],{"xmlns":1484},[1487,48883,48884,48940],{},[1490,48885,48886,48898,48900,48902,48910,48926],{},[1697,48887,48888,48890,48892],{},[1493,48889,1668],{},[1680,48891,8542],{},[1490,48893,48894,48896],{},[1506,48895,6927],{"mathvariant":1516},[1506,48897,6927],{"mathvariant":1516},[1506,48899,1508],{},[1506,48901,1888],{},[1869,48903,48904],{"scriptlevel":1871,"displaystyle":1552},[1510,48905,48906,48908],{},[1680,48907,1682],{},[1680,48909,4007],{},[1697,48911,48912,48914,48916],{},[1493,48913,1520],{},[1680,48915,1682],{},[1490,48917,48918,48920,48922,48924],{},[1506,48919,1888],{},[1680,48921,3201],{},[1493,48923,1709],{"mathvariant":1516},[1680,48925,1691],{},[1697,48927,48928,48930,48932],{},[1493,48929,1520],{},[1680,48931,1691],{},[1490,48933,48934,48936,48938],{},[1680,48935,1682],{},[1493,48937,1709],{"mathvariant":1516},[1680,48939,1691],{},[1528,48941,48942],{"encoding":1530},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F2}",[1035,48944,48946],{"className":48945},[1480],[1482,48947,48948],{"xmlns":1484},[1487,48949,48950,49006],{},[1490,48951,48952,48964,48966,48968,48976,48990],{},[1697,48953,48954,48956,48958],{},[1493,48955,1668],{},[1680,48957,9923],{},[1490,48959,48960,48962],{},[1506,48961,6927],{"mathvariant":1516},[1506,48963,6927],{"mathvariant":1516},[1506,48965,1508],{},[1506,48967,1888],{},[1869,48969,48970],{"scriptlevel":1871,"displaystyle":1552},[1510,48971,48972,48974],{},[1680,48973,1682],{},[1680,48975,4007],{},[1697,48977,48978,48980,48982],{},[1493,48979,1520],{},[1680,48981,1682],{},[1490,48983,48984,48986,48988],{},[1680,48985,1682],{},[1493,48987,1709],{"mathvariant":1516},[1680,48989,1691],{},[1697,48991,48992,48994,48996],{},[1493,48993,1520],{},[1680,48995,1691],{},[1490,48997,48998,49000,49002,49004],{},[1506,48999,1888],{},[1680,49001,3201],{},[1493,49003,1709],{"mathvariant":1516},[1680,49005,1691],{},[1528,49007,49008],{"encoding":1530},"U''_{22} = -\\tfrac{1}{4} Q_1^{1\u002F2} Q_2^{-3\u002F2}",[1035,49010,49012],{"className":49011},[1480],[1482,49013,49014],{"xmlns":1484},[1487,49015,49016,49072],{},[1490,49017,49018,49030,49032,49040,49056],{},[1697,49019,49020,49022,49024],{},[1493,49021,1668],{},[1680,49023,6797],{},[1490,49025,49026,49028],{},[1506,49027,6927],{"mathvariant":1516},[1506,49029,6927],{"mathvariant":1516},[1506,49031,1508],{},[1869,49033,49034],{"scriptlevel":1871,"displaystyle":1552},[1510,49035,49036,49038],{},[1680,49037,1682],{},[1680,49039,4007],{},[1697,49041,49042,49044,49046],{},[1493,49043,1520],{},[1680,49045,1682],{},[1490,49047,49048,49050,49052,49054],{},[1506,49049,1888],{},[1680,49051,1682],{},[1493,49053,1709],{"mathvariant":1516},[1680,49055,1691],{},[1697,49057,49058,49060,49062],{},[1493,49059,1520],{},[1680,49061,1691],{},[1490,49063,49064,49066,49068,49070],{},[1506,49065,1888],{},[1680,49067,1682],{},[1493,49069,1709],{"mathvariant":1516},[1680,49071,1691],{},[1528,49073,49074],{"encoding":1530},"U''_{12} = \\tfrac{1}{4} Q_1^{-1\u002F2} Q_2^{-1\u002F2}",". Po dosazení ",[1035,49077,49079],{"className":49078},[1480],[1482,49080,49081],{"xmlns":1484},[1487,49082,49083,49110],{},[1490,49084,49085,49087,49089,49091,49093,49095,49097,49099,49101,49103,49106,49108],{},[1493,49086,3712],{},[1506,49088,1553],{"stretchy":1552},[1680,49090,4007],{},[1506,49092,1559],{"separator":1041},[1680,49094,1682],{},[1506,49096,1559],{"separator":1041},[1680,49098,1682],{},[1506,49100,1564],{"stretchy":1552},[1506,49102,1508],{},[1680,49104,49105],{},"0,28125",[1506,49107,2796],{},[1680,49109,1871],{},[1528,49111,49112],{"encoding":1530},"D(4, 1, 1) = 0{,}28125 > 0"," — v bodě ",[1035,49115,49117],{"className":49116},[1480],[1482,49118,49119],{"xmlns":1484},[1487,49120,49121,49133],{},[1490,49122,49123,49125,49127,49129,49131],{},[1506,49124,14314],{"stretchy":1552},[1680,49126,4007],{},[1506,49128,1559],{"separator":1041},[1680,49130,1682],{},[1506,49132,14323],{"stretchy":1552},[1528,49134,49135],{"encoding":1530},"[4, 1]"," je vázané ",[1047,49138,19195],{},[1065,49140,49142],{"id":49141},"poptávka-minimalizující-výdaje-hicksova","Poptávka minimalizující výdaje (Hicksova)",[1030,49144,49145],{},"Obecně:",[1035,49147,49149],{"className":49148},[1480],[1482,49150,49151],{"xmlns":1484,"display":1485},[1487,49152,49153,49248],{},[19617,49154,49155],{"width":19619},[19621,49156,49157,49159,49241,49243],{},[19624,49158],{"width":19626},[19624,49160,49161],{},[1490,49162,49163,49169,49171,49177,49179,49185,49187,49193,49195,49197,49199,49201,49203,49209,49211,49217,49219,49225,49227,49233,49235,49237,49239],{},[1497,49164,49165,49167],{},[1493,49166,1520],{},[1680,49168,1682],{},[1506,49170,1508],{},[1497,49172,49173,49175],{},[1493,49174,3712],{},[1680,49176,1682],{},[1506,49178,1553],{"stretchy":1552},[1497,49180,49181,49183],{},[1493,49182,1501],{},[1680,49184,1682],{},[1506,49186,1559],{"separator":1041},[1497,49188,49189,49191],{},[1493,49190,1501],{},[1680,49192,1691],{},[1506,49194,1559],{"separator":1041},[1493,49196,1668],{},[1506,49198,1564],{"stretchy":1552},[1506,49200,1559],{"separator":1041},[1912,49202],{"width":2108},[1497,49204,49205,49207],{},[1493,49206,1520],{},[1680,49208,1691],{},[1506,49210,1508],{},[1497,49212,49213,49215],{},[1493,49214,3712],{},[1680,49216,1691],{},[1506,49218,1553],{"stretchy":1552},[1497,49220,49221,49223],{},[1493,49222,1501],{},[1680,49224,1682],{},[1506,49226,1559],{"separator":1041},[1497,49228,49229,49231],{},[1493,49230,1501],{},[1680,49232,1691],{},[1506,49234,1559],{"separator":1041},[1493,49236,1668],{},[1506,49238,1564],{"stretchy":1552},[1506,49240,1559],{"separator":1041},[19624,49242],{"width":19626},[19624,49244,49245],{},[1988,49246,49247],{},"(6.27)",[1528,49249,49250],{"encoding":1530},"Q_1 = D_1(P_1, P_2, U), \\quad Q_2 = D_2(P_1, P_2, U), \\tag{6.27}",[1035,49252,49254],{"className":49253},[1480],[1482,49255,49256],{"xmlns":1484,"display":1485},[1487,49257,49258,49305],{},[19617,49259,49260],{"width":19619},[19621,49261,49262,49264,49298,49300],{},[19624,49263],{"width":19626},[19624,49265,49266],{},[1490,49267,49268,49270,49272,49274,49276,49282,49284,49290,49292,49294,49296],{},[1493,49269,32598],{},[1506,49271,1508],{},[1493,49273,32598],{},[1506,49275,1553],{"stretchy":1552},[1497,49277,49278,49280],{},[1493,49279,1501],{},[1680,49281,1682],{},[1506,49283,1559],{"separator":1041},[1497,49285,49286,49288],{},[1493,49287,1501],{},[1680,49289,1691],{},[1506,49291,1559],{"separator":1041},[1493,49293,1668],{},[1506,49295,1564],{"stretchy":1552},[1493,49297,2632],{"mathvariant":1516},[19624,49299],{"width":19626},[19624,49301,49302],{},[1988,49303,49304],{},"(6.28)",[1528,49306,49307],{"encoding":1530},"\\lambda = \\lambda(P_1, P_2, U). \\tag{6.28}",[1030,49309,49310,49311,1656,49314,49327,49328,49341],{},"Hicksova poptávka závisí na ",[1047,49312,49313],{},"hladině užitečnosti",[1035,49315,49317],{"className":49316},[1480],[1482,49318,49319],{"xmlns":1484},[1487,49320,49321,49325],{},[1490,49322,49323],{},[1493,49324,1668],{},[1528,49326,1668],{"encoding":1530}," (nikoli na důchodu ",[1035,49329,49331],{"className":49330},[1480],[1482,49332,49333],{"xmlns":1484},[1487,49334,49335,49339],{},[1490,49336,49337],{},[1493,49338,1791],{},[1528,49340,1791],{"encoding":1530}," jako u Marshallovy). Fyzická interpretace: jaké množství zboží koupit při daných cenách, abych dosáhl předem stanovené úrovně uspokojení s minimálními výdaji.",[1065,49343,49345,49346],{"id":49344},"příklad-68-obecné-odvození-pro-uq112q212u-q_112-q_212","Příklad 6.8 — obecné odvození pro ",[1035,49347,49349],{"className":49348},[1480],[1482,49350,49351],{"xmlns":1484},[1487,49352,49353,49387],{},[1490,49354,49355,49357,49359,49373],{},[1493,49356,1668],{},[1506,49358,1508],{},[1697,49360,49361,49363,49365],{},[1493,49362,1520],{},[1680,49364,1682],{},[1490,49366,49367,49369,49371],{},[1680,49368,1682],{},[1493,49370,1709],{"mathvariant":1516},[1680,49372,1691],{},[1697,49374,49375,49377,49379],{},[1493,49376,1520],{},[1680,49378,1691],{},[1490,49380,49381,49383,49385],{},[1680,49382,1682],{},[1493,49384,1709],{"mathvariant":1516},[1680,49386,1691],{},[1528,49388,5197],{"encoding":1530},[1030,49390,49391,49421],{},[1035,49392,49394],{"className":49393},[1480],[1482,49395,49396],{"xmlns":1484},[1487,49397,49398,49418],{},[1490,49399,49400,49406,49408,49414,49416],{},[1497,49401,49402,49404],{},[1493,49403,1501],{},[1680,49405,1682],{},[1506,49407,1559],{"separator":1041},[1497,49409,49410,49412],{},[1493,49411,1501],{},[1680,49413,1691],{},[1506,49415,1559],{"separator":1041},[1493,49417,1668],{},[1528,49419,49420],{"encoding":1530},"P_1, P_2, U"," jsou parametry. Lagrangeova funkce:",[1035,49423,49425],{"className":49424},[1480],[1482,49426,49427],{"xmlns":1484,"display":1485},[1487,49428,49429,49503],{},[1490,49430,49431,49433,49435,49441,49447,49449,49455,49461,49463,49465,49467,49469,49471,49485,49499,49501],{},[1493,49432,1556],{"mathvariant":44114},[1506,49434,1508],{},[1497,49436,49437,49439],{},[1493,49438,1501],{},[1680,49440,1682],{},[1497,49442,49443,49445],{},[1493,49444,1520],{},[1680,49446,1682],{},[1506,49448,2162],{},[1497,49450,49451,49453],{},[1493,49452,1501],{},[1680,49454,1691],{},[1497,49456,49457,49459],{},[1493,49458,1520],{},[1680,49460,1691],{},[1506,49462,2162],{},[1493,49464,32598],{},[1506,49466,1553],{"stretchy":1552},[1493,49468,1668],{},[1506,49470,1888],{},[1697,49472,49473,49475,49477],{},[1493,49474,1520],{},[1680,49476,1682],{},[1490,49478,49479,49481,49483],{},[1680,49480,1682],{},[1493,49482,1709],{"mathvariant":1516},[1680,49484,1691],{},[1697,49486,49487,49489,49491],{},[1493,49488,1520],{},[1680,49490,1691],{},[1490,49492,49493,49495,49497],{},[1680,49494,1682],{},[1493,49496,1709],{"mathvariant":1516},[1680,49498,1691],{},[1506,49500,1564],{"stretchy":1552},[1493,49502,2632],{"mathvariant":1516},[1528,49504,49505],{"encoding":1530},"\\mathcal{L} = P_1 Q_1 + P_2 Q_2 + \\lambda(U - Q_1^{1\u002F2} Q_2^{1\u002F2}).",[1030,49507,45755],{},[1035,49509,49511],{"className":49510},[1480],[1482,49512,49513],{"xmlns":1484,"display":1485},[1487,49514,49515,49737],{},[19617,49516,49517,49597,49677],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,49518,49519,49531],{},[19624,49520,49521],{},[1869,49522,49523],{"scriptlevel":1871,"displaystyle":1041},[1697,49524,49525,49527,49529],{},[1493,49526,1556],{"mathvariant":44114},[1680,49528,1682],{},[1506,49530,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,49532,49533],{},[1869,49534,49535],{"scriptlevel":1871,"displaystyle":1041},[1490,49536,49537,49539,49541,49547,49549,49551,49553,49561,49577,49591,49593,49595],{},[1490,49538],{},[1506,49540,1508],{},[1497,49542,49543,49545],{},[1493,49544,1501],{},[1680,49546,1682],{},[1506,49548,1888],{},[1493,49550,32598],{},[1506,49552,1714],{},[1869,49554,49555],{"scriptlevel":1871,"displaystyle":1552},[1510,49556,49557,49559],{},[1680,49558,1682],{},[1680,49560,1691],{},[1697,49562,49563,49565,49567],{},[1493,49564,1520],{},[1680,49566,1682],{},[1490,49568,49569,49571,49573,49575],{},[1506,49570,1888],{},[1680,49572,1682],{},[1493,49574,1709],{"mathvariant":1516},[1680,49576,1691],{},[1697,49578,49579,49581,49583],{},[1493,49580,1520],{},[1680,49582,1691],{},[1490,49584,49585,49587,49589],{},[1680,49586,1682],{},[1493,49588,1709],{"mathvariant":1516},[1680,49590,1691],{},[1506,49592,1508],{},[1680,49594,1871],{},[1506,49596,1559],{"separator":1041},[19621,49598,49599,49611],{},[19624,49600,49601],{},[1869,49602,49603],{"scriptlevel":1871,"displaystyle":1041},[1697,49604,49605,49607,49609],{},[1493,49606,1556],{"mathvariant":44114},[1680,49608,1691],{},[1506,49610,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,49612,49613],{},[1869,49614,49615],{"scriptlevel":1871,"displaystyle":1041},[1490,49616,49617,49619,49621,49627,49629,49631,49633,49641,49655,49671,49673,49675],{},[1490,49618],{},[1506,49620,1508],{},[1497,49622,49623,49625],{},[1493,49624,1501],{},[1680,49626,1691],{},[1506,49628,1888],{},[1493,49630,32598],{},[1506,49632,1714],{},[1869,49634,49635],{"scriptlevel":1871,"displaystyle":1552},[1510,49636,49637,49639],{},[1680,49638,1682],{},[1680,49640,1691],{},[1697,49642,49643,49645,49647],{},[1493,49644,1520],{},[1680,49646,1682],{},[1490,49648,49649,49651,49653],{},[1680,49650,1682],{},[1493,49652,1709],{"mathvariant":1516},[1680,49654,1691],{},[1697,49656,49657,49659,49661],{},[1493,49658,1520],{},[1680,49660,1691],{},[1490,49662,49663,49665,49667,49669],{},[1506,49664,1888],{},[1680,49666,1682],{},[1493,49668,1709],{"mathvariant":1516},[1680,49670,1691],{},[1506,49672,1508],{},[1680,49674,1871],{},[1506,49676,1559],{"separator":1041},[19621,49678,49679,49691],{},[19624,49680,49681],{},[1869,49682,49683],{"scriptlevel":1871,"displaystyle":1041},[1697,49684,49685,49687,49689],{},[1493,49686,1556],{"mathvariant":44114},[1493,49688,32598],{},[1506,49690,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[19624,49692,49693],{},[1869,49694,49695],{"scriptlevel":1871,"displaystyle":1041},[1490,49696,49697,49699,49701,49703,49705,49719,49733,49735],{},[1490,49698],{},[1506,49700,1508],{},[1493,49702,1668],{},[1506,49704,1888],{},[1697,49706,49707,49709,49711],{},[1493,49708,1520],{},[1680,49710,1682],{},[1490,49712,49713,49715,49717],{},[1680,49714,1682],{},[1493,49716,1709],{"mathvariant":1516},[1680,49718,1691],{},[1697,49720,49721,49723,49725],{},[1493,49722,1520],{},[1680,49724,1691],{},[1490,49726,49727,49729,49731],{},[1680,49728,1682],{},[1493,49730,1709],{"mathvariant":1516},[1680,49732,1691],{},[1506,49734,1508],{},[1680,49736,28945],{},[1528,49738,49739],{"encoding":1530},"\\begin{aligned}\n\\mathcal{L}'_1 &= P_1 - \\lambda \\cdot \\tfrac{1}{2} Q_1^{-1\u002F2} Q_2^{1\u002F2} = 0, \\\\\n\\mathcal{L}'_2 &= P_2 - \\lambda \\cdot \\tfrac{1}{2} Q_1^{1\u002F2} Q_2^{-1\u002F2} = 0, \\\\\n\\mathcal{L}'_\\lambda &= U - Q_1^{1\u002F2} Q_2^{1\u002F2} = 0.\n\\end{aligned}",[1030,49741,49742,49743,49813,49814,49872],{},"Podílem rovnic: ",[1035,49744,49746],{"className":49745},[1480],[1482,49747,49748],{"xmlns":1484},[1487,49749,49750,49810],{},[1490,49751,49752,49758,49760,49766,49768,49774,49776,49782,49784,49790,49796,49798,49804],{},[1497,49753,49754,49756],{},[1493,49755,1501],{},[1680,49757,1682],{},[1493,49759,1709],{"mathvariant":1516},[1497,49761,49762,49764],{},[1493,49763,1501],{},[1680,49765,1691],{},[1506,49767,1508],{},[1497,49769,49770,49772],{},[1493,49771,1520],{},[1680,49773,1691],{},[1493,49775,1709],{"mathvariant":1516},[1497,49777,49778,49780],{},[1493,49779,1520],{},[1680,49781,1682],{},[1506,49783,2183],{},[1497,49785,49786,49788],{},[1493,49787,1501],{},[1680,49789,1682],{},[1497,49791,49792,49794],{},[1493,49793,1520],{},[1680,49795,1682],{},[1506,49797,1508],{},[1497,49799,49800,49802],{},[1493,49801,1501],{},[1680,49803,1691],{},[1497,49805,49806,49808],{},[1493,49807,1520],{},[1680,49809,1691],{},[1528,49811,49812],{"encoding":1530},"P_1\u002FP_2 = Q_2\u002FQ_1 \\Rightarrow P_1 Q_1 = P_2 Q_2",", tedy celkové výdaje ",[1035,49815,49817],{"className":49816},[1480],[1482,49818,49819],{"xmlns":1484},[1487,49820,49821,49869],{},[1490,49822,49823,49825,49827,49833,49839,49841,49847,49853,49855,49857,49863],{},[1493,49824,2711],{},[1506,49826,1508],{},[1497,49828,49829,49831],{},[1493,49830,1501],{},[1680,49832,1682],{},[1497,49834,49835,49837],{},[1493,49836,1520],{},[1680,49838,1682],{},[1506,49840,2162],{},[1497,49842,49843,49845],{},[1493,49844,1501],{},[1680,49846,1691],{},[1497,49848,49849,49851],{},[1493,49850,1520],{},[1680,49852,1691],{},[1506,49854,1508],{},[1680,49856,1691],{},[1497,49858,49859,49861],{},[1493,49860,1501],{},[1680,49862,1682],{},[1497,49864,49865,49867],{},[1493,49866,1520],{},[1680,49868,1682],{},[1528,49870,49871],{"encoding":1530},"E = P_1 Q_1 + P_2 Q_2 = 2 P_1 Q_1",". Odtud",[1035,49874,49876],{"className":49875},[1480],[1482,49877,49878],{"xmlns":1484,"display":1485},[1487,49879,49880,49947],{},[19617,49881,49882],{"width":19619},[19621,49883,49884,49886,49940,49942],{},[19624,49885],{"width":19626},[19624,49887,49888],{},[1490,49889,49890,49896,49898,49912,49914,49916,49922,49924,49938],{},[1497,49891,49892,49894],{},[1493,49893,1520],{},[1680,49895,1682],{},[1506,49897,1508],{},[1510,49899,49900,49902],{},[1493,49901,2711],{},[1490,49903,49904,49906],{},[1680,49905,1691],{},[1497,49907,49908,49910],{},[1493,49909,1501],{},[1680,49911,1682],{},[1506,49913,1559],{"separator":1041},[1912,49915],{"width":2108},[1497,49917,49918,49920],{},[1493,49919,1520],{},[1680,49921,1691],{},[1506,49923,1508],{},[1510,49925,49926,49928],{},[1493,49927,2711],{},[1490,49929,49930,49932],{},[1680,49931,1691],{},[1497,49933,49934,49936],{},[1493,49935,1501],{},[1680,49937,1691],{},[1493,49939,2632],{"mathvariant":1516},[19624,49941],{"width":19626},[19624,49943,49944],{},[1988,49945,49946],{},"(6.29)",[1528,49948,49949],{"encoding":1530},"Q_1 = \\frac{E}{2 P_1}, \\quad Q_2 = \\frac{E}{2 P_2}. \\tag{6.29}",[1030,49951,49952,49953,33723,50035,50071],{},"Ze třetí rovnice ",[1035,49954,49956],{"className":49955},[1480],[1482,49957,49958],{"xmlns":1484},[1487,49959,49960,50032],{},[1490,49961,49962,49964,49966,50004,50006],{},[1493,49963,1668],{},[1506,49965,1508],{},[2324,49967,49968],{},[1490,49969,49970,49986,49988],{},[1869,49971,49972],{"scriptlevel":1871,"displaystyle":1552},[1510,49973,49974,49976],{},[1493,49975,2711],{},[1490,49977,49978,49980],{},[1680,49979,1691],{},[1497,49981,49982,49984],{},[1493,49983,1501],{},[1680,49985,1682],{},[1506,49987,1714],{},[1869,49989,49990],{"scriptlevel":1871,"displaystyle":1552},[1510,49991,49992,49994],{},[1493,49993,2711],{},[1490,49995,49996,49998],{},[1680,49997,1691],{},[1497,49999,50000,50002],{},[1493,50001,1501],{},[1680,50003,1691],{},[1506,50005,1508],{},[1869,50007,50008],{"scriptlevel":1871,"displaystyle":1552},[1510,50009,50010,50012],{},[1493,50011,2711],{},[1490,50013,50014,50016],{},[1680,50015,1691],{},[2324,50017,50018],{},[1490,50019,50020,50026],{},[1497,50021,50022,50024],{},[1493,50023,1501],{},[1680,50025,1682],{},[1497,50027,50028,50030],{},[1493,50029,1501],{},[1680,50031,1691],{},[1528,50033,50034],{"encoding":1530},"U = \\sqrt{\\tfrac{E}{2 P_1} \\cdot \\tfrac{E}{2 P_2}} = \\tfrac{E}{2\\sqrt{P_1 P_2}}",[1035,50036,50038],{"className":50037},[1480],[1482,50039,50040],{"xmlns":1484},[1487,50041,50042,50068],{},[1490,50043,50044,50046,50048,50050,50052],{},[1493,50045,2711],{},[1506,50047,1508],{},[1680,50049,1691],{},[1493,50051,1668],{},[2324,50053,50054],{},[1490,50055,50056,50062],{},[1497,50057,50058,50060],{},[1493,50059,1501],{},[1680,50061,1682],{},[1497,50063,50064,50066],{},[1493,50065,1501],{},[1680,50067,1691],{},[1528,50069,50070],{"encoding":1530},"E = 2 U \\sqrt{P_1 P_2}",". Dosazením:",[1035,50073,50075],{"className":50074},[1480],[1482,50076,50077],{"xmlns":1484,"display":1485},[1487,50078,50079,50224],{},[19617,50080,50081],{"width":19619},[19621,50082,50083,50085,50217,50219],{},[19624,50084],{"width":19626},[19624,50086,50087],{},[1976,50088,50089],{"notation":1978},[1869,50090,50091],{"scriptlevel":1871,"displaystyle":1552},[1869,50092,50093],{"scriptlevel":1871,"displaystyle":1552},[1869,50094,50095],{"scriptlevel":1871,"displaystyle":1041},[1490,50096,50097,50099,50105,50107,50109,50125,50127,50133,50135,50141,50143,50149,50151,50153,50155,50157,50159,50165,50167,50169,50185,50187,50193,50195,50201,50203,50209,50211,50213,50215],{},[1988,50098,1990],{},[1497,50100,50101,50103],{},[1493,50102,1520],{},[1680,50104,1682],{},[1506,50106,1508],{},[1493,50108,1668],{},[2324,50110,50111],{},[1510,50112,50113,50119],{},[1497,50114,50115,50117],{},[1493,50116,1501],{},[1680,50118,1691],{},[1497,50120,50121,50123],{},[1493,50122,1501],{},[1680,50124,1682],{},[1506,50126,1508],{},[1497,50128,50129,50131],{},[1493,50130,3712],{},[1680,50132,1682],{},[1506,50134,1553],{"stretchy":1552},[1497,50136,50137,50139],{},[1493,50138,1501],{},[1680,50140,1682],{},[1506,50142,1559],{"separator":1041},[1497,50144,50145,50147],{},[1493,50146,1501],{},[1680,50148,1691],{},[1506,50150,1559],{"separator":1041},[1493,50152,1668],{},[1506,50154,1564],{"stretchy":1552},[1506,50156,1559],{"separator":1041},[1912,50158],{"width":2108},[1497,50160,50161,50163],{},[1493,50162,1520],{},[1680,50164,1691],{},[1506,50166,1508],{},[1493,50168,1668],{},[2324,50170,50171],{},[1510,50172,50173,50179],{},[1497,50174,50175,50177],{},[1493,50176,1501],{},[1680,50178,1682],{},[1497,50180,50181,50183],{},[1493,50182,1501],{},[1680,50184,1691],{},[1506,50186,1508],{},[1497,50188,50189,50191],{},[1493,50190,3712],{},[1680,50192,1691],{},[1506,50194,1553],{"stretchy":1552},[1497,50196,50197,50199],{},[1493,50198,1501],{},[1680,50200,1682],{},[1506,50202,1559],{"separator":1041},[1497,50204,50205,50207],{},[1493,50206,1501],{},[1680,50208,1691],{},[1506,50210,1559],{"separator":1041},[1493,50212,1668],{},[1506,50214,1564],{"stretchy":1552},[1988,50216,1990],{},[19624,50218],{"width":19626},[19624,50220,50221],{},[1988,50222,50223],{},"(6.30)",[1528,50225,50226],{"encoding":1530},"\\boxed{\\; Q_1 = U \\sqrt{\\frac{P_2}{P_1}} = D_1(P_1, P_2, U), \\quad Q_2 = U \\sqrt{\\frac{P_1}{P_2}} = D_2(P_1, P_2, U) \\;} \\tag{6.30}",[1065,50228,50230],{"id":50229},"vztah-primární-a-duální-úlohy","Vztah primární a duální úlohy",[1030,50232,50233,50234,50247,50248,50265,50266,50279,50280,50297,50298,50301,50302,50341,50342,50371],{},"Primární (max ",[1035,50235,50237],{"className":50236},[1480],[1482,50238,50239],{"xmlns":1484},[1487,50240,50241,50245],{},[1490,50242,50243],{},[1493,50244,1668],{},[1528,50246,1668],{"encoding":1530}," při rozpočtu ",[1035,50249,50251],{"className":50250},[1480],[1482,50252,50253],{"xmlns":1484},[1487,50254,50255,50263],{},[1490,50256,50257],{},[2315,50258,50259,50261],{},[1493,50260,1791],{},[1506,50262,2287],{},[1528,50264,43593],{"encoding":1530},") a duální (min ",[1035,50267,50269],{"className":50268},[1480],[1482,50270,50271],{"xmlns":1484},[1487,50272,50273,50277],{},[1490,50274,50275],{},[1493,50276,2711],{},[1528,50278,2711],{"encoding":1530}," při užitečnosti ",[1035,50281,50283],{"className":50282},[1480],[1482,50284,50285],{"xmlns":1484},[1487,50286,50287,50295],{},[1490,50288,50289],{},[2315,50290,50291,50293],{},[1493,50292,1668],{},[1506,50294,2287],{},[1528,50296,43527],{"encoding":1530},") úloha jsou ",[1047,50299,50300],{},"ekvivalentní",": mají tentýž bod optima ",[1035,50303,50305],{"className":50304},[1480],[1482,50306,50307],{"xmlns":1484},[1487,50308,50309,50339],{},[1490,50310,50311,50317,50319,50327,50329,50337],{},[2315,50312,50313,50315],{},[1493,50314,1520],{},[1506,50316,2287],{},[1506,50318,14314],{"stretchy":1552},[1697,50320,50321,50323,50325],{},[1493,50322,1520],{},[1680,50324,1682],{},[1506,50326,2287],{},[1506,50328,1559],{"separator":1041},[1697,50330,50331,50333,50335],{},[1493,50332,1520],{},[1680,50334,1691],{},[1506,50336,2287],{},[1506,50338,14323],{"stretchy":1552},[1528,50340,43893],{"encoding":1530}," a v obou platí ",[1035,50343,50345],{"className":50344},[1480],[1482,50346,50347],{"xmlns":1484},[1487,50348,50349,50369],{},[1490,50350,50351,50353,50355,50361,50363],{},[1988,50352,13960],{},[1506,50354,1508],{},[1497,50356,50357,50359],{},[1493,50358,1501],{},[1680,50360,1682],{},[1493,50362,1709],{"mathvariant":1516},[1497,50364,50365,50367],{},[1493,50366,1501],{},[1680,50368,1691],{},[1528,50370,43563],{"encoding":1530},". Rozdíl je v tom, která veličina je zadána a která se optimalizuje:",[1030,50373,50374],{},[18014,50375],{"alt":50376,"className":50377,"src":50378},"imek-primarni-vs-dualni",[1055,18018],"\u002Fwiki-assets\u002Fimek-primarni-vs-dualni.jpeg",[1203,50380,50381,50492],{},[1206,50382,50383,50386,50387,50400,50401,50441,50442,2632],{},[1047,50384,50385],{},"Primární"," (Marshall): zadáno ",[1035,50388,50390],{"className":50389},[1480],[1482,50391,50392],{"xmlns":1484},[1487,50393,50394,50398],{},[1490,50395,50396],{},[1493,50397,1791],{},[1528,50399,1791],{"encoding":1530},", hledáme maximální ",[1035,50402,50404],{"className":50403},[1480],[1482,50405,50406],{"xmlns":1484},[1487,50407,50408,50438],{},[1490,50409,50410,50416,50418,50424,50426,50432,50434,50436],{},[2315,50411,50412,50414],{},[1493,50413,1668],{},[1506,50415,2287],{},[1506,50417,1553],{"stretchy":1552},[1497,50419,50420,50422],{},[1493,50421,1501],{},[1680,50423,1682],{},[1506,50425,1559],{"separator":1041},[1497,50427,50428,50430],{},[1493,50429,1501],{},[1680,50431,1691],{},[1506,50433,1559],{"separator":1041},[1493,50435,1791],{},[1506,50437,1564],{"stretchy":1552},[1528,50439,50440],{"encoding":1530},"U^*(P_1, P_2, Y)"," a poptávku ",[1035,50443,50445],{"className":50444},[1480],[1482,50446,50447],{"xmlns":1484},[1487,50448,50449,50489],{},[1490,50450,50451,50457,50459,50467,50469,50475,50477,50483,50485,50487],{},[1497,50452,50453,50455],{},[1493,50454,1520],{},[1493,50456,6277],{},[1506,50458,1508],{},[1697,50460,50461,50463,50465],{},[1493,50462,3712],{},[1493,50464,6277],{},[1493,50466,1495],{},[1506,50468,1553],{"stretchy":1552},[1497,50470,50471,50473],{},[1493,50472,1501],{},[1680,50474,1682],{},[1506,50476,1559],{"separator":1041},[1497,50478,50479,50481],{},[1493,50480,1501],{},[1680,50482,1691],{},[1506,50484,1559],{"separator":1041},[1493,50486,1791],{},[1506,50488,1564],{"stretchy":1552},[1528,50490,50491],{"encoding":1530},"Q_i = D_i^M(P_1, P_2, Y)",[1206,50493,50494,50497,50498,50511,50512,50441,50552,2632],{},[1047,50495,50496],{},"Duální"," (Hicks): zadáno ",[1035,50499,50501],{"className":50500},[1480],[1482,50502,50503],{"xmlns":1484},[1487,50504,50505,50509],{},[1490,50506,50507],{},[1493,50508,1668],{},[1528,50510,1668],{"encoding":1530},", hledáme minimální ",[1035,50513,50515],{"className":50514},[1480],[1482,50516,50517],{"xmlns":1484},[1487,50518,50519,50549],{},[1490,50520,50521,50527,50529,50535,50537,50543,50545,50547],{},[2315,50522,50523,50525],{},[1493,50524,2711],{},[1506,50526,2287],{},[1506,50528,1553],{"stretchy":1552},[1497,50530,50531,50533],{},[1493,50532,1501],{},[1680,50534,1682],{},[1506,50536,1559],{"separator":1041},[1497,50538,50539,50541],{},[1493,50540,1501],{},[1680,50542,1691],{},[1506,50544,1559],{"separator":1041},[1493,50546,1668],{},[1506,50548,1564],{"stretchy":1552},[1528,50550,50551],{"encoding":1530},"E^*(P_1, P_2, U)",[1035,50553,50555],{"className":50554},[1480],[1482,50556,50557],{"xmlns":1484},[1487,50558,50559,50599],{},[1490,50560,50561,50567,50569,50577,50579,50585,50587,50593,50595,50597],{},[1497,50562,50563,50565],{},[1493,50564,1520],{},[1493,50566,6277],{},[1506,50568,1508],{},[1697,50570,50571,50573,50575],{},[1493,50572,3712],{},[1493,50574,6277],{},[1493,50576,9900],{},[1506,50578,1553],{"stretchy":1552},[1497,50580,50581,50583],{},[1493,50582,1501],{},[1680,50584,1682],{},[1506,50586,1559],{"separator":1041},[1497,50588,50589,50591],{},[1493,50590,1501],{},[1680,50592,1691],{},[1506,50594,1559],{"separator":1041},[1493,50596,1668],{},[1506,50598,1564],{"stretchy":1552},[1528,50600,50601],{"encoding":1530},"Q_i = D_i^H(P_1, P_2, U)",[1030,50603,50604,50605,50608,50609,50612],{},"Proč se studují obě? Marshallova poptávka je ",[1047,50606,50607],{},"pozorovatelná"," (lze odhadnout z dat o spotřebě a důchodech), zatímco Hicksova umožňuje čistě oddělit ",[1047,50610,50611],{},"substituční efekt"," změny ceny od efektu důchodového — je klíčová pro teorii blahobytu a cenové indexy.",[1065,50614,50616],{"id":50615},"úlohy-k-optimalizaci","Úlohy k optimalizaci",[1304,50618,50620],{"id":50619},"maximalizace-užitečnosti-a-marshallova-poptávka","Maximalizace užitečnosti a Marshallova poptávka",[1030,50622,50623,50626,50627,50659,50660,50698,50699,1827],{},[1047,50624,50625],{},"6.8"," Jsou dány užitečnost ",[1035,50628,50630],{"className":50629},[1480],[1482,50631,50632],{"xmlns":1484},[1487,50633,50634,50656],{},[1490,50635,50636,50638,50640,50648],{},[1493,50637,1668],{},[1506,50639,1508],{},[1697,50641,50642,50644,50646],{},[1493,50643,1520],{},[1680,50645,1682],{},[1680,50647,3687],{},[1697,50649,50650,50652,50654],{},[1493,50651,1520],{},[1680,50653,1691],{},[1680,50655,3687],{},[1528,50657,50658],{"encoding":1530},"U = Q_1^{0{,}5} Q_2^{0{,}5}",", ceny ",[1035,50661,50663],{"className":50662},[1480],[1482,50664,50665],{"xmlns":1484},[1487,50666,50667,50695],{},[1490,50668,50669,50677,50679,50681,50683,50691,50693],{},[1697,50670,50671,50673,50675],{},[1493,50672,1501],{},[1680,50674,1682],{},[1506,50676,2287],{},[1506,50678,1508],{},[1680,50680,4007],{},[1506,50682,1559],{"separator":1041},[1697,50684,50685,50687,50689],{},[1493,50686,1501],{},[1680,50688,1691],{},[1506,50690,2287],{},[1506,50692,1508],{},[1680,50694,1775],{},[1528,50696,50697],{"encoding":1530},"P_1^* = 4, P_2^* = 10"," za jednotku zboží a důchod spotřebitele 200. Určete množství ",[1035,50700,50702],{"className":50701},[1480],[1482,50703,50704],{"xmlns":1484},[1487,50705,50706,50722],{},[1490,50707,50708,50714,50716],{},[1497,50709,50710,50712],{},[1493,50711,1520],{},[1680,50713,1682],{},[1506,50715,1559],{"separator":1041},[1497,50717,50718,50720],{},[1493,50719,1520],{},[1680,50721,1691],{},[1528,50723,1826],{"encoding":1530},[1030,50725,50726,50729,50730,50772,50773,50804,50805,50827,50828,2632],{},[1047,50727,50728],{},"6.9"," Jsou dány rozpočtové omezení ",[1035,50731,50733],{"className":50732},[1480],[1482,50734,50735],{"xmlns":1484},[1487,50736,50737,50769],{},[1490,50738,50739,50741,50743,50749,50755,50757,50763],{},[1493,50740,1791],{},[1506,50742,1508],{},[1497,50744,50745,50747],{},[1493,50746,1501],{},[1680,50748,1682],{},[1497,50750,50751,50753],{},[1493,50752,1520],{},[1680,50754,1682],{},[1506,50756,2162],{},[1497,50758,50759,50761],{},[1493,50760,1501],{},[1680,50762,1691],{},[1497,50764,50765,50767],{},[1493,50766,1520],{},[1680,50768,1691],{},[1528,50770,50771],{"encoding":1530},"Y = P_1 Q_1 + P_2 Q_2"," a užitečnost ",[1035,50774,50776],{"className":50775},[1480],[1482,50777,50778],{"xmlns":1484},[1487,50779,50780,50802],{},[1490,50781,50782,50784,50786,50794],{},[1493,50783,1668],{},[1506,50785,1508],{},[1697,50787,50788,50790,50792],{},[1493,50789,1520],{},[1680,50791,1682],{},[1680,50793,3687],{},[1697,50795,50796,50798,50800],{},[1493,50797,1520],{},[1680,50799,1691],{},[1680,50801,3687],{},[1528,50803,50658],{"encoding":1530},". (a) Odvoďte funkce poptávky maximalizující užitečnost. (b) Najděte funkce poptávky pro důchod ",[1035,50806,50808],{"className":50807},[1480],[1482,50809,50810],{"xmlns":1484},[1487,50811,50812,50824],{},[1490,50813,50814,50820,50822],{},[2315,50815,50816,50818],{},[1493,50817,1791],{},[1506,50819,2287],{},[1506,50821,1508],{},[1680,50823,1796],{},[1528,50825,50826],{"encoding":1530},"Y^* = 500",". (c) Najděte Engelovy funkce pro ceny ",[1035,50829,50831],{"className":50830},[1480],[1482,50832,50833],{"xmlns":1484},[1487,50834,50835,50863],{},[1490,50836,50837,50845,50847,50849,50851,50859,50861],{},[1697,50838,50839,50841,50843],{},[1493,50840,1501],{},[1680,50842,1682],{},[1506,50844,2287],{},[1506,50846,1508],{},[1680,50848,1752],{},[1506,50850,1559],{"separator":1041},[1697,50852,50853,50855,50857],{},[1493,50854,1501],{},[1680,50856,1691],{},[1506,50858,2287],{},[1506,50860,1508],{},[1680,50862,1775],{},[1528,50864,50865],{"encoding":1530},"P_1^* = 5, P_2^* = 10",[1030,50867,50868,50871,50872,37188,50903,50933,50934,2632],{},[1047,50869,50870],{},"6.10"," Odvoďte funkce poptávky pro Cobb-Douglasovy funkce užitečnosti ",[1035,50873,50875],{"className":50874},[1480],[1482,50876,50877],{"xmlns":1484},[1487,50878,50879,50901],{},[1490,50880,50881,50883,50885,50893],{},[1493,50882,1668],{},[1506,50884,1508],{},[1697,50886,50887,50889,50891],{},[1493,50888,1520],{},[1680,50890,1682],{},[1493,50892,1052],{},[1697,50894,50895,50897,50899],{},[1493,50896,1520],{},[1680,50898,1691],{},[1493,50900,2394],{},[1528,50902,2397],{"encoding":1530},[1035,50904,50906],{"className":50905},[1480],[1482,50907,50908],{"xmlns":1484},[1487,50909,50910,50930],{},[1490,50911,50912,50914,50916,50918,50920,50922,50924,50926,50928],{},[1493,50913,1052],{},[1506,50915,1559],{"separator":1041},[1493,50917,2394],{},[1506,50919,22378],{},[1506,50921,21034],{"stretchy":1552},[1680,50923,1871],{},[1506,50925,1559],{"separator":1041},[1680,50927,1682],{},[1506,50929,21051],{"stretchy":1552},[1528,50931,50932],{"encoding":1530},"a, b \\in \\langle 0, 1 \\rangle"," a rozpočtové omezení ",[1035,50935,50937],{"className":50936},[1480],[1482,50938,50939],{"xmlns":1484},[1487,50940,50941,50973],{},[1490,50942,50943,50945,50947,50953,50959,50961,50967],{},[1493,50944,1791],{},[1506,50946,1508],{},[1497,50948,50949,50951],{},[1493,50950,1501],{},[1680,50952,1682],{},[1497,50954,50955,50957],{},[1493,50956,1520],{},[1680,50958,1682],{},[1506,50960,2162],{},[1497,50962,50963,50965],{},[1493,50964,1501],{},[1680,50966,1691],{},[1497,50968,50969,50971],{},[1493,50970,1520],{},[1680,50972,1691],{},[1528,50974,50771],{"encoding":1530},[1030,50976,50977,50980,50981,37188,51015,50933,51033,2632],{},[1047,50978,50979],{},"6.11"," Odvoďte funkce poptávky pro funkce užitečnosti CES typu ",[1035,50982,50984],{"className":50983},[1480],[1482,50985,50986],{"xmlns":1484},[1487,50987,50988,51012],{},[1490,50989,50990,50992,50994,51002,51004],{},[1493,50991,1668],{},[1506,50993,1508],{},[1697,50995,50996,50998,51000],{},[1493,50997,1520],{},[1680,50999,1682],{},[1493,51001,1052],{},[1506,51003,2162],{},[1697,51005,51006,51008,51010],{},[1493,51007,1520],{},[1680,51009,1691],{},[1493,51011,1052],{},[1528,51013,51014],{"encoding":1530},"U = Q_1^a + Q_2^a",[1035,51016,51018],{"className":51017},[1480],[1482,51019,51020],{"xmlns":1484},[1487,51021,51022,51030],{},[1490,51023,51024,51026,51028],{},[1493,51025,1052],{},[1506,51027,18796],{"mathvariant":1516},[1680,51029,1871],{},[1528,51031,51032],{"encoding":1530},"a \\neq 0",[1035,51034,51036],{"className":51035},[1480],[1482,51037,51038],{"xmlns":1484},[1487,51039,51040,51072],{},[1490,51041,51042,51044,51046,51052,51058,51060,51066],{},[1493,51043,1791],{},[1506,51045,1508],{},[1497,51047,51048,51050],{},[1493,51049,1501],{},[1680,51051,1682],{},[1497,51053,51054,51056],{},[1493,51055,1520],{},[1680,51057,1682],{},[1506,51059,2162],{},[1497,51061,51062,51064],{},[1493,51063,1501],{},[1680,51065,1691],{},[1497,51067,51068,51070],{},[1493,51069,1520],{},[1680,51071,1691],{},[1528,51073,50771],{"encoding":1530},[1304,51075,51077],{"id":51076},"minimalizace-výdajů-a-hicksova-poptávka","Minimalizace výdajů a Hicksova poptávka",[1030,51079,51080,50626,51083,1732,51110,51131,51132,1732,51155,51179,51180,51205,51206,2632],{},[1047,51081,51082],{},"6.12",[1035,51084,51086],{"className":51085},[1480],[1482,51087,51088],{"xmlns":1484},[1487,51089,51090,51108],{},[1490,51091,51092,51094,51096,51102],{},[1493,51093,1668],{},[1506,51095,1508],{},[1497,51097,51098,51100],{},[1493,51099,1520],{},[1680,51101,1682],{},[1497,51103,51104,51106],{},[1493,51105,1520],{},[1680,51107,1691],{},[1528,51109,45550],{"encoding":1530},[1035,51111,51113],{"className":51112},[1480],[1482,51114,51115],{"xmlns":1484},[1487,51116,51117,51129],{},[1490,51118,51119,51125,51127],{},[2315,51120,51121,51123],{},[1493,51122,1668],{},[1506,51124,2287],{},[1506,51126,1508],{},[1680,51128,1775],{},[1528,51130,4048],{"encoding":1530}," hladina užitečnosti a ceny ",[1035,51133,51135],{"className":51134},[1480],[1482,51136,51137],{"xmlns":1484},[1487,51138,51139,51153],{},[1490,51140,51141,51149,51151],{},[1697,51142,51143,51145,51147],{},[1493,51144,1501],{},[1680,51146,1682],{},[1506,51148,2287],{},[1506,51150,1508],{},[1680,51152,1691],{},[1528,51154,45623],{"encoding":1530},[1035,51156,51158],{"className":51157},[1480],[1482,51159,51160],{"xmlns":1484},[1487,51161,51162,51176],{},[1490,51163,51164,51172,51174],{},[1697,51165,51166,51168,51170],{},[1493,51167,1501],{},[1680,51169,1691],{},[1506,51171,2287],{},[1506,51173,1508],{},[1680,51175,4007],{},[1528,51177,51178],{"encoding":1530},"P_2^* = 4",". Určete množství ",[1035,51181,51183],{"className":51182},[1480],[1482,51184,51185],{"xmlns":1484},[1487,51186,51187,51203],{},[1490,51188,51189,51195,51197],{},[1497,51190,51191,51193],{},[1493,51192,1520],{},[1680,51194,1682],{},[1506,51196,1559],{"separator":1041},[1497,51198,51199,51201],{},[1493,51200,1520],{},[1680,51202,1691],{},[1528,51204,1826],{"encoding":1530}," minimalizující výdaje spotřebitele ",[1035,51207,51209],{"className":51208},[1480],[1482,51210,51211],{"xmlns":1484},[1487,51212,51213,51233],{},[1490,51214,51215,51217,51219,51225,51227],{},[1493,51216,1668],{},[1506,51218,1508],{},[1497,51220,51221,51223],{},[1493,51222,1520],{},[1680,51224,1682],{},[1506,51226,1714],{},[1497,51228,51229,51231],{},[1493,51230,1520],{},[1680,51232,1691],{},[1528,51234,51235],{"encoding":1530},"U = Q_1 \\cdot Q_2",[1030,51237,51238,51241,51242,51283,51284,51306,51307,2632],{},[1047,51239,51240],{},"6.13"," Jsou dány výdaje spotřebitele ",[1035,51243,51245],{"className":51244},[1480],[1482,51246,51247],{"xmlns":1484},[1487,51248,51249,51281],{},[1490,51250,51251,51253,51255,51261,51267,51269,51275],{},[1493,51252,2711],{},[1506,51254,1508],{},[1497,51256,51257,51259],{},[1493,51258,1501],{},[1680,51260,1682],{},[1497,51262,51263,51265],{},[1493,51264,1520],{},[1680,51266,1682],{},[1506,51268,2162],{},[1497,51270,51271,51273],{},[1493,51272,1501],{},[1680,51274,1691],{},[1497,51276,51277,51279],{},[1493,51278,1520],{},[1680,51280,1691],{},[1528,51282,4208],{"encoding":1530}," a užitečnost. (a) Najděte funkce poptávky minimalizující výdaje spotřebitele. (b) Určete funkce poptávky pro užitečnost ",[1035,51285,51287],{"className":51286},[1480],[1482,51288,51289],{"xmlns":1484},[1487,51290,51291,51303],{},[1490,51292,51293,51299,51301],{},[2315,51294,51295,51297],{},[1493,51296,1668],{},[1506,51298,2287],{},[1506,51300,1508],{},[1680,51302,2309],{},[1528,51304,51305],{"encoding":1530},"U^* = 25"," a stanovte příslušné výdaje spotřebitele při cenách ",[1035,51308,51310],{"className":51309},[1480],[1482,51311,51312],{"xmlns":1484},[1487,51313,51314,51342],{},[1490,51315,51316,51324,51326,51328,51330,51338,51340],{},[1697,51317,51318,51320,51322],{},[1493,51319,1501],{},[1680,51321,1682],{},[1506,51323,2287],{},[1506,51325,1508],{},[1680,51327,8436],{},[1506,51329,1559],{"separator":1041},[1697,51331,51332,51334,51336],{},[1493,51333,1501],{},[1680,51335,1691],{},[1506,51337,2287],{},[1506,51339,1508],{},[1680,51341,9787],{},[1528,51343,51344],{"encoding":1530},"P_1^* = 20, P_2^* = 15",[1065,51346,31885],{"id":31884},[1203,51348,51349,51406,51445,51465,51500,51554,51559,51565,51661,51706],{},[1206,51350,51351,1656,51354,51403,51404,2632],{},[1047,51352,51353],{},"Rozpočtové omezení (budget constraint)",[1035,51355,51357],{"className":51356},[1480],[1482,51358,51359],{"xmlns":1484},[1487,51360,51361,51401],{},[1490,51362,51363,51369,51371,51379,51385,51387,51395],{},[2315,51364,51365,51367],{},[1493,51366,1791],{},[1506,51368,2287],{},[1506,51370,1508],{},[1697,51372,51373,51375,51377],{},[1493,51374,1501],{},[1680,51376,1682],{},[1506,51378,2287],{},[1497,51380,51381,51383],{},[1493,51382,1520],{},[1680,51384,1682],{},[1506,51386,2162],{},[1697,51388,51389,51391,51393],{},[1493,51390,1501],{},[1680,51392,1691],{},[1506,51394,2287],{},[1497,51396,51397,51399],{},[1493,51398,1520],{},[1680,51400,1691],{},[1528,51402,33447],{"encoding":1530}," — (6.12); ",[1047,51405,43697],{},[1206,51407,51408,51411,51412,2632],{},[1047,51409,51410],{},"Úloha o maximalizaci užitečnosti"," (primární) — Lagrangeova funkce (6.13), soustava (6.14), podmínka optimality ",[1035,51413,51415],{"className":51414},[1480],[1482,51416,51417],{"xmlns":1484},[1487,51418,51419,51443],{},[1490,51420,51421,51423,51425,51433,51435],{},[1988,51422,13960],{},[1506,51424,1508],{},[1697,51426,51427,51429,51431],{},[1493,51428,1501],{},[1680,51430,1682],{},[1506,51432,2287],{},[1493,51434,1709],{"mathvariant":1516},[1697,51436,51437,51439,51441],{},[1493,51438,1501],{},[1680,51440,1691],{},[1506,51442,2287],{},[1528,51444,44551],{"encoding":1530},[1206,51446,51447,51462,51463,2632],{},[1047,51448,44692,51449],{},[1035,51450,51452],{"className":51451},[1480],[1482,51453,51454],{"xmlns":1484},[1487,51455,51456,51460],{},[1490,51457,51458],{},[1493,51459,32598],{},[1528,51461,32651],{"encoding":1530}," — stínová cena uvolnění omezení; u maximalizace ",[1047,51464,44714],{},[1206,51466,51467,51470,51471,2632],{},[1047,51468,51469],{},"Podmínka tečnosti"," — sklon indiferenční křivky = sklon rozpočtové přímky; ",[1035,51472,51474],{"className":51473},[1480],[1482,51475,51476],{"xmlns":1484},[1487,51477,51478,51498],{},[1490,51479,51480,51482,51484,51490,51492],{},[1988,51481,13960],{},[1506,51483,1508],{},[1497,51485,51486,51488],{},[1493,51487,1501],{},[1680,51489,1682],{},[1493,51491,1709],{"mathvariant":1516},[1497,51493,51494,51496],{},[1493,51495,1501],{},[1680,51497,1691],{},[1528,51499,43563],{"encoding":1530},[1206,51501,51502,22970,51505,51553],{},[1047,51503,51504],{},"Poptávka maximalizující užitečnost (Marshallova)",[1035,51506,51508],{"className":51507},[1480],[1482,51509,51510],{"xmlns":1484},[1487,51511,51512,51550],{},[1490,51513,51514,51520,51522,51528,51530,51536,51538,51544,51546,51548],{},[1497,51515,51516,51518],{},[1493,51517,1520],{},[1493,51519,6277],{},[1506,51521,1508],{},[1497,51523,51524,51526],{},[1493,51525,3712],{},[1493,51527,6277],{},[1506,51529,1553],{"stretchy":1552},[1497,51531,51532,51534],{},[1493,51533,1501],{},[1680,51535,1682],{},[1506,51537,1559],{"separator":1041},[1497,51539,51540,51542],{},[1493,51541,1501],{},[1680,51543,1691],{},[1506,51545,1559],{"separator":1041},[1493,51547,1791],{},[1506,51549,1564],{"stretchy":1552},[1528,51551,51552],{"encoding":1530},"Q_i = D_i(P_1, P_2, Y)"," — (6.15).",[1206,51555,51556,51558],{},[1047,51557,46829],{}," — poptávka jako funkce důchodu při pevných cenách.",[1206,51560,51561,51564],{},[1047,51562,51563],{},"Úloha o minimalizaci výdajů"," (duální) — Lagrangeova funkce (6.24), soustava (6.25), postačující podmínka (6.26).",[1206,51566,51567,22970,51569,51616,51617,51660],{},[1047,51568,49142],{},[1035,51570,51572],{"className":51571},[1480],[1482,51573,51574],{"xmlns":1484},[1487,51575,51576,51614],{},[1490,51577,51578,51584,51586,51592,51594,51600,51602,51608,51610,51612],{},[1497,51579,51580,51582],{},[1493,51581,1520],{},[1493,51583,6277],{},[1506,51585,1508],{},[1497,51587,51588,51590],{},[1493,51589,3712],{},[1493,51591,6277],{},[1506,51593,1553],{"stretchy":1552},[1497,51595,51596,51598],{},[1493,51597,1501],{},[1680,51599,1682],{},[1506,51601,1559],{"separator":1041},[1497,51603,51604,51606],{},[1493,51605,1501],{},[1680,51607,1691],{},[1506,51609,1559],{"separator":1041},[1493,51611,1668],{},[1506,51613,1564],{"stretchy":1552},[1528,51615,33967],{"encoding":1530}," — (6.27); obecný výsledek pro ",[1035,51618,51620],{"className":51619},[1480],[1482,51621,51622],{"xmlns":1484},[1487,51623,51624,51658],{},[1490,51625,51626,51628,51630,51644],{},[1493,51627,1668],{},[1506,51629,1508],{},[1697,51631,51632,51634,51636],{},[1493,51633,1520],{},[1680,51635,1682],{},[1490,51637,51638,51640,51642],{},[1680,51639,1682],{},[1493,51641,1709],{"mathvariant":1516},[1680,51643,1691],{},[1697,51645,51646,51648,51650],{},[1493,51647,1520],{},[1680,51649,1691],{},[1490,51651,51652,51654,51656],{},[1680,51653,1682],{},[1493,51655,1709],{"mathvariant":1516},[1680,51657,1691],{},[1528,51659,5197],{"encoding":1530},": (6.30).",[1206,51662,51663,51705],{},[1047,51664,51665,51666],{},"Bod dotyku ",[1035,51667,51669],{"className":51668},[1480],[1482,51670,51671],{"xmlns":1484},[1487,51672,51673,51703],{},[1490,51674,51675,51681,51683,51691,51693,51701],{},[2315,51676,51677,51679],{},[1493,51678,1520],{},[1506,51680,2287],{},[1506,51682,14314],{"stretchy":1552},[1697,51684,51685,51687,51689],{},[1493,51686,1520],{},[1680,51688,1682],{},[1506,51690,2287],{},[1506,51692,1559],{"separator":1041},[1697,51694,51695,51697,51699],{},[1493,51696,1520],{},[1680,51698,1691],{},[1506,51700,2287],{},[1506,51702,14323],{"stretchy":1552},[1528,51704,43893],{"encoding":1530}," — řešení obou úloh; totožný pro primární i duální formulaci.",[1206,51707,51708,51711,51712,51725,51726,51739],{},[1047,51709,51710],{},"Dualita"," — ekvivalence max ",[1035,51713,51715],{"className":51714},[1480],[1482,51716,51717],{"xmlns":1484},[1487,51718,51719,51723],{},[1490,51720,51721],{},[1493,51722,1668],{},[1528,51724,1668],{"encoding":1530}," a min ",[1035,51727,51729],{"className":51728},[1480],[1482,51730,51731],{"xmlns":1484},[1487,51732,51733,51737],{},[1490,51734,51735],{},[1493,51736,2711],{},[1528,51738,2711],{"encoding":1530},"; Marshallova a Hicksova poptávka.",[1065,51741,17159],{"id":17158},[1203,51743,51744,51767,51782,51795,51806],{},[1206,51745,51746,1656,51749,51752,51753,51766],{},[1047,51747,51748],{},"Teorie před optimalizací:",[1052,51750,6615],{"className":51751,"dataFsResolvedFilePath":6613,"href":6614},[1055]," (funkce ",[1035,51754,51756],{"className":51755},[1480],[1482,51757,51758],{"xmlns":1484},[1487,51759,51760,51764],{},[1490,51761,51762],{},[1493,51763,1668],{},[1528,51765,1668],{"encoding":1530},", indiferenční křivky, MRCS).",[1206,51768,51769,1656,51771,51774,51775,51778,51779,2632],{},[1047,51770,17249],{},[1052,51772,17267],{"className":51773,"dataFsResolvedFilePath":17265,"href":17266},[1055]," (vázaná optimalizace), ",[1052,51776,9472],{"className":51777,"dataFsResolvedFilePath":9470,"href":9471},[1055]," (parciální derivace), ",[1052,51780,3506],{"className":51781,"dataFsResolvedFilePath":16621,"href":16622},[1055],[1206,51783,51784,1656,51787,51790,51791,51794],{},[1047,51785,51786],{},"Paralely:",[1052,51788,6836],{"className":51789,"dataFsResolvedFilePath":1572,"href":1573},[1055]," (MRTS ↔ MRCS, izokvanty ↔ IC, Eulerova věta pro CD), ",[1052,51792,17211],{"className":51793,"dataFsResolvedFilePath":3487,"href":3488},[1055]," (Marshallova poptávka jako vstup tržního modelu).",[1206,51796,51797,1656,51800,1732,51803],{},[1047,51798,51799],{},"Přednášky:",[1052,51801,17196],{"className":51802,"dataFsResolvedFilePath":17194,"href":17195},[1055],[1052,51804,17202],{"className":51805,"dataFsResolvedFilePath":17200,"href":17201},[1055],[1206,51807,51808,1656,51810],{},[1047,51809,17176],{},[1052,51811,1058],{"className":51812,"dataFsResolvedFilePath":1056,"href":1057},[1055],{"title":17269,"searchDepth":141,"depth":141,"links":51814},[51815,51816,51817,51822,51823,51824,51826,51829,51832,51834,51835,51837,51838,51842,51843],{"id":28491,"depth":141,"text":1042},{"id":43571,"depth":141,"text":43572},{"id":43970,"depth":141,"text":43971,"children":51818},[51819,51820],{"id":44090,"depth":96,"text":44091},{"id":44675,"depth":96,"text":51821},"Interpretace λ\\lambda — mezní užitečnost důchodu",{"id":45139,"depth":141,"text":45140},{"id":45205,"depth":141,"text":45206},{"id":45521,"depth":141,"text":51825},"Příklad 6.6 — maximalizace užitečnosti pro U=Q1Q2U = Q_1 Q_2",{"id":46072,"depth":141,"text":46073,"children":51827},[51828],{"id":46828,"depth":96,"text":46829},{"id":47008,"depth":141,"text":47009,"children":51830},[51831],{"id":47265,"depth":96,"text":47266},{"id":48218,"depth":141,"text":51833},"Příklad 6.7 — minimalizace výdajů pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":49141,"depth":141,"text":49142},{"id":49344,"depth":141,"text":51836},"Příklad 6.8 — obecné odvození pro U=Q11\u002F2Q21\u002F2U = Q_1^{1\u002F2} Q_2^{1\u002F2}",{"id":50229,"depth":141,"text":50230},{"id":50615,"depth":141,"text":50616,"children":51839},[51840,51841],{"id":50619,"depth":96,"text":50620},{"id":51076,"depth":96,"text":51077},{"id":31884,"depth":141,"text":31885},{"id":17158,"depth":141,"text":17159},{},"\u002Ftopics\u002Foptimalizace-spotrebitele",{"title":43333,"description":17269},[26098,32431],"topics\u002Foptimalizace-spotrebitele",[9,774,62,93,806,706,181],"au3wlPl5K1NDHMB00blHngLTd3z3NjSmXTirELSkjkE",{"id":51852,"title":3489,"body":51853,"course":9,"courses":17424,"created":26093,"description":17269,"extension":17426,"meta":65147,"navigation":17428,"path":65148,"seo":65149,"sources":65150,"stem":65151,"tags":65152,"type":19275,"updated":26102,"__hash__":65153},"topics\u002Ftopics\u002Fpoptavka-nabidka.md",{"type":1016,"value":51854,"toc":65103},[51855,51858,51888,51892,51899,52049,52063,52065,52067,52159,52163,52199,52272,52293,52418,52434,52447,52451,52456,52486,52548,52557,52561,52623,52634,52658,52776,52780,52783,52842,52957,52962,52993,53054,53102,53106,53127,53151,53155,53167,53171,53281,53285,53301,53342,53353,53512,53522,53526,53653,53663,53670,53674,53752,53769,53848,53854,53861,54000,54007,54010,54014,54092,54138,54182,54188,54192,54195,54390,54394,54630,54633,54638,54786,54791,54939,54941,54943,55028,55031,55136,55205,55214,55218,55221,55282,55291,55295,55328,55410,55414,55463,55517,55521,55550,55579,55631,55638,55691,55695,55738,55805,55849,55953,55955,55959,56072,56074,56142,56191,56198,56202,56274,56279,56327,56513,56517,56522,56698,56703,56762,56867,56871,56898,56902,56909,57072,57158,57163,57165,57169,57274,57424,57496,57570,57572,57576,57595,57599,57732,57787,57899,57903,57960,58063,58122,58283,58287,58362,58434,58532,58590,58643,58664,58718,58723,58801,58848,58935,58973,59061,59214,59250,59256,59258,59260,59314,59321,59329,59416,59425,59512,59519,59521,59525,59750,59752,59756,59760,59829,59880,60080,60086,60097,60165,60171,60593,60597,60661,60685,60881,60887,60901,60969,60972,61012,61235,61303,61605,62014,62091,62257,62263,62266,62341,62795,62846,63252,63356,64019,64022,64099,64107,64181,64212,64214,64218,64262,64264,64266,64270,64499,64503,64594,64599,64693,64698,64871,64875,64993,64998,65047,65049,65051],[1019,51856,3489],{"id":51857},"poptávka-nabídka-a-tržní-rovnováha",[1023,51859,51861,51867],{"className":51860,"dataCallout":582},[1026,1186],[1030,51862,51864,1042],{"className":51863},[1033],[1035,51865],{"className":51866,"ariaHidden":1041},[1038,1193,1040],[1030,51868,51869,51870,51873,51874,51876,51877,51880,51881,51883,51884,51887],{},"Kapitola buduje základní mikroekonomický model trhu: chování spotřebitele (",[1047,51871,51872],{},"poptávka",") a výrobce (",[1047,51875,16507],{},"), jejich interakci v ",[1047,51878,51879],{},"tržní rovnováze"," a kvantitativní analýzu reakce modelu na změnu exogenních proměnných (posuny, zdanění, ",[1047,51882,34120],{},"). Uzavírá ji pojem ",[1047,51885,51886],{},"přebytku spotřebitele a výrobce"," jako míry čistého prospěchu obou stran trhu.",[1065,51889,51891],{"id":51890},"úvod-model-a-proměnné","Úvod — model a proměnné",[1030,51893,51894,51895,51898],{},"Cílem je popsat chování spotřebitele a výrobce za předpokladu racionality jedince (",[1176,51896,51897],{},"homo economicus","). Mezi hlavní proměnné patří:",[1203,51900,51901,51918,51959,51975],{},[1206,51902,51903,51904,51917],{},"cena ",[1035,51905,51907],{"className":51906},[1480],[1482,51908,51909],{"xmlns":1484},[1487,51910,51911,51915],{},[1490,51912,51913],{},[1493,51914,1501],{},[1528,51916,1501],{"encoding":1530}," zkoumaného zboží,",[1206,51919,51920,51921,1559],{},"ceny alternativních zboží ",[1035,51922,51924],{"className":51923},[1480],[1482,51925,51926],{"xmlns":1484},[1487,51927,51928,51956],{},[1490,51929,51930,51936,51938,51944,51946,51948,51950],{},[1497,51931,51932,51934],{},[1493,51933,1501],{},[1680,51935,1682],{},[1506,51937,1559],{"separator":1041},[1497,51939,51940,51942],{},[1493,51941,1501],{},[1680,51943,1691],{},[1506,51945,1559],{"separator":1041},[1506,51947,26181],{},[1506,51949,1559],{"separator":1041},[1497,51951,51952,51954],{},[1493,51953,1501],{},[1493,51955,7781],{},[1528,51957,51958],{"encoding":1530},"P_1, P_2, \\dots, P_n",[1206,51960,51961,51962,1559],{},"důchod ",[1035,51963,51965],{"className":51964},[1480],[1482,51966,51967],{"xmlns":1484},[1487,51968,51969,51973],{},[1490,51970,51971],{},[1493,51972,1791],{},[1528,51974,1791],{"encoding":1530},[1206,51976,51977,51978,51991,51992,52005,52006,52019,52020,52034,52035,52048],{},"preference, očekávání, populace, výrobní faktory (práce ",[1035,51979,51981],{"className":51980},[1480],[1482,51982,51983],{"xmlns":1484},[1487,51984,51985,51989],{},[1490,51986,51987],{},[1493,51988,1556],{},[1528,51990,1556],{"encoding":1530},", kapitál ",[1035,51993,51995],{"className":51994},[1480],[1482,51996,51997],{"xmlns":1484},[1487,51998,51999,52003],{},[1490,52000,52001],{},[1493,52002,1504],{},[1528,52004,1504],{"encoding":1530},", půda ",[1035,52007,52009],{"className":52008},[1480],[1482,52010,52011],{"xmlns":1484},[1487,52012,52013,52017],{},[1490,52014,52015],{},[1493,52016,2711],{},[1528,52018,2711],{"encoding":1530},"), technologie, počet výrobců ",[1035,52021,52023],{"className":52022},[1480],[1482,52024,52025],{"xmlns":1484},[1487,52026,52027,52032],{},[1490,52028,52029],{},[1493,52030,52031],{},"O",[1528,52033,52031],{"encoding":1530},", počasí ",[1035,52036,52038],{"className":52037},[1480],[1482,52039,52040],{"xmlns":1484},[1487,52041,52042,52046],{},[1490,52043,52044],{},[1493,52045,15148],{},[1528,52047,15148],{"encoding":1530}," atd.",[1030,52050,52051,52052,52055,52056,52059,52060,2632],{},"Vybereme-li právě jeden z faktorů jako endogenní (",[1176,52053,52054],{},"ceteris paribus","), hovoříme o ",[1047,52057,52058],{},"jednofaktorovém modelu","; jinak jde o model ",[1047,52061,52062],{},"vícefaktorový",[1246,52064],{},[1065,52066,29638],{"id":51872},[1023,52068,52070,52076],{"className":52069,"dataCallout":582},[1026,1186],[1030,52071,52073,1042],{"className":52072},[1033],[1035,52074],{"className":52075,"ariaHidden":1041},[1038,1193,1040],[1030,52077,52078,52079,52092,52093,52106,52107,52110,52111,52134,52135,2632],{},"Poptávka vyjadřuje závislost nakupovaného množství ",[1035,52080,52082],{"className":52081},[1480],[1482,52083,52084],{"xmlns":1484},[1487,52085,52086,52090],{},[1490,52087,52088],{},[1493,52089,1520],{},[1528,52091,1520],{"encoding":1530}," na ceně ",[1035,52094,52096],{"className":52095},[1480],[1482,52097,52098],{"xmlns":1484},[1487,52099,52100,52104],{},[1490,52101,52102],{},[1493,52103,1501],{},[1528,52105,1501],{"encoding":1530}," (případně dalších proměnných). Základní vlastností je ",[1047,52108,52109],{},"zákon klesající poptávky",": při růstu ceny množství klesá. Z důvodu přehlednosti se pracuje s jednofaktorovým modelem ",[1035,52112,52114],{"className":52113},[1480],[1482,52115,52116],{"xmlns":1484},[1487,52117,52118,52132],{},[1490,52119,52120,52122,52124,52126,52128,52130],{},[1493,52121,1520],{},[1506,52123,1508],{},[1493,52125,3712],{},[1506,52127,1553],{"stretchy":1552},[1493,52129,1501],{},[1506,52131,1564],{"stretchy":1552},[1528,52133,19607],{"encoding":1530}," a jeho lineární verzí ",[1035,52136,52138],{"className":52137},[1480],[1482,52139,52140],{"xmlns":1484},[1487,52141,52142,52156],{},[1490,52143,52144,52146,52148,52150,52152,52154],{},[1493,52145,1501],{},[1506,52147,1508],{},[1493,52149,1052],{},[1493,52151,1520],{},[1506,52153,2162],{},[1493,52155,2394],{},[1528,52157,52158],{"encoding":1530},"P = aQ + b",[1304,52160,52162],{"id":52161},"obecný-vícefaktorový-model","Obecný vícefaktorový model",[1030,52164,52165,52166,52179,52180,52193,52194,7606,52196,18579],{},"Ve vícefaktorovém modelu uvažujeme, že poptávané množství ",[1035,52167,52169],{"className":52168},[1480],[1482,52170,52171],{"xmlns":1484},[1487,52172,52173,52177],{},[1490,52174,52175],{},[1493,52176,1520],{},[1528,52178,1520],{"encoding":1530}," závisí na ceně ",[1035,52181,52183],{"className":52182},[1480],[1482,52184,52185],{"xmlns":1484},[1487,52186,52187,52191],{},[1490,52188,52189],{},[1493,52190,1501],{},[1528,52192,1501],{"encoding":1530},", na cenách alternativních zboží a důchodu. Závislost vyjadřuje ",[1047,52195,43567],{},[1176,52197,52198],{},"demand function",[1035,52200,52202],{"className":52201},[1480],[1482,52203,52204],{"xmlns":1484,"display":1485},[1487,52205,52206,52269],{},[19617,52207,52208],{"width":19619},[19621,52209,52210,52212,52262,52264],{},[19624,52211],{"width":19626},[19624,52213,52214],{},[1490,52215,52216,52218,52220,52222,52224,52226,52228,52234,52236,52242,52244,52246,52248,52254,52256,52258,52260],{},[1493,52217,1520],{},[1506,52219,1508],{},[1493,52221,3712],{},[1506,52223,1553],{"stretchy":1552},[1493,52225,1501],{},[1506,52227,1559],{"separator":1041},[1497,52229,52230,52232],{},[1493,52231,1501],{},[1680,52233,1682],{},[1506,52235,1559],{"separator":1041},[1497,52237,52238,52240],{},[1493,52239,1501],{},[1680,52241,1691],{},[1506,52243,1559],{"separator":1041},[1506,52245,26181],{},[1506,52247,1559],{"separator":1041},[1497,52249,52250,52252],{},[1493,52251,1501],{},[1493,52253,7781],{},[1506,52255,1559],{"separator":1041},[1493,52257,1791],{},[1506,52259,1564],{"stretchy":1552},[1493,52261,2632],{"mathvariant":1516},[19624,52263],{"width":19626},[19624,52265,52266],{},[1988,52267,52268],{},"(2.1)",[1528,52270,52271],{"encoding":1530},"Q = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.1}",[1030,52273,52274,52275,52278,52279,52292],{},"Důležitou vlastností je ",[1047,52276,52277],{},"homogenita",": změní-li se všechny nezávisle proměnné ",[1035,52280,52282],{"className":52281},[1480],[1482,52283,52284],{"xmlns":1484},[1487,52285,52286,52290],{},[1490,52287,52288],{},[1493,52289,7740],{},[1528,52291,7740],{"encoding":1530},"-krát, poptávané množství se nezmění,",[1035,52294,52296],{"className":52295},[1480],[1482,52297,52298],{"xmlns":1484,"display":1485},[1487,52299,52300,52415],{},[19617,52301,52302],{"width":19619},[19621,52303,52304,52306,52408,52410],{},[19624,52305],{"width":19626},[19624,52307,52308],{},[1490,52309,52310,52312,52314,52316,52318,52320,52322,52324,52326,52332,52334,52336,52342,52344,52346,52348,52350,52356,52358,52360,52362,52364,52366,52368,52370,52372,52374,52380,52382,52388,52390,52392,52394,52400,52402,52404,52406],{},[1493,52311,1520],{},[1506,52313,1508],{},[1493,52315,3712],{},[1506,52317,1553],{"stretchy":1552},[1493,52319,7740],{},[1493,52321,1501],{},[1506,52323,1559],{"separator":1041},[1493,52325,7740],{},[1497,52327,52328,52330],{},[1493,52329,1501],{},[1680,52331,1682],{},[1506,52333,1559],{"separator":1041},[1493,52335,7740],{},[1497,52337,52338,52340],{},[1493,52339,1501],{},[1680,52341,1691],{},[1506,52343,1559],{"separator":1041},[1506,52345,26181],{},[1506,52347,1559],{"separator":1041},[1493,52349,7740],{},[1497,52351,52352,52354],{},[1493,52353,1501],{},[1493,52355,7781],{},[1506,52357,1559],{"separator":1041},[1493,52359,7740],{},[1493,52361,1791],{},[1506,52363,1564],{"stretchy":1552},[1506,52365,1508],{},[1493,52367,3712],{},[1506,52369,1553],{"stretchy":1552},[1493,52371,1501],{},[1506,52373,1559],{"separator":1041},[1497,52375,52376,52378],{},[1493,52377,1501],{},[1680,52379,1682],{},[1506,52381,1559],{"separator":1041},[1497,52383,52384,52386],{},[1493,52385,1501],{},[1680,52387,1691],{},[1506,52389,1559],{"separator":1041},[1506,52391,26181],{},[1506,52393,1559],{"separator":1041},[1497,52395,52396,52398],{},[1493,52397,1501],{},[1493,52399,7781],{},[1506,52401,1559],{"separator":1041},[1493,52403,1791],{},[1506,52405,1564],{"stretchy":1552},[1493,52407,2632],{"mathvariant":1516},[19624,52409],{"width":19626},[19624,52411,52412],{},[1988,52413,52414],{},"(2.2)",[1528,52416,52417],{"encoding":1530},"Q = D(rP, rP_1, rP_2, \\dots, rP_n, rY) = D(P, P_1, P_2, \\dots, P_n, Y). \\tag{2.2}",[1023,52419,52421,52428],{"className":52420,"dataCallout":1155},[1026,1154],[1030,52422,52424,52427],{"className":52423},[1033],[1035,52425],{"className":52426,"ariaHidden":1041},[1038,1162,1040],"Pozor",[1030,52429,52430,52431,2632],{},"Homogenita platí pouze v zidealizovaném vícefaktorovém modelu; ",[1047,52432,52433],{},"v jednofaktorových modelech neplatí",[1030,52435,52436,52437,1732,52440,1586,52443,52446],{},"Rozlišuje se poptávka ",[1047,52438,52439],{},"individuální",[1047,52441,52442],{},"tržní",[1047,52444,52445],{},"agregátní"," (není-li specifikováno, rozumí se tržní).",[1304,52448,52450],{"id":52449},"jednofaktorové-modely","Jednofaktorové modely",[52452,52453,52455],"h4",{"id":52454},"funkce-poptávky-v-užším-slova-smyslu","Funkce poptávky v užším slova smyslu",[1030,52457,52458,52459,52472,52473,1274],{},"Poptávané množství ",[1035,52460,52462],{"className":52461},[1480],[1482,52463,52464],{"xmlns":1484},[1487,52465,52466,52470],{},[1490,52467,52468],{},[1493,52469,1520],{},[1528,52471,1520],{"encoding":1530}," závisí pouze na ceně ",[1035,52474,52476],{"className":52475},[1480],[1482,52477,52478],{"xmlns":1484},[1487,52479,52480,52484],{},[1490,52481,52482],{},[1493,52483,1501],{},[1528,52485,1501],{"encoding":1530},[1035,52487,52489],{"className":52488},[1480],[1482,52490,52491],{"xmlns":1484,"display":1485},[1487,52492,52493,52545],{},[19617,52494,52495],{"width":19619},[19621,52496,52497,52499,52538,52540],{},[19624,52498],{"width":19626},[19624,52500,52501],{},[1490,52502,52503,52505,52507,52509,52511,52513,52515,52517,52519,52522,52524,52526,52528,52530,52532,52534,52536],{},[1493,52504,1520],{},[1506,52506,1508],{},[1493,52508,3712],{},[1506,52510,1553],{"stretchy":1552},[1493,52512,1501],{},[1506,52514,1564],{"stretchy":1552},[1506,52516,1559],{"separator":1041},[1912,52518],{"width":1914},[1988,52520,52521],{},"resp.",[1912,52523],{"width":1914},[1493,52525,1501],{},[1506,52527,1508],{},[1493,52529,3712],{},[1506,52531,1553],{"stretchy":1552},[1493,52533,1520],{},[1506,52535,1564],{"stretchy":1552},[1493,52537,2632],{"mathvariant":1516},[19624,52539],{"width":19626},[19624,52541,52542],{},[1988,52543,52544],{},"(2.3)",[1528,52546,52547],{"encoding":1530},"Q = D(P), \\qquad \\text{resp.} \\qquad P = D(Q). \\tag{2.3}",[1030,52549,52550,52551,7606,52554,16623],{},"Graf této funkce se nazývá ",[1047,52552,52553],{},"křivka poptávky",[1176,52555,52556],{},"demand curve",[52452,52558,52560],{"id":52559},"zákon-klesající-poptávky","Zákon klesající poptávky",[19516,52562,52563],{},[1030,52564,52565],{},[1047,52566,52567,52568,52581,52582,52595,52596,52581,52609,52622],{},"Roste-li cena ",[1035,52569,52571],{"className":52570},[1480],[1482,52572,52573],{"xmlns":1484},[1487,52574,52575,52579],{},[1490,52576,52577],{},[1493,52578,1501],{},[1528,52580,1501],{"encoding":1530},", pak množství ",[1035,52583,52585],{"className":52584},[1480],[1482,52586,52587],{"xmlns":1484},[1487,52588,52589,52593],{},[1490,52590,52591],{},[1493,52592,1520],{},[1528,52594,1520],{"encoding":1530}," klesá; klesá-li cena ",[1035,52597,52599],{"className":52598},[1480],[1482,52600,52601],{"xmlns":1484},[1487,52602,52603,52607],{},[1490,52604,52605],{},[1493,52606,1501],{},[1528,52608,1501],{"encoding":1530},[1035,52610,52612],{"className":52611},[1480],[1482,52613,52614],{"xmlns":1484},[1487,52615,52616,52620],{},[1490,52617,52618],{},[1493,52619,1520],{},[1528,52621,1520],{"encoding":1530}," roste.",[1030,52624,52625,52626,52629,52630,52633],{},"Spotřebitelé jsou ochotni nakoupit větší množství za nižší cenu (mezní užitečnost — viz ",[1052,52627,93],{"className":52628,"dataFsResolvedFilePath":6613,"href":6614},[1055],"). Zákon platí za ",[1047,52631,52632],{},"normálních podmínek","; první kvantitativní formulaci podal Marshall (1890).",[1023,52635,52637,52644],{"className":52636,"dataCallout":582},[1026,1186],[1030,52638,52640,52643],{"className":52639},[1033],[1035,52641],{"className":52642,"ariaHidden":1041},[1038,1193,1040],"Intuice — proč zákon platí",[1203,52645,52646,52652],{},[1206,52647,52648,52651],{},[1047,52649,52650],{},"Substituční efekt"," — růst ceny vede ke snaze nahradit zboží jiným.",[1206,52653,52654,52657],{},[1047,52655,52656],{},"Důchodový efekt"," — růst ceny způsobí nevítaný úbytek reálného důchodu.",[1030,52659,52660,52661,52674,52675,52688,52689,52715,52716,52742,52743,8994,52769,52772,52773,2632],{},"Každá funkce poptávky je tedy klesající. Cena ",[1035,52662,52664],{"className":52663},[1480],[1482,52665,52666],{"xmlns":1484},[1487,52667,52668,52672],{},[1490,52669,52670],{},[1493,52671,1501],{},[1528,52673,1501],{"encoding":1530}," se vynáší na svislou osu, množství ",[1035,52676,52678],{"className":52677},[1480],[1482,52679,52680],{"xmlns":1484},[1487,52681,52682,52686],{},[1490,52683,52684],{},[1493,52685,1520],{},[1528,52687,1520],{"encoding":1530}," na vodorovnou. Hypotetická křivka prochází body ",[1035,52690,52692],{"className":52691},[1480],[1482,52693,52694],{"xmlns":1484},[1487,52695,52696,52712],{},[1490,52697,52698,52700,52702,52704,52710],{},[1506,52699,14314],{"stretchy":1552},[1680,52701,1871],{},[1506,52703,1559],{"separator":1041},[1497,52705,52706,52708],{},[1493,52707,1501],{},[1680,52709,1871],{},[1506,52711,14323],{"stretchy":1552},[1528,52713,52714],{"encoding":1530},"[0, P_0]"," (cena, při níž je zboží neprodejné) a ",[1035,52717,52719],{"className":52718},[1480],[1482,52720,52721],{"xmlns":1484},[1487,52722,52723,52739],{},[1490,52724,52725,52727,52733,52735,52737],{},[1506,52726,14314],{"stretchy":1552},[1497,52728,52729,52731],{},[1493,52730,1520],{},[1680,52732,1871],{},[1506,52734,1559],{"separator":1041},[1680,52736,1871],{},[1506,52738,14323],{"stretchy":1552},[1528,52740,52741],{"encoding":1530},"[Q_0, 0]"," (teoretický objem při nulové ceně). Interval ",[1035,52744,52746],{"className":52745},[1480],[1482,52747,52748],{"xmlns":1484},[1487,52749,52750,52766],{},[1490,52751,52752,52754,52756,52758,52764],{},[1506,52753,1553],{"stretchy":1552},[1680,52755,1871],{},[1506,52757,1559],{"separator":1041},[1497,52759,52760,52762],{},[1493,52761,1501],{},[1680,52763,1871],{},[1506,52765,1564],{"stretchy":1552},[1528,52767,52768],{"encoding":1530},"(0, P_0)",[1047,52770,52771],{},"reálné cenové rozpětí",". Za teoretických předpokladů je křivka ",[1047,52774,52775],{},"konvexní",[52452,52777,52779],{"id":52778},"lineární-model-poptávky","Lineární model poptávky",[1030,52781,52782],{},"Nejjednodušší závislostí je",[1035,52784,52786],{"className":52785},[1480],[1482,52787,52788],{"xmlns":1484,"display":1485},[1487,52789,52790,52839],{},[19617,52791,52792],{"width":19619},[19621,52793,52794,52796,52832,52834],{},[19624,52795],{"width":19626},[19624,52797,52798],{},[1490,52799,52800,52802,52804,52806,52808,52810,52812,52814,52816,52818,52820,52822,52824,52826,52828,52830],{},[1493,52801,1501],{},[1506,52803,1508],{},[1493,52805,1052],{},[1493,52807,1520],{},[1506,52809,2162],{},[1493,52811,2394],{},[1506,52813,1559],{"separator":1041},[1912,52815],{"width":1914},[1493,52817,1052],{},[1506,52819,3961],{},[1680,52821,1871],{},[1506,52823,1559],{"separator":1041},[1988,52825,10922],{},[1493,52827,2394],{},[1506,52829,2796],{},[1680,52831,28945],{},[19624,52833],{"width":19626},[19624,52835,52836],{},[1988,52837,52838],{},"(2.4)",[1528,52840,52841],{"encoding":1530},"P = aQ + b, \\qquad a \u003C 0,\\ b > 0. \\tag{2.4}",[1030,52843,52844,52845,37188,52881,1586,52905,23990,52931,52953,52954,2632],{},"Křivka poptávky je přímka se záporným sklonem. Alternativně ",[1035,52846,52848],{"className":52847},[1480],[1482,52849,52850],{"xmlns":1484},[1487,52851,52852,52878],{},[1490,52853,52854,52856,52858,52866,52868,52870],{},[1493,52855,1520],{},[1506,52857,1508],{},[1869,52859,52860],{"scriptlevel":1871,"displaystyle":1552},[1510,52861,52862,52864],{},[1680,52863,1682],{},[1493,52865,1052],{},[1493,52867,1501],{},[1506,52869,1888],{},[1869,52871,52872],{"scriptlevel":1871,"displaystyle":1552},[1510,52873,52874,52876],{},[1493,52875,2394],{},[1493,52877,1052],{},[1528,52879,52880],{"encoding":1530},"Q = \\tfrac{1}{a}P - \\tfrac{b}{a}",[1035,52882,52884],{"className":52883},[1480],[1482,52885,52886],{"xmlns":1484},[1487,52887,52888,52902],{},[1490,52889,52890,52898,52900],{},[1869,52891,52892],{"scriptlevel":1871,"displaystyle":1552},[1510,52893,52894,52896],{},[1680,52895,1682],{},[1493,52897,1052],{},[1506,52899,3961],{},[1680,52901,1871],{},[1528,52903,52904],{"encoding":1530},"\\tfrac{1}{a} \u003C 0",[1035,52906,52908],{"className":52907},[1480],[1482,52909,52910],{"xmlns":1484},[1487,52911,52912,52928],{},[1490,52913,52914,52916,52924,52926],{},[1506,52915,1888],{},[1869,52917,52918],{"scriptlevel":1871,"displaystyle":1552},[1510,52919,52920,52922],{},[1493,52921,2394],{},[1493,52923,1052],{},[1506,52925,2796],{},[1680,52927,1871],{},[1528,52929,52930],{"encoding":1530},"-\\tfrac{b}{a} > 0",[1035,52932,52934],{"className":52933},[1480],[1482,52935,52936],{"xmlns":1484},[1487,52937,52938,52950],{},[1490,52939,52940,52942,52944,52946,52948],{},[1506,52941,1553],{"stretchy":1552},[1680,52943,1871],{},[1506,52945,1559],{"separator":1041},[1493,52947,2394],{},[1506,52949,1564],{"stretchy":1552},[1528,52951,52952],{"encoding":1530},"(0, b)",". Tento model odpovídá ",[1047,52955,52956],{},"nedokonalé konkurenci",[52958,52959,52961],"h5",{"id":52960},"příklad-21","Příklad 2.1",[1030,52963,52964,52966,52967,2632],{},[1047,52965,1263],{}," Lineární poptávka ",[1035,52968,52970],{"className":52969},[1480],[1482,52971,52972],{"xmlns":1484},[1487,52973,52974,52990],{},[1490,52975,52976,52978,52980,52982,52984,52986,52988],{},[1493,52977,1501],{},[1506,52979,1508],{},[1506,52981,1888],{},[1680,52983,1691],{},[1493,52985,1520],{},[1506,52987,2162],{},[1680,52989,4965],{},[1528,52991,52992],{"encoding":1530},"P = -2Q + 60",[1030,52994,52995,52998,52999,53021,53022,2632],{},[1047,52996,52997],{},"Řešení:"," Reálné cenové rozpětí je ",[1035,53000,53002],{"className":53001},[1480],[1482,53003,53004],{"xmlns":1484},[1487,53005,53006,53018],{},[1490,53007,53008,53010,53012,53014,53016],{},[1506,53009,1553],{"stretchy":1552},[1680,53011,1871],{},[1506,53013,1559],{"separator":1041},[1680,53015,4965],{},[1506,53017,1564],{"stretchy":1552},[1528,53019,53020],{"encoding":1530},"(0, 60)","; alternativní tvar je ",[1035,53023,53025],{"className":53024},[1480],[1482,53026,53027],{"xmlns":1484},[1487,53028,53029,53051],{},[1490,53030,53031,53033,53035,53037,53045,53047,53049],{},[1493,53032,1520],{},[1506,53034,1508],{},[1506,53036,1888],{},[1869,53038,53039],{"scriptlevel":1871,"displaystyle":1552},[1510,53040,53041,53043],{},[1680,53042,1682],{},[1680,53044,1691],{},[1493,53046,1501],{},[1506,53048,2162],{},[1680,53050,6956],{},[1528,53052,53053],{"encoding":1530},"Q = -\\tfrac{1}{2}P + 30",[1073,53055,53056,53079],{},[1076,53057,53058],{},[1079,53059,53060,53075,53077],{},[1082,53061,53062],{},[1035,53063,53065],{"className":53064},[1480],[1482,53066,53067],{"xmlns":1484},[1487,53068,53069,53073],{},[1490,53070,53071],{},[1493,53072,1501],{},[1528,53074,1501],{"encoding":1530},[1082,53076,7380],{},[1082,53078,8436],{},[1092,53080,53081],{},[1079,53082,53083,53098,53100],{},[1097,53084,53085],{},[1035,53086,53088],{"className":53087},[1480],[1482,53089,53090],{"xmlns":1484},[1487,53091,53092,53096],{},[1490,53093,53094],{},[1493,53095,1520],{},[1528,53097,1520],{"encoding":1530},[1097,53099,1775],{},[1097,53101,8436],{},[52452,53103,53105],{"id":53104},"poptávka-při-dokonalé-konkurenci","Poptávka při dokonalé konkurenci",[1030,53107,53108,53109,53126],{},"Přebírá-li každý účastník trhu pevnou tržní cenu ",[1035,53110,53112],{"className":53111},[1480],[1482,53113,53114],{"xmlns":1484},[1487,53115,53116,53124],{},[1490,53117,53118],{},[2315,53119,53120,53122],{},[1493,53121,1501],{},[1506,53123,2287],{},[1528,53125,20114],{"encoding":1530},", je funkce poptávky konstantní:",[1035,53128,53130],{"className":53129},[1480],[1482,53131,53132],{"xmlns":1484,"display":1485},[1487,53133,53134,53148],{},[1490,53135,53136,53138,53140,53146],{},[1493,53137,1501],{},[1506,53139,1508],{},[2315,53141,53142,53144],{},[1493,53143,1501],{},[1506,53145,2287],{},[1493,53147,2632],{"mathvariant":1516},[1528,53149,53150],{"encoding":1530},"P = P^*.",[52452,53152,53154],{"id":53153},"giffenův-statek","Giffenův statek",[1030,53156,53157,53158,53160,53161,53163,53164,2632],{},"Existují zboží, u nichž je křivka poptávky ",[1047,53159,3482],{}," — tzv. ",[1047,53162,53154],{},". Jde o případy, kdy důchodový efekt převáží substituční (klasický příklad: rýže u chudých asijských spotřebitelů). Giffenův statek patří k ",[1047,53165,53166],{},"podřadnému zboží",[52958,53168,53170],{"id":53169},"příklad-22","Příklad 2.2",[1030,53172,53173,53176,53177,53195,53196,53218,53219,53237,53238,53256,53257,53280],{},[1047,53174,53175],{},"Zadání a popis:"," Křivka ",[1035,53178,53180],{"className":53179},[1480],[1482,53181,53182],{"xmlns":1484},[1487,53183,53184,53192],{},[1490,53185,53186],{},[1497,53187,53188,53190],{},[1493,53189,3712],{},[1680,53191,1682],{},[1528,53193,53194],{"encoding":1530},"D_1"," reprezentuje poptávku rodiny po cukru s reálným cenovým rozpětím ",[1035,53197,53199],{"className":53198},[1480],[1482,53200,53201],{"xmlns":1484},[1487,53202,53203,53215],{},[1490,53204,53205,53207,53209,53211,53213],{},[1506,53206,1553],{"stretchy":1552},[1680,53208,1871],{},[1506,53210,1559],{"separator":1041},[1680,53212,9787],{},[1506,53214,1564],{"stretchy":1552},[1528,53216,53217],{"encoding":1530},"(0, 15)"," pencí za libru; je nejprve konvexní, od inflexního bodu ",[1035,53220,53222],{"className":53221},[1480],[1482,53223,53224],{"xmlns":1484},[1487,53225,53226,53234],{},[1490,53227,53228],{},[1497,53229,53230,53232],{},[1493,53231,1520],{},[1680,53233,1871],{},[1528,53235,53236],{"encoding":1530},"Q_0"," konkávní, se saturací kolem 17 liber. Křivka ",[1035,53239,53241],{"className":53240},[1480],[1482,53242,53243],{"xmlns":1484},[1487,53244,53245,53253],{},[1490,53246,53247],{},[1497,53248,53249,53251],{},[1493,53250,3712],{},[1680,53252,1691],{},[1528,53254,53255],{"encoding":1530},"D_2"," na širším trhu je konvexní klesající z bodu ",[1035,53258,53260],{"className":53259},[1480],[1482,53261,53262],{"xmlns":1484},[1487,53263,53264,53277],{},[1490,53265,53266,53268,53270,53272,53275],{},[1506,53267,14314],{"stretchy":1552},[1680,53269,1871],{},[1506,53271,1559],{"separator":1041},[1680,53273,53274],{},"21",[1506,53276,14323],{"stretchy":1552},[1528,53278,53279],{"encoding":1530},"[0, 21]"," centů.",[1304,53282,53284],{"id":53283},"engelova-funkce-závislost-na-důchodu","Engelova funkce (závislost na důchodu)",[1030,53286,53287,53288,1274],{},"Druhý jednofaktorový model předpokládá závislost množství pouze na důchodu ",[1035,53289,53291],{"className":53290},[1480],[1482,53292,53293],{"xmlns":1484},[1487,53294,53295,53299],{},[1490,53296,53297],{},[1493,53298,1791],{},[1528,53300,1791],{"encoding":1530},[1035,53302,53304],{"className":53303},[1480],[1482,53305,53306],{"xmlns":1484,"display":1485},[1487,53307,53308,53339],{},[19617,53309,53310],{"width":19619},[19621,53311,53312,53314,53332,53334],{},[19624,53313],{"width":19626},[19624,53315,53316],{},[1490,53317,53318,53320,53322,53324,53326,53328,53330],{},[1493,53319,1520],{},[1506,53321,1508],{},[1493,53323,2711],{},[1506,53325,1553],{"stretchy":1552},[1493,53327,1791],{},[1506,53329,1564],{"stretchy":1552},[1493,53331,2632],{"mathvariant":1516},[19624,53333],{"width":19626},[19624,53335,53336],{},[1988,53337,53338],{},"(2.5)",[1528,53340,53341],{"encoding":1530},"Q = E(Y). \\tag{2.5}",[1030,53343,53344,53345,53348,53349,53352],{},"Funkce se nazývá ",[1047,53346,53347],{},"Engelova",", její graf ",[1047,53350,53351],{},"Engelova křivka",". Tvar závisí na typu zboží:",[1203,53354,53355,53487],{},[1206,53356,53357,22970,53360,53373,53374,53387,53388,53405,53406],{},[1047,53358,53359],{},"Normální (superior) zboží",[1035,53361,53363],{"className":53362},[1480],[1482,53364,53365],{"xmlns":1484},[1487,53366,53367,53371],{},[1490,53368,53369],{},[1493,53370,1520],{},[1528,53372,1520],{"encoding":1530}," roste s ",[1035,53375,53377],{"className":53376},[1480],[1482,53378,53379],{"xmlns":1484},[1487,53380,53381,53385],{},[1490,53382,53383],{},[1493,53384,1791],{},[1528,53386,1791],{"encoding":1530},", nepřesáhne hodnotu ",[1035,53389,53391],{"className":53390},[1480],[1482,53392,53393],{"xmlns":1484},[1487,53394,53395,53403],{},[1490,53396,53397],{},[1497,53398,53399,53401],{},[1493,53400,1520],{},[1680,53402,1871],{},[1528,53404,53236],{"encoding":1530},":\n",[1203,53407,53408,53440],{},[1206,53409,53410,53413,53414,53417,53418,2632],{},[1047,53411,53412],{},"Nezbytné zboží"," (potraviny, léky) — malá citlivost, ",[1047,53415,53416],{},"konkávní"," křivka, autonomní spotřeba ",[1035,53419,53421],{"className":53420},[1480],[1482,53422,53423],{"xmlns":1484},[1487,53424,53425,53437],{},[1490,53426,53427,53433,53435],{},[1497,53428,53429,53431],{},[1493,53430,1520],{},[1680,53432,1682],{},[1506,53434,2796],{},[1680,53436,1871],{},[1528,53438,53439],{"encoding":1530},"Q_1 > 0",[1206,53441,53442,53445,53446,53464,53465,53467,53468,1656,53485,2632],{},[1047,53443,53444],{},"Luxusní zboží"," — velká citlivost až od hladiny ",[1035,53447,53449],{"className":53448},[1480],[1482,53450,53451],{"xmlns":1484},[1487,53452,53453,53461],{},[1490,53454,53455],{},[1497,53456,53457,53459],{},[1493,53458,1791],{},[1680,53460,1682],{},[1528,53462,53463],{"encoding":1530},"Y_1",", křivka je nejprve ",[1047,53466,52775],{}," a od ",[1035,53469,53471],{"className":53470},[1480],[1482,53472,53473],{"xmlns":1484},[1487,53474,53475,53483],{},[1490,53476,53477],{},[1497,53478,53479,53481],{},[1493,53480,1791],{},[1680,53482,1682],{},[1528,53484,53463],{"encoding":1530},[1047,53486,53416],{},[1206,53488,53489,53492,53493,53511],{},[1047,53490,53491],{},"Podřadné (inferior) zboží"," — od hladiny ",[1035,53494,53496],{"className":53495},[1480],[1482,53497,53498],{"xmlns":1484},[1487,53499,53500,53508],{},[1490,53501,53502],{},[1497,53503,53504,53506],{},[1493,53505,1791],{},[1680,53507,1871],{},[1528,53509,53510],{"encoding":1530},"Y_0"," množství s růstem důchodu klesá.",[1030,53513,53514,53515,53518,53519,16623],{},"Mírou citlivosti je ",[1176,53516,53517],{},"důchodová elasticita"," (viz ",[1052,53520,79],{"className":53521,"dataFsResolvedFilePath":3807,"href":3808},[1055],[52452,53523,53525],{"id":53524},"intuice-co-vlastně-znamená-podřadné","Intuice — co vlastně znamená „podřadné\"?",[1023,53527,53529,53536,53604,53647],{"className":53528,"dataCallout":1155},[1026,1154],[1030,53530,53532,53535],{"className":53531},[1033],[1035,53533],{"className":53534,"ariaHidden":1041},[1038,1162,1040],"Pozor — nezbytné ≠ podřadné",[1030,53537,53538,1656,53541,1656,53554,21432,53556,53569,53570,53573,53574,2632],{},[1047,53539,53540],{},"Nezbytné zboží:",[1035,53542,53544],{"className":53543},[1480],[1482,53545,53546],{"xmlns":1484},[1487,53547,53548,53552],{},[1490,53549,53550],{},[1493,53551,1520],{},[1528,53553,1520],{"encoding":1530},[1047,53555,7685],{},[1035,53557,53559],{"className":53558},[1480],[1482,53560,53561],{"xmlns":1484},[1487,53562,53563,53567],{},[1490,53564,53565],{},[1493,53566,1791],{},[1528,53568,1791],{"encoding":1530},", ale ",[1047,53571,53572],{},"pomaleji"," než důchod (2× plat → třeba 1,3× spotřeba). ",[1035,53575,53577],{"className":53576},[1480],[1482,53578,53579],{"xmlns":1484},[1487,53580,53581,53601],{},[1490,53582,53583,53589,53591,53593,53595,53597,53599],{},[1497,53584,53585,53587],{},[1493,53586,2711],{},[1493,53588,1791],{},[1506,53590,22378],{},[1506,53592,1553],{"stretchy":1552},[1680,53594,1871],{},[1506,53596,1559],{"separator":1041},[1680,53598,1682],{},[1506,53600,1564],{"stretchy":1552},[1528,53602,53603],{"encoding":1530},"E_Y \\in (0, 1)",[1030,53605,53606,1656,53609,1656,53622,53624,53625,2632],{},[1047,53607,53608],{},"Podřadné zboží:",[1035,53610,53612],{"className":53611},[1480],[1482,53613,53614],{"xmlns":1484},[1487,53615,53616,53620],{},[1490,53617,53618],{},[1493,53619,1520],{},[1528,53621,1520],{"encoding":1530},[1047,53623,23295],{}," v absolutních číslech (2× plat → třeba 0,7× spotřeba). ",[1035,53626,53628],{"className":53627},[1480],[1482,53629,53630],{"xmlns":1484},[1487,53631,53632,53644],{},[1490,53633,53634,53640,53642],{},[1497,53635,53636,53638],{},[1493,53637,2711],{},[1493,53639,1791],{},[1506,53641,3961],{},[1680,53643,1871],{},[1528,53645,53646],{"encoding":1530},"E_Y \u003C 0",[1030,53648,53649,53650,2632],{},"Klíčový rozdíl: u podřadného zboží si při vyšším důchodu kupuješ ",[1047,53651,53652],{},"méně kusů, ne jen proporčně méně",[1030,53654,53655,53658,53659,53662],{},[1047,53656,53657],{},"Mechanismus — substituce „nahoru\"."," Samotné zboží se nezhoršilo, jen si teď můžeš dovolit ",[1047,53660,53661],{},"kvalitnější alternativu",". Růst důchodu → přesun k prémiovému substitutu → absolutní pokles nákupu „levnější verze\".",[1030,53664,53665],{},[18014,53666],{"alt":53667,"className":53668,"src":53669},"imek-engelovy-krivky-3typy",[1055,18018],"\u002Fwiki-assets\u002Fimek-engelovy-krivky-3typy.jpeg",[52958,53671,53673],{"id":53672},"české-příklady","České příklady",[1073,53675,53676,53686],{},[1076,53677,53678],{},[1079,53679,53680,53683],{},[1082,53681,53682],{},"Podřadné",[1082,53684,53685],{},"Nahradí se za",[1092,53687,53688,53696,53704,53712,53720,53728,53736,53744],{},[1079,53689,53690,53693],{},[1097,53691,53692],{},"Instantní polévky, ramen",[1097,53694,53695],{},"Čerstvé jídlo, restaurace",[1079,53697,53698,53701],{},[1097,53699,53700],{},"MHD (autobus, tramvaj)",[1097,53702,53703],{},"Vlastní auto, Uber, taxi",[1079,53705,53706,53709],{},[1097,53707,53708],{},"Mražené polotovary, pizza z mrazáku",[1097,53710,53711],{},"Čerstvé suroviny, hotovky",[1079,53713,53714,53717],{},[1097,53715,53716],{},"Privátní značky supermarketů (K-Classic, Clever)",[1097,53718,53719],{},"Značkové produkty",[1079,53721,53722,53725],{},[1097,53723,53724],{},"Paštika Májka, obyčejný měkký salám",[1097,53726,53727],{},"Kvalitní uzeniny, šunka od kosti",[1079,53729,53730,53733],{},[1097,53731,53732],{},"Second hand oblečení",[1097,53734,53735],{},"Nové oblečení, značky",[1079,53737,53738,53741],{},[1097,53739,53740],{},"Krabicové víno, nejlevnější pivo",[1097,53742,53743],{},"Lahvové víno, řemeslná piva",[1079,53745,53746,53749],{},[1097,53747,53748],{},"Ojetá auta nižších tříd",[1097,53750,53751],{},"Nová auta, prémiové značky",[1023,53753,53755,53762],{"className":53754,"dataCallout":1443},[1026,1442],[1030,53756,53758,53761],{"className":53757},[1033],[1035,53759],{"className":53760,"ariaHidden":1041},[1038,1450,1040],"Test 50 milionů",[1030,53763,53764,53765,53768],{},"Představ si, že vyhraješ 50 milionů. ",[1047,53766,53767],{},"Čeho si najednou koupíš méně"," (nebo vůbec)? To je tvoje podřadné zboží.",[1030,53770,53771,53774,53775,7606,53778,53799,53800,7606,53803,53824,53825,53843,53844,53847],{},[1047,53772,53773],{},"Pozor — podřadné je relativní k osobě."," Stejný produkt může být pro různé lidi v různých kategoriích. McDonald's je pro studenta s 15k platem možná ",[1047,53776,53777],{},"luxus",[1035,53779,53781],{"className":53780},[1480],[1482,53782,53783],{"xmlns":1484},[1487,53784,53785,53797],{},[1490,53786,53787,53793,53795],{},[1497,53788,53789,53791],{},[1493,53790,2711],{},[1493,53792,1791],{},[1506,53794,2796],{},[1680,53796,1682],{},[1528,53798,15819],{"encoding":1530},"), pro manažera s 200k platem ",[1047,53801,53802],{},"podřadné",[1035,53804,53806],{"className":53805},[1480],[1482,53807,53808],{"xmlns":1484},[1487,53809,53810,53822],{},[1490,53811,53812,53818,53820],{},[1497,53813,53814,53816],{},[1493,53815,2711],{},[1493,53817,1791],{},[1506,53819,3961],{},[1680,53821,1871],{},[1528,53823,53646],{"encoding":1530},"). Proto je ",[1035,53826,53828],{"className":53827},[1480],[1482,53829,53830],{"xmlns":1484},[1487,53831,53832,53840],{},[1490,53833,53834],{},[1497,53835,53836,53838],{},[1493,53837,2711],{},[1493,53839,1791],{},[1528,53841,53842],{"encoding":1530},"E_Y"," vždy ",[1047,53845,53846],{},"lokální veličina"," — platí pro danou úroveň důchodu, ne absolutně.",[1030,53849,53850,53851,53853],{},"Extrémním případem podřadného zboží, kde substituční efekt převáží už na straně ceny, je ",[1047,53852,53154],{}," (viz níže) — tam poptávková křivka dokonce roste.",[1304,53855,53857,53858,1564],{"id":53856},"posun-poptávky-shift-of-demand","Posun poptávky (",[1176,53859,53860],{},"shift of demand",[1030,53862,53863,53864,53882,53883,53900,53901,53914,53915,18139,53928,53950,53951,53968,53969,53995,53996,53999],{},"Při změně exogenní proměnné (např. důchodu) se celá křivka poptávky posouvá. Uvažujme normální zboží. Ceně ",[1035,53865,53867],{"className":53866},[1480],[1482,53868,53869],{"xmlns":1484},[1487,53870,53871,53879],{},[1490,53872,53873],{},[1497,53874,53875,53877],{},[1493,53876,1501],{},[1680,53878,1871],{},[1528,53880,53881],{"encoding":1530},"P_0"," odpovídá množství ",[1035,53884,53886],{"className":53885},[1480],[1482,53887,53888],{"xmlns":1484},[1487,53889,53890,53898],{},[1490,53891,53892],{},[1497,53893,53894,53896],{},[1493,53895,1520],{},[1680,53897,1871],{},[1528,53899,53236],{"encoding":1530}," na křivce ",[1035,53902,53904],{"className":53903},[1480],[1482,53905,53906],{"xmlns":1484},[1487,53907,53908,53912],{},[1490,53909,53910],{},[1493,53911,3712],{},[1528,53913,3712],{"encoding":1530},"; vzroste-li důchod z ",[1035,53916,53918],{"className":53917},[1480],[1482,53919,53920],{"xmlns":1484},[1487,53921,53922,53926],{},[1490,53923,53924],{},[1493,53925,1791],{},[1528,53927,1791],{"encoding":1530},[1035,53929,53931],{"className":53930},[1480],[1482,53932,53933],{"xmlns":1484},[1487,53934,53935,53947],{},[1490,53936,53937,53943,53945],{},[1497,53938,53939,53941],{},[1493,53940,1791],{},[1680,53942,1682],{},[1506,53944,2796],{},[1493,53946,1791],{},[1528,53948,53949],{"encoding":1530},"Y_1 > Y",", pak stejné ceně ",[1035,53952,53954],{"className":53953},[1480],[1482,53955,53956],{"xmlns":1484},[1487,53957,53958,53966],{},[1490,53959,53960],{},[1497,53961,53962,53964],{},[1493,53963,1501],{},[1680,53965,1871],{},[1528,53967,53881],{"encoding":1530}," odpovídá vyšší ",[1035,53970,53972],{"className":53971},[1480],[1482,53973,53974],{"xmlns":1484},[1487,53975,53976,53992],{},[1490,53977,53978,53984,53986],{},[1497,53979,53980,53982],{},[1493,53981,1520],{},[1680,53983,1682],{},[1506,53985,2796],{},[1497,53987,53988,53990],{},[1493,53989,1520],{},[1680,53991,1871],{},[1528,53993,53994],{"encoding":1530},"Q_1 > Q_0"," — křivka se ",[1047,53997,53998],{},"posouvá doprava",". Pokles důchodu vede k posunu doleva.",[1030,54001,54002],{},[18014,54003],{"alt":54004,"className":54005,"src":54006},"imek-posun-vs-pohyb-po-krivce",[1055,18018],"\u002Fwiki-assets\u002Fimek-posun-vs-pohyb-po-krivce.jpeg",[1030,54008,54009],{},"Posun může být způsoben i jinými faktory (např. zdaněním spotřebitele — viz dále).",[52958,54011,54013],{"id":54012},"příklad-23-zdanění-kupujícího","Příklad 2.3 — zdanění kupujícího",[1030,54015,54016,54018,54019,54042,54043,54060,54061,54078,54079,2632],{},[1047,54017,1263],{}," Poptávce ",[1035,54020,54022],{"className":54021},[1480],[1482,54023,54024],{"xmlns":1484},[1487,54025,54026,54040],{},[1490,54027,54028,54030,54032,54034,54036,54038],{},[1493,54029,1501],{},[1506,54031,1508],{},[1493,54033,3712],{},[1506,54035,1553],{"stretchy":1552},[1493,54037,1520],{},[1506,54039,1564],{"stretchy":1552},[1528,54041,20356],{"encoding":1530}," odpovídá ceně ",[1035,54044,54046],{"className":54045},[1480],[1482,54047,54048],{"xmlns":1484},[1487,54049,54050,54058],{},[1490,54051,54052],{},[1497,54053,54054,54056],{},[1493,54055,1501],{},[1680,54057,1871],{},[1528,54059,53881],{"encoding":1530}," množství ",[1035,54062,54064],{"className":54063},[1480],[1482,54065,54066],{"xmlns":1484},[1487,54067,54068,54076],{},[1490,54069,54070],{},[1497,54071,54072,54074],{},[1493,54073,1520],{},[1680,54075,1871],{},[1528,54077,53236],{"encoding":1530},". Na kupujícího je uložena jednotková daň ",[1035,54080,54082],{"className":54081},[1480],[1482,54083,54084],{"xmlns":1484},[1487,54085,54086,54090],{},[1490,54087,54088],{},[1493,54089,5289],{},[1528,54091,5289],{"encoding":1530},[1030,54093,54094,54096,54097,54114,54115,54137],{},[1047,54095,52997],{}," Kupující nakupuje množství ",[1035,54098,54100],{"className":54099},[1480],[1482,54101,54102],{"xmlns":1484},[1487,54103,54104,54112],{},[1490,54105,54106],{},[1497,54107,54108,54110],{},[1493,54109,1520],{},[1680,54111,1682],{},[1528,54113,6702],{"encoding":1530},", které odpovídá ceně ",[1035,54116,54118],{"className":54117},[1480],[1482,54119,54120],{"xmlns":1484},[1487,54121,54122,54134],{},[1490,54123,54124,54130,54132],{},[1497,54125,54126,54128],{},[1493,54127,1501],{},[1680,54129,1871],{},[1506,54131,2162],{},[1493,54133,5289],{},[1528,54135,54136],{"encoding":1530},"P_0 + T"," na původní křivce. Nová poptávka je",[1035,54139,54141],{"className":54140},[1480],[1482,54142,54143],{"xmlns":1484,"display":1485},[1487,54144,54145,54179],{},[1490,54146,54147,54149,54151,54157,54159,54161,54163,54165,54167,54169,54171,54173,54175,54177],{},[1493,54148,1501],{},[1506,54150,1508],{},[1497,54152,54153,54155],{},[1493,54154,3712],{},[1680,54156,1682],{},[1506,54158,1553],{"stretchy":1552},[1493,54160,1520],{},[1506,54162,1564],{"stretchy":1552},[1506,54164,1508],{},[1493,54166,3712],{},[1506,54168,1553],{"stretchy":1552},[1493,54170,1520],{},[1506,54172,1564],{"stretchy":1552},[1506,54174,1888],{},[1493,54176,5289],{},[1506,54178,1559],{"separator":1041},[1528,54180,54181],{"encoding":1530},"P = D_1(Q) = D(Q) - T,",[1030,54183,54184,54185,2632],{},"tj. dojde k ",[1047,54186,54187],{},"posunu poptávky doleva",[1304,54189,54191],{"id":54190},"vícekomoditní-dvoukomoditní-trh","Vícekomoditní (dvoukomoditní) trh",[1030,54193,54194],{},"Uvažujme dvě tržně závislá zboží s lineárními funkcemi poptávky:",[1035,54196,54198],{"className":54197},[1480],[1482,54199,54200],{"xmlns":1484,"display":1485},[1487,54201,54202,54387],{},[19617,54203,54204],{"width":19619},[19621,54205,54206,54208,54380,54382],{},[19624,54207],{"width":19626},[19624,54209,54210],{},[19617,54211,54212,54296],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,54213,54214,54224],{},[19624,54215,54216],{},[1869,54217,54218],{"scriptlevel":1871,"displaystyle":1041},[1497,54219,54220,54222],{},[1493,54221,1520],{},[1680,54223,1682],{},[19624,54225,54226],{},[1869,54227,54228],{"scriptlevel":1871,"displaystyle":1041},[1490,54229,54230,54232,54234,54240,54242,54248,54250,54256,54258,54260,54266,54268,54274,54280,54282,54288,54294],{},[1490,54231],{},[1506,54233,1508],{},[1497,54235,54236,54238],{},[1493,54237,3712],{},[1680,54239,1682],{},[1506,54241,1553],{"stretchy":1552},[1497,54243,54244,54246],{},[1493,54245,1501],{},[1680,54247,1682],{},[1506,54249,1559],{"separator":1041},[1497,54251,54252,54254],{},[1493,54253,1501],{},[1680,54255,1691],{},[1506,54257,1564],{"stretchy":1552},[1506,54259,1508],{},[1497,54261,54262,54264],{},[1493,54263,1052],{},[1680,54265,1682],{},[1506,54267,2162],{},[1497,54269,54270,54272],{},[1493,54271,2394],{},[1680,54273,1682],{},[1497,54275,54276,54278],{},[1493,54277,1501],{},[1680,54279,1682],{},[1506,54281,2162],{},[1497,54283,54284,54286],{},[1493,54285,8730],{},[1680,54287,1682],{},[1497,54289,54290,54292],{},[1493,54291,1501],{},[1680,54293,1691],{},[1506,54295,1559],{"separator":1041},[19621,54297,54298,54308],{},[19624,54299,54300],{},[1869,54301,54302],{"scriptlevel":1871,"displaystyle":1041},[1497,54303,54304,54306],{},[1493,54305,1520],{},[1680,54307,1691],{},[19624,54309,54310],{},[1869,54311,54312],{"scriptlevel":1871,"displaystyle":1041},[1490,54313,54314,54316,54318,54324,54326,54332,54334,54340,54342,54344,54350,54352,54358,54364,54366,54372,54378],{},[1490,54315],{},[1506,54317,1508],{},[1497,54319,54320,54322],{},[1493,54321,3712],{},[1680,54323,1691],{},[1506,54325,1553],{"stretchy":1552},[1497,54327,54328,54330],{},[1493,54329,1501],{},[1680,54331,1682],{},[1506,54333,1559],{"separator":1041},[1497,54335,54336,54338],{},[1493,54337,1501],{},[1680,54339,1691],{},[1506,54341,1564],{"stretchy":1552},[1506,54343,1508],{},[1497,54345,54346,54348],{},[1493,54347,1052],{},[1680,54349,1691],{},[1506,54351,2162],{},[1497,54353,54354,54356],{},[1493,54355,2394],{},[1680,54357,1691],{},[1497,54359,54360,54362],{},[1493,54361,1501],{},[1680,54363,1682],{},[1506,54365,2162],{},[1497,54367,54368,54370],{},[1493,54369,8730],{},[1680,54371,1691],{},[1497,54373,54374,54376],{},[1493,54375,1501],{},[1680,54377,1691],{},[1493,54379,2632],{"mathvariant":1516},[19624,54381],{"width":19626},[19624,54383,54384],{},[1988,54385,54386],{},"(2.6)",[1528,54388,54389],{"encoding":1530},"\\begin{aligned}\nQ_1 &= D_1(P_1, P_2) = a_1 + b_1 P_1 + c_1 P_2, \\\\\nQ_2 &= D_2(P_1, P_2) = a_2 + b_2 P_1 + c_2 P_2.\n\\end{aligned}\n\\tag{2.6}",[52452,54391,54393],{"id":54392},"znaménková-analýza-parametrů","Znaménková analýza parametrů",[1203,54395,54396,54443,54490],{},[1206,54397,54398,1732,54420,54442],{},[1035,54399,54401],{"className":54400},[1480],[1482,54402,54403],{"xmlns":1484},[1487,54404,54405,54417],{},[1490,54406,54407,54413,54415],{},[1497,54408,54409,54411],{},[1493,54410,1052],{},[1680,54412,1682],{},[1506,54414,2796],{},[1680,54416,1871],{},[1528,54418,54419],{"encoding":1530},"a_1 > 0",[1035,54421,54423],{"className":54422},[1480],[1482,54424,54425],{"xmlns":1484},[1487,54426,54427,54439],{},[1490,54428,54429,54435,54437],{},[1497,54430,54431,54433],{},[1493,54432,1052],{},[1680,54434,1691],{},[1506,54436,2796],{},[1680,54438,1871],{},[1528,54440,54441],{"encoding":1530},"a_2 > 0"," (při nulových cenách je poptávané množství kladné),",[1206,54444,54445,1732,54467,54489],{},[1035,54446,54448],{"className":54447},[1480],[1482,54449,54450],{"xmlns":1484},[1487,54451,54452,54464],{},[1490,54453,54454,54460,54462],{},[1497,54455,54456,54458],{},[1493,54457,2394],{},[1680,54459,1682],{},[1506,54461,3961],{},[1680,54463,1871],{},[1528,54465,54466],{"encoding":1530},"b_1 \u003C 0",[1035,54468,54470],{"className":54469},[1480],[1482,54471,54472],{"xmlns":1484},[1487,54473,54474,54486],{},[1490,54475,54476,54482,54484],{},[1497,54477,54478,54480],{},[1493,54479,8730],{},[1680,54481,1691],{},[1506,54483,3961],{},[1680,54485,1871],{},[1528,54487,54488],{"encoding":1530},"c_2 \u003C 0"," (vlastní koeficienty — zákon klesající poptávky),",[1206,54491,54492,54493,1732,54511,54529,54530],{},"zkřížené koeficienty ",[1035,54494,54496],{"className":54495},[1480],[1482,54497,54498],{"xmlns":1484},[1487,54499,54500,54508],{},[1490,54501,54502],{},[1497,54503,54504,54506],{},[1493,54505,8730],{},[1680,54507,1682],{},[1528,54509,54510],{"encoding":1530},"c_1",[1035,54512,54514],{"className":54513},[1480],[1482,54515,54516],{"xmlns":1484},[1487,54517,54518,54526],{},[1490,54519,54520],{},[1497,54521,54522,54524],{},[1493,54523,2394],{},[1680,54525,1691],{},[1528,54527,54528],{"encoding":1530},"b_2"," určují povahu vztahu:\n",[1203,54531,54532,54581],{},[1206,54533,54534,54536,54537,1732,54559,1559],{},[1047,54535,3899],{}," (máslo vs. margarín): ",[1035,54538,54540],{"className":54539},[1480],[1482,54541,54542],{"xmlns":1484},[1487,54543,54544,54556],{},[1490,54545,54546,54552,54554],{},[1497,54547,54548,54550],{},[1493,54549,8730],{},[1680,54551,1682],{},[1506,54553,2796],{},[1680,54555,1871],{},[1528,54557,54558],{"encoding":1530},"c_1 > 0",[1035,54560,54562],{"className":54561},[1480],[1482,54563,54564],{"xmlns":1484},[1487,54565,54566,54578],{},[1490,54567,54568,54574,54576],{},[1497,54569,54570,54572],{},[1493,54571,2394],{},[1680,54573,1691],{},[1506,54575,2796],{},[1680,54577,1871],{},[1528,54579,54580],{"encoding":1530},"b_2 > 0",[1206,54582,54583,54585,54586,1732,54608,2632],{},[1047,54584,8866],{}," (auto vs. benzín): ",[1035,54587,54589],{"className":54588},[1480],[1482,54590,54591],{"xmlns":1484},[1487,54592,54593,54605],{},[1490,54594,54595,54601,54603],{},[1497,54596,54597,54599],{},[1493,54598,8730],{},[1680,54600,1682],{},[1506,54602,3961],{},[1680,54604,1871],{},[1528,54606,54607],{"encoding":1530},"c_1 \u003C 0",[1035,54609,54611],{"className":54610},[1480],[1482,54612,54613],{"xmlns":1484},[1487,54614,54615,54627],{},[1490,54616,54617,54623,54625],{},[1497,54618,54619,54621],{},[1493,54620,2394],{},[1680,54622,1691],{},[1506,54624,3961],{},[1680,54626,1871],{},[1528,54628,54629],{"encoding":1530},"b_2 \u003C 0",[1030,54631,54632],{},"Schematicky:",[1030,54634,54635],{},[1047,54636,54637],{},"Substituty",[1035,54639,54641],{"className":54640},[1480],[1482,54642,54643],{"xmlns":1484,"display":1485},[1487,54644,54645,54783],{},[1490,54646,54647,54653,54655,54669,54671,54691,54693,54713,54715,54717,54723,54725,54739,54741,54761,54763],{},[1497,54648,54649,54651],{},[1493,54650,1520],{},[1680,54652,1682],{},[1506,54654,1508],{},[1493,54656,54657],{},[3151,54658,54659,54667],{},[1506,54660,54661],{},[1497,54662,54663,54665],{},[1493,54664,1052],{},[1680,54666,1682],{},[1506,54668,2162],{"lspace":6926,"rspace":6926},[1506,54670,2162],{},[1493,54672,54673],{},[3151,54674,54675,54689],{},[1506,54676,54677,54683],{},[1497,54678,54679,54681],{},[1493,54680,2394],{},[1680,54682,1682],{},[1497,54684,54685,54687],{},[1493,54686,1501],{},[1680,54688,1682],{},[1506,54690,1888],{"lspace":6926,"rspace":6926},[1506,54692,2162],{},[1493,54694,54695],{},[3151,54696,54697,54711],{},[1506,54698,54699,54705],{},[1497,54700,54701,54703],{},[1493,54702,8730],{},[1680,54704,1682],{},[1497,54706,54707,54709],{},[1493,54708,1501],{},[1680,54710,1691],{},[1506,54712,2162],{"lspace":6926,"rspace":6926},[1506,54714,1559],{"separator":1041},[1912,54716],{"width":1914},[1497,54718,54719,54721],{},[1493,54720,1520],{},[1680,54722,1691],{},[1506,54724,1508],{},[1493,54726,54727],{},[3151,54728,54729,54737],{},[1506,54730,54731],{},[1497,54732,54733,54735],{},[1493,54734,1052],{},[1680,54736,1691],{},[1506,54738,2162],{"lspace":6926,"rspace":6926},[1506,54740,2162],{},[1493,54742,54743],{},[3151,54744,54745,54759],{},[1506,54746,54747,54753],{},[1497,54748,54749,54751],{},[1493,54750,2394],{},[1680,54752,1691],{},[1497,54754,54755,54757],{},[1493,54756,1501],{},[1680,54758,1682],{},[1506,54760,2162],{"lspace":6926,"rspace":6926},[1506,54762,2162],{},[1493,54764,54765],{},[3151,54766,54767,54781],{},[1506,54768,54769,54775],{},[1497,54770,54771,54773],{},[1493,54772,8730],{},[1680,54774,1691],{},[1497,54776,54777,54779],{},[1493,54778,1501],{},[1680,54780,1691],{},[1506,54782,1888],{"lspace":6926,"rspace":6926},[1528,54784,54785],{"encoding":1530},"Q_1 = \\underset{+}{a_1} + \\underset{-}{b_1 P_1} + \\underset{+}{c_1 P_2}, \\qquad Q_2 = \\underset{+}{a_2} + \\underset{+}{b_2 P_1} + \\underset{-}{c_2 P_2}",[1030,54787,54788],{},[1047,54789,54790],{},"Komplementy",[1035,54792,54794],{"className":54793},[1480],[1482,54795,54796],{"xmlns":1484,"display":1485},[1487,54797,54798,54936],{},[1490,54799,54800,54806,54808,54822,54824,54844,54846,54866,54868,54870,54876,54878,54892,54894,54914,54916],{},[1497,54801,54802,54804],{},[1493,54803,1520],{},[1680,54805,1682],{},[1506,54807,1508],{},[1493,54809,54810],{},[3151,54811,54812,54820],{},[1506,54813,54814],{},[1497,54815,54816,54818],{},[1493,54817,1052],{},[1680,54819,1682],{},[1506,54821,2162],{"lspace":6926,"rspace":6926},[1506,54823,2162],{},[1493,54825,54826],{},[3151,54827,54828,54842],{},[1506,54829,54830,54836],{},[1497,54831,54832,54834],{},[1493,54833,2394],{},[1680,54835,1682],{},[1497,54837,54838,54840],{},[1493,54839,1501],{},[1680,54841,1682],{},[1506,54843,1888],{"lspace":6926,"rspace":6926},[1506,54845,2162],{},[1493,54847,54848],{},[3151,54849,54850,54864],{},[1506,54851,54852,54858],{},[1497,54853,54854,54856],{},[1493,54855,8730],{},[1680,54857,1682],{},[1497,54859,54860,54862],{},[1493,54861,1501],{},[1680,54863,1691],{},[1506,54865,1888],{"lspace":6926,"rspace":6926},[1506,54867,1559],{"separator":1041},[1912,54869],{"width":1914},[1497,54871,54872,54874],{},[1493,54873,1520],{},[1680,54875,1691],{},[1506,54877,1508],{},[1493,54879,54880],{},[3151,54881,54882,54890],{},[1506,54883,54884],{},[1497,54885,54886,54888],{},[1493,54887,1052],{},[1680,54889,1691],{},[1506,54891,2162],{"lspace":6926,"rspace":6926},[1506,54893,2162],{},[1493,54895,54896],{},[3151,54897,54898,54912],{},[1506,54899,54900,54906],{},[1497,54901,54902,54904],{},[1493,54903,2394],{},[1680,54905,1691],{},[1497,54907,54908,54910],{},[1493,54909,1501],{},[1680,54911,1682],{},[1506,54913,1888],{"lspace":6926,"rspace":6926},[1506,54915,2162],{},[1493,54917,54918],{},[3151,54919,54920,54934],{},[1506,54921,54922,54928],{},[1497,54923,54924,54926],{},[1493,54925,8730],{},[1680,54927,1691],{},[1497,54929,54930,54932],{},[1493,54931,1501],{},[1680,54933,1691],{},[1506,54935,1888],{"lspace":6926,"rspace":6926},[1528,54937,54938],{"encoding":1530},"Q_1 = \\underset{+}{a_1} + \\underset{-}{b_1 P_1} + \\underset{-}{c_1 P_2}, \\qquad Q_2 = \\underset{+}{a_2} + \\underset{-}{b_2 P_1} + \\underset{-}{c_2 P_2}",[1246,54940],{},[1065,54942,29604],{"id":16507},[1023,54944,54946,54952],{"className":54945,"dataCallout":582},[1026,1186],[1030,54947,54949,1042],{"className":54948},[1033],[1035,54950],{"className":54951,"ariaHidden":1041},[1038,1193,1040],[1030,54953,54954,54955,52092,54968,52106,54981,54984,54985,21432,55009,55027],{},"Nabídka vyjadřuje závislost nabízeného množství ",[1035,54956,54958],{"className":54957},[1480],[1482,54959,54960],{"xmlns":1484},[1487,54961,54962,54966],{},[1490,54963,54964],{},[1493,54965,1520],{},[1528,54967,1520],{"encoding":1530},[1035,54969,54971],{"className":54970},[1480],[1482,54972,54973],{"xmlns":1484},[1487,54974,54975,54979],{},[1490,54976,54977],{},[1493,54978,1501],{},[1528,54980,1501],{"encoding":1530},[1047,54982,54983],{},"zákon rostoucí nabídky",": při vyšší ceně je výrobce ochoten nabídnout více. Lineární model ",[1035,54986,54988],{"className":54987},[1480],[1482,54989,54990],{"xmlns":1484},[1487,54991,54992,55006],{},[1490,54993,54994,54996,54998,55000,55002,55004],{},[1493,54995,1501],{},[1506,54997,1508],{},[1493,54999,8730],{},[1493,55001,1520],{},[1506,55003,2162],{},[1493,55005,3384],{},[1528,55007,55008],{"encoding":1530},"P = cQ + d",[1035,55010,55012],{"className":55011},[1480],[1482,55013,55014],{"xmlns":1484},[1487,55015,55016,55024],{},[1490,55017,55018,55020,55022],{},[1493,55019,8730],{},[1506,55021,2796],{},[1680,55023,1871],{},[1528,55025,55026],{"encoding":1530},"c > 0"," je standardní aproximací.",[1304,55029,52162],{"id":55030},"obecný-vícefaktorový-model-1",[1030,55032,55033,7606,55036,55039,55040,55053,55054,51991,55067,52005,55080,55093,55094,55108,55109,52034,55122,55135],{},[1047,55034,55035],{},"Nabízené množství",[1176,55037,55038],{},"quantity supplied",") závisí na ceně ",[1035,55041,55043],{"className":55042},[1480],[1482,55044,55045],{"xmlns":1484},[1487,55046,55047,55051],{},[1490,55048,55049],{},[1493,55050,1501],{},[1528,55052,1501],{"encoding":1530},", cenách výrobních faktorů (práce ",[1035,55055,55057],{"className":55056},[1480],[1482,55058,55059],{"xmlns":1484},[1487,55060,55061,55065],{},[1490,55062,55063],{},[1493,55064,1556],{},[1528,55066,1556],{"encoding":1530},[1035,55068,55070],{"className":55069},[1480],[1482,55071,55072],{"xmlns":1484},[1487,55073,55074,55078],{},[1490,55075,55076],{},[1493,55077,1504],{},[1528,55079,1504],{"encoding":1530},[1035,55081,55083],{"className":55082},[1480],[1482,55084,55085],{"xmlns":1484},[1487,55086,55087,55091],{},[1490,55088,55089],{},[1493,55090,2711],{},[1528,55092,2711],{"encoding":1530},"), očekávání ",[1035,55095,55097],{"className":55096},[1480],[1482,55098,55099],{"xmlns":1484},[1487,55100,55101,55106],{},[1490,55102,55103],{},[1493,55104,55105],{},"V",[1528,55107,55105],{"encoding":1530},", počtu výrobců ",[1035,55110,55112],{"className":55111},[1480],[1482,55113,55114],{"xmlns":1484},[1487,55115,55116,55120],{},[1490,55117,55118],{},[1493,55119,52031],{},[1528,55121,52031],{"encoding":1530},[1035,55123,55125],{"className":55124},[1480],[1482,55126,55127],{"xmlns":1484},[1487,55128,55129,55133],{},[1490,55130,55131],{},[1493,55132,15148],{},[1528,55134,15148],{"encoding":1530}," a dalších:",[1035,55137,55139],{"className":55138},[1480],[1482,55140,55141],{"xmlns":1484,"display":1485},[1487,55142,55143,55202],{},[19617,55144,55145],{"width":19619},[19621,55146,55147,55149,55195,55197],{},[19624,55148],{"width":19626},[19624,55150,55151],{},[1490,55152,55153,55155,55157,55159,55161,55163,55165,55167,55169,55171,55173,55175,55177,55179,55181,55183,55185,55187,55189,55191,55193],{},[1493,55154,1520],{},[1506,55156,1508],{},[1493,55158,2001],{},[1506,55160,1553],{"stretchy":1552},[1493,55162,1501],{},[1506,55164,1559],{"separator":1041},[1493,55166,1556],{},[1506,55168,1559],{"separator":1041},[1493,55170,1504],{},[1506,55172,1559],{"separator":1041},[1493,55174,2711],{},[1506,55176,1559],{"separator":1041},[1493,55178,55105],{},[1506,55180,1559],{"separator":1041},[1493,55182,52031],{},[1506,55184,1559],{"separator":1041},[1493,55186,15148],{},[1506,55188,1559],{"separator":1041},[1506,55190,26181],{},[1506,55192,1564],{"stretchy":1552},[1493,55194,2632],{"mathvariant":1516},[19624,55196],{"width":19626},[19624,55198,55199],{},[1988,55200,55201],{},"(2.7)",[1528,55203,55204],{"encoding":1530},"Q = S(P, L, K, E, V, O, W, \\ldots). \\tag{2.7}",[1030,55206,53344,55207,7606,55210,55213],{},[1047,55208,55209],{},"funkce nabídky",[1176,55211,55212],{},"supply function",") v širším slova smyslu.",[1304,55215,55217],{"id":55216},"jednofaktorový-model","Jednofaktorový model",[1030,55219,55220],{},"V nejpřirozenějším jednofaktorovém modelu",[1035,55222,55224],{"className":55223},[1480],[1482,55225,55226],{"xmlns":1484,"display":1485},[1487,55227,55228,55279],{},[19617,55229,55230],{"width":19619},[19621,55231,55232,55234,55272,55274],{},[19624,55233],{"width":19626},[19624,55235,55236],{},[1490,55237,55238,55240,55242,55244,55246,55248,55250,55252,55254,55256,55258,55260,55262,55264,55266,55268,55270],{},[1493,55239,1520],{},[1506,55241,1508],{},[1493,55243,2001],{},[1506,55245,1553],{"stretchy":1552},[1493,55247,1501],{},[1506,55249,1564],{"stretchy":1552},[1506,55251,1559],{"separator":1041},[1912,55253],{"width":1914},[1988,55255,52521],{},[1912,55257],{"width":1914},[1493,55259,1501],{},[1506,55261,1508],{},[1493,55263,2001],{},[1506,55265,1553],{"stretchy":1552},[1493,55267,1520],{},[1506,55269,1564],{"stretchy":1552},[1493,55271,2632],{"mathvariant":1516},[19624,55273],{"width":19626},[19624,55275,55276],{},[1988,55277,55278],{},"(2.8)",[1528,55280,55281],{"encoding":1530},"Q = S(P), \\qquad \\text{resp.} \\qquad P = S(Q). \\tag{2.8}",[1030,55283,55284,55285,7606,55288,16623],{},"Graf je ",[1047,55286,55287],{},"křivka nabídky",[1176,55289,55290],{},"supply curve",[52452,55292,55294],{"id":55293},"zákon-rostoucí-nabídky","Zákon rostoucí nabídky",[19516,55296,55297],{},[1030,55298,55299],{},[1047,55300,52567,55301,55314,55315,52622],{},[1035,55302,55304],{"className":55303},[1480],[1482,55305,55306],{"xmlns":1484},[1487,55307,55308,55312],{},[1490,55309,55310],{},[1493,55311,1501],{},[1528,55313,1501],{"encoding":1530},", pak nabízené množství ",[1035,55316,55318],{"className":55317},[1480],[1482,55319,55320],{"xmlns":1484},[1487,55321,55322,55326],{},[1490,55323,55324],{},[1493,55325,1520],{},[1528,55327,1520],{"encoding":1530},[1030,55329,55330,55331,55334,55335,55360,55361,55391,55392,55409],{},"Výrobce je ochoten zvýšit produkci jen za vyšší cenu, neboť rostou mezní náklady (viz ",[1052,55332,820],{"className":55333,"dataFsResolvedFilePath":1299,"href":1300},[1055],"). Funkce nabídky je proto rostoucí. Křivka nabídky vychází z bodu ",[1035,55336,55338],{"className":55337},[1480],[1482,55339,55340],{"xmlns":1484},[1487,55341,55342,55358],{},[1490,55343,55344,55346,55348,55350,55356],{},[1506,55345,14314],{"stretchy":1552},[1680,55347,1871],{},[1506,55349,1559],{"separator":1041},[1497,55351,55352,55354],{},[1493,55353,1501],{},[1680,55355,1871],{},[1506,55357,14323],{"stretchy":1552},[1528,55359,52714],{"encoding":1530}," na svislé ose (případně z ",[1035,55362,55364],{"className":55363},[1480],[1482,55365,55366],{"xmlns":1484},[1487,55367,55368,55388],{},[1490,55369,55370,55372,55378,55380,55386],{},[1506,55371,14314],{"stretchy":1552},[1497,55373,55374,55376],{},[1493,55375,1520],{},[1680,55377,1682],{},[1506,55379,1559],{"separator":1041},[1497,55381,55382,55384],{},[1493,55383,1501],{},[1680,55385,1682],{},[1506,55387,14323],{"stretchy":1552},[1528,55389,55390],{"encoding":1530},"[Q_1, P_1]","), kde ",[1035,55393,55395],{"className":55394},[1480],[1482,55396,55397],{"xmlns":1484},[1487,55398,55399,55407],{},[1490,55400,55401],{},[1497,55402,55403,55405],{},[1493,55404,1501],{},[1680,55406,1871],{},[1528,55408,53881],{"encoding":1530}," je minimální cena, při které je výrobce ochoten vyrábět.",[52452,55411,55413],{"id":55412},"lineární-model-nabídky","Lineární model nabídky",[1035,55415,55417],{"className":55416},[1480],[1482,55418,55419],{"xmlns":1484,"display":1485},[1487,55420,55421,55460],{},[19617,55422,55423],{"width":19619},[19621,55424,55425,55427,55453,55455],{},[19624,55426],{"width":19626},[19624,55428,55429],{},[1490,55430,55431,55433,55435,55437,55439,55441,55443,55445,55447,55449,55451],{},[1493,55432,1501],{},[1506,55434,1508],{},[1493,55436,8730],{},[1493,55438,1520],{},[1506,55440,2162],{},[1493,55442,3384],{},[1506,55444,1559],{"separator":1041},[1912,55446],{"width":1914},[1493,55448,8730],{},[1506,55450,2796],{},[1680,55452,28945],{},[19624,55454],{"width":19626},[19624,55456,55457],{},[1988,55458,55459],{},"(2.9)",[1528,55461,55462],{"encoding":1530},"P = cQ + d, \\qquad c > 0. \\tag{2.9}",[1030,55464,55465,55466,55502,55503,55516],{},"Alternativně ",[1035,55467,55469],{"className":55468},[1480],[1482,55470,55471],{"xmlns":1484},[1487,55472,55473,55499],{},[1490,55474,55475,55477,55479,55487,55489,55491],{},[1493,55476,1520],{},[1506,55478,1508],{},[1869,55480,55481],{"scriptlevel":1871,"displaystyle":1552},[1510,55482,55483,55485],{},[1680,55484,1682],{},[1493,55486,8730],{},[1493,55488,1501],{},[1506,55490,1888],{},[1869,55492,55493],{"scriptlevel":1871,"displaystyle":1552},[1510,55494,55495,55497],{},[1493,55496,3384],{},[1493,55498,8730],{},[1528,55500,55501],{"encoding":1530},"Q = \\tfrac{1}{c}P - \\tfrac{d}{c}","; znaménko koeficientu u ",[1035,55504,55506],{"className":55505},[1480],[1482,55507,55508],{"xmlns":1484},[1487,55509,55510,55514],{},[1490,55511,55512],{},[1493,55513,1501],{},[1528,55515,1501],{"encoding":1530}," zůstává, znaménko absolutního členu se mění.",[52958,55518,55520],{"id":55519},"příklad-25","Příklad 2.5",[1030,55522,55523,55525,55526,2632],{},[1047,55524,1263],{}," Lineární nabídka ",[1035,55527,55529],{"className":55528},[1480],[1482,55530,55531],{"xmlns":1484},[1487,55532,55533,55547],{},[1490,55534,55535,55537,55539,55541,55543,55545],{},[1493,55536,1501],{},[1506,55538,1508],{},[1680,55540,3687],{},[1493,55542,1520],{},[1506,55544,2162],{},[1680,55546,2309],{},[1528,55548,55549],{"encoding":1530},"P = 0{,}5Q + 25",[1030,55551,55552,55554,55555,2632],{},[1047,55553,52997],{}," Alternativní tvar ",[1035,55556,55558],{"className":55557},[1480],[1482,55559,55560],{"xmlns":1484},[1487,55561,55562,55576],{},[1490,55563,55564,55566,55568,55570,55572,55574],{},[1493,55565,1520],{},[1506,55567,1508],{},[1680,55569,1691],{},[1493,55571,1501],{},[1506,55573,1888],{},[1680,55575,2292],{},[1528,55577,55578],{"encoding":1530},"Q = 2P - 50",[1073,55580,55581,55606],{},[1076,55582,55583],{},[1079,55584,55585,55600,55602,55604],{},[1082,55586,55587],{},[1035,55588,55590],{"className":55589},[1480],[1482,55591,55592],{"xmlns":1484},[1487,55593,55594,55598],{},[1490,55595,55596],{},[1493,55597,1501],{},[1528,55599,1501],{"encoding":1530},[1082,55601,6956],{},[1082,55603,5603],{},[1082,55605,7380],{},[1092,55607,55608],{},[1079,55609,55610,55625,55627,55629],{},[1097,55611,55612],{},[1035,55613,55615],{"className":55614},[1480],[1482,55616,55617],{"xmlns":1484},[1487,55618,55619,55623],{},[1490,55620,55621],{},[1493,55622,1520],{},[1528,55624,1520],{"encoding":1530},[1097,55626,1775],{},[1097,55628,8436],{},[1097,55630,6956],{},[1304,55632,55634,55635,1564],{"id":55633},"posun-nabídky-shift-of-supply","Posun nabídky (",[1176,55636,55637],{},"shift of supply",[1030,55639,55640,55641,55643,55644,55661,55662,55687,55688,2632],{},"Posun nastává při změně exogenních proměnných — nová technologie snižuje náklady (posun ",[1047,55642,476],{},": při stejné ceně ",[1035,55645,55647],{"className":55646},[1480],[1482,55648,55649],{"xmlns":1484},[1487,55650,55651,55659],{},[1490,55652,55653],{},[1497,55654,55655,55657],{},[1493,55656,1501],{},[1680,55658,1871],{},[1528,55660,53881],{"encoding":1530}," vyrobí výrobce větší ",[1035,55663,55665],{"className":55664},[1480],[1482,55666,55667],{"xmlns":1484},[1487,55668,55669,55685],{},[1490,55670,55671,55677,55679],{},[1497,55672,55673,55675],{},[1493,55674,1520],{},[1680,55676,1682],{},[1506,55678,2796],{},[1497,55680,55681,55683],{},[1493,55682,1520],{},[1680,55684,1871],{},[1528,55686,53994],{"encoding":1530},"); zdražení vstupů posune křivku ",[1047,55689,55690],{},"doleva",[52958,55692,55694],{"id":55693},"příklad-26-zdanění-výrobce","Příklad 2.6 — zdanění výrobce",[1030,55696,55697,55699,55700,55724,55725,2632],{},[1047,55698,1263],{}," Nabídka ",[1035,55701,55703],{"className":55702},[1480],[1482,55704,55705],{"xmlns":1484},[1487,55706,55707,55721],{},[1490,55708,55709,55711,55713,55715,55717,55719],{},[1493,55710,1501],{},[1506,55712,1508],{},[1493,55714,2001],{},[1506,55716,1553],{"stretchy":1552},[1493,55718,1520],{},[1506,55720,1564],{"stretchy":1552},[1528,55722,55723],{"encoding":1530},"P = S(Q)","; na výrobce je uložena jednotková daň ",[1035,55726,55728],{"className":55727},[1480],[1482,55729,55730],{"xmlns":1484},[1487,55731,55732,55736],{},[1490,55733,55734],{},[1493,55735,5289],{},[1528,55737,5289],{"encoding":1530},[1030,55739,55740,55742,55743,55756,55757,55775,55776,55804],{},[1047,55741,52997],{}," Spotřebitel zaplatí ",[1035,55744,55746],{"className":55745},[1480],[1482,55747,55748],{"xmlns":1484},[1487,55749,55750,55754],{},[1490,55751,55752],{},[1493,55753,1501],{},[1528,55755,1501],{"encoding":1530},", výrobce obdrží ",[1035,55758,55760],{"className":55759},[1480],[1482,55761,55762],{"xmlns":1484},[1487,55763,55764,55772],{},[1490,55765,55766,55768,55770],{},[1493,55767,1501],{},[1506,55769,1888],{},[1493,55771,5289],{},[1528,55773,55774],{"encoding":1530},"P - T",". Z podmínky ",[1035,55777,55779],{"className":55778},[1480],[1482,55780,55781],{"xmlns":1484},[1487,55782,55783,55801],{},[1490,55784,55785,55787,55789,55791,55793,55795,55797,55799],{},[1493,55786,1501],{},[1506,55788,1888],{},[1493,55790,5289],{},[1506,55792,1508],{},[1493,55794,2001],{},[1506,55796,1553],{"stretchy":1552},[1493,55798,1520],{},[1506,55800,1564],{"stretchy":1552},[1528,55802,55803],{"encoding":1530},"P - T = S(Q)"," plyne",[1035,55806,55808],{"className":55807},[1480],[1482,55809,55810],{"xmlns":1484,"display":1485},[1487,55811,55812,55846],{},[1490,55813,55814,55816,55818,55824,55826,55828,55830,55832,55834,55836,55838,55840,55842,55844],{},[1493,55815,1501],{},[1506,55817,1508],{},[1497,55819,55820,55822],{},[1493,55821,2001],{},[1680,55823,1682],{},[1506,55825,1553],{"stretchy":1552},[1493,55827,1520],{},[1506,55829,1564],{"stretchy":1552},[1506,55831,1508],{},[1493,55833,2001],{},[1506,55835,1553],{"stretchy":1552},[1493,55837,1520],{},[1506,55839,1564],{"stretchy":1552},[1506,55841,2162],{},[1493,55843,5289],{},[1493,55845,2632],{"mathvariant":1516},[1528,55847,55848],{"encoding":1530},"P = S_1(Q) = S(Q) + T.",[1030,55850,55851,55852,55865,55866,1656,55879,55882,55883,1586,55903,8994,55921,2632],{},"Křivka ",[1035,55853,55855],{"className":55854},[1480],[1482,55856,55857],{"xmlns":1484},[1487,55858,55859,55863],{},[1490,55860,55861],{},[1493,55862,2001],{},[1528,55864,2001],{"encoding":1530}," se tedy posune o ",[1035,55867,55869],{"className":55868},[1480],[1482,55870,55871],{"xmlns":1484},[1487,55872,55873,55877],{},[1490,55874,55875],{},[1493,55876,5289],{},[1528,55878,5289],{"encoding":1530},[1047,55880,55881],{},"svisle nahoru"," (tj. doleva). Např. pro ",[1035,55884,55886],{"className":55885},[1480],[1482,55887,55888],{"xmlns":1484},[1487,55889,55890,55900],{},[1490,55891,55892,55894,55896,55898],{},[1493,55893,1501],{},[1506,55895,1508],{},[1680,55897,1691],{},[1493,55899,1520],{},[1528,55901,55902],{"encoding":1530},"P = 2Q",[1035,55904,55906],{"className":55905},[1480],[1482,55907,55908],{"xmlns":1484},[1487,55909,55910,55918],{},[1490,55911,55912,55914,55916],{},[1493,55913,5289],{},[1506,55915,1508],{},[1680,55917,7508],{},[1528,55919,55920],{"encoding":1530},"T = 6",[1035,55922,55924],{"className":55923},[1480],[1482,55925,55926],{"xmlns":1484},[1487,55927,55928,55950],{},[1490,55929,55930,55936,55938,55940,55942,55944,55946,55948],{},[1497,55931,55932,55934],{},[1493,55933,2001],{},[1680,55935,1682],{},[1506,55937,1274],{},[1493,55939,1501],{},[1506,55941,1508],{},[1680,55943,1691],{},[1493,55945,1520],{},[1506,55947,2162],{},[1680,55949,7508],{},[1528,55951,55952],{"encoding":1530},"S_1: P = 2Q + 6",[1246,55954],{},[1065,55956,55958],{"id":55957},"tržní-rovnováha","Tržní rovnováha",[1023,55960,55962,55968],{"className":55961,"dataCallout":582},[1026,1186],[1030,55963,55965,1042],{"className":55964},[1033],[1035,55966],{"className":55967,"ariaHidden":1041},[1038,1193,1040],[1030,55969,55970,55971,1656,55974,56006,56007,1732,56030,56053,56054,56057,56058,56071],{},"V ",[1047,55972,55973],{},"rovnovážném bodě",[1035,55975,55977],{"className":55976},[1480],[1482,55978,55979],{"xmlns":1484},[1487,55980,55981,56003],{},[1490,55982,55983,55985,55987,55993,55995,56001],{},[1493,55984,2711],{},[1506,55986,14314],{"stretchy":1552},[2315,55988,55989,55991],{},[1493,55990,1520],{},[1493,55992,2711],{},[1506,55994,1559],{"separator":1041},[2315,55996,55997,55999],{},[1493,55998,1501],{},[1493,56000,2711],{},[1506,56002,14323],{"stretchy":1552},[1528,56004,56005],{"encoding":1530},"E[Q^E, P^E]"," se poptávané a nabízené množství rovnají. Najde se jako řešení soustavy ",[1035,56008,56010],{"className":56009},[1480],[1482,56011,56012],{"xmlns":1484},[1487,56013,56014,56028],{},[1490,56015,56016,56018,56020,56022,56024,56026],{},[1493,56017,1501],{},[1506,56019,1508],{},[1493,56021,3712],{},[1506,56023,1553],{"stretchy":1552},[1493,56025,1520],{},[1506,56027,1564],{"stretchy":1552},[1528,56029,20356],{"encoding":1530},[1035,56031,56033],{"className":56032},[1480],[1482,56034,56035],{"xmlns":1484},[1487,56036,56037,56051],{},[1490,56038,56039,56041,56043,56045,56047,56049],{},[1493,56040,1501],{},[1506,56042,1508],{},[1493,56044,2001],{},[1506,56046,1553],{"stretchy":1552},[1493,56048,1520],{},[1506,56050,1564],{"stretchy":1552},[1528,56052,55723],{"encoding":1530},". Čtyři ",[1047,56055,56056],{},"pravidla komparativní statiky"," popisují, jak se ",[1035,56059,56061],{"className":56060},[1480],[1482,56062,56063],{"xmlns":1484},[1487,56064,56065,56069],{},[1490,56066,56067],{},[1493,56068,2711],{},[1528,56070,2711],{"encoding":1530}," posune při změně poptávky nebo nabídky.",[1304,56073,1476],{"id":1475},[1030,56075,56076,7606,56078,56081,56082,1656,56085,56103,56104,56135,56136,7606,56139,16623],{},[1047,56077,55958],{},[1176,56079,56080],{},"market equilibrium",") je stav, kdy poptávané množství = nabízené množství. Při ",[1047,56083,56084],{},"rovnovážné ceně",[1035,56086,56088],{"className":56087},[1480],[1482,56089,56090],{"xmlns":1484},[1487,56091,56092,56100],{},[1490,56093,56094],{},[2315,56095,56096,56098],{},[1493,56097,1501],{},[1493,56099,2711],{},[1528,56101,56102],{"encoding":1530},"P^E"," není přebytek ani nedostatek zboží. Bod ",[1035,56105,56107],{"className":56106},[1480],[1482,56108,56109],{"xmlns":1484},[1487,56110,56111,56133],{},[1490,56112,56113,56115,56117,56123,56125,56131],{},[1493,56114,2711],{},[1506,56116,14314],{"stretchy":1552},[2315,56118,56119,56121],{},[1493,56120,1520],{},[1493,56122,2711],{},[1506,56124,1559],{"separator":1041},[2315,56126,56127,56129],{},[1493,56128,1501],{},[1493,56130,2711],{},[1506,56132,14323],{"stretchy":1552},[1528,56134,56005],{"encoding":1530}," se nazývá ",[1047,56137,56138],{},"rovnovážný bod",[1176,56140,56141],{},"equilibrium point",[1030,56143,56144,56145,1732,56168,2632],{},"Rovnovážný bod je průsečíkem křivek poptávky a nabídky; nalézá se jako řešení soustavy ",[1035,56146,56148],{"className":56147},[1480],[1482,56149,56150],{"xmlns":1484},[1487,56151,56152,56166],{},[1490,56153,56154,56156,56158,56160,56162,56164],{},[1493,56155,1501],{},[1506,56157,1508],{},[1493,56159,3712],{},[1506,56161,1553],{"stretchy":1552},[1493,56163,1520],{},[1506,56165,1564],{"stretchy":1552},[1528,56167,20356],{"encoding":1530},[1035,56169,56171],{"className":56170},[1480],[1482,56172,56173],{"xmlns":1484},[1487,56174,56175,56189],{},[1490,56176,56177,56179,56181,56183,56185,56187],{},[1493,56178,1501],{},[1506,56180,1508],{},[1493,56182,2001],{},[1506,56184,1553],{"stretchy":1552},[1493,56186,1520],{},[1506,56188,1564],{"stretchy":1552},[1528,56190,55723],{"encoding":1530},[1030,56192,56193],{},[18014,56194],{"alt":56195,"className":56196,"src":56197},"imek-poptavka-nabidka-rovnovaha",[1055,18018],"\u002Fwiki-assets\u002Fimek-poptavka-nabidka-rovnovaha.jpeg",[1304,56199,56201],{"id":56200},"příklad-27-kvadratický-model","Příklad 2.7 (kvadratický model)",[1030,56203,56204,56206,56207,56241,56242,2632],{},[1047,56205,1263],{}," Poptávka ",[1035,56208,56210],{"className":56209},[1480],[1482,56211,56212],{"xmlns":1484},[1487,56213,56214,56238],{},[1490,56215,56216,56218,56220,56222,56228,56230,56232,56234,56236],{},[1493,56217,1501],{},[1506,56219,1508],{},[1506,56221,1888],{},[2315,56223,56224,56226],{},[1493,56225,1520],{},[1680,56227,1691],{},[1506,56229,1888],{},[1680,56231,1775],{},[1493,56233,1520],{},[1506,56235,2162],{},[1680,56237,5551],{},[1528,56239,56240],{"encoding":1530},"P = -Q^2 - 10Q + 150",", nabídka ",[1035,56243,56245],{"className":56244},[1480],[1482,56246,56247],{"xmlns":1484},[1487,56248,56249,56271],{},[1490,56250,56251,56253,56255,56261,56263,56265,56267,56269],{},[1493,56252,1501],{},[1506,56254,1508],{},[2315,56256,56257,56259],{},[1493,56258,1520],{},[1680,56260,1691],{},[1506,56262,2162],{},[1680,56264,38539],{},[1493,56266,1520],{},[1506,56268,2162],{},[1680,56270,9923],{},[1528,56272,56273],{"encoding":1530},"P = Q^2 + 14Q + 22",[1030,56275,56276,56278],{},[1047,56277,52997],{}," Z rovnosti",[1035,56280,56282],{"className":56281},[1480],[1482,56283,56284],{"xmlns":1484,"display":1485},[1487,56285,56286,56324],{},[1490,56287,56288,56290,56296,56298,56300,56302,56304,56306,56308,56314,56316,56318,56320,56322],{},[1506,56289,1888],{},[2315,56291,56292,56294],{},[1493,56293,1520],{},[1680,56295,1691],{},[1506,56297,1888],{},[1680,56299,1775],{},[1493,56301,1520],{},[1506,56303,2162],{},[1680,56305,5551],{},[1506,56307,1508],{},[2315,56309,56310,56312],{},[1493,56311,1520],{},[1680,56313,1691],{},[1506,56315,2162],{},[1680,56317,38539],{},[1493,56319,1520],{},[1506,56321,2162],{},[1680,56323,9923],{},[1528,56325,56326],{"encoding":1530},"-Q^2 - 10Q + 150 = Q^2 + 14Q + 22",[1030,56328,56329,56330,56364,56365,56397,56398,56414,56415,56428,56429,1732,56451,56488,56489,2632],{},"dostaneme ",[1035,56331,56333],{"className":56332},[1480],[1482,56334,56335],{"xmlns":1484},[1487,56336,56337,56361],{},[1490,56338,56339,56341,56347,56349,56351,56353,56355,56357,56359],{},[1680,56340,1691],{},[2315,56342,56343,56345],{},[1493,56344,1520],{},[1680,56346,1691],{},[1506,56348,2162],{},[1680,56350,7201],{},[1493,56352,1520],{},[1506,56354,1888],{},[1680,56356,21380],{},[1506,56358,1508],{},[1680,56360,1871],{},[1528,56362,56363],{"encoding":1530},"2Q^2 + 24Q - 128 = 0",", resp. ",[1035,56366,56368],{"className":56367},[1480],[1482,56369,56370],{"xmlns":1484},[1487,56371,56372,56394],{},[1490,56373,56374,56380,56382,56384,56386,56388,56390,56392],{},[2315,56375,56376,56378],{},[1493,56377,1520],{},[1680,56379,1691],{},[1506,56381,2162],{},[1680,56383,6797],{},[1493,56385,1520],{},[1506,56387,1888],{},[1680,56389,7466],{},[1506,56391,1508],{},[1680,56393,1871],{},[1528,56395,56396],{"encoding":1530},"Q^2 + 12Q - 64 = 0",". Kořeny jsou ",[1035,56399,56401],{"className":56400},[1480],[1482,56402,56403],{"xmlns":1484},[1487,56404,56405,56411],{},[1490,56406,56407,56409],{},[1506,56408,1888],{},[1680,56410,9961],{},[1528,56412,56413],{"encoding":1530},"-16"," (nevyhovuje) a ",[1035,56416,56418],{"className":56417},[1480],[1482,56419,56420],{"xmlns":1484},[1487,56421,56422,56426],{},[1490,56423,56424],{},[1680,56425,4007],{},[1528,56427,4007],{"encoding":1530},". Tedy ",[1035,56430,56432],{"className":56431},[1480],[1482,56433,56434],{"xmlns":1484},[1487,56435,56436,56448],{},[1490,56437,56438,56444,56446],{},[2315,56439,56440,56442],{},[1493,56441,1520],{},[1493,56443,2711],{},[1506,56445,1508],{},[1680,56447,4007],{},[1528,56449,56450],{"encoding":1530},"Q^E = 4",[1035,56452,56454],{"className":56453},[1480],[1482,56455,56456],{"xmlns":1484},[1487,56457,56458,56485],{},[1490,56459,56460,56466,56468,56470,56472,56474,56476,56478,56480,56482],{},[2315,56461,56462,56464],{},[1493,56463,1501],{},[1493,56465,2711],{},[1506,56467,1508],{},[1506,56469,1888],{},[1680,56471,9961],{},[1506,56473,1888],{},[1680,56475,7380],{},[1506,56477,2162],{},[1680,56479,5551],{},[1506,56481,1508],{},[1680,56483,56484],{},"94",[1528,56486,56487],{"encoding":1530},"P^E = -16 - 40 + 150 = 94",", rovnovážný bod ",[1035,56490,56492],{"className":56491},[1480],[1482,56493,56494],{"xmlns":1484},[1487,56495,56496,56510],{},[1490,56497,56498,56500,56502,56504,56506,56508],{},[1493,56499,2711],{},[1506,56501,14314],{"stretchy":1552},[1680,56503,4007],{},[1506,56505,1559],{"separator":1041},[1680,56507,56484],{},[1506,56509,14323],{"stretchy":1552},[1528,56511,56512],{"encoding":1530},"E[4, 94]",[1304,56514,56516],{"id":56515},"příklad-28-dvoukomoditní-trh","Příklad 2.8 (dvoukomoditní trh)",[1030,56518,56519,56521],{},[1047,56520,1263],{}," Poptávky a nabídky dvou zboží",[1035,56523,56525],{"className":56524},[1480],[1482,56526,56527],{"xmlns":1484,"display":1485},[1487,56528,56529,56695],{},[19617,56530,56533,56621],{"rowspacing":36473,"columnalign":56531,"columnspacing":56532},"right left right left","0em 1em 0em",[19621,56534,56535,56545,56577,56587],{},[19624,56536,56537],{},[1869,56538,56539],{"scriptlevel":1871,"displaystyle":1041},[1497,56540,56541,56543],{},[1493,56542,1520],{},[1680,56544,1682],{},[19624,56546,56547],{},[1869,56548,56549],{"scriptlevel":1871,"displaystyle":1041},[1490,56550,56551,56553,56555,56557,56559,56561,56567,56569,56575],{},[1490,56552],{},[1506,56554,1508],{},[1680,56556,7380],{},[1506,56558,1888],{},[1680,56560,1752],{},[1497,56562,56563,56565],{},[1493,56564,1501],{},[1680,56566,1682],{},[1506,56568,1888],{},[1497,56570,56571,56573],{},[1493,56572,1501],{},[1680,56574,1691],{},[1506,56576,1559],{"separator":1041},[19624,56578,56579],{},[1869,56580,56581],{"scriptlevel":1871,"displaystyle":1041},[1497,56582,56583,56585],{},[1493,56584,1520],{},[1680,56586,1691],{},[19624,56588,56589],{},[1869,56590,56591],{"scriptlevel":1871,"displaystyle":1041},[1490,56592,56593,56595,56597,56599,56601,56603,56609,56611,56613,56619],{},[1490,56594],{},[1506,56596,1508],{},[1680,56598,2292],{},[1506,56600,1888],{},[1680,56602,1691],{},[1497,56604,56605,56607],{},[1493,56606,1501],{},[1680,56608,1682],{},[1506,56610,1888],{},[1680,56612,4007],{},[1497,56614,56615,56617],{},[1493,56616,1501],{},[1680,56618,1691],{},[1506,56620,1559],{"separator":1041},[19621,56622,56623,56633,56659,56669],{},[19624,56624,56625],{},[1869,56626,56627],{"scriptlevel":1871,"displaystyle":1041},[1497,56628,56629,56631],{},[1493,56630,1520],{},[1680,56632,1682],{},[19624,56634,56635],{},[1869,56636,56637],{"scriptlevel":1871,"displaystyle":1041},[1490,56638,56639,56641,56643,56645,56647,56649,56651,56657],{},[1490,56640],{},[1506,56642,1508],{},[1506,56644,1888],{},[1680,56646,3201],{},[1506,56648,2162],{},[1680,56650,4007],{},[1497,56652,56653,56655],{},[1493,56654,1501],{},[1680,56656,1682],{},[1506,56658,1559],{"separator":1041},[19624,56660,56661],{},[1869,56662,56663],{"scriptlevel":1871,"displaystyle":1041},[1497,56664,56665,56667],{},[1493,56666,1520],{},[1680,56668,1691],{},[19624,56670,56671],{},[1869,56672,56673],{"scriptlevel":1871,"displaystyle":1041},[1490,56674,56675,56677,56679,56681,56683,56685,56687,56693],{},[1490,56676],{},[1506,56678,1508],{},[1506,56680,1888],{},[1680,56682,16580],{},[1506,56684,2162],{},[1680,56686,3201],{},[1497,56688,56689,56691],{},[1493,56690,1501],{},[1680,56692,1691],{},[1493,56694,2632],{"mathvariant":1516},[1528,56696,56697],{"encoding":1530},"\\begin{aligned}\nQ_1 &= 40 - 5P_1 - P_2, & Q_2 &= 50 - 2P_1 - 4P_2, \\\\\nQ_1 &= -3 + 4P_1, & Q_2 &= -7 + 3P_2.\n\\end{aligned}",[1030,56699,56700,56702],{},[1047,56701,52997],{}," Z rovností poptávek a nabídek dostaneme",[1035,56704,56706],{"className":56705},[1480],[1482,56707,56708],{"xmlns":1484,"display":1485},[1487,56709,56710,56759],{},[1490,56711,56712,56714,56720,56722,56728,56730,56732,56734,56736,56738,56744,56746,56748,56754,56756],{},[1680,56713,14365],{},[1497,56715,56716,56718],{},[1493,56717,1501],{},[1680,56719,1682],{},[1506,56721,2162],{},[1497,56723,56724,56726],{},[1493,56725,1501],{},[1680,56727,1691],{},[1506,56729,1508],{},[1680,56731,36914],{},[1506,56733,1559],{"separator":1041},[1912,56735],{"width":1914},[1680,56737,1691],{},[1497,56739,56740,56742],{},[1493,56741,1501],{},[1680,56743,1682],{},[1506,56745,2162],{},[1680,56747,16580],{},[1497,56749,56750,56752],{},[1493,56751,1501],{},[1680,56753,1691],{},[1506,56755,1508],{},[1680,56757,56758],{},"57.",[1528,56760,56761],{"encoding":1530},"9P_1 + P_2 = 43, \\qquad 2P_1 + 7P_2 = 57.",[1030,56763,56764,56765,1732,56789,56813,56814,1732,56839,56863,56864,56866],{},"Řešením je ",[1035,56766,56768],{"className":56767},[1480],[1482,56769,56770],{"xmlns":1484},[1487,56771,56772,56786],{},[1490,56773,56774,56782,56784],{},[1697,56775,56776,56778,56780],{},[1493,56777,1501],{},[1680,56779,1682],{},[1493,56781,2711],{},[1506,56783,1508],{},[1680,56785,4007],{},[1528,56787,56788],{"encoding":1530},"P_1^E = 4",[1035,56790,56792],{"className":56791},[1480],[1482,56793,56794],{"xmlns":1484},[1487,56795,56796,56810],{},[1490,56797,56798,56806,56808],{},[1697,56799,56800,56802,56804],{},[1493,56801,1501],{},[1680,56803,1691],{},[1493,56805,2711],{},[1506,56807,1508],{},[1680,56809,16580],{},[1528,56811,56812],{"encoding":1530},"P_2^E = 7","; zpětným dosazením ",[1035,56815,56817],{"className":56816},[1480],[1482,56818,56819],{"xmlns":1484},[1487,56820,56821,56836],{},[1490,56822,56823,56831,56833],{},[1697,56824,56825,56827,56829],{},[1493,56826,1520],{},[1680,56828,1682],{},[1493,56830,2711],{},[1506,56832,1508],{},[1680,56834,56835],{},"13",[1528,56837,56838],{"encoding":1530},"Q_1^E = 13",[1035,56840,56842],{"className":56841},[1480],[1482,56843,56844],{"xmlns":1484},[1487,56845,56846,56860],{},[1490,56847,56848,56856,56858],{},[1697,56849,56850,56852,56854],{},[1493,56851,1520],{},[1680,56853,1691],{},[1493,56855,2711],{},[1506,56857,1508],{},[1680,56859,38539],{},[1528,56861,56862],{"encoding":1530},"Q_2^E = 14",". Zboží jsou ",[1047,56865,8866],{}," (zkřížené koeficienty v poptávce jsou záporné).",[1304,56868,56870],{"id":56869},"dynamický-model-pavučinový-teorém","Dynamický model — pavučinový teorém",[1030,56872,56873,56874,56891,56892,7606,56895,16623],{},"Rovnovážná cena se obecně liší od tržní ceny, která vzniká působením tržních sil v čase. Za podmínky stability se tržní cena přibližuje k ",[1035,56875,56877],{"className":56876},[1480],[1482,56878,56879],{"xmlns":1484},[1487,56880,56881,56889],{},[1490,56882,56883],{},[2315,56884,56885,56887],{},[1493,56886,1501],{},[1493,56888,2711],{},[1528,56890,56102],{"encoding":1530},"; mechanismus popisuje ",[1047,56893,56894],{},"teorém pavučiny",[1176,56896,56897],{},"cobweb model",[1304,56899,56901],{"id":56900},"pravidla-komparativní-statiky-14","Pravidla komparativní statiky (1–4)",[1030,56903,56904],{},[18014,56905],{"alt":56906,"className":56907,"src":56908},"imek-komparativni-statika-4pripady",[1055,18018],"\u002Fwiki-assets\u002Fimek-komparativni-statika-4pripady.jpeg",[19516,56910,56911,56951,56991,57031],{},[1030,56912,56913,56916,56917,22060,56934,2632],{},[1047,56914,56915],{},"Pravidlo 1:"," Růst poptávky ⟹ růst ",[1035,56918,56920],{"className":56919},[1480],[1482,56921,56922],{"xmlns":1484},[1487,56923,56924,56932],{},[1490,56925,56926],{},[2315,56927,56928,56930],{},[1493,56929,1501],{},[1493,56931,2711],{},[1528,56933,56102],{"encoding":1530},[1035,56935,56937],{"className":56936},[1480],[1482,56938,56939],{"xmlns":1484},[1487,56940,56941,56949],{},[1490,56942,56943],{},[2315,56944,56945,56947],{},[1493,56946,1520],{},[1493,56948,2711],{},[1528,56950,14059],{"encoding":1530},[1030,56952,56953,56956,56957,22060,56974,2632],{},[1047,56954,56955],{},"Pravidlo 2:"," Pokles poptávky ⟹ pokles ",[1035,56958,56960],{"className":56959},[1480],[1482,56961,56962],{"xmlns":1484},[1487,56963,56964,56972],{},[1490,56965,56966],{},[2315,56967,56968,56970],{},[1493,56969,1501],{},[1493,56971,2711],{},[1528,56973,56102],{"encoding":1530},[1035,56975,56977],{"className":56976},[1480],[1482,56978,56979],{"xmlns":1484},[1487,56980,56981,56989],{},[1490,56982,56983],{},[2315,56984,56985,56987],{},[1493,56986,1520],{},[1493,56988,2711],{},[1528,56990,14059],{"encoding":1530},[1030,56992,56993,56996,56997,25653,57014,2632],{},[1047,56994,56995],{},"Pravidlo 3:"," Růst nabídky ⟹ pokles ",[1035,56998,57000],{"className":56999},[1480],[1482,57001,57002],{"xmlns":1484},[1487,57003,57004,57012],{},[1490,57005,57006],{},[2315,57007,57008,57010],{},[1493,57009,1501],{},[1493,57011,2711],{},[1528,57013,56102],{"encoding":1530},[1035,57015,57017],{"className":57016},[1480],[1482,57018,57019],{"xmlns":1484},[1487,57020,57021,57029],{},[1490,57022,57023],{},[2315,57024,57025,57027],{},[1493,57026,1520],{},[1493,57028,2711],{},[1528,57030,14059],{"encoding":1530},[1030,57032,57033,57036,57037,57054,57055,2632],{},[1047,57034,57035],{},"Pravidlo 4:"," Pokles nabídky ⟹ růst ",[1035,57038,57040],{"className":57039},[1480],[1482,57041,57042],{"xmlns":1484},[1487,57043,57044,57052],{},[1490,57045,57046],{},[2315,57047,57048,57050],{},[1493,57049,1501],{},[1493,57051,2711],{},[1528,57053,56102],{"encoding":1530},", pokles ",[1035,57056,57058],{"className":57057},[1480],[1482,57059,57060],{"xmlns":1484},[1487,57061,57062,57070],{},[1490,57063,57064],{},[2315,57065,57066,57068],{},[1493,57067,1520],{},[1493,57069,2711],{},[1528,57071,14059],{"encoding":1530},[1073,57073,57074,57118],{},[1076,57075,57076],{},[1079,57077,57078,57080,57099],{},[1082,57079,13501],{},[1082,57081,57082],{},[1035,57083,57085],{"className":57084},[1480],[1482,57086,57087],{"xmlns":1484},[1487,57088,57089,57097],{},[1490,57090,57091],{},[2315,57092,57093,57095],{},[1493,57094,1501],{},[1493,57096,2711],{},[1528,57098,56102],{"encoding":1530},[1082,57100,57101],{},[1035,57102,57104],{"className":57103},[1480],[1482,57105,57106],{"xmlns":1484},[1487,57107,57108,57116],{},[1490,57109,57110],{},[2315,57111,57112,57114],{},[1493,57113,1520],{},[1493,57115,2711],{},[1528,57117,14059],{"encoding":1530},[1092,57119,57120,57130,57140,57149],{},[1079,57121,57122,57125,57128],{},[1097,57123,57124],{},"Růst poptávky",[1097,57126,57127],{},"↑",[1097,57129,57127],{},[1079,57131,57132,57135,57138],{},[1097,57133,57134],{},"Pokles poptávky",[1097,57136,57137],{},"↓",[1097,57139,57137],{},[1079,57141,57142,57145,57147],{},[1097,57143,57144],{},"Růst nabídky",[1097,57146,57137],{},[1097,57148,57127],{},[1079,57150,57151,57154,57156],{},[1097,57152,57153],{},"Pokles nabídky",[1097,57155,57127],{},[1097,57157,57137],{},[1030,57159,57160],{},[1176,57161,57162],{},"Obrázky 2.15–2.18 ilustrují všechny čtyři situace pomocí posunu jedné z křivek.",[1246,57164],{},[1065,57166,57168],{"id":57167},"zdanění-trhu","Zdanění trhu",[1023,57170,57172,57178,57263],{"className":57171,"dataCallout":582},[1026,1186],[1030,57173,57175,1042],{"className":57174},[1033],[1035,57176],{"className":57177,"ariaHidden":1041},[1038,1193,1040],[1030,57179,57180,57181,57194,57195,18367,57208,57211,57212,51873,57234,57258,57259,57262],{},"Jednotková daň ",[1035,57182,57184],{"className":57183},[1480],[1482,57185,57186],{"xmlns":1484},[1487,57187,57188,57192],{},[1490,57189,57190],{},[1493,57191,5289],{},[1528,57193,5289],{"encoding":1530}," uložená na každou prodanou jednotku způsobí posun jedné z křivek o ",[1035,57196,57198],{"className":57197},[1480],[1482,57199,57200],{"xmlns":1484},[1487,57201,57202,57206],{},[1490,57203,57204],{},[1493,57205,5289],{},[1528,57207,5289],{"encoding":1530},[1047,57209,57210],{},"Daňové břemeno"," se dělí mezi spotřebitele (",[1035,57213,57215],{"className":57214},[1480],[1482,57216,57217],{"xmlns":1484},[1487,57218,57219,57231],{},[1490,57220,57221],{},[1497,57222,57223,57225],{},[1493,57224,5289],{},[1490,57226,57227,57229],{},[1493,57228,25906],{},[1493,57230,1030],{},[1528,57232,57233],{"encoding":1530},"T_{sp}",[1035,57235,57237],{"className":57236},[1480],[1482,57238,57239],{"xmlns":1484},[1487,57240,57241,57255],{},[1490,57242,57243],{},[1497,57244,57245,57247],{},[1493,57246,5289],{},[1490,57248,57249,57251,57253],{},[1493,57250,25950],{},[1493,57252,3052],{},[1493,57254,7740],{},[1528,57256,57257],{"encoding":1530},"T_{vyr}","). Klíčová vlastnost — ",[1047,57260,57261],{},"ekvivalence zdanění",": výsledné rovnovážné množství i čistá cena pro výrobce jsou stejné bez ohledu na to, zda je daň uložena výrobci, či spotřebiteli.",[1030,57264,57265],{},[1176,57266,57267,57268,2632],{},"Pro detail, úplné odvození, Příklady 2.9 a 2.10 a geometrickou interpretaci viz ",[1052,57269,57273],{"className":57270,"dataFsResolvedFilePath":57271,"href":57272},[1055],"topics\u002Fzdaneni-trhu.md","\u002Fwiki\u002Fzdaneni-trhu","zdaneni-trhu",[1030,57275,57276,57277,57280,57281,57307,57308,57311,57312,57338,57339,57356,57357,57397,57398,1586,57411,2632],{},"Existují dvě formy zdanění — daň uložená ",[1047,57278,57279],{},"výrobci"," (posun nabídky ",[1035,57282,57284],{"className":57283},[1480],[1482,57285,57286],{"xmlns":1484},[1487,57287,57288,57304],{},[1490,57289,57290,57296,57298,57300,57302],{},[1497,57291,57292,57294],{},[1493,57293,2001],{},[1680,57295,1682],{},[1506,57297,1508],{},[1493,57299,2001],{},[1506,57301,2162],{},[1493,57303,5289],{},[1528,57305,57306],{"encoding":1530},"S_1 = S + T"," svisle nahoru) a daň uložená ",[1047,57309,57310],{},"spotřebiteli"," (posun poptávky ",[1035,57313,57315],{"className":57314},[1480],[1482,57316,57317],{"xmlns":1484},[1487,57318,57319,57335],{},[1490,57320,57321,57327,57329,57331,57333],{},[1497,57322,57323,57325],{},[1493,57324,3712],{},[1680,57326,1691],{},[1506,57328,1508],{},[1493,57330,3712],{},[1506,57332,1888],{},[1493,57334,5289],{},[1528,57336,57337],{"encoding":1530},"D_2 = D - T"," svisle dolů). V obou případech nové rovnovážné množství ",[1035,57340,57342],{"className":57341},[1480],[1482,57343,57344],{"xmlns":1484},[1487,57345,57346,57354],{},[1490,57347,57348],{},[2315,57349,57350,57352],{},[1493,57351,1520],{},[1493,57353,2711],{},[1528,57355,14059],{"encoding":1530}," klesá a vzniká rozklad daně ",[1035,57358,57360],{"className":57359},[1480],[1482,57361,57362],{"xmlns":1484},[1487,57363,57364,57394],{},[1490,57365,57366,57368,57370,57380,57382],{},[1493,57367,5289],{},[1506,57369,1508],{},[1497,57371,57372,57374],{},[1493,57373,5289],{},[1490,57375,57376,57378],{},[1493,57377,25906],{},[1493,57379,1030],{},[1506,57381,2162],{},[1497,57383,57384,57386],{},[1493,57385,5289],{},[1490,57387,57388,57390,57392],{},[1493,57389,25950],{},[1493,57391,3052],{},[1493,57393,7740],{},[1528,57395,57396],{"encoding":1530},"T = T_{sp} + T_{vyr}"," mezi obě strany trhu, určený relativními sklony křivek ",[1035,57399,57401],{"className":57400},[1480],[1482,57402,57403],{"xmlns":1484},[1487,57404,57405,57409],{},[1490,57406,57407],{},[1493,57408,3712],{},[1528,57410,3712],{"encoding":1530},[1035,57412,57414],{"className":57413},[1480],[1482,57415,57416],{"xmlns":1484},[1487,57417,57418,57422],{},[1490,57419,57420],{},[1493,57421,2001],{},[1528,57423,2001],{"encoding":1530},[1030,57425,57426,57427,57430,57431,1586,57461,57495],{},"Zásadním výsledkem kapitoly je ",[1047,57428,57429],{},"věta o ekvivalenci zdanění",": ať je daň uvalena formálně na kohokoli, rovnovážné množství i reálné rozdělení břemene jsou identické — ",[1035,57432,57434],{"className":57433},[1480],[1482,57435,57436],{"xmlns":1484},[1487,57437,57438,57458],{},[1490,57439,57440,57448,57450],{},[1697,57441,57442,57444,57446],{},[1493,57443,1520],{},[1680,57445,1682],{},[1493,57447,2711],{},[1506,57449,1508],{},[1697,57451,57452,57454,57456],{},[1493,57453,1520],{},[1680,57455,1691],{},[1493,57457,2711],{},[1528,57459,57460],{"encoding":1530},"Q_1^E = Q_2^E",[1035,57462,57464],{"className":57463},[1480],[1482,57465,57466],{"xmlns":1484},[1487,57467,57468,57492],{},[1490,57469,57470,57478,57480,57482,57484],{},[1697,57471,57472,57474,57476],{},[1493,57473,1501],{},[1680,57475,1682],{},[1493,57477,2711],{},[1506,57479,1888],{},[1493,57481,5289],{},[1506,57483,1508],{},[1697,57485,57486,57488,57490],{},[1493,57487,1501],{},[1680,57489,1691],{},[1493,57491,2711],{},[1528,57493,57494],{"encoding":1530},"P_1^E - T = P_2^E",". Otázka, \"kdo má platit daň\", je tedy z hlediska trhu formální; skutečné rozdělení určuje struktura trhu, nikoli znění zákona.",[1030,57497,57498,57499,57502,57503,57529,57530,57558,57559,57562,57563,57566,57567,2632],{},"Podrobný výklad, Příklady ",[1047,57500,57501],{},"2.9"," (daň výrobci, ",[1035,57504,57506],{"className":57505},[1480],[1482,57507,57508],{"xmlns":1484},[1487,57509,57510,57526],{},[1490,57511,57512,57522,57524],{},[1497,57513,57514,57516],{},[1493,57515,5289],{},[1490,57517,57518,57520],{},[1493,57519,25906],{},[1493,57521,1030],{},[1506,57523,1508],{},[1680,57525,1691],{},[1528,57527,57528],{"encoding":1530},"T_{sp} = 2"," Kč, ",[1035,57531,57533],{"className":57532},[1480],[1482,57534,57535],{"xmlns":1484},[1487,57536,57537,57555],{},[1490,57538,57539,57551,57553],{},[1497,57540,57541,57543],{},[1493,57542,5289],{},[1490,57544,57545,57547,57549],{},[1493,57546,25950],{},[1493,57548,3052],{},[1493,57550,7740],{},[1506,57552,1508],{},[1680,57554,4007],{},[1528,57556,57557],{"encoding":1530},"T_{vyr} = 4"," Kč) a ",[1047,57560,57561],{},"2.10"," (táž daň, ale na spotřebitele), postup výpočtu rozkladu břemene a ",[1047,57564,57565],{},"Obrázky 2.17–2.21"," jsou na samostatné stránce ",[1052,57568,57273],{"className":57569,"dataFsResolvedFilePath":57271,"href":57272},[1055],[1246,57571],{},[1065,57573,57575],{"id":57574},"multiplikátory-pro-mikroekonomické-proměnné","Multiplikátory pro mikroekonomické proměnné",[1023,57577,57579,57585],{"className":57578,"dataCallout":582},[1026,1186],[1030,57580,57582,1042],{"className":57581},[1033],[1035,57583],{"className":57584,"ariaHidden":1041},[1038,1193,1040],[1030,57586,57587,57588,57591,57592,57594],{},"Multiplikátory jsou ",[1047,57589,57590],{},"parciální derivace redukovaného tvaru"," endogenní proměnné podle exogenních parametrů. Udávají přibližnou odezvu rovnovážného bodu na jednotkovou změnu parametru (",[1176,57593,52054],{},"). Kvalitativní smysl (znaménko) je invariantní, kvantitativní závisí na konkrétních hodnotách.",[1304,57596,57598],{"id":57597},"redukovaný-tvar","Redukovaný tvar",[1030,57600,57601,57602,7606,57625,1732,57643,28611,57660,7606,57683,57700,57701,57731],{},"Pro lineární model ",[1035,57603,57605],{"className":57604},[1480],[1482,57606,57607],{"xmlns":1484},[1487,57608,57609,57623],{},[1490,57610,57611,57613,57615,57617,57619,57621],{},[1493,57612,1501],{},[1506,57614,1508],{},[1493,57616,1052],{},[1493,57618,1520],{},[1506,57620,2162],{},[1493,57622,2394],{},[1528,57624,52158],{"encoding":1530},[1035,57626,57628],{"className":57627},[1480],[1482,57629,57630],{"xmlns":1484},[1487,57631,57632,57640],{},[1490,57633,57634,57636,57638],{},[1493,57635,1052],{},[1506,57637,3961],{},[1680,57639,1871],{},[1528,57641,57642],{"encoding":1530},"a \u003C 0",[1035,57644,57646],{"className":57645},[1480],[1482,57647,57648],{"xmlns":1484},[1487,57649,57650,57658],{},[1490,57651,57652,57654,57656],{},[1493,57653,2394],{},[1506,57655,2796],{},[1680,57657,1871],{},[1528,57659,34950],{"encoding":1530},[1035,57661,57663],{"className":57662},[1480],[1482,57664,57665],{"xmlns":1484},[1487,57666,57667,57681],{},[1490,57668,57669,57671,57673,57675,57677,57679],{},[1493,57670,1501],{},[1506,57672,1508],{},[1493,57674,8730],{},[1493,57676,1520],{},[1506,57678,2162],{},[1493,57680,3384],{},[1528,57682,55008],{"encoding":1530},[1035,57684,57686],{"className":57685},[1480],[1482,57687,57688],{"xmlns":1484},[1487,57689,57690,57698],{},[1490,57691,57692,57694,57696],{},[1493,57693,8730],{},[1506,57695,2796],{},[1680,57697,1871],{},[1528,57699,55026],{"encoding":1530},") dává podmínka rovnováhy ",[1035,57702,57704],{"className":57703},[1480],[1482,57705,57706],{"xmlns":1484},[1487,57707,57708,57728],{},[1490,57709,57710,57712,57714,57716,57718,57720,57722,57724,57726],{},[1493,57711,1052],{},[1493,57713,1520],{},[1506,57715,2162],{},[1493,57717,2394],{},[1506,57719,1508],{},[1493,57721,8730],{},[1493,57723,1520],{},[1506,57725,2162],{},[1493,57727,3384],{},[1528,57729,57730],{"encoding":1530},"aQ + b = cQ + d",", odkud",[1035,57733,57735],{"className":57734},[1480],[1482,57736,57737],{"xmlns":1484,"display":1485},[1487,57738,57739,57784],{},[19617,57740,57741],{"width":19619},[19621,57742,57743,57745,57777,57779],{},[19624,57744],{"width":19626},[19624,57746,57747],{},[1490,57748,57749,57755,57757,57775],{},[2315,57750,57751,57753],{},[1493,57752,1520],{},[1493,57754,2711],{},[1506,57756,1508],{},[1510,57758,57759,57767],{},[1490,57760,57761,57763,57765],{},[1493,57762,2394],{},[1506,57764,1888],{},[1493,57766,3384],{},[1490,57768,57769,57771,57773],{},[1493,57770,8730],{},[1506,57772,1888],{},[1493,57774,1052],{},[1493,57776,2632],{"mathvariant":1516},[19624,57778],{"width":19626},[19624,57780,57781],{},[1988,57782,57783],{},"(2.10)",[1528,57785,57786],{"encoding":1530},"Q^E = \\frac{b - d}{c - a}. \\tag{2.10}",[1030,57788,57789,57790,7606,57792,57795,57796,57813,57814,1656,57817,57843,57844,57857,57858,57876,57877,16623],{},"Vztah (2.10) je ",[1047,57791,36669],{},[1176,57793,57794],{},"reduced form",") pro ",[1035,57797,57799],{"className":57798},[1480],[1482,57800,57801],{"xmlns":1484},[1487,57802,57803,57811],{},[1490,57804,57805],{},[2315,57806,57807,57809],{},[1493,57808,1520],{},[1493,57810,2711],{},[1528,57812,14059],{"encoding":1530},": endogenní proměnná je vyjádřena pomocí exogenních ",[1047,57815,57816],{},"parametrů",[1035,57818,57820],{"className":57819},[1480],[1482,57821,57822],{"xmlns":1484},[1487,57823,57824,57840],{},[1490,57825,57826,57828,57830,57832,57834,57836,57838],{},[1493,57827,1052],{},[1506,57829,1559],{"separator":1041},[1493,57831,2394],{},[1506,57833,1559],{"separator":1041},[1493,57835,8730],{},[1506,57837,1559],{"separator":1041},[1493,57839,3384],{},[1528,57841,57842],{"encoding":1530},"a, b, c, d",". Aby ",[1035,57845,57847],{"className":57846},[1480],[1482,57848,57849],{"xmlns":1484},[1487,57850,57851,57855],{},[1490,57852,57853],{},[1493,57854,2711],{},[1528,57856,2711],{"encoding":1530}," ležel v 1. kvadrantu, musí platit ",[1035,57859,57861],{"className":57860},[1480],[1482,57862,57863],{"xmlns":1484},[1487,57864,57865,57873],{},[1490,57866,57867,57869,57871],{},[1493,57868,2394],{},[1506,57870,2796],{},[1493,57872,3384],{},[1528,57874,57875],{"encoding":1530},"b > d"," (neboť ",[1035,57878,57880],{"className":57879},[1480],[1482,57881,57882],{"xmlns":1484},[1487,57883,57884,57896],{},[1490,57885,57886,57888,57890,57892,57894],{},[1493,57887,8730],{},[1506,57889,1888],{},[1493,57891,1052],{},[1506,57893,2796],{},[1680,57895,1871],{},[1528,57897,57898],{"encoding":1530},"c - a > 0",[1304,57900,57902],{"id":57901},"definice-multiplikátorů","Definice multiplikátorů",[1030,57904,57905,57906,57931,57932,57945,57946,57959],{},"V komparativní statice jsou ",[1035,57907,57909],{"className":57908},[1480],[1482,57910,57911],{"xmlns":1484},[1487,57912,57913,57929],{},[1490,57914,57915,57917,57919,57921,57923,57925,57927],{},[1493,57916,1052],{},[1506,57918,1559],{"separator":1041},[1493,57920,2394],{},[1506,57922,1559],{"separator":1041},[1493,57924,8730],{},[1506,57926,1559],{"separator":1041},[1493,57928,3384],{},[1528,57930,57842],{"encoding":1530}," exogenní proměnné a ",[1035,57933,57935],{"className":57934},[1480],[1482,57936,57937],{"xmlns":1484},[1487,57938,57939,57943],{},[1490,57940,57941],{},[1493,57942,1520],{},[1528,57944,1520],{"encoding":1530}," endogenní. Přibližná změna ",[1035,57947,57949],{"className":57948},[1480],[1482,57950,57951],{"xmlns":1484},[1487,57952,57953,57957],{},[1490,57954,57955],{},[1493,57956,1520],{},[1528,57958,1520],{"encoding":1530}," se rovná totálnímu diferenciálu:",[1035,57961,57963],{"className":57962},[1480],[1482,57964,57965],{"xmlns":1484,"display":1485},[1487,57966,57967,58060],{},[19617,57968,57969],{"width":19619},[19621,57970,57971,57973,58053,58055],{},[19624,57972],{"width":19626},[19624,57974,57975],{},[1490,57976,57977,57979,57981,57983,57985,57987,57989,57997,57999,58001,58003,58005,58013,58015,58017,58019,58021,58029,58031,58033,58035,58037,58045,58047,58049,58051],{},[1493,57978,2976],{"mathvariant":1516},[1493,57980,1520],{},[1506,57982,2343],{},[1493,57984,3384],{},[1493,57986,1520],{},[1506,57988,1508],{},[1697,57990,57991,57993,57995],{},[1493,57992,1520],{},[1493,57994,1052],{},[1506,57996,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1988,57998,5016],{},[1493,58000,3384],{},[1493,58002,1052],{},[1506,58004,2162],{},[1697,58006,58007,58009,58011],{},[1493,58008,1520],{},[1493,58010,2394],{},[1506,58012,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1988,58014,5016],{},[1493,58016,3384],{},[1493,58018,2394],{},[1506,58020,2162],{},[1697,58022,58023,58025,58027],{},[1493,58024,1520],{},[1493,58026,8730],{},[1506,58028,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1988,58030,5016],{},[1493,58032,3384],{},[1493,58034,8730],{},[1506,58036,2162],{},[1697,58038,58039,58041,58043],{},[1493,58040,1520],{},[1493,58042,3384],{},[1506,58044,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1988,58046,5016],{},[1493,58048,3384],{},[1493,58050,3384],{},[1493,58052,2632],{"mathvariant":1516},[19624,58054],{"width":19626},[19624,58056,58057],{},[1988,58058,58059],{},"(2.11)",[1528,58061,58062],{"encoding":1530},"\\Delta Q \\approx dQ = Q'_a\\,da + Q'_b\\,db + Q'_c\\,dc + Q'_d\\,dd. \\tag{2.11}",[1030,58064,58065,58066,58116,58117,7606,58119,18579],{},"Parciální derivace ",[1035,58067,58069],{"className":58068},[1480],[1482,58070,58071],{"xmlns":1484},[1487,58072,58073,58113],{},[1490,58074,58075,58083,58085,58093,58095,58103,58105],{},[1697,58076,58077,58079,58081],{},[1493,58078,1520],{},[1493,58080,1052],{},[1506,58082,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,58084,1559],{"separator":1041},[1697,58086,58087,58089,58091],{},[1493,58088,1520],{},[1493,58090,2394],{},[1506,58092,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,58094,1559],{"separator":1041},[1697,58096,58097,58099,58101],{},[1493,58098,1520],{},[1493,58100,8730],{},[1506,58102,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,58104,1559],{"separator":1041},[1697,58106,58107,58109,58111],{},[1493,58108,1520],{},[1493,58110,3384],{},[1506,58112,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,58114,58115],{"encoding":1530},"Q'_a, Q'_b, Q'_c, Q'_d"," se nazývají ",[1047,58118,34120],{},[1176,58120,58121],{},"multipliers",[1035,58123,58125],{"className":58124},[1480],[1482,58126,58127],{"xmlns":1484,"display":1485},[1487,58128,58129,58280],{},[19617,58130,58131],{"width":19619},[19621,58132,58133,58135,58273,58275],{},[19624,58134],{"width":19626},[19624,58136,58137],{},[1490,58138,58139,58147,58149,58175,58177,58179,58187,58189,58201,58203,58205,58213,58215,58217,58243,58245,58247,58255,58257,58259,58271],{},[1697,58140,58141,58143,58145],{},[1493,58142,1520],{},[1493,58144,1052],{},[1506,58146,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,58148,1508],{},[1510,58150,58151,58159],{},[1490,58152,58153,58155,58157],{},[1493,58154,2394],{},[1506,58156,1888],{},[1493,58158,3384],{},[1490,58160,58161,58163,58165,58167,58169],{},[1506,58162,1553],{"stretchy":1552},[1493,58164,8730],{},[1506,58166,1888],{},[1493,58168,1052],{},[2315,58170,58171,58173],{},[1506,58172,1564],{"stretchy":1552},[1680,58174,1691],{},[1506,58176,1559],{"separator":1041},[1912,58178],{"width":2108},[1697,58180,58181,58183,58185],{},[1493,58182,1520],{},[1493,58184,2394],{},[1506,58186,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,58188,1508],{},[1510,58190,58191,58193],{},[1680,58192,1682],{},[1490,58194,58195,58197,58199],{},[1493,58196,8730],{},[1506,58198,1888],{},[1493,58200,1052],{},[1506,58202,1559],{"separator":1041},[1912,58204],{"width":2108},[1697,58206,58207,58209,58211],{},[1493,58208,1520],{},[1493,58210,8730],{},[1506,58212,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,58214,1508],{},[1506,58216,1888],{},[1510,58218,58219,58227],{},[1490,58220,58221,58223,58225],{},[1493,58222,2394],{},[1506,58224,1888],{},[1493,58226,3384],{},[1490,58228,58229,58231,58233,58235,58237],{},[1506,58230,1553],{"stretchy":1552},[1493,58232,8730],{},[1506,58234,1888],{},[1493,58236,1052],{},[2315,58238,58239,58241],{},[1506,58240,1564],{"stretchy":1552},[1680,58242,1691],{},[1506,58244,1559],{"separator":1041},[1912,58246],{"width":2108},[1697,58248,58249,58251,58253],{},[1493,58250,1520],{},[1493,58252,3384],{},[1506,58254,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,58256,1508],{},[1506,58258,1888],{},[1510,58260,58261,58263],{},[1680,58262,1682],{},[1490,58264,58265,58267,58269],{},[1493,58266,8730],{},[1506,58268,1888],{},[1493,58270,1052],{},[1493,58272,2632],{"mathvariant":1516},[19624,58274],{"width":19626},[19624,58276,58277],{},[1988,58278,58279],{},"(2.12)",[1528,58281,58282],{"encoding":1530},"Q'_a = \\frac{b - d}{(c - a)^2}, \\quad Q'_b = \\frac{1}{c - a}, \\quad Q'_c = -\\frac{b - d}{(c - a)^2}, \\quad Q'_d = -\\frac{1}{c - a}. \\tag{2.12}",[1304,58284,58286],{"id":58285},"znaménka-a-interpretace","Znaménka a interpretace",[1030,58288,58289,58290,1732,58307,1732,58324,1732,58341,58358,58359,18579],{},"Za podmínek ",[1035,58291,58293],{"className":58292},[1480],[1482,58294,58295],{"xmlns":1484},[1487,58296,58297,58305],{},[1490,58298,58299,58301,58303],{},[1493,58300,1052],{},[1506,58302,3961],{},[1680,58304,1871],{},[1528,58306,57642],{"encoding":1530},[1035,58308,58310],{"className":58309},[1480],[1482,58311,58312],{"xmlns":1484},[1487,58313,58314,58322],{},[1490,58315,58316,58318,58320],{},[1493,58317,2394],{},[1506,58319,2796],{},[1680,58321,1871],{},[1528,58323,34950],{"encoding":1530},[1035,58325,58327],{"className":58326},[1480],[1482,58328,58329],{"xmlns":1484},[1487,58330,58331,58339],{},[1490,58332,58333,58335,58337],{},[1493,58334,8730],{},[1506,58336,2796],{},[1680,58338,1871],{},[1528,58340,55026],{"encoding":1530},[1035,58342,58344],{"className":58343},[1480],[1482,58345,58346],{"xmlns":1484},[1487,58347,58348,58356],{},[1490,58349,58350,58352,58354],{},[1493,58351,2394],{},[1506,58353,2796],{},[1493,58355,3384],{},[1528,58357,57875],{"encoding":1530}," platí (znaménka se ",[1047,58360,58361],{},"nemění",[1035,58363,58365],{"className":58364},[1480],[1482,58366,58367],{"xmlns":1484,"display":1485},[1487,58368,58369,58431],{},[1490,58370,58371,58379,58381,58383,58385,58387,58395,58397,58399,58401,58403,58411,58413,58415,58417,58419,58427,58429],{},[1697,58372,58373,58375,58377],{},[1493,58374,1520],{},[1493,58376,1052],{},[1506,58378,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,58380,2796],{},[1680,58382,1871],{},[1506,58384,1559],{"separator":1041},[1912,58386],{"width":1914},[1697,58388,58389,58391,58393],{},[1493,58390,1520],{},[1493,58392,2394],{},[1506,58394,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,58396,2796],{},[1680,58398,1871],{},[1506,58400,1559],{"separator":1041},[1912,58402],{"width":1914},[1697,58404,58405,58407,58409],{},[1493,58406,1520],{},[1493,58408,8730],{},[1506,58410,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,58412,3961],{},[1680,58414,1871],{},[1506,58416,1559],{"separator":1041},[1912,58418],{"width":1914},[1697,58420,58421,58423,58425],{},[1493,58422,1520],{},[1493,58424,3384],{},[1506,58426,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,58428,3961],{},[1680,58430,28945],{},[1528,58432,58433],{"encoding":1530},"Q'_a > 0, \\qquad Q'_b > 0, \\qquad Q'_c \u003C 0, \\qquad Q'_d \u003C 0.",[1203,58435,58436,58495],{},[1206,58437,58438,1656,58441,58461,58462,58479,58480,1732,58493,2632],{},[1047,58439,58440],{},"Kvantitativní smysl:",[1035,58442,58444],{"className":58443},[1480],[1482,58445,58446],{"xmlns":1484},[1487,58447,58448,58458],{},[1490,58449,58450],{},[1697,58451,58452,58454,58456],{},[1493,58453,1520],{},[1493,58455,17494],{},[1506,58457,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,58459,58460],{"encoding":1530},"Q'_x"," udává, o kolik přibližně vzroste ",[1035,58463,58465],{"className":58464},[1480],[1482,58466,58467],{"xmlns":1484},[1487,58468,58469,58477],{},[1490,58470,58471],{},[2315,58472,58473,58475],{},[1493,58474,1520],{},[1493,58476,2711],{},[1528,58478,14059],{"encoding":1530}," při jednotkové změně parametru ",[1035,58481,58483],{"className":58482},[1480],[1482,58484,58485],{"xmlns":1484},[1487,58486,58487,58491],{},[1490,58488,58489],{},[1493,58490,17494],{},[1528,58492,17494],{"encoding":1530},[1176,58494,52054],{},[1206,58496,58497,58500,58501,58518,58519,2632],{},[1047,58498,58499],{},"Kvalitativní smysl:"," znaménko určuje směr reakce ",[1035,58502,58504],{"className":58503},[1480],[1482,58505,58506],{"xmlns":1484},[1487,58507,58508,58516],{},[1490,58509,58510],{},[2315,58511,58512,58514],{},[1493,58513,1520],{},[1493,58515,2711],{},[1528,58517,14059],{"encoding":1530}," na růst ",[1035,58520,58522],{"className":58521},[1480],[1482,58523,58524],{"xmlns":1484},[1487,58525,58526,58530],{},[1490,58527,58528],{},[1493,58529,17494],{},[1528,58531,17494],{"encoding":1530},[1030,58533,58534,58535,58548,58549,57876,58566,16623],{},"Např. růst ",[1035,58536,58538],{"className":58537},[1480],[1482,58539,58540],{"xmlns":1484},[1487,58541,58542,58546],{},[1490,58543,58544],{},[1493,58545,8730],{},[1528,58547,8730],{"encoding":1530}," (strmější nabídka) ⟹ pokles ",[1035,58550,58552],{"className":58551},[1480],[1482,58553,58554],{"xmlns":1484},[1487,58555,58556,58564],{},[1490,58557,58558],{},[2315,58559,58560,58562],{},[1493,58561,1520],{},[1493,58563,2711],{},[1528,58565,14059],{"encoding":1530},[1035,58567,58569],{"className":58568},[1480],[1482,58570,58571],{"xmlns":1484},[1487,58572,58573,58587],{},[1490,58574,58575,58583,58585],{},[1697,58576,58577,58579,58581],{},[1493,58578,1520],{},[1493,58580,8730],{},[1506,58582,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,58584,3961],{},[1680,58586,1871],{},[1528,58588,58589],{"encoding":1530},"Q'_c \u003C 0",[1030,58591,58592,58593,58625,58626,2632],{},"Při změně jediné proměnné se (2.11) redukuje např. na ",[1035,58594,58596],{"className":58595},[1480],[1482,58597,58598],{"xmlns":1484},[1487,58599,58600,58622],{},[1490,58601,58602,58604,58606,58608,58616,58618,58620],{},[1493,58603,2976],{"mathvariant":1516},[1493,58605,1520],{},[1506,58607,2343],{},[1697,58609,58610,58612,58614],{},[1493,58611,1520],{},[1493,58613,2394],{},[1506,58615,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1988,58617,5016],{},[1493,58619,3384],{},[1493,58621,2394],{},[1528,58623,58624],{"encoding":1530},"\\Delta Q \\approx Q'_b\\,db",". Analogicky lze odvodit multiplikátory pro ",[1035,58627,58629],{"className":58628},[1480],[1482,58630,58631],{"xmlns":1484},[1487,58632,58633,58641],{},[1490,58634,58635],{},[2315,58636,58637,58639],{},[1493,58638,1501],{},[1493,58640,2711],{},[1528,58642,56102],{"encoding":1530},[1304,58644,58646,58647],{"id":58645},"příklad-211-komparativní-statika-pro-qeqe","Příklad 2.11 — komparativní statika pro ",[1035,58648,58650],{"className":58649},[1480],[1482,58651,58652],{"xmlns":1484},[1487,58653,58654,58662],{},[1490,58655,58656],{},[2315,58657,58658,58660],{},[1493,58659,1520],{},[1493,58661,2711],{},[1528,58663,14059],{"encoding":1530},[1030,58665,58666,56206,58668,56241,58694,2632],{},[1047,58667,1263],{},[1035,58669,58671],{"className":58670},[1480],[1482,58672,58673],{"xmlns":1484},[1487,58674,58675,58691],{},[1490,58676,58677,58679,58681,58683,58685,58687,58689],{},[1493,58678,1501],{},[1506,58680,1508],{},[1506,58682,1888],{},[1680,58684,3201],{},[1493,58686,1520],{},[1506,58688,2162],{},[1680,58690,7380],{},[1528,58692,58693],{"encoding":1530},"P = -3Q + 40",[1035,58695,58697],{"className":58696},[1480],[1482,58698,58699],{"xmlns":1484},[1487,58700,58701,58715],{},[1490,58702,58703,58705,58707,58709,58711,58713],{},[1493,58704,1501],{},[1506,58706,1508],{},[1680,58708,3687],{},[1493,58710,1520],{},[1506,58712,2162],{},[1680,58714,1775],{},[1528,58716,58717],{"encoding":1530},"P = 0{,}5Q + 10",[1030,58719,58720,58722],{},[1047,58721,52997],{}," Rovnovážné množství",[1035,58724,58726],{"className":58725},[1480],[1482,58727,58728],{"xmlns":1484,"display":1485},[1487,58729,58730,58798],{},[1490,58731,58732,58738,58740,58758,58760,58784,58786,58793,58795],{},[2315,58733,58734,58736],{},[1493,58735,1520],{},[1493,58737,2711],{},[1506,58739,1508],{},[1510,58741,58742,58750],{},[1490,58743,58744,58746,58748],{},[1493,58745,2394],{},[1506,58747,1888],{},[1493,58749,3384],{},[1490,58751,58752,58754,58756],{},[1493,58753,8730],{},[1506,58755,1888],{},[1493,58757,1052],{},[1506,58759,1508],{},[1510,58761,58762,58770],{},[1490,58763,58764,58766,58768],{},[1680,58765,7380],{},[1506,58767,1888],{},[1680,58769,1775],{},[1490,58771,58772,58774,58776,58778,58780,58782],{},[1680,58773,3687],{},[1506,58775,1888],{},[1506,58777,1553],{"stretchy":1552},[1506,58779,1888],{},[1680,58781,3201],{},[1506,58783,1564],{"stretchy":1552},[1506,58785,1508],{},[1510,58787,58788,58790],{},[1680,58789,6956],{},[1680,58791,58792],{},"3,5",[1506,58794,2343],{},[1680,58796,58797],{},"8,571.",[1528,58799,58800],{"encoding":1530},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\approx 8{,}571.",[1030,58802,58803,58847],{},[1047,58804,58805,58806,18125,58819,18139,58833,3864],{},"(a) Změna ",[1035,58807,58809],{"className":58808},[1480],[1482,58810,58811],{"xmlns":1484},[1487,58812,58813,58817],{},[1490,58814,58815],{},[1493,58816,8730],{},[1528,58818,8730],{"encoding":1530},[1035,58820,58822],{"className":58821},[1480],[1482,58823,58824],{"xmlns":1484},[1487,58825,58826,58830],{},[1490,58827,58828],{},[1680,58829,3687],{},[1528,58831,58832],{"encoding":1530},"0{,}5",[1035,58834,58836],{"className":58835},[1480],[1482,58837,58838],{"xmlns":1484},[1487,58839,58840,58844],{},[1490,58841,58842],{},[1680,58843,3332],{},[1528,58845,58846],{"encoding":1530},"0{,}6"," Dle (2.12):",[1035,58849,58851],{"className":58850},[1480],[1482,58852,58853],{"xmlns":1484,"display":1485},[1487,58854,58855,58932],{},[1490,58856,58857,58865,58867,58869,58871,58873,58875,58901,58903,58905,58907,58909,58911,58921,58923,58925,58927,58929],{},[1697,58858,58859,58861,58863],{},[1493,58860,1520],{},[1493,58862,8730],{},[1506,58864,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1988,58866,5016],{},[1493,58868,3384],{},[1493,58870,8730],{},[1506,58872,1508],{},[1506,58874,1888],{},[1510,58876,58877,58885],{},[1490,58878,58879,58881,58883],{},[1493,58880,2394],{},[1506,58882,1888],{},[1493,58884,3384],{},[1490,58886,58887,58889,58891,58893,58895],{},[1506,58888,1553],{"stretchy":1552},[1493,58890,8730],{},[1506,58892,1888],{},[1493,58894,1052],{},[2315,58896,58897,58899],{},[1506,58898,1564],{"stretchy":1552},[1680,58900,1691],{},[1988,58902,5016],{},[1493,58904,3384],{},[1493,58906,8730],{},[1506,58908,1508],{},[1506,58910,1888],{},[1510,58912,58913,58915],{},[1680,58914,6956],{},[2315,58916,58917,58919],{},[1680,58918,58792],{},[1680,58920,1691],{},[1506,58922,1714],{},[1680,58924,13237],{},[1506,58926,2343],{},[1506,58928,1888],{},[1680,58930,58931],{},"0,245.",[1528,58933,58934],{"encoding":1530},"Q'_c\\,dc = -\\frac{b - d}{(c - a)^2}\\,dc = -\\frac{30}{3{,}5^2}\\cdot 0{,}1 \\approx -0{,}245.",[1030,58936,58937,58938,2632],{},"Nové rovnovážné množství ",[1035,58939,58941],{"className":58940},[1480],[1482,58942,58943],{"xmlns":1484},[1487,58944,58945,58970],{},[1490,58946,58947,58955,58957,58960,58962,58965,58967],{},[1697,58948,58949,58951,58953],{},[1493,58950,1520],{},[1680,58952,1682],{},[1493,58954,2711],{},[1506,58956,2343],{},[1680,58958,58959],{},"8,571",[1506,58961,1888],{},[1680,58963,58964],{},"0,245",[1506,58966,1508],{},[1680,58968,58969],{},"8,326",[1528,58971,58972],{"encoding":1530},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326",[1030,58974,58975,59060],{},[1047,58976,58977,58978,1732,58998,1732,59020,1732,59040,2632],{},"(b) Současné změny ",[1035,58979,58981],{"className":58980},[1480],[1482,58982,58983],{"xmlns":1484},[1487,58984,58985,58995],{},[1490,58986,58987,58989,58991,58993],{},[1493,58988,3384],{},[1493,58990,1052],{},[1506,58992,1508],{},[1680,58994,3687],{},[1528,58996,58997],{"encoding":1530},"da = 0{,}5",[1035,58999,59001],{"className":59000},[1480],[1482,59002,59003],{"xmlns":1484},[1487,59004,59005,59017],{},[1490,59006,59007,59009,59011,59013,59015],{},[1493,59008,3384],{},[1493,59010,2394],{},[1506,59012,1508],{},[1506,59014,1888],{},[1680,59016,1752],{},[1528,59018,59019],{"encoding":1530},"db = -5",[1035,59021,59023],{"className":59022},[1480],[1482,59024,59025],{"xmlns":1484},[1487,59026,59027,59037],{},[1490,59028,59029,59031,59033,59035],{},[1493,59030,3384],{},[1493,59032,8730],{},[1506,59034,1508],{},[1680,59036,13237],{},[1528,59038,59039],{"encoding":1530},"dc = 0{,}1",[1035,59041,59043],{"className":59042},[1480],[1482,59044,59045],{"xmlns":1484},[1487,59046,59047,59057],{},[1490,59048,59049,59051,59053,59055],{},[1493,59050,3384],{},[1493,59052,3384],{},[1506,59054,1508],{},[1680,59056,1682],{},[1528,59058,59059],{"encoding":1530},"dd = 1"," Dosazením do (2.11):",[1035,59062,59064],{"className":59063},[1480],[1482,59065,59066],{"xmlns":1484,"display":1485},[1487,59067,59068,59211],{},[19617,59069,59070,59152,59188],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,59071,59072,59082],{},[19624,59073,59074],{},[1869,59075,59076],{"scriptlevel":1871,"displaystyle":1041},[1490,59077,59078,59080],{},[1493,59079,2976],{"mathvariant":1516},[1493,59081,1520],{},[19624,59083,59084],{},[1869,59085,59086],{"scriptlevel":1871,"displaystyle":1041},[1490,59087,59088,59090,59092,59102,59104,59106,59108,59114,59116,59118,59120,59122,59124,59126,59136,59138,59140,59142,59148,59150],{},[1490,59089],{},[1506,59091,2343],{},[1510,59093,59094,59096],{},[1680,59095,6956],{},[2315,59097,59098,59100],{},[1680,59099,58792],{},[1680,59101,1691],{},[1506,59103,1714],{},[1680,59105,3687],{},[1506,59107,2162],{},[1510,59109,59110,59112],{},[1680,59111,1682],{},[1680,59113,58792],{},[1506,59115,1714],{},[1506,59117,1553],{"stretchy":1552},[1506,59119,1888],{},[1680,59121,1752],{},[1506,59123,1564],{"stretchy":1552},[1506,59125,1888],{},[1510,59127,59128,59130],{},[1680,59129,6956],{},[2315,59131,59132,59134],{},[1680,59133,58792],{},[1680,59135,1691],{},[1506,59137,1714],{},[1680,59139,13237],{},[1506,59141,1888],{},[1510,59143,59144,59146],{},[1680,59145,1682],{},[1680,59147,58792],{},[1506,59149,1714],{},[1680,59151,1682],{},[19621,59153,59154,59160],{},[19624,59155,59156],{},[1869,59157,59158],{"scriptlevel":1871,"displaystyle":1041},[1490,59159],{},[19624,59161,59162],{},[1869,59163,59164],{"scriptlevel":1871,"displaystyle":1041},[1490,59165,59166,59168,59170,59173,59175,59178,59180,59183,59185],{},[1490,59167],{},[1506,59169,1508],{},[1680,59171,59172],{},"1,2245",[1506,59174,1888],{},[1680,59176,59177],{},"1,4286",[1506,59179,1888],{},[1680,59181,59182],{},"0,2449",[1506,59184,1888],{},[1680,59186,59187],{},"0,2857",[19621,59189,59190,59196],{},[19624,59191,59192],{},[1869,59193,59194],{"scriptlevel":1871,"displaystyle":1041},[1490,59195],{},[19624,59197,59198],{},[1869,59199,59200],{"scriptlevel":1871,"displaystyle":1041},[1490,59201,59202,59204,59206,59208],{},[1490,59203],{},[1506,59205,2343],{},[1506,59207,1888],{},[1680,59209,59210],{},"0,735.",[1528,59212,59213],{"encoding":1530},"\\begin{aligned}\n\\Delta Q &\\approx \\frac{30}{3{,}5^2}\\cdot 0{,}5 + \\frac{1}{3{,}5}\\cdot(-5) - \\frac{30}{3{,}5^2}\\cdot 0{,}1 - \\frac{1}{3{,}5}\\cdot 1 \\\\\n&= 1{,}2245 - 1{,}4286 - 0{,}2449 - 0{,}2857 \\\\\n&\\approx -0{,}735.\n\\end{aligned}",[1030,59215,45390,59216,2632],{},[1035,59217,59219],{"className":59218},[1480],[1482,59220,59221],{"xmlns":1484},[1487,59222,59223,59247],{},[1490,59224,59225,59233,59235,59237,59239,59242,59244],{},[1697,59226,59227,59229,59231],{},[1493,59228,1520],{},[1680,59230,1682],{},[1493,59232,2711],{},[1506,59234,2343],{},[1680,59236,58959],{},[1506,59238,1888],{},[1680,59240,59241],{},"0,735",[1506,59243,1508],{},[1680,59245,59246],{},"7,836",[1528,59248,59249],{"encoding":1530},"Q_1^E \\approx 8{,}571 - 0{,}735 = 7{,}836",[1030,59251,59252,59253,16623],{},"Princip multiplikátorů lze uplatnit na libovolné ekonomické proměnné — analogicky v makroekonomii (viz ",[1052,59254,265],{"className":59255,"dataFsResolvedFilePath":2622,"href":2623},[1055],[1246,59257],{},[1065,59259,28281],{"id":28280},[1023,59261,59263,59269],{"className":59262,"dataCallout":582},[1026,1186],[1030,59264,59266,1042],{"className":59265},[1033],[1035,59267],{"className":59268,"ariaHidden":1041},[1038,1193,1040],[1030,59270,59271,7606,59274,28611,59290,7606,59293,59309,59310,2632],{},[1047,59272,59273],{},"Přebytek spotřebitele",[1035,59275,59277],{"className":59276},[1480],[1482,59278,59279],{"xmlns":1484},[1487,59280,59281,59287],{},[1490,59282,59283,59285],{},[1493,59284,1998],{},[1493,59286,2001],{},[1528,59288,59289],{"encoding":1530},"CS",[1047,59291,59292],{},"přebytek výrobce",[1035,59294,59296],{"className":59295},[1480],[1482,59297,59298],{"xmlns":1484},[1487,59299,59300,59306],{},[1490,59301,59302,59304],{},[1493,59303,1501],{},[1493,59305,2001],{},[1528,59307,59308],{"encoding":1530},"PS",") jsou míry čistého prospěchu stran trhu, definované pomocí určitého integrálu a geometricky odpovídající plochám mezi rovnovážnou cenou a příslušnou křivkou. Podrobný výklad je na samostatné stránce ",[1052,59311,59313],{"className":59312,"dataFsResolvedFilePath":17231,"href":17232},[1055],"prebytek-spotrebitele-vyrobce",[1030,59315,59316],{},[18014,59317],{"alt":59318,"className":59319,"src":59320},"imek-prebytky-cs-ps",[1055,18018],"\u002Fwiki-assets\u002Fimek-prebytky-cs-ps.jpeg",[1030,59322,59323,7606,59325,59328],{},[1047,59324,59273],{},[1176,59326,59327],{},"consumer surplus",") — rozdíl mezi ochotou platit a skutečnou platbou:",[1035,59330,59332],{"className":59331},[1480],[1482,59333,59334],{"xmlns":1484,"display":1485},[1487,59335,59336,59413],{},[19617,59337,59338],{"width":19619},[19621,59339,59340,59342,59406,59408],{},[19624,59341],{"width":19626},[19624,59343,59344],{},[1490,59345,59346,59348,59350,59352,59358,59360,59362,59374,59376,59378,59380,59382,59384,59386,59388,59390,59396,59398,59404],{},[1493,59347,1998],{},[1493,59349,2001],{},[1506,59351,1553],{"stretchy":1552},[1497,59353,59354,59356],{},[1493,59355,1520],{},[1680,59357,1871],{},[1506,59359,1564],{"stretchy":1552},[1506,59361,1508],{},[1697,59363,59364,59366,59368],{},[1506,59365,10857],{},[1680,59367,1871],{},[1497,59369,59370,59372],{},[1493,59371,1520],{},[1680,59373,1871],{},[1493,59375,3712],{},[1506,59377,1553],{"stretchy":1552},[1493,59379,1520],{},[1506,59381,1564],{"stretchy":1552},[1988,59383,5016],{},[1493,59385,3384],{},[1493,59387,1520],{},[1506,59389,1888],{},[1497,59391,59392,59394],{},[1493,59393,1501],{},[1680,59395,1871],{},[1988,59397,5016],{},[1497,59399,59400,59402],{},[1493,59401,1520],{},[1680,59403,1871],{},[1493,59405,2632],{"mathvariant":1516},[19624,59407],{"width":19626},[19624,59409,59410],{},[1988,59411,59412],{},"(2.14)",[1528,59414,59415],{"encoding":1530},"CS(Q_0) = \\int_0^{Q_0} D(Q)\\,dQ - P_0\\,Q_0. \\tag{2.14}",[1030,59417,59418,7606,59421,59424],{},[1047,59419,59420],{},"Přebytek výrobce",[1176,59422,59423],{},"producer surplus",") — rozdíl mezi tržbou a minimální cenou:",[1035,59426,59428],{"className":59427},[1480],[1482,59429,59430],{"xmlns":1484,"display":1485},[1487,59431,59432,59509],{},[19617,59433,59434],{"width":19619},[19621,59435,59436,59438,59502,59504],{},[19624,59437],{"width":19626},[19624,59439,59440],{},[1490,59441,59442,59444,59446,59448,59454,59456,59458,59464,59466,59472,59474,59486,59488,59490,59492,59494,59496,59498,59500],{},[1493,59443,1501],{},[1493,59445,2001],{},[1506,59447,1553],{"stretchy":1552},[1497,59449,59450,59452],{},[1493,59451,1520],{},[1680,59453,1871],{},[1506,59455,1564],{"stretchy":1552},[1506,59457,1508],{},[1497,59459,59460,59462],{},[1493,59461,1501],{},[1680,59463,1871],{},[1988,59465,5016],{},[1497,59467,59468,59470],{},[1493,59469,1520],{},[1680,59471,1871],{},[1506,59473,1888],{},[1697,59475,59476,59478,59480],{},[1506,59477,10857],{},[1680,59479,1871],{},[1497,59481,59482,59484],{},[1493,59483,1520],{},[1680,59485,1871],{},[1493,59487,2001],{},[1506,59489,1553],{"stretchy":1552},[1493,59491,1520],{},[1506,59493,1564],{"stretchy":1552},[1988,59495,5016],{},[1493,59497,3384],{},[1493,59499,1520],{},[1493,59501,2632],{"mathvariant":1516},[19624,59503],{"width":19626},[19624,59505,59506],{},[1988,59507,59508],{},"(2.15)",[1528,59510,59511],{"encoding":1530},"PS(Q_0) = P_0\\,Q_0 - \\int_0^{Q_0} S(Q)\\,dQ. \\tag{2.15}",[1030,59513,59514,59515,2632],{},"Geometricky jde o plochy mezi rovnovážnou cenou a příslušnou křivkou; výpočet využívá aparát ",[1052,59516,59518],{"className":59517,"dataFsResolvedFilePath":17256,"href":17257},[1055],"určitého integrálu",[1246,59520],{},[1065,59522,59524],{"id":59523},"příklady-z-knihy-přehled","Příklady z knihy — přehled",[1203,59526,59527,59558,59563,59569,59597,59603,59632,59638,59718,59744],{},[1206,59528,59529,59531,59532,59557],{},[1047,59530,52961],{}," — lineární poptávka ",[1035,59533,59535],{"className":59534},[1480],[1482,59536,59537],{"xmlns":1484},[1487,59538,59539,59555],{},[1490,59540,59541,59543,59545,59547,59549,59551,59553],{},[1493,59542,1501],{},[1506,59544,1508],{},[1506,59546,1888],{},[1680,59548,1691],{},[1493,59550,1520],{},[1506,59552,2162],{},[1680,59554,4965],{},[1528,59556,52992],{"encoding":1530},", alternativní tvar, cenové rozpětí.",[1206,59559,59560,59562],{},[1047,59561,53170],{}," — empirické křivky poptávky po cukru (rodina vs. trh).",[1206,59564,59565,59568],{},[1047,59566,59567],{},"Příklad 2.3"," — posun poptávky při zdanění kupujícího.",[1206,59570,59571,59573,59574,2632],{},[1047,59572,55520],{}," — lineární nabídka ",[1035,59575,59577],{"className":59576},[1480],[1482,59578,59579],{"xmlns":1484},[1487,59580,59581,59595],{},[1490,59582,59583,59585,59587,59589,59591,59593],{},[1493,59584,1501],{},[1506,59586,1508],{},[1680,59588,3687],{},[1493,59590,1520],{},[1506,59592,2162],{},[1680,59594,2309],{},[1528,59596,55549],{"encoding":1530},[1206,59598,59599,59602],{},[1047,59600,59601],{},"Příklad 2.6"," — posun nabídky při zdanění výrobce.",[1206,59604,59605,59608,59609,2632],{},[1047,59606,59607],{},"Příklad 2.7"," — kvadratická rovnováha, ",[1035,59610,59612],{"className":59611},[1480],[1482,59613,59614],{"xmlns":1484},[1487,59615,59616,59630],{},[1490,59617,59618,59620,59622,59624,59626,59628],{},[1493,59619,2711],{},[1506,59621,14314],{"stretchy":1552},[1680,59623,4007],{},[1506,59625,1559],{"separator":1041},[1680,59627,56484],{},[1506,59629,14323],{"stretchy":1552},[1528,59631,56512],{"encoding":1530},[1206,59633,59634,59637],{},[1047,59635,59636],{},"Příklad 2.8"," — dvoukomoditní trh, soustava rovnic, komplementy.",[1206,59639,59640,59643,59644,59661,59662,1732,59687,59714,59715,7909],{},[1047,59641,59642],{},"Příklad 2.9"," — daň ",[1035,59645,59647],{"className":59646},[1480],[1482,59648,59649],{"xmlns":1484},[1487,59650,59651,59659],{},[1490,59652,59653,59655,59657],{},[1493,59654,5289],{},[1506,59656,1508],{},[1680,59658,7508],{},[1528,59660,55920],{"encoding":1530}," na výrobce; rozklad ",[1035,59663,59665],{"className":59664},[1480],[1482,59666,59667],{"xmlns":1484},[1487,59668,59669,59685],{},[1490,59670,59671,59681,59683],{},[1497,59672,59673,59675],{},[1493,59674,5289],{},[1490,59676,59677,59679],{},[1493,59678,25906],{},[1493,59680,1030],{},[1506,59682,1508],{},[1680,59684,1691],{},[1528,59686,57528],{"encoding":1530},[1035,59688,59690],{"className":59689},[1480],[1482,59691,59692],{"xmlns":1484},[1487,59693,59694,59712],{},[1490,59695,59696,59708,59710],{},[1497,59697,59698,59700],{},[1493,59699,5289],{},[1490,59701,59702,59704,59706],{},[1493,59703,25950],{},[1493,59705,3052],{},[1493,59707,7740],{},[1506,59709,1508],{},[1680,59711,4007],{},[1528,59713,57557],{"encoding":1530},". (Viz ",[1052,59716,57273],{"className":59717,"dataFsResolvedFilePath":57271,"href":57272},[1055],[1206,59719,59720,59643,59723,59740,59741,7909],{},[1047,59721,59722],{},"Příklad 2.10",[1035,59724,59726],{"className":59725},[1480],[1482,59727,59728],{"xmlns":1484},[1487,59729,59730,59738],{},[1490,59731,59732,59734,59736],{},[1493,59733,5289],{},[1506,59735,1508],{},[1680,59737,7508],{},[1528,59739,55920],{"encoding":1530}," na spotřebitele; stejné čisté ceny i množství. (Viz ",[1052,59742,57273],{"className":59743,"dataFsResolvedFilePath":57271,"href":57272},[1055],[1206,59745,59746,59749],{},[1047,59747,59748],{},"Příklad 2.11"," — komparativní statika, multiplikátory, změny parametrů.",[1246,59751],{},[1065,59753,59755],{"id":59754},"úlohy-k-samostatnému-řešení","Úlohy k samostatnému řešení",[1304,59757,59759],{"id":59758},"základní-analýza-poptávky","Základní analýza poptávky",[1030,59761,59762,59765,59766,59801,59802,59828],{},[1047,59763,59764],{},"2.1"," Je dána poptávka ",[1035,59767,59769],{"className":59768},[1480],[1482,59770,59771],{"xmlns":1484},[1487,59772,59773,59798],{},[1490,59774,59775,59777,59779,59781,59783,59785,59787,59789,59792,59794,59796],{},[1493,59776,1520],{},[1506,59778,1508],{},[1493,59780,3712],{},[1506,59782,1553],{"stretchy":1552},[1493,59784,1501],{},[1506,59786,1564],{"stretchy":1552},[1506,59788,1508],{},[1680,59790,59791],{},"75",[1506,59793,1888],{},[1680,59795,1752],{},[1493,59797,1501],{},[1528,59799,59800],{"encoding":1530},"Q = D(P) = 75 - 5P",". (a) Načrtněte křivku poptávky. (b) Stanovte reálné cenové rozpětí. (c) Vypočtěte množství při cenách ",[1035,59803,59805],{"className":59804},[1480],[1482,59806,59807],{"xmlns":1484},[1487,59808,59809,59825],{},[1490,59810,59811,59813,59815,59817,59819,59821,59823],{},[1680,59812,1871],{},[1506,59814,1559],{"separator":1041},[1680,59816,1752],{},[1506,59818,1559],{"separator":1041},[1680,59820,1775],{},[1506,59822,1559],{"separator":1041},[1680,59824,9787],{},[1528,59826,59827],{"encoding":1530},"0, 5, 10, 15"," a výsledky vyznačte na křivku poptávky.",[1030,59830,59831,59834,59835,59853,59854,18579],{},[1047,59832,59833],{},"2.2"," Ověřte, že uvedené funkce vyjadřují (s případným omezením pro ",[1035,59836,59838],{"className":59837},[1480],[1482,59839,59840],{"xmlns":1484},[1487,59841,59842,59850],{},[1490,59843,59844,59846,59848],{},[1493,59845,1501],{},[1506,59847,1559],{"separator":1041},[1493,59849,1520],{},[1528,59851,59852],{"encoding":1530},"P, Q",") poptávku (využijte testu na zápornost derivace), charakterizujte tvar křivky poptávky a vyjádřete ve tvaru poptávky v alternativním tvaru (",[1035,59855,59857],{"className":59856},[1480],[1482,59858,59859],{"xmlns":1484},[1487,59860,59861,59877],{},[1490,59862,59863,59865,59867,59869,59871,59873,59875],{},[1493,59864,1052],{},[1506,59866,1559],{"separator":1041},[1493,59868,2394],{},[1506,59870,1559],{"separator":1041},[1493,59872,8730],{},[1506,59874,2796],{},[1680,59876,1871],{},[1528,59878,59879],{"encoding":1530},"a, b, c > 0",[1203,59881,59882,59914,59945,59979,60010,60045],{},[1206,59883,10671,59884],{},[1035,59885,59887],{"className":59886},[1480],[1482,59888,59889],{"xmlns":1484},[1487,59890,59891,59911],{},[1490,59892,59893,59895,59897],{},[1493,59894,1520],{},[1506,59896,1508],{},[1869,59898,59899],{"scriptlevel":1871,"displaystyle":1041},[1510,59900,59901,59903],{},[1493,59902,1052],{},[1490,59904,59905,59907,59909],{},[1493,59906,1501],{},[1506,59908,2162],{},[1493,59910,8730],{},[1528,59912,59913],{"encoding":1530},"Q = \\dfrac{a}{P + c}",[1206,59915,59916,59917],{},"(b) ",[1035,59918,59920],{"className":59919},[1480],[1482,59921,59922],{"xmlns":1484},[1487,59923,59924,59942],{},[1490,59925,59926,59928,59930],{},[1493,59927,1520],{},[1506,59929,1508],{},[2324,59931,59932],{},[1490,59933,59934,59936,59938,59940],{},[1493,59935,1052],{},[1506,59937,1888],{},[1493,59939,2394],{},[1493,59941,1520],{},[1528,59943,59944],{"encoding":1530},"Q = \\sqrt{a - bQ}",[1206,59946,13176,59947],{},[1035,59948,59950],{"className":59949},[1480],[1482,59951,59952],{"xmlns":1484},[1487,59953,59954,59976],{},[1490,59955,59956,59958,59960],{},[1493,59957,1520],{},[1506,59959,1508],{},[1869,59961,59962],{"scriptlevel":1871,"displaystyle":1041},[1510,59963,59964,59974],{},[1490,59965,59966,59968,59970],{},[1493,59967,1052],{},[1506,59969,1888],{},[2324,59971,59972],{},[1493,59973,1501],{},[1493,59975,2394],{},[1528,59977,59978],{"encoding":1530},"Q = \\dfrac{a - \\sqrt{P}}{b}",[1206,59980,59981,59982],{},"(d) ",[1035,59983,59985],{"className":59984},[1480],[1482,59986,59987],{"xmlns":1484},[1487,59988,59989,60007],{},[1490,59990,59991,59993,59995,59997,59999,60001],{},[1493,59992,1501],{},[1506,59994,1508],{},[1493,59996,1052],{},[1506,59998,1888],{},[1493,60000,2394],{},[2315,60002,60003,60005],{},[1493,60004,1520],{},[1680,60006,1691],{},[1528,60008,60009],{"encoding":1530},"P = a - bQ^2",[1206,60011,60012,60013],{},"(e) ",[1035,60014,60016],{"className":60015},[1480],[1482,60017,60018],{"xmlns":1484},[1487,60019,60020,60042],{},[1490,60021,60022,60024,60026,60028,60038,60040],{},[1493,60023,1520],{},[1506,60025,1508],{},[1493,60027,2394],{},[2315,60029,60030,60032],{},[1493,60031,1501],{},[1490,60033,60034,60036],{},[1506,60035,1888],{},[1493,60037,1052],{},[1506,60039,2162],{},[1493,60041,8730],{},[1528,60043,60044],{"encoding":1530},"Q = bP^{-a} + c",[1206,60046,60047,60048],{},"(f) ",[1035,60049,60051],{"className":60050},[1480],[1482,60052,60053],{"xmlns":1484},[1487,60054,60055,60077],{},[1490,60056,60057,60059,60061,60063,60065],{},[1493,60058,1520],{},[1506,60060,1508],{},[1493,60062,1052],{},[1506,60064,1714],{},[2315,60066,60067,60069],{},[1493,60068,8584],{},[1490,60070,60071,60073,60075],{},[1506,60072,1888],{},[1493,60074,2394],{},[1493,60076,1501],{},[1528,60078,60079],{"encoding":1530},"Q = a \\cdot e^{-bP}",[1030,60081,60082,60085],{},[1047,60083,60084],{},"2.3"," Rozhodněte, jak se změní křivka poptávky, jestliže se zvýší (ceteris paribus):",[1203,60087,60088,60091,60094],{},[1206,60089,60090],{},"(a) Cena substitutu.",[1206,60092,60093],{},"(b) Cena komplementu.",[1206,60095,60096],{},"(c) Výdaje na reklamu.",[1030,60098,60099,59765,60101,60135,60136,60164],{},[1047,60100,40215],{},[1035,60102,60104],{"className":60103},[1480],[1482,60105,60106],{"xmlns":1484},[1487,60107,60108,60132],{},[1490,60109,60110,60112,60114,60116,60118,60120,60122,60124,60126,60128,60130],{},[1493,60111,1501],{},[1506,60113,1508],{},[1493,60115,3712],{},[1506,60117,1553],{"stretchy":1552},[1493,60119,1520],{},[1506,60121,1564],{"stretchy":1552},[1506,60123,1508],{},[1680,60125,6797],{},[1506,60127,1888],{},[1680,60129,1691],{},[1493,60131,1520],{},[1528,60133,60134],{"encoding":1530},"P = D(Q) = 12 - 2Q",". Najděte novou poptávku ",[1035,60137,60139],{"className":60138},[1480],[1482,60140,60141],{"xmlns":1484},[1487,60142,60143,60161],{},[1490,60144,60145,60147,60149,60155,60157,60159],{},[1493,60146,1501],{},[1506,60148,1508],{},[2315,60150,60151,60153],{},[1493,60152,3712],{},[1506,60154,2287],{},[1506,60156,1553],{"stretchy":1552},[1493,60158,1520],{},[1506,60160,1564],{"stretchy":1552},[1528,60162,60163],{"encoding":1530},"P = D^*(Q)",", na kterou se změní původní poptávka v důsledku uložení daně 6 Kč na kupujícího na každou jednotku zboží. Graficky interpretujte.",[1030,60166,60167,60170],{},[1047,60168,60169],{},"2.5"," Pro zadané dvojice funkcí rozhodněte, zda vyjadřují funkce poptávky ve dvoukomoditním trhu dvou závislých zboží. V kladném případě určete, zda jde o substituty, resp. komplementy a specifikujte zadané proměnné:",[1203,60172,60173,60257,60333,60419,60507],{},[1206,60174,10671,60175,1732,60215,2632],{},[1035,60176,60178],{"className":60177},[1480],[1482,60179,60180],{"xmlns":1484},[1487,60181,60182,60212],{},[1490,60183,60184,60190,60192,60194,60196,60198,60204,60206],{},[1497,60185,60186,60188],{},[1493,60187,11353],{},[1680,60189,1682],{},[1506,60191,1508],{},[1680,60193,8436],{},[1506,60195,1888],{},[1680,60197,4007],{},[1497,60199,60200,60202],{},[1493,60201,3633],{},[1680,60203,1682],{},[1506,60205,2162],{},[1497,60207,60208,60210],{},[1493,60209,3633],{},[1680,60211,1691],{},[1528,60213,60214],{"encoding":1530},"B_1 = 20 - 4A_1 + A_2",[1035,60216,60218],{"className":60217},[1480],[1482,60219,60220],{"xmlns":1484},[1487,60221,60222,60254],{},[1490,60223,60224,60230,60232,60234,60236,60238,60244,60246,60248],{},[1497,60225,60226,60228],{},[1493,60227,11353],{},[1680,60229,1691],{},[1506,60231,1508],{},[1680,60233,1775],{},[1506,60235,2162],{},[1680,60237,1691],{},[1497,60239,60240,60242],{},[1493,60241,3633],{},[1680,60243,1682],{},[1506,60245,1888],{},[1680,60247,4007],{},[1497,60249,60250,60252],{},[1493,60251,3633],{},[1680,60253,1691],{},[1528,60255,60256],{"encoding":1530},"B_2 = 10 + 2A_1 - 4A_2",[1206,60258,59916,60259,1732,60301,2632],{},[1035,60260,60262],{"className":60261},[1480],[1482,60263,60264],{"xmlns":1484},[1487,60265,60266,60298],{},[1490,60267,60268,60274,60276,60278,60280,60282,60288,60290,60292],{},[1497,60269,60270,60272],{},[1493,60271,11353],{},[1680,60273,1682],{},[1506,60275,1508],{},[1680,60277,2292],{},[1506,60279,1888],{},[1680,60281,1775],{},[1497,60283,60284,60286],{},[1493,60285,3633],{},[1680,60287,1682],{},[1506,60289,1888],{},[1680,60291,7508],{},[1497,60293,60294,60296],{},[1493,60295,3633],{},[1680,60297,1691],{},[1528,60299,60300],{"encoding":1530},"B_1 = 50 - 10A_1 - 6A_2",[1035,60302,60304],{"className":60303},[1480],[1482,60305,60306],{"xmlns":1484},[1487,60307,60308,60330],{},[1490,60309,60310,60316,60318,60320,60322,60324],{},[1497,60311,60312,60314],{},[1493,60313,11353],{},[1680,60315,1691],{},[1506,60317,1508],{},[1680,60319,9787],{},[1506,60321,1888],{},[1680,60323,1775],{},[1497,60325,60326,60328],{},[1493,60327,3633],{},[1680,60329,1691],{},[1528,60331,60332],{"encoding":1530},"B_2 = 15 - 10A_2",[1206,60334,13176,60335,1732,60377,2632],{},[1035,60336,60338],{"className":60337},[1480],[1482,60339,60340],{"xmlns":1484},[1487,60341,60342,60374],{},[1490,60343,60344,60350,60352,60354,60356,60358,60364,60366,60368],{},[1497,60345,60346,60348],{},[1493,60347,11353],{},[1680,60349,1682],{},[1506,60351,1508],{},[1680,60353,6956],{},[1506,60355,1888],{},[1680,60357,1691],{},[1497,60359,60360,60362],{},[1493,60361,3633],{},[1680,60363,1682],{},[1506,60365,1888],{},[1680,60367,4007],{},[1497,60369,60370,60372],{},[1493,60371,3633],{},[1680,60373,1691],{},[1528,60375,60376],{"encoding":1530},"B_1 = 30 - 2A_1 - 4A_2",[1035,60378,60380],{"className":60379},[1480],[1482,60381,60382],{"xmlns":1484},[1487,60383,60384,60416],{},[1490,60385,60386,60392,60394,60396,60398,60400,60406,60408,60410],{},[1497,60387,60388,60390],{},[1493,60389,11353],{},[1680,60391,1691],{},[1506,60393,1508],{},[1680,60395,9787],{},[1506,60397,2162],{},[1680,60399,1691],{},[1497,60401,60402,60404],{},[1493,60403,3633],{},[1680,60405,1682],{},[1506,60407,1888],{},[1680,60409,1691],{},[1497,60411,60412,60414],{},[1493,60413,3633],{},[1680,60415,1691],{},[1528,60417,60418],{"encoding":1530},"B_2 = 15 + 2A_1 - 2A_2",[1206,60420,59981,60421,1732,60465,2632],{},[1035,60422,60424],{"className":60423},[1480],[1482,60425,60426],{"xmlns":1484},[1487,60427,60428,60462],{},[1490,60429,60430,60436,60438,60440,60442,60444,60446,60452,60454,60456],{},[1497,60431,60432,60434],{},[1493,60433,11353],{},[1680,60435,1682],{},[1506,60437,1508],{},[1506,60439,1888],{},[1680,60441,8436],{},[1506,60443,1888],{},[1680,60445,1691],{},[1497,60447,60448,60450],{},[1493,60449,3633],{},[1680,60451,1682],{},[1506,60453,2162],{},[1680,60455,3201],{},[1497,60457,60458,60460],{},[1493,60459,3633],{},[1680,60461,1691],{},[1528,60463,60464],{"encoding":1530},"B_1 = -20 - 2A_1 + 3A_2",[1035,60466,60468],{"className":60467},[1480],[1482,60469,60470],{"xmlns":1484},[1487,60471,60472,60504],{},[1490,60473,60474,60480,60482,60484,60486,60488,60494,60496,60498],{},[1497,60475,60476,60478],{},[1493,60477,11353],{},[1680,60479,1691],{},[1506,60481,1508],{},[1680,60483,1775],{},[1506,60485,2162],{},[1680,60487,1691],{},[1497,60489,60490,60492],{},[1493,60491,3633],{},[1680,60493,1682],{},[1506,60495,1888],{},[1680,60497,1691],{},[1497,60499,60500,60502],{},[1493,60501,3633],{},[1680,60503,1691],{},[1528,60505,60506],{"encoding":1530},"B_2 = 10 + 2A_1 - 2A_2",[1206,60508,60012,60509,1732,60551,2632],{},[1035,60510,60512],{"className":60511},[1480],[1482,60513,60514],{"xmlns":1484},[1487,60515,60516,60548],{},[1490,60517,60518,60524,60526,60528,60530,60532,60538,60540,60542],{},[1497,60519,60520,60522],{},[1493,60521,11353],{},[1680,60523,1682],{},[1506,60525,1508],{},[1680,60527,8436],{},[1506,60529,2162],{},[1680,60531,1691],{},[1497,60533,60534,60536],{},[1493,60535,3633],{},[1680,60537,1682],{},[1506,60539,2162],{},[1680,60541,4007],{},[1497,60543,60544,60546],{},[1493,60545,3633],{},[1680,60547,1691],{},[1528,60549,60550],{"encoding":1530},"B_1 = 20 + 2A_1 + 4A_2",[1035,60552,60554],{"className":60553},[1480],[1482,60555,60556],{"xmlns":1484},[1487,60557,60558,60590],{},[1490,60559,60560,60566,60568,60570,60572,60574,60580,60582,60584],{},[1497,60561,60562,60564],{},[1493,60563,11353],{},[1680,60565,1691],{},[1506,60567,1508],{},[1680,60569,7380],{},[1506,60571,1888],{},[1680,60573,3201],{},[1497,60575,60576,60578],{},[1493,60577,3633],{},[1680,60579,1682],{},[1506,60581,2162],{},[1680,60583,1752],{},[1497,60585,60586,60588],{},[1493,60587,3633],{},[1680,60589,1691],{},[1528,60591,60592],{"encoding":1530},"B_2 = 40 - 3A_1 + 5A_2",[1304,60594,60596],{"id":60595},"základní-analýza-nabídky","Základní analýza nabídky",[1030,60598,60599,60602,60603,60637,60638,60660],{},[1047,60600,60601],{},"2.6"," Je dána nabídka ",[1035,60604,60606],{"className":60605},[1480],[1482,60607,60608],{"xmlns":1484},[1487,60609,60610,60634],{},[1490,60611,60612,60614,60616,60618,60620,60622,60624,60626,60628,60630,60632],{},[1493,60613,1501],{},[1506,60615,1508],{},[1493,60617,2001],{},[1506,60619,1553],{"stretchy":1552},[1493,60621,1520],{},[1506,60623,1564],{"stretchy":1552},[1506,60625,1508],{},[1680,60627,8436],{},[1506,60629,2162],{},[1680,60631,2929],{},[1493,60633,1520],{},[1528,60635,60636],{"encoding":1530},"P = S(Q) = 20 + 0{,}2Q",". (a) Načrtněte křivku nabídky. (b) Vypočtěte množství při cenách ",[1035,60639,60641],{"className":60640},[1480],[1482,60642,60643],{"xmlns":1484},[1487,60644,60645,60657],{},[1490,60646,60647,60649,60651,60653,60655],{},[1680,60648,2309],{},[1506,60650,1559],{"separator":1041},[1680,60652,6956],{},[1506,60654,1559],{"separator":1041},[1680,60656,5603],{},[1528,60658,60659],{"encoding":1530},"25, 30, 35"," a vyznačte výsledky na křivku nabídky.",[1030,60662,60663,60666,60667,60684],{},[1047,60664,60665],{},"2.7"," Ověřte, že zadané funkce vyjadřují (s případným omezením na ",[1035,60668,60670],{"className":60669},[1480],[1482,60671,60672],{"xmlns":1484},[1487,60673,60674,60682],{},[1490,60675,60676,60678,60680],{},[1493,60677,1501],{},[1506,60679,1559],{"separator":1041},[1493,60681,1520],{},[1528,60683,59852],{"encoding":1530},") nabídku (využijte testu na kladnost derivace), charakterizujte tvar křivky nabídky a vyjádřete nabídku v alternativním tvaru:",[1203,60686,60687,60713,60741,60774,60808,60844],{},[1206,60688,10671,60689],{},[1035,60690,60692],{"className":60691},[1480],[1482,60693,60694],{"xmlns":1484},[1487,60695,60696,60710],{},[1490,60697,60698,60700,60702,60704,60706,60708],{},[1493,60699,1501],{},[1506,60701,1508],{},[1680,60703,6956],{},[1506,60705,2162],{},[1680,60707,1691],{},[1493,60709,1520],{},[1528,60711,60712],{"encoding":1530},"P = 30 + 2Q",[1206,60714,59916,60715],{},[1035,60716,60718],{"className":60717},[1480],[1482,60719,60720],{"xmlns":1484},[1487,60721,60722,60738],{},[1490,60723,60724,60726,60728,60730,60732,60734,60736],{},[1493,60725,1520],{},[1506,60727,1508],{},[1506,60729,1888],{},[1680,60731,3201],{},[1506,60733,2162],{},[1680,60735,6797],{},[1493,60737,1501],{},[1528,60739,60740],{"encoding":1530},"Q = -3 + 12P",[1206,60742,13176,60743],{},[1035,60744,60746],{"className":60745},[1480],[1482,60747,60748],{"xmlns":1484},[1487,60749,60750,60772],{},[1490,60751,60752,60754,60756,60762,60764,60766,60768,60770],{},[1493,60753,1501],{},[1506,60755,1508],{},[2315,60757,60758,60760],{},[1493,60759,1520],{},[1680,60761,1691],{},[1506,60763,2162],{},[1680,60765,38539],{},[1493,60767,1520],{},[1506,60769,2162],{},[1680,60771,9923],{},[1528,60773,56273],{"encoding":1530},[1206,60775,59981,60776],{},[1035,60777,60779],{"className":60778},[1480],[1482,60780,60781],{"xmlns":1484},[1487,60782,60783,60805],{},[1490,60784,60785,60787,60789,60795,60797,60799,60801,60803],{},[1493,60786,1501],{},[1506,60788,1508],{},[2315,60790,60791,60793],{},[1493,60792,1520],{},[1680,60794,1691],{},[1506,60796,2162],{},[1680,60798,1691],{},[1493,60800,1520],{},[1506,60802,2162],{},[1680,60804,6797],{},[1528,60806,60807],{"encoding":1530},"P = Q^2 + 2Q + 12",[1206,60809,60012,60810],{},[1035,60811,60813],{"className":60812},[1480],[1482,60814,60815],{"xmlns":1484},[1487,60816,60817,60841],{},[1490,60818,60819,60821,60823,60825,60827,60829,60831,60833,60835],{},[1493,60820,1520],{},[1506,60822,1508],{},[1680,60824,5551],{},[1506,60826,2162],{},[1680,60828,1752],{},[1493,60830,1501],{},[1506,60832,2162],{},[1680,60834,13237],{},[2315,60836,60837,60839],{},[1493,60838,1501],{},[1680,60840,1691],{},[1528,60842,60843],{"encoding":1530},"Q = 150 + 5P + 0{,}1P^2",[1206,60845,60047,60846],{},[1035,60847,60849],{"className":60848},[1480],[1482,60850,60851],{"xmlns":1484},[1487,60852,60853,60878],{},[1490,60854,60855,60857,60859,60861,60863,60865,60867,60869,60872],{},[1493,60856,1520],{},[1506,60858,1508],{},[1680,60860,16580],{},[1506,60862,2162],{},[1680,60864,13237],{},[1493,60866,1501],{},[1506,60868,2162],{},[1680,60870,60871],{},"0,004",[2315,60873,60874,60876],{},[1493,60875,1501],{},[1680,60877,1691],{},[1528,60879,60880],{"encoding":1530},"Q = 7 + 0{,}1P + 0{,}004P^2",[1030,60882,60883,60886],{},[1047,60884,60885],{},"2.8"," Rozhodněte, jak se změní křivka nabídky, jestliže se (ceteris paribus):",[1203,60888,60889,60892,60895,60898],{},[1206,60890,60891],{},"(a) Sníží ceny surovin — vstupů.",[1206,60893,60894],{},"(b) Zavede nová ekologičtější technologie zvyšující výrobní náklady.",[1206,60896,60897],{},"(c) Zvýší ceny všech energií.",[1206,60899,60900],{},"(d) Sníží daňové odvody státu.",[1030,60902,60903,60602,60905,60939,60940,60968],{},[1047,60904,57501],{},[1035,60906,60908],{"className":60907},[1480],[1482,60909,60910],{"xmlns":1484},[1487,60911,60912,60936],{},[1490,60913,60914,60916,60918,60920,60922,60924,60926,60928,60930,60932,60934],{},[1493,60915,1501],{},[1506,60917,1508],{},[1493,60919,2001],{},[1506,60921,1553],{"stretchy":1552},[1493,60923,1520],{},[1506,60925,1564],{"stretchy":1552},[1506,60927,1508],{},[1680,60929,3687],{},[1493,60931,1520],{},[1506,60933,2162],{},[1680,60935,9787],{},[1528,60937,60938],{"encoding":1530},"P = S(Q) = 0{,}5Q + 15",". Najděte novou nabídku ",[1035,60941,60943],{"className":60942},[1480],[1482,60944,60945],{"xmlns":1484},[1487,60946,60947,60965],{},[1490,60948,60949,60951,60953,60959,60961,60963],{},[1493,60950,1501],{},[1506,60952,1508],{},[2315,60954,60955,60957],{},[1493,60956,2001],{},[1506,60958,2287],{},[1506,60960,1553],{"stretchy":1552},[1493,60962,1520],{},[1506,60964,1564],{"stretchy":1552},[1528,60966,60967],{"encoding":1530},"P = S^*(Q)",", na kterou se změní původní nabídka v důsledku uložení daně 5 Kč na výrobce na každou jednotku zboží. Graficky interpretujte.",[1304,60970,55958],{"id":60971},"tržní-rovnováha-1",[1030,60973,60974,60976,60977,60994,60995,1274],{},[1047,60975,57561],{}," Pro zadanou poptávku a nabídku najděte rovnovážné množství ",[1035,60978,60980],{"className":60979},[1480],[1482,60981,60982],{"xmlns":1484},[1487,60983,60984,60992],{},[1490,60985,60986],{},[2315,60987,60988,60990],{},[1493,60989,1520],{},[1493,60991,2711],{},[1528,60993,14059],{"encoding":1530}," a rovnovážnou cenu ",[1035,60996,60998],{"className":60997},[1480],[1482,60999,61000],{"xmlns":1484},[1487,61001,61002,61010],{},[1490,61003,61004],{},[2315,61005,61006,61008],{},[1493,61007,1501],{},[1493,61009,2711],{},[1528,61011,56102],{"encoding":1530},[1203,61013,61014,61066,61117,61176],{},[1206,61015,10671,61016,1732,61042,2632],{},[1035,61017,61019],{"className":61018},[1480],[1482,61020,61021],{"xmlns":1484},[1487,61022,61023,61039],{},[1490,61024,61025,61027,61029,61031,61033,61035,61037],{},[1493,61026,1501],{},[1506,61028,1508],{},[1506,61030,1888],{},[1680,61032,1752],{},[1493,61034,1520],{},[1506,61036,2162],{},[1680,61038,11232],{},[1528,61040,61041],{"encoding":1530},"P = -5Q + 80",[1035,61043,61045],{"className":61044},[1480],[1482,61046,61047],{"xmlns":1484},[1487,61048,61049,61063],{},[1490,61050,61051,61053,61055,61057,61059,61061],{},[1493,61052,1501],{},[1506,61054,1508],{},[1680,61056,1691],{},[1493,61058,1520],{},[1506,61060,2162],{},[1680,61062,1775],{},[1528,61064,61065],{"encoding":1530},"P = 2Q + 10",[1206,61067,59916,61068,1732,61094,2632],{},[1035,61069,61071],{"className":61070},[1480],[1482,61072,61073],{"xmlns":1484},[1487,61074,61075,61091],{},[1490,61076,61077,61079,61081,61083,61085,61087,61089],{},[1493,61078,1520],{},[1506,61080,1508],{},[1506,61082,1888],{},[1680,61084,3687],{},[1493,61086,1501],{},[1506,61088,2162],{},[1680,61090,2309],{},[1528,61092,61093],{"encoding":1530},"Q = -0{,}5P + 25",[1035,61095,61097],{"className":61096},[1480],[1482,61098,61099],{"xmlns":1484},[1487,61100,61101,61115],{},[1490,61102,61103,61105,61107,61109,61111,61113],{},[1493,61104,1520],{},[1506,61106,1508],{},[1680,61108,1691],{},[1493,61110,1501],{},[1506,61112,1888],{},[1680,61114,2292],{},[1528,61116,55578],{"encoding":1530},[1206,61118,13176,61119,1732,61145,2632],{},[1035,61120,61122],{"className":61121},[1480],[1482,61123,61124],{"xmlns":1484},[1487,61125,61126,61142],{},[1490,61127,61128,61130,61132,61134,61136,61138,61140],{},[1493,61129,1501],{},[1506,61131,1508],{},[1506,61133,1888],{},[1680,61135,4007],{},[1493,61137,1520],{},[1506,61139,2162],{},[1680,61141,10797],{},[1528,61143,61144],{"encoding":1530},"P = -4Q + 120",[1035,61146,61148],{"className":61147},[1480],[1482,61149,61150],{"xmlns":1484},[1487,61151,61152,61173],{},[1490,61153,61154,61156,61158,61166,61168,61170],{},[1493,61155,1501],{},[1506,61157,1508],{},[1869,61159,61160],{"scriptlevel":1871,"displaystyle":1552},[1510,61161,61162,61164],{},[1680,61163,1682],{},[1680,61165,3201],{},[1493,61167,1520],{},[1506,61169,2162],{},[1680,61171,61172],{},"29",[1528,61174,61175],{"encoding":1530},"P = \\tfrac{1}{3}Q + 29",[1206,61177,59981,61178,1732,61207,2632],{},[1035,61179,61181],{"className":61180},[1480],[1482,61182,61183],{"xmlns":1484},[1487,61184,61185,61204],{},[1490,61186,61187,61189,61191,61193,61199,61201],{},[1493,61188,1501],{},[1506,61190,1508],{},[1506,61192,1888],{},[2315,61194,61195,61197],{},[1493,61196,1520],{},[1680,61198,1691],{},[1506,61200,2162],{},[1680,61202,61203],{},"52",[1528,61205,61206],{"encoding":1530},"P = -Q^2 + 52",[1035,61208,61210],{"className":61209},[1480],[1482,61211,61212],{"xmlns":1484},[1487,61213,61214,61232],{},[1490,61215,61216,61218,61220,61222,61228,61230],{},[1493,61217,1501],{},[1506,61219,1508],{},[1680,61221,1691],{},[2315,61223,61224,61226],{},[1493,61225,1520],{},[1680,61227,1691],{},[1506,61229,2162],{},[1680,61231,1775],{},[1528,61233,61234],{"encoding":1530},"P = 2Q^2 + 10",[1030,61236,61237,61240,61241,61271,61272,61302],{},[1047,61238,61239],{},"2.11"," Pro zadanou poptávku a nabídku dvou závislých zboží najděte rovnovážná množství ",[1035,61242,61244],{"className":61243},[1480],[1482,61245,61246],{"xmlns":1484},[1487,61247,61248,61268],{},[1490,61249,61250,61258,61260],{},[1697,61251,61252,61254,61256],{},[1493,61253,1520],{},[1680,61255,1682],{},[1493,61257,2711],{},[1506,61259,1559],{"separator":1041},[1697,61261,61262,61264,61266],{},[1493,61263,1520],{},[1680,61265,1691],{},[1493,61267,2711],{},[1528,61269,61270],{"encoding":1530},"Q_1^E, Q_2^E"," a rovnovážné ceny ",[1035,61273,61275],{"className":61274},[1480],[1482,61276,61277],{"xmlns":1484},[1487,61278,61279,61299],{},[1490,61280,61281,61289,61291],{},[1697,61282,61283,61285,61287],{},[1493,61284,1501],{},[1680,61286,1682],{},[1493,61288,2711],{},[1506,61290,1559],{"separator":1041},[1697,61292,61293,61295,61297],{},[1493,61294,1501],{},[1680,61296,1691],{},[1493,61298,2711],{},[1528,61300,61301],{"encoding":1530},"P_1^E, P_2^E"," (index 1 přísluší prvnímu, index 2 druhému zboží):",[1203,61304,61305,61457],{},[1206,61306,10671,61307,1732,61347,1732,61389,1732,61423,2632],{},[1035,61308,61310],{"className":61309},[1480],[1482,61311,61312],{"xmlns":1484},[1487,61313,61314,61344],{},[1490,61315,61316,61322,61324,61326,61328,61330,61336,61338],{},[1497,61317,61318,61320],{},[1493,61319,1520],{},[1680,61321,1682],{},[1506,61323,1508],{},[1680,61325,1775],{},[1506,61327,1888],{},[1680,61329,1691],{},[1497,61331,61332,61334],{},[1493,61333,1501],{},[1680,61335,1682],{},[1506,61337,2162],{},[1497,61339,61340,61342],{},[1493,61341,1501],{},[1680,61343,1691],{},[1528,61345,61346],{"encoding":1530},"Q_1 = 10 - 2P_1 + P_2",[1035,61348,61350],{"className":61349},[1480],[1482,61351,61352],{"xmlns":1484},[1487,61353,61354,61386],{},[1490,61355,61356,61362,61364,61366,61368,61370,61376,61378,61380],{},[1497,61357,61358,61360],{},[1493,61359,1520],{},[1680,61361,1691],{},[1506,61363,1508],{},[1680,61365,1752],{},[1506,61367,2162],{},[1680,61369,1691],{},[1497,61371,61372,61374],{},[1493,61373,1501],{},[1680,61375,1682],{},[1506,61377,1888],{},[1680,61379,1691],{},[1497,61381,61382,61384],{},[1493,61383,1501],{},[1680,61385,1691],{},[1528,61387,61388],{"encoding":1530},"Q_2 = 5 + 2P_1 - 2P_2",[1035,61390,61392],{"className":61391},[1480],[1482,61393,61394],{"xmlns":1484},[1487,61395,61396,61420],{},[1490,61397,61398,61404,61406,61408,61410,61412,61414],{},[1497,61399,61400,61402],{},[1493,61401,1520],{},[1680,61403,1682],{},[1506,61405,1508],{},[1506,61407,1888],{},[1680,61409,3201],{},[1506,61411,2162],{},[1680,61413,1691],{},[1497,61415,61416,61418],{},[1493,61417,1501],{},[1680,61419,1682],{},[1528,61421,61422],{"encoding":1530},"Q_1 = -3 + 2P_1",[1035,61424,61426],{"className":61425},[1480],[1482,61427,61428],{"xmlns":1484},[1487,61429,61430,61454],{},[1490,61431,61432,61438,61440,61442,61444,61446,61448],{},[1497,61433,61434,61436],{},[1493,61435,1520],{},[1680,61437,1691],{},[1506,61439,1508],{},[1506,61441,1888],{},[1680,61443,1691],{},[1506,61445,2162],{},[1680,61447,3201],{},[1497,61449,61450,61452],{},[1493,61451,1501],{},[1680,61453,1691],{},[1528,61455,61456],{"encoding":1530},"Q_2 = -2 + 3P_2",[1206,61458,59916,61459,1732,61499,1732,61541,1732,61573,2632],{},[1035,61460,61462],{"className":61461},[1480],[1482,61463,61464],{"xmlns":1484},[1487,61465,61466,61496],{},[1490,61467,61468,61474,61476,61478,61480,61482,61488,61490],{},[1497,61469,61470,61472],{},[1493,61471,1520],{},[1680,61473,1682],{},[1506,61475,1508],{},[1680,61477,2916],{},[1506,61479,1888],{},[1680,61481,1691],{},[1497,61483,61484,61486],{},[1493,61485,1501],{},[1680,61487,1682],{},[1506,61489,2162],{},[1497,61491,61492,61494],{},[1493,61493,1501],{},[1680,61495,1691],{},[1528,61497,61498],{"encoding":1530},"Q_1 = 100 - 2P_1 + P_2",[1035,61500,61502],{"className":61501},[1480],[1482,61503,61504],{"xmlns":1484},[1487,61505,61506,61538],{},[1490,61507,61508,61514,61516,61518,61520,61522,61528,61530,61532],{},[1497,61509,61510,61512],{},[1493,61511,1520],{},[1680,61513,1691],{},[1506,61515,1508],{},[1680,61517,1752],{},[1506,61519,2162],{},[1680,61521,1691],{},[1497,61523,61524,61526],{},[1493,61525,1501],{},[1680,61527,1682],{},[1506,61529,1888],{},[1680,61531,3201],{},[1497,61533,61534,61536],{},[1493,61535,1501],{},[1680,61537,1691],{},[1528,61539,61540],{"encoding":1530},"Q_2 = 5 + 2P_1 - 3P_2",[1035,61542,61544],{"className":61543},[1480],[1482,61545,61546],{"xmlns":1484},[1487,61547,61548,61570],{},[1490,61549,61550,61556,61558,61560,61562,61564],{},[1497,61551,61552,61554],{},[1493,61553,1520],{},[1680,61555,1682],{},[1506,61557,1508],{},[1506,61559,1888],{},[1680,61561,1775],{},[1506,61563,2162],{},[1497,61565,61566,61568],{},[1493,61567,1501],{},[1680,61569,1682],{},[1528,61571,61572],{"encoding":1530},"Q_1 = -10 + P_1",[1035,61574,61576],{"className":61575},[1480],[1482,61577,61578],{"xmlns":1484},[1487,61579,61580,61602],{},[1490,61581,61582,61588,61590,61592,61594,61596],{},[1497,61583,61584,61586],{},[1493,61585,1520],{},[1680,61587,1691],{},[1506,61589,1508],{},[1680,61591,1752],{},[1506,61593,2162],{},[1680,61595,7508],{},[1497,61597,61598,61600],{},[1493,61599,1501],{},[1680,61601,1691],{},[1528,61603,61604],{"encoding":1530},"Q_2 = 5 + 6P_2",[1030,61606,61607,61610,61611,1732,61659,1732,61705,61755,61756,1732,61788,1732,61822,37188,61856,1586,61874,61892,61893,61906,61907,61933,61934,61271,61974,2632],{},[1047,61608,61609],{},"2.12"," Pro tři závislá zboží jsou dány poptávky rovnicemi ",[1035,61612,61614],{"className":61613},[1480],[1482,61615,61616],{"xmlns":1484},[1487,61617,61618,61656],{},[1490,61619,61620,61626,61628,61630,61632,61638,61640,61642,61648,61650],{},[1497,61621,61622,61624],{},[1493,61623,1520],{},[1680,61625,1682],{},[1506,61627,1508],{},[1680,61629,9787],{},[1506,61631,1888],{},[1497,61633,61634,61636],{},[1493,61635,1501],{},[1680,61637,1682],{},[1506,61639,2162],{},[1680,61641,1691],{},[1497,61643,61644,61646],{},[1493,61645,1501],{},[1680,61647,1691],{},[1506,61649,2162],{},[1497,61651,61652,61654],{},[1493,61653,1501],{},[1680,61655,3201],{},[1528,61657,61658],{"encoding":1530},"Q_1 = 15 - P_1 + 2P_2 + P_3",[1035,61660,61662],{"className":61661},[1480],[1482,61663,61664],{"xmlns":1484},[1487,61665,61666,61702],{},[1490,61667,61668,61674,61676,61678,61680,61686,61688,61694,61696],{},[1497,61669,61670,61672],{},[1493,61671,1520],{},[1680,61673,1691],{},[1506,61675,1508],{},[1680,61677,14365],{},[1506,61679,2162],{},[1497,61681,61682,61684],{},[1493,61683,1501],{},[1680,61685,1682],{},[1506,61687,1888],{},[1497,61689,61690,61692],{},[1493,61691,1501],{},[1680,61693,1691],{},[1506,61695,1888],{},[1497,61697,61698,61700],{},[1493,61699,1501],{},[1680,61701,3201],{},[1528,61703,61704],{"encoding":1530},"Q_2 = 9 + P_1 - P_2 - P_3",[1035,61706,61708],{"className":61707},[1480],[1482,61709,61710],{"xmlns":1484},[1487,61711,61712,61752],{},[1490,61713,61714,61720,61722,61724,61726,61728,61734,61736,61742,61744,61746],{},[1497,61715,61716,61718],{},[1493,61717,1520],{},[1680,61719,3201],{},[1506,61721,1508],{},[1680,61723,6138],{},[1506,61725,2162],{},[1680,61727,1691],{},[1497,61729,61730,61732],{},[1493,61731,1501],{},[1680,61733,1682],{},[1506,61735,1888],{},[1497,61737,61738,61740],{},[1493,61739,1501],{},[1680,61741,1691],{},[1506,61743,1888],{},[1680,61745,4007],{},[1497,61747,61748,61750],{},[1493,61749,1501],{},[1680,61751,3201],{},[1528,61753,61754],{"encoding":1530},"Q_3 = 8 + 2P_1 - P_2 - 4P_3"," a nabídky rovnicemi ",[1035,61757,61759],{"className":61758},[1480],[1482,61760,61761],{"xmlns":1484},[1487,61762,61763,61785],{},[1490,61764,61765,61771,61773,61775,61777,61779],{},[1497,61766,61767,61769],{},[1493,61768,1520],{},[1680,61770,1682],{},[1506,61772,1508],{},[1506,61774,1888],{},[1680,61776,16580],{},[1506,61778,2162],{},[1497,61780,61781,61783],{},[1493,61782,1501],{},[1680,61784,1682],{},[1528,61786,61787],{"encoding":1530},"Q_1 = -7 + P_1",[1035,61789,61791],{"className":61790},[1480],[1482,61792,61793],{"xmlns":1484},[1487,61794,61795,61819],{},[1490,61796,61797,61803,61805,61807,61809,61811,61813],{},[1497,61798,61799,61801],{},[1493,61800,1520],{},[1680,61802,1691],{},[1506,61804,1508],{},[1506,61806,1888],{},[1680,61808,4007],{},[1506,61810,2162],{},[1680,61812,4007],{},[1497,61814,61815,61817],{},[1493,61816,1501],{},[1680,61818,1691],{},[1528,61820,61821],{"encoding":1530},"Q_2 = -4 + 4P_2",[1035,61823,61825],{"className":61824},[1480],[1482,61826,61827],{"xmlns":1484},[1487,61828,61829,61853],{},[1490,61830,61831,61837,61839,61841,61843,61845,61847],{},[1497,61832,61833,61835],{},[1493,61834,1520],{},[1680,61836,3201],{},[1506,61838,1508],{},[1506,61840,1888],{},[1680,61842,1752],{},[1506,61844,2162],{},[1680,61846,1691],{},[1497,61848,61849,61851],{},[1493,61850,1501],{},[1680,61852,3201],{},[1528,61854,61855],{"encoding":1530},"Q_3 = -5 + 2P_3",[1035,61857,61859],{"className":61858},[1480],[1482,61860,61861],{"xmlns":1484},[1487,61862,61863,61871],{},[1490,61864,61865],{},[1497,61866,61867,61869],{},[1493,61868,1520],{},[1493,61870,6277],{},[1528,61872,61873],{"encoding":1530},"Q_i",[1035,61875,61877],{"className":61876},[1480],[1482,61878,61879],{"xmlns":1484},[1487,61880,61881,61889],{},[1490,61882,61883],{},[1497,61884,61885,61887],{},[1493,61886,1501],{},[1493,61888,6277],{},[1528,61890,61891],{"encoding":1530},"P_i"," značí příslušné množství a ceny ",[1035,61894,61896],{"className":61895},[1480],[1482,61897,61898],{"xmlns":1484},[1487,61899,61900,61904],{},[1490,61901,61902],{},[1493,61903,6277],{},[1528,61905,6277],{"encoding":1530},"-tého zboží, ",[1035,61908,61910],{"className":61909},[1480],[1482,61911,61912],{"xmlns":1484},[1487,61913,61914,61930],{},[1490,61915,61916,61918,61920,61922,61924,61926,61928],{},[1493,61917,6277],{},[1506,61919,1508],{},[1680,61921,1682],{},[1506,61923,1559],{"separator":1041},[1680,61925,1691],{},[1506,61927,1559],{"separator":1041},[1680,61929,3201],{},[1528,61931,61932],{"encoding":1530},"i = 1, 2, 3",". Najděte rovnovážná množství ",[1035,61935,61937],{"className":61936},[1480],[1482,61938,61939],{"xmlns":1484},[1487,61940,61941,61971],{},[1490,61942,61943,61951,61953,61961,61963],{},[1697,61944,61945,61947,61949],{},[1493,61946,1520],{},[1680,61948,1682],{},[1493,61950,2711],{},[1506,61952,1559],{"separator":1041},[1697,61954,61955,61957,61959],{},[1493,61956,1520],{},[1680,61958,1691],{},[1493,61960,2711],{},[1506,61962,1559],{"separator":1041},[1697,61964,61965,61967,61969],{},[1493,61966,1520],{},[1680,61968,3201],{},[1493,61970,2711],{},[1528,61972,61973],{"encoding":1530},"Q_1^E, Q_2^E, Q_3^E",[1035,61975,61977],{"className":61976},[1480],[1482,61978,61979],{"xmlns":1484},[1487,61980,61981,62011],{},[1490,61982,61983,61991,61993,62001,62003],{},[1697,61984,61985,61987,61989],{},[1493,61986,1501],{},[1680,61988,1682],{},[1493,61990,2711],{},[1506,61992,1559],{"separator":1041},[1697,61994,61995,61997,61999],{},[1493,61996,1501],{},[1680,61998,1691],{},[1493,62000,2711],{},[1506,62002,1559],{"separator":1041},[1697,62004,62005,62007,62009],{},[1493,62006,1501],{},[1680,62008,3201],{},[1493,62010,2711],{},[1528,62012,62013],{"encoding":1530},"P_1^E, P_2^E, P_3^E",[1030,62015,62016,62019,62020,62056,62057,2632],{},[1047,62017,62018],{},"2.13"," Jsou dány poptávka ",[1035,62021,62023],{"className":62022},[1480],[1482,62024,62025],{"xmlns":1484},[1487,62026,62027,62053],{},[1490,62028,62029,62031,62033,62035,62037,62039,62041,62043,62045,62047,62049,62051],{},[1493,62030,1501],{},[1506,62032,1508],{},[1493,62034,3712],{},[1506,62036,1553],{"stretchy":1552},[1493,62038,1520],{},[1506,62040,1564],{"stretchy":1552},[1506,62042,1508],{},[1506,62044,1888],{},[1680,62046,4007],{},[1493,62048,1520],{},[1506,62050,2162],{},[1680,62052,11232],{},[1528,62054,62055],{"encoding":1530},"P = D(Q) = -4Q + 80"," a nabídka ",[1035,62058,62060],{"className":62059},[1480],[1482,62061,62062],{"xmlns":1484},[1487,62063,62064,62088],{},[1490,62065,62066,62068,62070,62072,62074,62076,62078,62080,62082,62084,62086],{},[1493,62067,1501],{},[1506,62069,1508],{},[1493,62071,2001],{},[1506,62073,1553],{"stretchy":1552},[1493,62075,1520],{},[1506,62077,1564],{"stretchy":1552},[1506,62079,1508],{},[1680,62081,3201],{},[1493,62083,1520],{},[1506,62085,2162],{},[1680,62087,1775],{},[1528,62089,62090],{"encoding":1530},"P = S(Q) = 3Q + 10",[1203,62092,62093,62130,62194,62254],{},[1206,62094,62095,62096,60994,62113,2632],{},"(a) Určete rovnovážné množství ",[1035,62097,62099],{"className":62098},[1480],[1482,62100,62101],{"xmlns":1484},[1487,62102,62103,62111],{},[1490,62104,62105],{},[2315,62106,62107,62109],{},[1493,62108,1520],{},[1493,62110,2711],{},[1528,62112,14059],{"encoding":1530},[1035,62114,62116],{"className":62115},[1480],[1482,62117,62118],{"xmlns":1484},[1487,62119,62120,62128],{},[1490,62121,62122],{},[2315,62123,62124,62126],{},[1493,62125,1501],{},[1493,62127,2711],{},[1528,62129,56102],{"encoding":1530},[1206,62131,62132,62133,62151,62152,62172,62173,62193],{},"(b) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží výrobci daň ",[1035,62134,62136],{"className":62135},[1480],[1482,62137,62138],{"xmlns":1484},[1487,62139,62140,62148],{},[1490,62141,62142,62144,62146],{},[1493,62143,5289],{},[1506,62145,1508],{},[1680,62147,16580],{},[1528,62149,62150],{"encoding":1530},"T = 7"," Kč na každou jednotku zboží, vypočtěte nové rovnovážné množství ",[1035,62153,62155],{"className":62154},[1480],[1482,62156,62157],{"xmlns":1484},[1487,62158,62159,62169],{},[1490,62160,62161],{},[1697,62162,62163,62165,62167],{},[1493,62164,1520],{},[1680,62166,1682],{},[1493,62168,2711],{},[1528,62170,62171],{"encoding":1530},"Q_1^E"," a novou rovnovážnou cenu ",[1035,62174,62176],{"className":62175},[1480],[1482,62177,62178],{"xmlns":1484},[1487,62179,62180,62190],{},[1490,62181,62182],{},[1697,62183,62184,62186,62188],{},[1493,62185,1501],{},[1680,62187,1682],{},[1493,62189,2711],{},[1528,62191,62192],{"encoding":1530},"P_1^E"," a určete, kolik z daňového zatížení zaplatí výrobce a kolik spotřebitel.",[1206,62195,62196,62197,62151,62214,62172,62234,62193],{},"(c) Stanovte, jak se změní poptávka a nabídka, jestliže vláda uloží spotřebiteli daň ",[1035,62198,62200],{"className":62199},[1480],[1482,62201,62202],{"xmlns":1484},[1487,62203,62204,62212],{},[1490,62205,62206,62208,62210],{},[1493,62207,5289],{},[1506,62209,1508],{},[1680,62211,16580],{},[1528,62213,62150],{"encoding":1530},[1035,62215,62217],{"className":62216},[1480],[1482,62218,62219],{"xmlns":1484},[1487,62220,62221,62231],{},[1490,62222,62223],{},[1697,62224,62225,62227,62229],{},[1493,62226,1520],{},[1680,62228,1691],{},[1493,62230,2711],{},[1528,62232,62233],{"encoding":1530},"Q_2^E",[1035,62235,62237],{"className":62236},[1480],[1482,62238,62239],{"xmlns":1484},[1487,62240,62241,62251],{},[1490,62242,62243],{},[1697,62244,62245,62247,62249],{},[1493,62246,1501],{},[1680,62248,1691],{},[1493,62250,2711],{},[1528,62252,62253],{"encoding":1530},"P_2^E",[1206,62255,62256],{},"(d) Proveďte analýzu dopadu daňového zatížení na spotřebitele a výrobce vyplývající z výsledků (b) a (c).",[1030,62258,62259,62260,2632],{},"Viz též ",[1052,62261,57273],{"className":62262,"dataFsResolvedFilePath":57271,"href":57272},[1055],[1304,62264,57575],{"id":62265},"multiplikátory-pro-mikroekonomické-proměnné-1",[1030,62267,62268,62019,62271,62056,62307,2632],{},[1047,62269,62270],{},"2.14",[1035,62272,62274],{"className":62273},[1480],[1482,62275,62276],{"xmlns":1484},[1487,62277,62278,62304],{},[1490,62279,62280,62282,62284,62286,62288,62290,62292,62294,62296,62298,62300,62302],{},[1493,62281,1501],{},[1506,62283,1508],{},[1493,62285,1052],{},[1493,62287,1520],{},[1506,62289,2162],{},[1493,62291,2394],{},[1506,62293,1508],{},[1506,62295,1888],{},[1680,62297,1691],{},[1493,62299,1520],{},[1506,62301,2162],{},[1680,62303,2292],{},[1528,62305,62306],{"encoding":1530},"P = aQ + b = -2Q + 50",[1035,62308,62310],{"className":62309},[1480],[1482,62311,62312],{"xmlns":1484},[1487,62313,62314,62338],{},[1490,62315,62316,62318,62320,62322,62324,62326,62328,62330,62332,62334,62336],{},[1493,62317,1501],{},[1506,62319,1508],{},[1493,62321,8730],{},[1493,62323,1520],{},[1506,62325,2162],{},[1493,62327,3384],{},[1506,62329,1508],{},[1680,62331,3332],{},[1493,62333,1520],{},[1506,62335,2162],{},[1680,62337,8436],{},[1528,62339,62340],{"encoding":1530},"P = cQ + d = 0{,}6Q + 20",[1203,62342,62343,62379,62382,62468,62521,62601,62655],{},[1206,62344,62095,62345,60994,62362,2632],{},[1035,62346,62348],{"className":62347},[1480],[1482,62349,62350],{"xmlns":1484},[1487,62351,62352,62360],{},[1490,62353,62354],{},[2315,62355,62356,62358],{},[1493,62357,1520],{},[1493,62359,2711],{},[1528,62361,14059],{"encoding":1530},[1035,62363,62365],{"className":62364},[1480],[1482,62366,62367],{"xmlns":1484},[1487,62368,62369,62377],{},[1490,62370,62371],{},[2315,62372,62373,62375],{},[1493,62374,1501],{},[1493,62376,2711],{},[1528,62378,56102],{"encoding":1530},[1206,62380,62381],{},"(b) Určete hodnoty multiplikátorů pro zadané parametry.",[1206,62383,62384,62385,62402,62403,18125,62416,18139,62432,62448,62449,2632],{},"(c) Určete přibližnou změnu rovnovážného množství ",[1035,62386,62388],{"className":62387},[1480],[1482,62389,62390],{"xmlns":1484},[1487,62391,62392,62400],{},[1490,62393,62394],{},[2315,62395,62396,62398],{},[1493,62397,1520],{},[1493,62399,2711],{},[1528,62401,14059],{"encoding":1530}," odpovídající změně ",[1035,62404,62406],{"className":62405},[1480],[1482,62407,62408],{"xmlns":1484},[1487,62409,62410,62414],{},[1490,62411,62412],{},[1493,62413,1052],{},[1528,62415,1052],{"encoding":1530},[1035,62417,62419],{"className":62418},[1480],[1482,62420,62421],{"xmlns":1484},[1487,62422,62423,62429],{},[1490,62424,62425,62427],{},[1506,62426,1888],{},[1680,62428,1691],{},[1528,62430,62431],{"encoding":1530},"-2",[1035,62433,62435],{"className":62434},[1480],[1482,62436,62437],{"xmlns":1484},[1487,62438,62439,62445],{},[1490,62440,62441,62443],{},[1506,62442,1888],{},[1680,62444,3201],{},[1528,62446,62447],{"encoding":1530},"-3"," (ceteris paribus) a stanovte nové rovnovážné množství ",[1035,62450,62452],{"className":62451},[1480],[1482,62453,62454],{"xmlns":1484},[1487,62455,62456,62466],{},[1490,62457,62458],{},[1697,62459,62460,62462,62464],{},[1493,62461,1520],{},[1680,62463,1682],{},[1493,62465,2711],{},[1528,62467,62171],{"encoding":1530},[1206,62469,62470,62471,62402,62488,62501,62502,2632],{},"(d) Určete přibližnou změnu rovnovážného množství ",[1035,62472,62474],{"className":62473},[1480],[1482,62475,62476],{"xmlns":1484},[1487,62477,62478,62486],{},[1490,62479,62480],{},[2315,62481,62482,62484],{},[1493,62483,1520],{},[1493,62485,2711],{},[1528,62487,14059],{"encoding":1530},[1035,62489,62491],{"className":62490},[1480],[1482,62492,62493],{"xmlns":1484},[1487,62494,62495,62499],{},[1490,62496,62497],{},[1493,62498,2394],{},[1528,62500,2394],{"encoding":1530}," z 50 na 60 (ceteris paribus) a stanovte nové rovnovážné množství ",[1035,62503,62505],{"className":62504},[1480],[1482,62506,62507],{"xmlns":1484},[1487,62508,62509,62519],{},[1490,62510,62511],{},[1697,62512,62513,62515,62517],{},[1493,62514,1520],{},[1680,62516,1691],{},[1493,62518,2711],{},[1528,62520,62233],{"encoding":1530},[1206,62522,62523,62524,62402,62541,18125,62554,18139,62567,62448,62581,2632],{},"(e) Určete přibližnou změnu rovnovážného množství ",[1035,62525,62527],{"className":62526},[1480],[1482,62528,62529],{"xmlns":1484},[1487,62530,62531,62539],{},[1490,62532,62533],{},[2315,62534,62535,62537],{},[1493,62536,1520],{},[1493,62538,2711],{},[1528,62540,14059],{"encoding":1530},[1035,62542,62544],{"className":62543},[1480],[1482,62545,62546],{"xmlns":1484},[1487,62547,62548,62552],{},[1490,62549,62550],{},[1493,62551,8730],{},[1528,62553,8730],{"encoding":1530},[1035,62555,62557],{"className":62556},[1480],[1482,62558,62559],{"xmlns":1484},[1487,62560,62561,62565],{},[1490,62562,62563],{},[1680,62564,3332],{},[1528,62566,58846],{"encoding":1530},[1035,62568,62570],{"className":62569},[1480],[1482,62571,62572],{"xmlns":1484},[1487,62573,62574,62578],{},[1490,62575,62576],{},[1680,62577,2939],{},[1528,62579,62580],{"encoding":1530},"0{,}8",[1035,62582,62584],{"className":62583},[1480],[1482,62585,62586],{"xmlns":1484},[1487,62587,62588,62598],{},[1490,62589,62590],{},[1697,62591,62592,62594,62596],{},[1493,62593,1520],{},[1680,62595,3201],{},[1493,62597,2711],{},[1528,62599,62600],{"encoding":1530},"Q_3^E",[1206,62602,62603,62604,62402,62621,62634,62635,2632],{},"(f) Určete přibližnou změnu rovnovážného množství ",[1035,62605,62607],{"className":62606},[1480],[1482,62608,62609],{"xmlns":1484},[1487,62610,62611,62619],{},[1490,62612,62613],{},[2315,62614,62615,62617],{},[1493,62616,1520],{},[1493,62618,2711],{},[1528,62620,14059],{"encoding":1530},[1035,62622,62624],{"className":62623},[1480],[1482,62625,62626],{"xmlns":1484},[1487,62627,62628,62632],{},[1490,62629,62630],{},[1493,62631,3384],{},[1528,62633,3384],{"encoding":1530}," z 20 na 10 (ceteris paribus) a stanovte nové rovnovážné množství ",[1035,62636,62638],{"className":62637},[1480],[1482,62639,62640],{"xmlns":1484},[1487,62641,62642,62652],{},[1490,62643,62644],{},[1697,62645,62646,62648,62650],{},[1493,62647,1520],{},[1680,62649,4007],{},[1493,62651,2711],{},[1528,62653,62654],{"encoding":1530},"Q_4^E",[1206,62656,62657,62658,62675,62676,62689,62690,37016,62703,1732,62719,37016,62732,1586,62746,37016,62759,62774,62775,2632],{},"(g) Určete přibližnou změnu rovnovážného množství ",[1035,62659,62661],{"className":62660},[1480],[1482,62662,62663],{"xmlns":1484},[1487,62664,62665,62673],{},[1490,62666,62667],{},[2315,62668,62669,62671],{},[1493,62670,1520],{},[1493,62672,2711],{},[1528,62674,14059],{"encoding":1530}," odpovídající změnám ",[1035,62677,62679],{"className":62678},[1480],[1482,62680,62681],{"xmlns":1484},[1487,62682,62683,62687],{},[1490,62684,62685],{},[1493,62686,1052],{},[1528,62688,1052],{"encoding":1530}," o 1, ",[1035,62691,62693],{"className":62692},[1480],[1482,62694,62695],{"xmlns":1484},[1487,62696,62697,62701],{},[1490,62698,62699],{},[1493,62700,2394],{},[1528,62702,2394],{"encoding":1530},[1035,62704,62706],{"className":62705},[1480],[1482,62707,62708],{"xmlns":1484},[1487,62709,62710,62716],{},[1490,62711,62712,62714],{},[1506,62713,1888],{},[1680,62715,1775],{},[1528,62717,62718],{"encoding":1530},"-10",[1035,62720,62722],{"className":62721},[1480],[1482,62723,62724],{"xmlns":1484},[1487,62725,62726,62730],{},[1490,62727,62728],{},[1493,62729,8730],{},[1528,62731,8730],{"encoding":1530},[1035,62733,62735],{"className":62734},[1480],[1482,62736,62737],{"xmlns":1484},[1487,62738,62739,62743],{},[1490,62740,62741],{},[1680,62742,13237],{},[1528,62744,62745],{"encoding":1530},"0{,}1",[1035,62747,62749],{"className":62748},[1480],[1482,62750,62751],{"xmlns":1484},[1487,62752,62753,62757],{},[1490,62754,62755],{},[1493,62756,3384],{},[1528,62758,3384],{"encoding":1530},[1035,62760,62762],{"className":62761},[1480],[1482,62763,62764],{"xmlns":1484},[1487,62765,62766,62772],{},[1490,62767,62768,62770],{},[1506,62769,1888],{},[1680,62771,1775],{},[1528,62773,62718],{"encoding":1530}," vzhledem k zadaným hodnotám a stanovte nové rovnovážné množství ",[1035,62776,62778],{"className":62777},[1480],[1482,62779,62780],{"xmlns":1484},[1487,62781,62782,62792],{},[1490,62783,62784],{},[1697,62785,62786,62788,62790],{},[1493,62787,1520],{},[1680,62789,1752],{},[1493,62791,2711],{},[1528,62793,62794],{"encoding":1530},"Q_5^E",[1030,62796,62797,62019,62800,62056,62823,2632],{},[1047,62798,62799],{},"2.15",[1035,62801,62803],{"className":62802},[1480],[1482,62804,62805],{"xmlns":1484},[1487,62806,62807,62821],{},[1490,62808,62809,62811,62813,62815,62817,62819],{},[1493,62810,1501],{},[1506,62812,1508],{},[1493,62814,1052],{},[1493,62816,1520],{},[1506,62818,2162],{},[1493,62820,2394],{},[1528,62822,52158],{"encoding":1530},[1035,62824,62826],{"className":62825},[1480],[1482,62827,62828],{"xmlns":1484},[1487,62829,62830,62844],{},[1490,62831,62832,62834,62836,62838,62840,62842],{},[1493,62833,1501],{},[1506,62835,1508],{},[1493,62837,8730],{},[1493,62839,1520],{},[1506,62841,2162],{},[1493,62843,3384],{},[1528,62845,55008],{"encoding":1530},[1203,62847,62848,62923,62940,63049,63102,63156],{},[1206,62849,62850,62851,62864,62865,62890,62891,62922],{},"(a) Odvoďte redukovaný tvar pro ",[1035,62852,62854],{"className":62853},[1480],[1482,62855,62856],{"xmlns":1484},[1487,62857,62858,62862],{},[1490,62859,62860],{},[1493,62861,1501],{},[1528,62863,1501],{"encoding":1530},". Stanovte podmínky pro ",[1035,62866,62868],{"className":62867},[1480],[1482,62869,62870],{"xmlns":1484},[1487,62871,62872,62888],{},[1490,62873,62874,62876,62878,62880,62882,62884,62886],{},[1493,62875,1052],{},[1506,62877,1559],{"separator":1041},[1493,62879,2394],{},[1506,62881,1559],{"separator":1041},[1493,62883,8730],{},[1506,62885,1559],{"separator":1041},[1493,62887,3384],{},[1528,62889,57842],{"encoding":1530}," tak, aby rovnovážný bod ",[1035,62892,62894],{"className":62893},[1480],[1482,62895,62896],{"xmlns":1484},[1487,62897,62898,62920],{},[1490,62899,62900,62902,62904,62910,62912,62918],{},[1493,62901,2711],{},[1506,62903,14314],{"stretchy":1552},[2315,62905,62906,62908],{},[1493,62907,1520],{},[1493,62909,2711],{},[1506,62911,1559],{"separator":1041},[2315,62913,62914,62916],{},[1493,62915,1501],{},[1493,62917,2711],{},[1506,62919,14323],{"stretchy":1552},[1528,62921,56005],{"encoding":1530}," patřil do 1. kvadrantu (využijte obrázku 2.22).",[1206,62924,62925,62926,62939],{},"(b) Vypočtěte multiplikátory pro ",[1035,62927,62929],{"className":62928},[1480],[1482,62930,62931],{"xmlns":1484},[1487,62932,62933,62937],{},[1490,62934,62935],{},[1493,62936,1501],{},[1528,62938,1501],{"encoding":1530}," a určete jejich znaménka (ověřte geometricky užitím obrázků 2.22, 2.23).",[1206,62941,62942,62943,1732,62963,1732,62981,1732,62999,63017,63018,63035,63036,2632],{},"(c) Pro hodnoty parametrů ",[1035,62944,62946],{"className":62945},[1480],[1482,62947,62948],{"xmlns":1484},[1487,62949,62950,62960],{},[1490,62951,62952,62954,62956,62958],{},[1493,62953,1052],{},[1506,62955,1508],{},[1506,62957,1888],{},[1680,62959,1691],{},[1528,62961,62962],{"encoding":1530},"a = -2",[1035,62964,62966],{"className":62965},[1480],[1482,62967,62968],{"xmlns":1484},[1487,62969,62970,62978],{},[1490,62971,62972,62974,62976],{},[1493,62973,2394],{},[1506,62975,1508],{},[1680,62977,7380],{},[1528,62979,62980],{"encoding":1530},"b = 40",[1035,62982,62984],{"className":62983},[1480],[1482,62985,62986],{"xmlns":1484},[1487,62987,62988,62996],{},[1490,62989,62990,62992,62994],{},[1493,62991,8730],{},[1506,62993,1508],{},[1680,62995,3687],{},[1528,62997,62998],{"encoding":1530},"c = 0{,}5",[1035,63000,63002],{"className":63001},[1480],[1482,63003,63004],{"xmlns":1484},[1487,63005,63006,63014],{},[1490,63007,63008,63010,63012],{},[1493,63009,3384],{},[1506,63011,1508],{},[1680,63013,1775],{},[1528,63015,63016],{"encoding":1530},"d = 10"," určete rovnovážnou cenu ",[1035,63019,63021],{"className":63020},[1480],[1482,63022,63023],{"xmlns":1484},[1487,63024,63025,63033],{},[1490,63026,63027],{},[2315,63028,63029,63031],{},[1493,63030,1501],{},[1493,63032,2711],{},[1528,63034,56102],{"encoding":1530}," a hodnoty multiplikátorů pro ",[1035,63037,63039],{"className":63038},[1480],[1482,63040,63041],{"xmlns":1484},[1487,63042,63043,63047],{},[1490,63044,63045],{},[1493,63046,1501],{},[1528,63048,1501],{"encoding":1530},[1206,63050,63051,63052,62402,63069,63082,63083,2632],{},"(d) Určete přibližnou změnu rovnovážné ceny ",[1035,63053,63055],{"className":63054},[1480],[1482,63056,63057],{"xmlns":1484},[1487,63058,63059,63067],{},[1490,63060,63061],{},[2315,63062,63063,63065],{},[1493,63064,1501],{},[1493,63066,2711],{},[1528,63068,56102],{"encoding":1530},[1035,63070,63072],{"className":63071},[1480],[1482,63073,63074],{"xmlns":1484},[1487,63075,63076,63080],{},[1490,63077,63078],{},[1493,63079,1052],{},[1528,63081,1052],{"encoding":1530}," o 5 (ceteris paribus) a stanovte novou rovnovážnou cenu ",[1035,63084,63086],{"className":63085},[1480],[1482,63087,63088],{"xmlns":1484},[1487,63089,63090,63100],{},[1490,63091,63092],{},[1697,63093,63094,63096,63098],{},[1493,63095,1501],{},[1680,63097,1682],{},[1493,63099,2711],{},[1528,63101,62192],{"encoding":1530},[1206,63103,63104,63105,63122,63123,63136,63137,2632],{},"(e) Určete přibližnou změnu rovnovážné ceny ",[1035,63106,63108],{"className":63107},[1480],[1482,63109,63110],{"xmlns":1484},[1487,63111,63112,63120],{},[1490,63113,63114],{},[2315,63115,63116,63118],{},[1493,63117,1501],{},[1493,63119,2711],{},[1528,63121,56102],{"encoding":1530}," odpovídající poklesu ",[1035,63124,63126],{"className":63125},[1480],[1482,63127,63128],{"xmlns":1484},[1487,63129,63130,63134],{},[1490,63131,63132],{},[1493,63133,1052],{},[1528,63135,1052],{"encoding":1530}," o 1 a stanovte novou rovnovážnou cenu ",[1035,63138,63140],{"className":63139},[1480],[1482,63141,63142],{"xmlns":1484},[1487,63143,63144,63154],{},[1490,63145,63146],{},[1697,63147,63148,63150,63152],{},[1493,63149,1501],{},[1680,63151,1691],{},[1493,63153,2711],{},[1528,63155,62253],{"encoding":1530},[1206,63157,63158,63159,62675,63176,63189,63190,18139,63203,1586,63218,63231,63232,2632],{},"(f) Určete přibližnou změnu rovnovážné ceny ",[1035,63160,63162],{"className":63161},[1480],[1482,63163,63164],{"xmlns":1484},[1487,63165,63166,63174],{},[1490,63167,63168],{},[2315,63169,63170,63172],{},[1493,63171,1501],{},[1493,63173,2711],{},[1528,63175,56102],{"encoding":1530},[1035,63177,63179],{"className":63178},[1480],[1482,63180,63181],{"xmlns":1484},[1487,63182,63183,63187],{},[1490,63184,63185],{},[1493,63186,1052],{},[1528,63188,1052],{"encoding":1530}," na 35, ",[1035,63191,63193],{"className":63192},[1480],[1482,63194,63195],{"xmlns":1484},[1487,63196,63197,63201],{},[1490,63198,63199],{},[1493,63200,8730],{},[1528,63202,8730],{"encoding":1530},[1035,63204,63206],{"className":63205},[1480],[1482,63207,63208],{"xmlns":1484},[1487,63209,63210,63215],{},[1490,63211,63212],{},[1680,63213,63214],{},"0,7",[1528,63216,63217],{"encoding":1530},"0{,}7",[1035,63219,63221],{"className":63220},[1480],[1482,63222,63223],{"xmlns":1484},[1487,63224,63225,63229],{},[1490,63226,63227],{},[1493,63228,3384],{},[1528,63230,3384],{"encoding":1530}," na 12 vzhledem k hodnotám dle (d) a stanovte novou rovnovážnou cenu ",[1035,63233,63235],{"className":63234},[1480],[1482,63236,63237],{"xmlns":1484},[1487,63238,63239,63249],{},[1490,63240,63241],{},[1697,63242,63243,63245,63247],{},[1493,63244,1501],{},[1680,63246,3201],{},[1493,63248,2711],{},[1528,63250,63251],{"encoding":1530},"P_3^E",[1030,63253,63254,62019,63257,62056,63285,37188,63313,1586,63339,2632],{},[1047,63255,63256],{},"2.16",[1035,63258,63260],{"className":63259},[1480],[1482,63261,63262],{"xmlns":1484},[1487,63263,63264,63282],{},[1490,63265,63266,63268,63270,63272,63274,63276],{},[1493,63267,1501],{},[1506,63269,1508],{},[1493,63271,1052],{},[1506,63273,2162],{},[1493,63275,2394],{},[2315,63277,63278,63280],{},[1493,63279,1520],{},[1680,63281,1691],{},[1528,63283,63284],{"encoding":1530},"P = a + bQ^2",[1035,63286,63288],{"className":63287},[1480],[1482,63289,63290],{"xmlns":1484},[1487,63291,63292,63310],{},[1490,63293,63294,63296,63298,63300,63302,63304],{},[1493,63295,1501],{},[1506,63297,1508],{},[1493,63299,8730],{},[1506,63301,2162],{},[1493,63303,3384],{},[2315,63305,63306,63308],{},[1493,63307,1520],{},[1680,63309,1691],{},[1528,63311,63312],{"encoding":1530},"P = c + dQ^2",[1035,63314,63316],{"className":63315},[1480],[1482,63317,63318],{"xmlns":1484},[1487,63319,63320,63336],{},[1490,63321,63322,63324,63326,63328,63330,63332,63334],{},[1493,63323,1052],{},[1506,63325,1559],{"separator":1041},[1493,63327,8730],{},[1506,63329,1559],{"separator":1041},[1493,63331,3384],{},[1506,63333,2796],{},[1680,63335,1871],{},[1528,63337,63338],{"encoding":1530},"a, c, d > 0",[1035,63340,63342],{"className":63341},[1480],[1482,63343,63344],{"xmlns":1484},[1487,63345,63346,63354],{},[1490,63347,63348,63350,63352],{},[1493,63349,2394],{},[1506,63351,3961],{},[1680,63353,1871],{},[1528,63355,13817],{"encoding":1530},[1203,63357,63358,63406,63422,63529,63581,63633,63742,63758,63857,63910],{},[1206,63359,62850,63360,63373,63374,63405],{},[1035,63361,63363],{"className":63362},[1480],[1482,63364,63365],{"xmlns":1484},[1487,63366,63367,63371],{},[1490,63368,63369],{},[1493,63370,1520],{},[1528,63372,1520],{"encoding":1530},". Načrtněte křivky poptávky a nabídky a stanovte podmínky, aby rovnovážný bod ",[1035,63375,63377],{"className":63376},[1480],[1482,63378,63379],{"xmlns":1484},[1487,63380,63381,63403],{},[1490,63382,63383,63385,63387,63393,63395,63401],{},[1493,63384,2711],{},[1506,63386,14314],{"stretchy":1552},[2315,63388,63389,63391],{},[1493,63390,1520],{},[1493,63392,2711],{},[1506,63394,1559],{"separator":1041},[2315,63396,63397,63399],{},[1493,63398,1501],{},[1493,63400,2711],{},[1506,63402,14323],{"stretchy":1552},[1528,63404,56005],{"encoding":1530}," patřil do 1. kvadrantu.",[1206,63407,62925,63408,63421],{},[1035,63409,63411],{"className":63410},[1480],[1482,63412,63413],{"xmlns":1484},[1487,63414,63415,63419],{},[1490,63416,63417],{},[1493,63418,1520],{},[1528,63420,1520],{"encoding":1530}," a určete jejich znaménka (ověřte geometricky užitím obrázků v (b)).",[1206,63423,62942,63424,1732,63442,1732,63462,1732,63480,63498,63499,63035,63516,2632],{},[1035,63425,63427],{"className":63426},[1480],[1482,63428,63429],{"xmlns":1484},[1487,63430,63431,63439],{},[1490,63432,63433,63435,63437],{},[1493,63434,1052],{},[1506,63436,1508],{},[1680,63438,2916],{},[1528,63440,63441],{"encoding":1530},"a = 100",[1035,63443,63445],{"className":63444},[1480],[1482,63446,63447],{"xmlns":1484},[1487,63448,63449,63459],{},[1490,63450,63451,63453,63455,63457],{},[1493,63452,2394],{},[1506,63454,1508],{},[1506,63456,1888],{},[1680,63458,1682],{},[1528,63460,63461],{"encoding":1530},"b = -1",[1035,63463,63465],{"className":63464},[1480],[1482,63466,63467],{"xmlns":1484},[1487,63468,63469,63477],{},[1490,63470,63471,63473,63475],{},[1493,63472,8730],{},[1506,63474,1508],{},[1680,63476,8436],{},[1528,63478,63479],{"encoding":1530},"c = 20",[1035,63481,63483],{"className":63482},[1480],[1482,63484,63485],{"xmlns":1484},[1487,63486,63487,63495],{},[1490,63488,63489,63491,63493],{},[1493,63490,3384],{},[1506,63492,1508],{},[1680,63494,1682],{},[1528,63496,63497],{"encoding":1530},"d = 1"," určete rovnovážné množství ",[1035,63500,63502],{"className":63501},[1480],[1482,63503,63504],{"xmlns":1484},[1487,63505,63506,63514],{},[1490,63507,63508],{},[2315,63509,63510,63512],{},[1493,63511,1520],{},[1493,63513,2711],{},[1528,63515,14059],{"encoding":1530},[1035,63517,63519],{"className":63518},[1480],[1482,63520,63521],{"xmlns":1484},[1487,63522,63523,63527],{},[1490,63524,63525],{},[1493,63526,1520],{},[1528,63528,1520],{"encoding":1530},[1206,63530,62470,63531,62402,63548,63561,63562,2632],{},[1035,63532,63534],{"className":63533},[1480],[1482,63535,63536],{"xmlns":1484},[1487,63537,63538,63546],{},[1490,63539,63540],{},[2315,63541,63542,63544],{},[1493,63543,1520],{},[1493,63545,2711],{},[1528,63547,14059],{"encoding":1530},[1035,63549,63551],{"className":63550},[1480],[1482,63552,63553],{"xmlns":1484},[1487,63554,63555,63559],{},[1490,63556,63557],{},[1493,63558,1052],{},[1528,63560,1052],{"encoding":1530}," na 110 (ceteris paribus) a stanovte nové rovnovážné množství ",[1035,63563,63565],{"className":63564},[1480],[1482,63566,63567],{"xmlns":1484},[1487,63568,63569,63579],{},[1490,63570,63571],{},[1697,63572,63573,63575,63577],{},[1493,63574,1520],{},[1680,63576,1682],{},[1493,63578,2711],{},[1528,63580,62171],{"encoding":1530},[1206,63582,62523,63583,62402,63600,63613,63614,2632],{},[1035,63584,63586],{"className":63585},[1480],[1482,63587,63588],{"xmlns":1484},[1487,63589,63590,63598],{},[1490,63591,63592],{},[2315,63593,63594,63596],{},[1493,63595,1520],{},[1493,63597,2711],{},[1528,63599,14059],{"encoding":1530},[1035,63601,63603],{"className":63602},[1480],[1482,63604,63605],{"xmlns":1484},[1487,63606,63607,63611],{},[1490,63608,63609],{},[1493,63610,8730],{},[1528,63612,8730],{"encoding":1530}," na 25 (ceteris paribus) a stanovte nové rovnovážné množství ",[1035,63615,63617],{"className":63616},[1480],[1482,63618,63619],{"xmlns":1484},[1487,63620,63621,63631],{},[1490,63622,63623],{},[1697,63624,63625,63627,63629],{},[1493,63626,1520],{},[1680,63628,1691],{},[1493,63630,2711],{},[1528,63632,62233],{"encoding":1530},[1206,63634,62603,63635,62675,63652,63665,63666,18139,63679,63694,63695,63708,63709,63722,63723,2632],{},[1035,63636,63638],{"className":63637},[1480],[1482,63639,63640],{"xmlns":1484},[1487,63641,63642,63650],{},[1490,63643,63644],{},[2315,63645,63646,63648],{},[1493,63647,1520],{},[1493,63649,2711],{},[1528,63651,14059],{"encoding":1530},[1035,63653,63655],{"className":63654},[1480],[1482,63656,63657],{"xmlns":1484},[1487,63658,63659,63663],{},[1490,63660,63661],{},[1493,63662,1052],{},[1528,63664,1052],{"encoding":1530}," na 110, poklesu ",[1035,63667,63669],{"className":63668},[1480],[1482,63670,63671],{"xmlns":1484},[1487,63672,63673,63677],{},[1490,63674,63675],{},[1493,63676,2394],{},[1528,63678,2394],{"encoding":1530},[1035,63680,63682],{"className":63681},[1480],[1482,63683,63684],{"xmlns":1484},[1487,63685,63686,63692],{},[1490,63687,63688,63690],{},[1506,63689,1888],{},[1680,63691,1691],{},[1528,63693,62431],{"encoding":1530},", růstu ",[1035,63696,63698],{"className":63697},[1480],[1482,63699,63700],{"xmlns":1484},[1487,63701,63702,63706],{},[1490,63703,63704],{},[1493,63705,8730],{},[1528,63707,8730],{"encoding":1530}," na 25 a růstu ",[1035,63710,63712],{"className":63711},[1480],[1482,63713,63714],{"xmlns":1484},[1487,63715,63716,63720],{},[1490,63717,63718],{},[1493,63719,3384],{},[1528,63721,3384],{"encoding":1530}," na 2 vzhledem k hladině dle (d) a stanovte nové rovnovážné množství ",[1035,63724,63726],{"className":63725},[1480],[1482,63727,63728],{"xmlns":1484},[1487,63729,63730,63740],{},[1490,63731,63732],{},[1697,63733,63734,63736,63738],{},[1493,63735,1520],{},[1680,63737,3201],{},[1493,63739,2711],{},[1528,63741,62600],{"encoding":1530},[1206,63743,63744,63745,63421],{},"(i) Vypočtěte multiplikátory pro ",[1035,63746,63748],{"className":63747},[1480],[1482,63749,63750],{"xmlns":1484},[1487,63751,63752,63756],{},[1490,63753,63754],{},[1493,63755,1501],{},[1528,63757,1501],{"encoding":1530},[1206,63759,63760,63761,63035,63778,63791,63792,62402,63809,18139,63822,63837,63838,2632],{},"(j) Pro hodnoty parametrů dle (b) určete rovnovážnou cenu ",[1035,63762,63764],{"className":63763},[1480],[1482,63765,63766],{"xmlns":1484},[1487,63767,63768,63776],{},[1490,63769,63770],{},[2315,63771,63772,63774],{},[1493,63773,1501],{},[1493,63775,2711],{},[1528,63777,56102],{"encoding":1530},[1035,63779,63781],{"className":63780},[1480],[1482,63782,63783],{"xmlns":1484},[1487,63784,63785,63789],{},[1490,63786,63787],{},[1493,63788,1501],{},[1528,63790,1501],{"encoding":1530},", přibližnou změnu rovnovážné ceny ",[1035,63793,63795],{"className":63794},[1480],[1482,63796,63797],{"xmlns":1484},[1487,63798,63799,63807],{},[1490,63800,63801],{},[2315,63802,63803,63805],{},[1493,63804,1501],{},[1493,63806,2711],{},[1528,63808,56102],{"encoding":1530},[1035,63810,63812],{"className":63811},[1480],[1482,63813,63814],{"xmlns":1484},[1487,63815,63816,63820],{},[1490,63817,63818],{},[1493,63819,1052],{},[1528,63821,1052],{"encoding":1530},[1035,63823,63825],{"className":63824},[1480],[1482,63826,63827],{"xmlns":1484},[1487,63828,63829,63835],{},[1490,63830,63831,63833],{},[1506,63832,1888],{},[1680,63834,3201],{},[1528,63836,62447],{"encoding":1530}," (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[1035,63839,63841],{"className":63840},[1480],[1482,63842,63843],{"xmlns":1484},[1487,63844,63845,63855],{},[1490,63846,63847],{},[1697,63848,63849,63851,63853],{},[1493,63850,1501],{},[1680,63852,1682],{},[1493,63854,2711],{},[1528,63856,62192],{"encoding":1530},[1206,63858,63859,63860,62402,63877,63890,63891,2632],{},"(k) Určete přibližnou změnu rovnovážné ceny ",[1035,63861,63863],{"className":63862},[1480],[1482,63864,63865],{"xmlns":1484},[1487,63866,63867,63875],{},[1490,63868,63869],{},[2315,63870,63871,63873],{},[1493,63872,1501],{},[1493,63874,2711],{},[1528,63876,56102],{"encoding":1530},[1035,63878,63880],{"className":63879},[1480],[1482,63881,63882],{"xmlns":1484},[1487,63883,63884,63888],{},[1490,63885,63886],{},[1493,63887,1052],{},[1528,63889,1052],{"encoding":1530}," na 2 (ceteris paribus) vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[1035,63892,63894],{"className":63893},[1480],[1482,63895,63896],{"xmlns":1484},[1487,63897,63898,63908],{},[1490,63899,63900],{},[1697,63901,63902,63904,63906],{},[1493,63903,1501],{},[1680,63905,1691],{},[1493,63907,2711],{},[1528,63909,62253],{"encoding":1530},[1206,63911,63912,63913,63122,63930,63943,63944,18139,63957,63694,63972,63985,63986,63999,64000,2632],{},"(l) Určete přibližnou změnu rovnovážné ceny ",[1035,63914,63916],{"className":63915},[1480],[1482,63917,63918],{"xmlns":1484},[1487,63919,63920,63928],{},[1490,63921,63922],{},[2315,63923,63924,63926],{},[1493,63925,1501],{},[1493,63927,2711],{},[1528,63929,56102],{"encoding":1530},[1035,63931,63933],{"className":63932},[1480],[1482,63934,63935],{"xmlns":1484},[1487,63936,63937,63941],{},[1490,63938,63939],{},[1493,63940,1052],{},[1528,63942,1052],{"encoding":1530}," na 90, poklesu ",[1035,63945,63947],{"className":63946},[1480],[1482,63948,63949],{"xmlns":1484},[1487,63950,63951,63955],{},[1490,63952,63953],{},[1493,63954,2394],{},[1528,63956,2394],{"encoding":1530},[1035,63958,63960],{"className":63959},[1480],[1482,63961,63962],{"xmlns":1484},[1487,63963,63964,63970],{},[1490,63965,63966,63968],{},[1506,63967,1888],{},[1680,63969,3201],{},[1528,63971,62447],{"encoding":1530},[1035,63973,63975],{"className":63974},[1480],[1482,63976,63977],{"xmlns":1484},[1487,63978,63979,63983],{},[1490,63980,63981],{},[1493,63982,8730],{},[1528,63984,8730],{"encoding":1530}," na 30 a růstu ",[1035,63987,63989],{"className":63988},[1480],[1482,63990,63991],{"xmlns":1484},[1487,63992,63993,63997],{},[1490,63994,63995],{},[1493,63996,3384],{},[1528,63998,3384],{"encoding":1530}," na 2 vzhledem k hladině dle (d) a stanovte novou rovnovážnou cenu ",[1035,64001,64003],{"className":64002},[1480],[1482,64004,64005],{"xmlns":1484},[1487,64006,64007,64017],{},[1490,64008,64009],{},[1697,64010,64011,64013,64015],{},[1493,64012,1501],{},[1680,64014,3201],{},[1493,64016,2711],{},[1528,64018,63251],{"encoding":1530},[1304,64020,28281],{"id":64021},"přebytek-spotřebitele-a-výrobce-1",[1030,64023,64024,62019,64027,62056,64063,2632],{},[1047,64025,64026],{},"2.17",[1035,64028,64030],{"className":64029},[1480],[1482,64031,64032],{"xmlns":1484},[1487,64033,64034,64060],{},[1490,64035,64036,64038,64040,64042,64044,64046,64048,64050,64052,64054],{},[1493,64037,1501],{},[1506,64039,1508],{},[1493,64041,3712],{},[1506,64043,1553],{"stretchy":1552},[1493,64045,1520],{},[1506,64047,1564],{"stretchy":1552},[1506,64049,1508],{},[1680,64051,5603],{},[1506,64053,1888],{},[2315,64055,64056,64058],{},[1493,64057,1520],{},[1680,64059,1691],{},[1528,64061,64062],{"encoding":1530},"P = D(Q) = 35 - Q^2",[1035,64064,64066],{"className":64065},[1480],[1482,64067,64068],{"xmlns":1484},[1487,64069,64070,64096],{},[1490,64071,64072,64074,64076,64078,64080,64082,64084,64086,64088,64090],{},[1493,64073,1501],{},[1506,64075,1508],{},[1493,64077,2001],{},[1506,64079,1553],{"stretchy":1552},[1493,64081,1520],{},[1506,64083,1564],{"stretchy":1552},[1506,64085,1508],{},[1680,64087,3201],{},[1506,64089,2162],{},[2315,64091,64092,64094],{},[1493,64093,1520],{},[1680,64095,1691],{},[1528,64097,64098],{"encoding":1530},"P = S(Q) = 3 + Q^2",[1203,64100,64101,64104],{},[1206,64102,64103],{},"(a) Vypočtěte přebytek spotřebitele při množství 4.",[1206,64105,64106],{},"(b) Vypočtěte přebytek výrobce při množství 4.",[1030,64108,64109,62019,64112,62056,64146,2632],{},[1047,64110,64111],{},"2.18",[1035,64113,64115],{"className":64114},[1480],[1482,64116,64117],{"xmlns":1484},[1487,64118,64119,64143],{},[1490,64120,64121,64123,64125,64127,64129,64131,64133,64135,64137,64139,64141],{},[1493,64122,1501],{},[1506,64124,1508],{},[1493,64126,3712],{},[1506,64128,1553],{"stretchy":1552},[1493,64130,1520],{},[1506,64132,1564],{"stretchy":1552},[1506,64134,1508],{},[1680,64136,9319],{},[1506,64138,1888],{},[1680,64140,1691],{},[1493,64142,1520],{},[1528,64144,64145],{"encoding":1530},"P = D(Q) = 18 - 2Q",[1035,64147,64149],{"className":64148},[1480],[1482,64150,64151],{"xmlns":1484},[1487,64152,64153,64179],{},[1490,64154,64155,64157,64159,64161,64163,64165,64167,64169,64171,64173],{},[1493,64156,1501],{},[1506,64158,1508],{},[1493,64160,2001],{},[1506,64162,1553],{"stretchy":1552},[1493,64164,1520],{},[1506,64166,1564],{"stretchy":1552},[1506,64168,1508],{},[1680,64170,3201],{},[1506,64172,2162],{},[2315,64174,64175,64177],{},[1493,64176,1520],{},[1680,64178,1691],{},[1528,64180,64098],{"encoding":1530},[1203,64182,64183,64203,64206,64209],{},[1206,64184,64185,64186,2632],{},"(a) Vypočtěte rovnovážné množství ",[1035,64187,64189],{"className":64188},[1480],[1482,64190,64191],{"xmlns":1484},[1487,64192,64193,64201],{},[1490,64194,64195],{},[2315,64196,64197,64199],{},[1493,64198,1520],{},[1493,64200,2711],{},[1528,64202,14059],{"encoding":1530},[1206,64204,64205],{},"(b) Vypočtěte přebytek spotřebitele při rovnovážném množství.",[1206,64207,64208],{},"(b) Vypočtěte přebytek výrobce při rovnovážném množství.",[1206,64210,64211],{},"(c) Graficky interpretujte.",[1246,64213],{},[1065,64215,64217],{"id":64216},"otázky-k-sebehodnocení","Otázky k sebehodnocení",[1276,64219,64220,64223,64226,64229,64232,64235,64238,64241,64244,64247,64250,64253,64256,64259],{},[1206,64221,64222],{},"Jaký je rozdíl mezi jednofaktorovým a vícefaktorovým modelem poptávky?",[1206,64224,64225],{},"Vyjádřete (vícefaktorovou) funkci poptávky. Jakou má vlastnost?",[1206,64227,64228],{},"Definujte funkci poptávky (jednofaktorovou). Jaká je její základní vlastnost? Zdůvodněte.",[1206,64230,64231],{},"Definujte Engelovu funkci. Na čem závisí tvar příslušné Engelovy křivky?",[1206,64233,64234],{},"Jaký charakter má odezva poptávky na změnu některé z exogenních proměnných?",[1206,64236,64237],{},"Definujte funkci nabídky. Jaká je její základní vlastnost? Zdůvodněte.",[1206,64239,64240],{},"Co znamená tržní rovnováha? Čím je reprezentována?",[1206,64242,64243],{},"Jak se určí rovnovážné množství a rovnovážná cena?",[1206,64245,64246],{},"Jaká jsou pravidla pro změnu rovnovážného bodu jako odezvy na posun poptávky, resp. nabídky?",[1206,64248,64249],{},"K čemu slouží multiplikátory?",[1206,64251,64252],{},"Jak se najde redukovaný tvar pro vybranou rovnovážnou veličinu?",[1206,64254,64255],{},"Jak se vypočtou multiplikátory? Mění se jejich znaménka?",[1206,64257,64258],{},"Co se rozumí přebytkem spotřebitele? Jak se vypočte?",[1206,64260,64261],{},"Co se rozumí přebytkem výrobce? Jak se vypočte?",[1246,64263],{},[1065,64265,31885],{"id":31884},[1030,64267,64268],{},[1047,64269,29638],{},[1203,64271,64272,64307,64312,64342,64347,64410,64436,64441,64471,64480,64487,64492],{},[1206,64273,64274,7606,64277,34788,64280,1656,64282,1732,64305],{},[1047,64275,64276],{},"Poptávané množství",[1176,64278,64279],{},"quantity demanded",[1047,64281,43567],{},[1035,64283,64285],{"className":64284},[1480],[1482,64286,64287],{"xmlns":1484},[1487,64288,64289,64303],{},[1490,64290,64291,64293,64295,64297,64299,64301],{},[1493,64292,1520],{},[1506,64294,1508],{},[1493,64296,3712],{},[1506,64298,1553],{"stretchy":1552},[1493,64300,1501],{},[1506,64302,1564],{"stretchy":1552},[1528,64304,19607],{"encoding":1530},[1047,64306,52553],{},[1206,64308,64309,64311],{},[1047,64310,52560],{}," — substituční + důchodový efekt",[1206,64313,64314,1656,64317],{},[1047,64315,64316],{},"Reálné cenové rozpětí",[1035,64318,64320],{"className":64319},[1480],[1482,64321,64322],{"xmlns":1484},[1487,64323,64324,64340],{},[1490,64325,64326,64328,64330,64332,64338],{},[1506,64327,1553],{"stretchy":1552},[1680,64329,1871],{},[1506,64331,1559],{"separator":1041},[1497,64333,64334,64336],{},[1493,64335,1501],{},[1680,64337,1871],{},[1506,64339,1564],{"stretchy":1552},[1528,64341,52768],{"encoding":1530},[1206,64343,64344,27611],{},[1047,64345,64346],{},"Homogenita poptávky",[1206,64348,64349,1656,64352,1732,64375,1732,64392,64409],{},[1047,64350,64351],{},"Lineární poptávka",[1035,64353,64355],{"className":64354},[1480],[1482,64356,64357],{"xmlns":1484},[1487,64358,64359,64373],{},[1490,64360,64361,64363,64365,64367,64369,64371],{},[1493,64362,1501],{},[1506,64364,1508],{},[1493,64366,1052],{},[1493,64368,1520],{},[1506,64370,2162],{},[1493,64372,2394],{},[1528,64374,52158],{"encoding":1530},[1035,64376,64378],{"className":64377},[1480],[1482,64379,64380],{"xmlns":1484},[1487,64381,64382,64390],{},[1490,64383,64384,64386,64388],{},[1493,64385,1052],{},[1506,64387,3961],{},[1680,64389,1871],{},[1528,64391,57642],{"encoding":1530},[1035,64393,64395],{"className":64394},[1480],[1482,64396,64397],{"xmlns":1484},[1487,64398,64399,64407],{},[1490,64400,64401,64403,64405],{},[1493,64402,2394],{},[1506,64404,2796],{},[1680,64406,1871],{},[1528,64408,34950],{"encoding":1530}," — nedokonalá konkurence",[1206,64411,64412,22970,64415],{},[1047,64413,64414],{},"Dokonalá konkurence",[1035,64416,64418],{"className":64417},[1480],[1482,64419,64420],{"xmlns":1484},[1487,64421,64422,64434],{},[1490,64423,64424,64426,64428],{},[1493,64425,1501],{},[1506,64427,1508],{},[2315,64429,64430,64432],{},[1493,64431,1501],{},[1506,64433,2287],{},[1528,64435,20068],{"encoding":1530},[1206,64437,64438,64440],{},[1047,64439,53154],{}," — rostoucí křivka poptávky (důchodový efekt > substituční)",[1206,64442,64443,1656,64445,1732,64469],{},[1047,64444,46829],{},[1035,64446,64448],{"className":64447},[1480],[1482,64449,64450],{"xmlns":1484},[1487,64451,64452,64466],{},[1490,64453,64454,64456,64458,64460,64462,64464],{},[1493,64455,1520],{},[1506,64457,1508],{},[1493,64459,2711],{},[1506,64461,1553],{"stretchy":1552},[1493,64463,1791],{},[1506,64465,1564],{"stretchy":1552},[1528,64467,64468],{"encoding":1530},"Q = E(Y)",[1047,64470,53351],{},[1206,64472,64473,64476,64477,64479],{},[1047,64474,64475],{},"Normální"," (nezbytné \u002F luxusní) vs. ",[1047,64478,53802],{}," zboží",[1206,64481,64482,1586,64484,64486],{},[1047,64483,54637],{},[1047,64485,8866],{}," — znaménka zkřížených koeficientů",[1206,64488,64489,64491],{},[1047,64490,8775],{}," (2.6)",[1206,64493,64494,7606,64497,1564],{},[1047,64495,64496],{},"Posun poptávky",[1176,64498,53860],{},[1030,64500,64501],{},[1047,64502,29604],{},[1203,64504,64505,64538,64542,64587],{},[1206,64506,64507,7606,64509,34788,64511,1656,64513,1732,64536],{},[1047,64508,55035],{},[1176,64510,55038],{},[1047,64512,55209],{},[1035,64514,64516],{"className":64515},[1480],[1482,64517,64518],{"xmlns":1484},[1487,64519,64520,64534],{},[1490,64521,64522,64524,64526,64528,64530,64532],{},[1493,64523,1520],{},[1506,64525,1508],{},[1493,64527,2001],{},[1506,64529,1553],{"stretchy":1552},[1493,64531,1501],{},[1506,64533,1564],{"stretchy":1552},[1528,64535,24691],{"encoding":1530},[1047,64537,55287],{},[1206,64539,64540],{},[1047,64541,55294],{},[1206,64543,64544,1656,64547,1732,64570],{},[1047,64545,64546],{},"Lineární nabídka",[1035,64548,64550],{"className":64549},[1480],[1482,64551,64552],{"xmlns":1484},[1487,64553,64554,64568],{},[1490,64555,64556,64558,64560,64562,64564,64566],{},[1493,64557,1501],{},[1506,64559,1508],{},[1493,64561,8730],{},[1493,64563,1520],{},[1506,64565,2162],{},[1493,64567,3384],{},[1528,64569,55008],{"encoding":1530},[1035,64571,64573],{"className":64572},[1480],[1482,64574,64575],{"xmlns":1484},[1487,64576,64577,64585],{},[1490,64578,64579,64581,64583],{},[1493,64580,8730],{},[1506,64582,2796],{},[1680,64584,1871],{},[1528,64586,55026],{"encoding":1530},[1206,64588,64589,7606,64592,1564],{},[1047,64590,64591],{},"Posun nabídky",[1176,64593,55637],{},[1030,64595,64596],{},[1047,64597,64598],{},"Rovnováha a komparativní statika",[1203,64600,64601,64680,64686],{},[1206,64602,64603,7606,64605,34788,64607,1656,64610,1732,64627,1656,64630,1732,64647,1656,64649],{},[1047,64604,55958],{},[1176,64606,56080],{},[1047,64608,64609],{},"rovnovážná cena",[1035,64611,64613],{"className":64612},[1480],[1482,64614,64615],{"xmlns":1484},[1487,64616,64617,64625],{},[1490,64618,64619],{},[2315,64620,64621,64623],{},[1493,64622,1501],{},[1493,64624,2711],{},[1528,64626,56102],{"encoding":1530},[1047,64628,64629],{},"rovnovážné množství",[1035,64631,64633],{"className":64632},[1480],[1482,64634,64635],{"xmlns":1484},[1487,64636,64637,64645],{},[1490,64638,64639],{},[2315,64640,64641,64643],{},[1493,64642,1520],{},[1493,64644,2711],{},[1528,64646,14059],{"encoding":1530},[1047,64648,56138],{},[1035,64650,64652],{"className":64651},[1480],[1482,64653,64654],{"xmlns":1484},[1487,64655,64656,64678],{},[1490,64657,64658,64660,64662,64668,64670,64676],{},[1493,64659,2711],{},[1506,64661,14314],{"stretchy":1552},[2315,64663,64664,64666],{},[1493,64665,1520],{},[1493,64667,2711],{},[1506,64669,1559],{"separator":1041},[2315,64671,64672,64674],{},[1493,64673,1501],{},[1493,64675,2711],{},[1506,64677,14323],{"stretchy":1552},[1528,64679,56005],{"encoding":1530},[1206,64681,64682,64685],{},[1047,64683,64684],{},"Pravidla 1–4"," komparativní statiky",[1206,64687,64688,7606,64691,1564],{},[1047,64689,64690],{},"Teorém pavučiny",[1176,64692,56897],{},[1030,64694,64695],{},[1047,64696,64697],{},"Zdanění",[1203,64699,64700,64756,64804],{},[1206,64701,64702,64704,64705,64730,64731,1564],{},[1047,64703,64697],{}," — daň výrobci (",[1035,64706,64708],{"className":64707},[1480],[1482,64709,64710],{"xmlns":1484},[1487,64711,64712,64728],{},[1490,64713,64714,64720,64722,64724,64726],{},[1497,64715,64716,64718],{},[1493,64717,2001],{},[1680,64719,1682],{},[1506,64721,1508],{},[1493,64723,2001],{},[1506,64725,2162],{},[1493,64727,5289],{},[1528,64729,57306],{"encoding":1530},") vs. daň spotřebiteli (",[1035,64732,64734],{"className":64733},[1480],[1482,64735,64736],{"xmlns":1484},[1487,64737,64738,64754],{},[1490,64739,64740,64746,64748,64750,64752],{},[1497,64741,64742,64744],{},[1493,64743,3712],{},[1680,64745,1691],{},[1506,64747,1508],{},[1493,64749,3712],{},[1506,64751,1888],{},[1493,64753,5289],{},[1528,64755,57337],{"encoding":1530},[1206,64757,64758,1656,64760,1732,64781],{},[1047,64759,57210],{},[1035,64761,64763],{"className":64762},[1480],[1482,64764,64765],{"xmlns":1484},[1487,64766,64767,64779],{},[1490,64768,64769],{},[1497,64770,64771,64773],{},[1493,64772,5289],{},[1490,64774,64775,64777],{},[1493,64776,25906],{},[1493,64778,1030],{},[1528,64780,57233],{"encoding":1530},[1035,64782,64784],{"className":64783},[1480],[1482,64785,64786],{"xmlns":1484},[1487,64787,64788,64802],{},[1490,64789,64790],{},[1497,64791,64792,64794],{},[1493,64793,5289],{},[1490,64795,64796,64798,64800],{},[1493,64797,25950],{},[1493,64799,3052],{},[1493,64801,7740],{},[1528,64803,57257],{"encoding":1530},[1206,64805,64806,1656,64809,1732,64838],{},[1047,64807,64808],{},"Ekvivalence zdanění",[1035,64810,64812],{"className":64811},[1480],[1482,64813,64814],{"xmlns":1484},[1487,64815,64816,64836],{},[1490,64817,64818,64826,64828],{},[1697,64819,64820,64822,64824],{},[1493,64821,1520],{},[1680,64823,1682],{},[1493,64825,2711],{},[1506,64827,1508],{},[1697,64829,64830,64832,64834],{},[1493,64831,1520],{},[1680,64833,1691],{},[1493,64835,2711],{},[1528,64837,57460],{"encoding":1530},[1035,64839,64841],{"className":64840},[1480],[1482,64842,64843],{"xmlns":1484},[1487,64844,64845,64869],{},[1490,64846,64847,64855,64857,64859,64861],{},[1697,64848,64849,64851,64853],{},[1493,64850,1501],{},[1680,64852,1682],{},[1493,64854,2711],{},[1506,64856,1888],{},[1493,64858,5289],{},[1506,64860,1508],{},[1697,64862,64863,64865,64867],{},[1493,64864,1501],{},[1680,64866,1691],{},[1493,64868,2711],{},[1528,64870,57494],{"encoding":1530},[1030,64872,64873],{},[1047,64874,17142],{},[1203,64876,64877,64923,64954,64959,64965,64972],{},[1206,64878,64879,1656,64881],{},[1047,64880,57598],{},[1035,64882,64884],{"className":64883},[1480],[1482,64885,64886],{"xmlns":1484},[1487,64887,64888,64920],{},[1490,64889,64890,64896,64898,64900,64902,64904,64906,64908,64910,64912,64914,64916,64918],{},[2315,64891,64892,64894],{},[1493,64893,1520],{},[1493,64895,2711],{},[1506,64897,1508],{},[1506,64899,1553],{"stretchy":1552},[1493,64901,2394],{},[1506,64903,1888],{},[1493,64905,3384],{},[1506,64907,1564],{"stretchy":1552},[1493,64909,1709],{"mathvariant":1516},[1506,64911,1553],{"stretchy":1552},[1493,64913,8730],{},[1506,64915,1888],{},[1493,64917,1052],{},[1506,64919,1564],{"stretchy":1552},[1528,64921,64922],{"encoding":1530},"Q^E = (b - d)\u002F(c - a)",[1206,64924,64925,1656,64928,64953],{},[1047,64926,64927],{},"Parametry",[1035,64929,64931],{"className":64930},[1480],[1482,64932,64933],{"xmlns":1484},[1487,64934,64935,64951],{},[1490,64936,64937,64939,64941,64943,64945,64947,64949],{},[1493,64938,1052],{},[1506,64940,1559],{"separator":1041},[1493,64942,2394],{},[1506,64944,1559],{"separator":1041},[1493,64946,8730],{},[1506,64948,1559],{"separator":1041},[1493,64950,3384],{},[1528,64952,57842],{"encoding":1530}," — exogenní proměnné",[1206,64955,64956],{},[1047,64957,64958],{},"Endogenní \u002F exogenní proměnná",[1206,64960,64961,64964],{},[1047,64962,64963],{},"Multiplikátor"," — parciální derivace redukovaného tvaru",[1206,64966,64967,1732,64970],{},[1047,64968,64969],{},"Komparativní statika",[1047,64971,52054],{},[1206,64973,64974,1656,64976,64992],{},[1047,64975,18393],{},[1035,64977,64979],{"className":64978},[1480],[1482,64980,64981],{"xmlns":1484},[1487,64982,64983,64989],{},[1490,64984,64985,64987],{},[1493,64986,3384],{},[1493,64988,1520],{},[1528,64990,64991],{"encoding":1530},"dQ"," (2.11)",[1030,64994,64995],{},[1047,64996,64997],{},"Přebytky a ostatní",[1203,64999,65000,65038],{},[1206,65001,65002,1656,65004,65019,65020,1656,65022,65037],{},[1047,65003,59273],{},[1035,65005,65007],{"className":65006},[1480],[1482,65008,65009],{"xmlns":1484},[1487,65010,65011,65017],{},[1490,65012,65013,65015],{},[1493,65014,1998],{},[1493,65016,2001],{},[1528,65018,59289],{"encoding":1530}," (2.14), ",[1047,65021,59292],{},[1035,65023,65025],{"className":65024},[1480],[1482,65026,65027],{"xmlns":1484},[1487,65028,65029,65035],{},[1490,65030,65031,65033],{},[1493,65032,1501],{},[1493,65034,2001],{},[1528,65036,59308],{"encoding":1530}," (2.15)",[1206,65039,65040,1732,65043,65046],{},[1047,65041,65042],{},"Homo economicus",[1047,65044,65045],{},"Marshallova formulace"," (1890)",[1246,65048],{},[1065,65050,17159],{"id":17158},[1203,65052,65053,65088,65096],{},[1206,65054,65055,1656,65058,65061,65062,1732,65065,65068,65069,65072,65073,65076,65077,65080,65081,65084,65085],{},[1047,65056,65057],{},"Související témata:",[1052,65059,57168],{"className":65060,"dataFsResolvedFilePath":57271,"href":57272},[1055]," (dopady daně, daňové břemeno, ekvivalence), ",[1052,65063,28281],{"className":65064,"dataFsResolvedFilePath":17231,"href":17232},[1055],[1052,65066,3506],{"className":65067,"dataFsResolvedFilePath":16621,"href":16622},[1055]," (zákon klesající\u002Frostoucí, monotonie), ",[1052,65070,17258],{"className":65071,"dataFsResolvedFilePath":17256,"href":17257},[1055]," (CS a PS), ",[1052,65074,9472],{"className":65075,"dataFsResolvedFilePath":9470,"href":9471},[1055]," (vícefaktorové modely, multiplikátory), ",[1052,65078,17267],{"className":65079,"dataFsResolvedFilePath":17265,"href":17266},[1055]," (optimalizace spotřebitele), ",[1052,65082,17218],{"className":65083,"dataFsResolvedFilePath":3807,"href":3808},[1055]," (důchodová a cenová citlivost), ",[1052,65086,1301],{"className":65087,"dataFsResolvedFilePath":1299,"href":1300},[1055],[1206,65089,65090,1656,65093],{},[1047,65091,65092],{},"Shrnutí přednášek:",[1052,65094,17190],{"className":65095,"dataFsResolvedFilePath":17188,"href":17189},[1055],[1206,65097,65098,1656,65100],{},[1047,65099,17176],{},[1052,65101,1058],{"className":65102,"dataFsResolvedFilePath":1056,"href":1057},[1055],{"title":17269,"searchDepth":141,"depth":141,"links":65104},[65105,65106,65114,65120,65127,65128,65135,65136,65137,65144,65145,65146],{"id":51890,"depth":141,"text":51891},{"id":51872,"depth":141,"text":29638,"children":65107},[65108,65109,65110,65111,65113],{"id":52161,"depth":96,"text":52162},{"id":52449,"depth":96,"text":52450},{"id":53283,"depth":96,"text":53284},{"id":53856,"depth":96,"text":65112},"Posun poptávky (shift of demand)",{"id":54190,"depth":96,"text":54191},{"id":16507,"depth":141,"text":29604,"children":65115},[65116,65117,65118],{"id":55030,"depth":96,"text":52162},{"id":55216,"depth":96,"text":55217},{"id":55633,"depth":96,"text":65119},"Posun nabídky (shift of supply)",{"id":55957,"depth":141,"text":55958,"children":65121},[65122,65123,65124,65125,65126],{"id":1475,"depth":96,"text":1476},{"id":56200,"depth":96,"text":56201},{"id":56515,"depth":96,"text":56516},{"id":56869,"depth":96,"text":56870},{"id":56900,"depth":96,"text":56901},{"id":57167,"depth":141,"text":57168},{"id":57574,"depth":141,"text":57575,"children":65129},[65130,65131,65132,65133],{"id":57597,"depth":96,"text":57598},{"id":57901,"depth":96,"text":57902},{"id":58285,"depth":96,"text":58286},{"id":58645,"depth":96,"text":65134},"Příklad 2.11 — komparativní statika pro QEQ^E",{"id":28280,"depth":141,"text":28281},{"id":59523,"depth":141,"text":59524},{"id":59754,"depth":141,"text":59755,"children":65138},[65139,65140,65141,65142,65143],{"id":59758,"depth":96,"text":59759},{"id":60595,"depth":96,"text":60596},{"id":60971,"depth":96,"text":55958},{"id":62265,"depth":96,"text":57575},{"id":64021,"depth":96,"text":28281},{"id":64216,"depth":141,"text":64217},{"id":31884,"depth":141,"text":31885},{"id":17158,"depth":141,"text":17159},{},"\u002Ftopics\u002Fpoptavka-nabidka",{"title":3489,"description":17269},[26098,19272],"topics\u002Fpoptavka-nabidka",[9,804,732,297,126,341,281],"PVsmM9zjzR6S_-atW_WPF2wpWDR_2TuwB4wE1ghAXQI",{"id":65155,"title":28281,"body":65156,"course":9,"courses":17424,"created":26093,"description":17269,"extension":17426,"meta":69287,"navigation":17428,"path":69288,"seo":69289,"sources":69290,"stem":69291,"tags":69292,"type":19275,"updated":26102,"__hash__":69293},"topics\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce.md",{"type":1016,"value":65157,"toc":69265},[65158,65160,65233,65283,65285,65289,65548,65626,65631,65633,65652,65656,65732,65817,65819,66133,66135,66154,66158,66232,66317,66320,66496,66498,66921,66923,66927,66931,67174,67218,67318,67384,67387,67420,67595,67657,67787,67865,67976,68010,68017,68113,68156,68175,68245,68249,68252,68297,68300,68417,68463,68465,68469,68816,68818,68820,69098,69100,69104,69139,69146,69219,69221,69223],[1019,65159,28281],{"id":28280},[1023,65161,65163,65169],{"className":65162,"dataCallout":1028},[1026,1027],[1030,65164,65166,1042],{"className":65165},[1033],[1035,65167],{"className":65168,"ariaHidden":1041},[1038,1039,1040],[1030,65170,65171,7606,65173,65188,65189,7606,65191,65206,65207,65229,65230,2632],{},[1047,65172,59273],{},[1035,65174,65176],{"className":65175},[1480],[1482,65177,65178],{"xmlns":1484},[1487,65179,65180,65186],{},[1490,65181,65182,65184],{},[1493,65183,1998],{},[1493,65185,2001],{},[1528,65187,59289],{"encoding":1530},") je rozdíl mezi tím, co byl spotřebitel ochoten zaplatit, a tím, co skutečně zaplatil. ",[1047,65190,59420],{},[1035,65192,65194],{"className":65193},[1480],[1482,65195,65196],{"xmlns":1484},[1487,65197,65198,65204],{},[1490,65199,65200,65202],{},[1493,65201,1501],{},[1493,65203,2001],{},[1528,65205,59308],{"encoding":1530},") je rozdíl mezi tím, co výrobce dostal, a minimální cenou, za kterou by byl ochoten prodávat. Geometricky jsou to plochy mezi křivkou poptávky \u002F nabídky a rovnovážnou cenou; početně určité integrály. Součet ",[1035,65208,65210],{"className":65209},[1480],[1482,65211,65212],{"xmlns":1484},[1487,65213,65214,65226],{},[1490,65215,65216,65218,65220,65222,65224],{},[1493,65217,1998],{},[1493,65219,2001],{},[1506,65221,2162],{},[1493,65223,1501],{},[1493,65225,2001],{},[1528,65227,65228],{"encoding":1530},"CS + PS"," měří ",[1047,65231,65232],{},"celkový blahobyt trhu",[1030,65234,65235,7606,65237,1732,65239,28611,65254,7606,65256,1732,65258,65273,65274,65278,65279,2632],{},[1047,65236,59273],{},[1176,65238,59327],{},[1035,65240,65242],{"className":65241},[1480],[1482,65243,65244],{"xmlns":1484},[1487,65245,65246,65252],{},[1490,65247,65248,65250],{},[1493,65249,1998],{},[1493,65251,2001],{},[1528,65253,59289],{"encoding":1530},[1047,65255,59292],{},[1176,65257,59423],{},[1035,65259,65261],{"className":65260},[1480],[1482,65262,65263],{"xmlns":1484},[1487,65264,65265,65271],{},[1490,65266,65267,65269],{},[1493,65268,1501],{},[1493,65270,2001],{},[1528,65272,59308],{"encoding":1530},") kvantifikují čistý prospěch jednotlivých stran trhu. Navazují na pojmy ",[1052,65275,65277],{"className":65276,"dataFsResolvedFilePath":3487,"href":3488},[1055],"tržní rovnováhy"," a využívají aparát ",[1052,65280,65282],{"className":65281,"dataFsResolvedFilePath":17256,"href":17257},[1055],"integrálního počtu",[1246,65284],{},[1065,65286,65288],{"id":65287},"úvod","Úvod",[1030,65290,65291,65292,65315,65316,65339,65340,65357,65358,19330,65390,65422,65423,65449,65450,65453,65454,65457,65458,30481,65492,37188,65514,2632],{},"Je dána funkce poptávky ",[1035,65293,65295],{"className":65294},[1480],[1482,65296,65297],{"xmlns":1484},[1487,65298,65299,65313],{},[1490,65300,65301,65303,65305,65307,65309,65311],{},[1493,65302,1501],{},[1506,65304,1508],{},[1493,65306,3712],{},[1506,65308,1553],{"stretchy":1552},[1493,65310,1520],{},[1506,65312,1564],{"stretchy":1552},[1528,65314,20356],{"encoding":1530},", resp. funkce nabídky ",[1035,65317,65319],{"className":65318},[1480],[1482,65320,65321],{"xmlns":1484},[1487,65322,65323,65337],{},[1490,65324,65325,65327,65329,65331,65333,65335],{},[1493,65326,1501],{},[1506,65328,1508],{},[1493,65330,2001],{},[1506,65332,1553],{"stretchy":1552},[1493,65334,1520],{},[1506,65336,1564],{"stretchy":1552},[1528,65338,55723],{"encoding":1530},". Pro pevně zadané množství ",[1035,65341,65343],{"className":65342},[1480],[1482,65344,65345],{"xmlns":1484},[1487,65346,65347,65355],{},[1490,65348,65349],{},[1497,65350,65351,65353],{},[1493,65352,1520],{},[1680,65354,1871],{},[1528,65356,53236],{"encoding":1530}," je odpovídající cena ",[1035,65359,65361],{"className":65360},[1480],[1482,65362,65363],{"xmlns":1484},[1487,65364,65365,65387],{},[1490,65366,65367,65373,65375,65377,65379,65385],{},[1497,65368,65369,65371],{},[1493,65370,1501],{},[1680,65372,1871],{},[1506,65374,1508],{},[1493,65376,3712],{},[1506,65378,1553],{"stretchy":1552},[1497,65380,65381,65383],{},[1493,65382,1520],{},[1680,65384,1871],{},[1506,65386,1564],{"stretchy":1552},[1528,65388,65389],{"encoding":1530},"P_0 = D(Q_0)",[1035,65391,65393],{"className":65392},[1480],[1482,65394,65395],{"xmlns":1484},[1487,65396,65397,65419],{},[1490,65398,65399,65405,65407,65409,65411,65417],{},[1497,65400,65401,65403],{},[1493,65402,1501],{},[1680,65404,1871],{},[1506,65406,1508],{},[1493,65408,2001],{},[1506,65410,1553],{"stretchy":1552},[1497,65412,65413,65415],{},[1493,65414,1520],{},[1680,65416,1871],{},[1506,65418,1564],{"stretchy":1552},[1528,65420,65421],{"encoding":1530},"P_0 = S(Q_0)","). Součin ",[1035,65424,65426],{"className":65425},[1480],[1482,65427,65428],{"xmlns":1484},[1487,65429,65430,65446],{},[1490,65431,65432,65438,65440],{},[1497,65433,65434,65436],{},[1493,65435,1501],{},[1680,65437,1871],{},[1988,65439,5016],{},[1497,65441,65442,65444],{},[1493,65443,1520],{},[1680,65445,1871],{},[1528,65447,65448],{"encoding":1530},"P_0 \\, Q_0"," reprezentuje buď ",[1047,65451,65452],{},"výdaje spotřebitele",", nebo ",[1047,65455,65456],{},"tržby výrobce"," a geometricky odpovídá obsahu obdélníka ",[1035,65459,65461],{"className":65460},[1480],[1482,65462,65463],{"xmlns":1484},[1487,65464,65465,65489],{},[1490,65466,65467,65469,65471,65477,65479,65481,65483],{},[1680,65468,1871],{},[1988,65470,5016],{},[1497,65472,65473,65475],{},[1493,65474,1520],{},[1680,65476,1871],{},[1988,65478,5016],{},[1493,65480,3633],{},[1988,65482,5016],{},[1497,65484,65485,65487],{},[1493,65486,1501],{},[1680,65488,1871],{},[1528,65490,65491],{"encoding":1530},"0\\,Q_0\\,A\\,P_0",[1035,65493,65495],{"className":65494},[1480],[1482,65496,65497],{"xmlns":1484},[1487,65498,65499,65511],{},[1490,65500,65501,65503,65505,65507,65509],{},[1506,65502,1553],{"stretchy":1552},[1493,65504,1520],{},[1506,65506,1559],{"separator":1041},[1493,65508,1501],{},[1506,65510,1564],{"stretchy":1552},[1528,65512,65513],{"encoding":1530},"(Q, P)",[1035,65515,65517],{"className":65516},[1480],[1482,65518,65519],{"xmlns":1484},[1487,65520,65521,65545],{},[1490,65522,65523,65525,65527,65529,65535,65537,65543],{},[1493,65524,3633],{},[1506,65526,1508],{},[1506,65528,14314],{"stretchy":1552},[1497,65530,65531,65533],{},[1493,65532,1520],{},[1680,65534,1871],{},[1506,65536,1559],{"separator":1041},[1497,65538,65539,65541],{},[1493,65540,1501],{},[1680,65542,1871],{},[1506,65544,14323],{"stretchy":1552},[1528,65546,65547],{"encoding":1530},"A = [Q_0, P_0]",[1023,65549,65551,65557,65615],{"className":65550,"dataCallout":582},[1026,1186],[1030,65552,65554,6749],{"className":65553},[1033],[1035,65555],{"className":65556,"ariaHidden":1041},[1038,1193,1040],[1203,65558,65559,65587],{},[1206,65560,65561,65562,65565,65566,65568,65569,65586],{},"Za jednotky zboží nakoupené ",[1047,65563,65564],{},"před"," posledním kusem je spotřebitel podle funkce poptávky ochoten platit ",[1176,65567,40840],{}," než ",[1035,65570,65572],{"className":65571},[1480],[1482,65573,65574],{"xmlns":1484},[1487,65575,65576,65584],{},[1490,65577,65578],{},[1497,65579,65580,65582],{},[1493,65581,1501],{},[1680,65583,1871],{},[1528,65585,53881],{"encoding":1530}," — rozdíl si „šetří do kapsy\" jako přebytek.",[1206,65588,65589,65590,65592,65593,65596,65597,65614],{},"Za jednotky zboží prodané ",[1047,65591,65564],{}," posledním kusem by výrobce podle funkce nabídky byl ochoten prodávat i za ",[1176,65594,65595],{},"nižší"," cenu než ",[1035,65598,65600],{"className":65599},[1480],[1482,65601,65602],{"xmlns":1484},[1487,65603,65604,65612],{},[1490,65605,65606],{},[1497,65607,65608,65610],{},[1493,65609,1501],{},[1680,65611,1871],{},[1528,65613,53881],{"encoding":1530}," — rozdíl je jeho přebytek.",[1030,65616,65617,65618,65621,65622,65625],{},"Přebytek je tedy rozdíl mezi ",[1176,65619,65620],{},"ochotou"," (platit \u002F prodávat) a ",[1176,65623,65624],{},"skutečností"," (zaplaceno \u002F obdrženo).",[1030,65627,65628],{},[18014,65629],{"alt":59318,"className":65630,"src":59320},[1055,18018],[1246,65632],{},[1065,65634,65636,65637,1564],{"id":65635},"přebytek-spotřebitele-cscs","Přebytek spotřebitele (",[1035,65638,65640],{"className":65639},[1480],[1482,65641,65642],{"xmlns":1484},[1487,65643,65644,65650],{},[1490,65645,65646,65648],{},[1493,65647,1998],{},[1493,65649,2001],{},[1528,65651,59289],{"encoding":1530},[1304,65653,65655],{"id":65654},"definice-vzorec-214","Definice (vzorec 2.14)",[1030,65657,65658,65659,65682,65683,65700,65701,1274],{},"Pro poptávku ",[1035,65660,65662],{"className":65661},[1480],[1482,65663,65664],{"xmlns":1484},[1487,65665,65666,65680],{},[1490,65667,65668,65670,65672,65674,65676,65678],{},[1493,65669,1501],{},[1506,65671,1508],{},[1493,65673,3712],{},[1506,65675,1553],{"stretchy":1552},[1493,65677,1520],{},[1506,65679,1564],{"stretchy":1552},[1528,65681,20356],{"encoding":1530}," a pevně zadané ",[1035,65684,65686],{"className":65685},[1480],[1482,65687,65688],{"xmlns":1484},[1487,65689,65690,65698],{},[1490,65691,65692],{},[1497,65693,65694,65696],{},[1493,65695,1520],{},[1680,65697,1871],{},[1528,65699,53236],{"encoding":1530}," s cenou ",[1035,65702,65704],{"className":65703},[1480],[1482,65705,65706],{"xmlns":1484},[1487,65707,65708,65730],{},[1490,65709,65710,65716,65718,65720,65722,65728],{},[1497,65711,65712,65714],{},[1493,65713,1501],{},[1680,65715,1871],{},[1506,65717,1508],{},[1493,65719,3712],{},[1506,65721,1553],{"stretchy":1552},[1497,65723,65724,65726],{},[1493,65725,1520],{},[1680,65727,1871],{},[1506,65729,1564],{"stretchy":1552},[1528,65731,65389],{"encoding":1530},[1035,65733,65735],{"className":65734},[1480],[1482,65736,65737],{"xmlns":1484,"display":1485},[1487,65738,65739,65815],{},[19617,65740,65741],{"width":19619},[19621,65742,65743,65745,65809,65811],{},[19624,65744],{"width":19626},[19624,65746,65747],{},[1490,65748,65749,65751,65753,65755,65761,65763,65765,65777,65779,65781,65783,65785,65787,65789,65791,65793,65799,65801,65807],{},[1493,65750,1998],{},[1493,65752,2001],{},[1506,65754,1553],{"stretchy":1552},[1497,65756,65757,65759],{},[1493,65758,1520],{},[1680,65760,1871],{},[1506,65762,1564],{"stretchy":1552},[1506,65764,1508],{},[1697,65766,65767,65769,65771],{},[1506,65768,10857],{},[1680,65770,1871],{},[1497,65772,65773,65775],{},[1493,65774,1520],{},[1680,65776,1871],{},[1493,65778,3712],{},[1506,65780,1553],{"stretchy":1552},[1493,65782,1520],{},[1506,65784,1564],{"stretchy":1552},[1988,65786,5016],{},[1493,65788,3384],{},[1493,65790,1520],{},[1506,65792,1888],{},[1497,65794,65795,65797],{},[1493,65796,1501],{},[1680,65798,1871],{},[1988,65800,5016],{},[1497,65802,65803,65805],{},[1493,65804,1520],{},[1680,65806,1871],{},[1493,65808,2632],{"mathvariant":1516},[19624,65810],{"width":19626},[19624,65812,65813],{},[1988,65814,59412],{},[1528,65816,59415],{"encoding":1530},[1304,65818,17903],{"id":17902},[1203,65820,65821,65913,65975],{},[1206,65822,65823,65863,65864,65890,65891,65894,65895,65912],{},[1035,65824,65826],{"className":65825},[1480],[1482,65827,65828],{"xmlns":1484},[1487,65829,65830,65860],{},[1490,65831,65832],{},[1869,65833,65834,65846,65848,65850,65852,65854,65856,65858],{"scriptlevel":1871,"displaystyle":1041},[1697,65835,65836,65838,65840],{},[1506,65837,10857],{},[1680,65839,1871],{},[1497,65841,65842,65844],{},[1493,65843,1520],{},[1680,65845,1871],{},[1493,65847,3712],{},[1506,65849,1553],{"stretchy":1552},[1493,65851,1520],{},[1506,65853,1564],{"stretchy":1552},[1988,65855,5016],{},[1493,65857,3384],{},[1493,65859,1520],{},[1528,65861,65862],{"encoding":1530},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ"," — plocha pod křivkou poptávky v intervalu ",[1035,65865,65867],{"className":65866},[1480],[1482,65868,65869],{"xmlns":1484},[1487,65870,65871,65887],{},[1490,65872,65873,65875,65877,65879,65885],{},[1506,65874,14314],{"stretchy":1552},[1680,65876,1871],{},[1506,65878,1559],{"separator":1041},[1497,65880,65881,65883],{},[1493,65882,1520],{},[1680,65884,1871],{},[1506,65886,14323],{"stretchy":1552},[1528,65888,65889],{"encoding":1530},"[0, Q_0]","; představuje celkovou ",[1047,65892,65893],{},"ochotu platit"," (maximální částku, kterou by spotřebitel za ",[1035,65896,65898],{"className":65897},[1480],[1482,65899,65900],{"xmlns":1484},[1487,65901,65902,65910],{},[1490,65903,65904],{},[1497,65905,65906,65908],{},[1493,65907,1520],{},[1680,65909,1871],{},[1528,65911,53236],{"encoding":1530}," jednotek byl ochoten zaplatit).",[1206,65914,65915,65941,65942,16623],{},[1035,65916,65918],{"className":65917},[1480],[1482,65919,65920],{"xmlns":1484},[1487,65921,65922,65938],{},[1490,65923,65924,65930,65932],{},[1497,65925,65926,65928],{},[1493,65927,1501],{},[1680,65929,1871],{},[1988,65931,5016],{},[1497,65933,65934,65936],{},[1493,65935,1520],{},[1680,65937,1871],{},[1528,65939,65940],{"encoding":1530},"P_0\\,Q_0"," — skutečně zaplacená částka (obdélník ",[1035,65943,65945],{"className":65944},[1480],[1482,65946,65947],{"xmlns":1484},[1487,65948,65949,65973],{},[1490,65950,65951,65953,65955,65961,65963,65965,65967],{},[1680,65952,1871],{},[1988,65954,5016],{},[1497,65956,65957,65959],{},[1493,65958,1520],{},[1680,65960,1871],{},[1988,65962,5016],{},[1493,65964,3633],{},[1988,65966,5016],{},[1497,65968,65969,65971],{},[1493,65970,1501],{},[1680,65972,1871],{},[1528,65974,65491],{"encoding":1530},[1206,65976,65977,65992,65993,66015,66016,66041,66042,37188,66068,1586,66100,2632],{},[1035,65978,65980],{"className":65979},[1480],[1482,65981,65982],{"xmlns":1484},[1487,65983,65984,65990],{},[1490,65985,65986,65988],{},[1493,65987,1998],{},[1493,65989,2001],{},[1528,65991,59289],{"encoding":1530}," je plocha mezi křivkou poptávky a vodorovnou přímkou ",[1035,65994,65996],{"className":65995},[1480],[1482,65997,65998],{"xmlns":1484},[1487,65999,66000,66012],{},[1490,66001,66002,66004,66006],{},[1493,66003,1501],{},[1506,66005,1508],{},[1497,66007,66008,66010],{},[1493,66009,1501],{},[1680,66011,1871],{},[1528,66013,66014],{"encoding":1530},"P = P_0"," v pásu ",[1035,66017,66019],{"className":66018},[1480],[1482,66020,66021],{"xmlns":1484},[1487,66022,66023,66039],{},[1490,66024,66025,66027,66029,66031,66037],{},[1506,66026,14314],{"stretchy":1552},[1680,66028,1871],{},[1506,66030,1559],{"separator":1041},[1497,66032,66033,66035],{},[1493,66034,1520],{},[1680,66036,1871],{},[1506,66038,14323],{"stretchy":1552},[1528,66040,65889],{"encoding":1530}," — „křivočarý trojúhelník\" ",[1035,66043,66045],{"className":66044},[1480],[1482,66046,66047],{"xmlns":1484},[1487,66048,66049,66065],{},[1490,66050,66051,66057,66059,66061,66063],{},[1497,66052,66053,66055],{},[1493,66054,1501],{},[1680,66056,1871],{},[1988,66058,5016],{},[1493,66060,11353],{},[1988,66062,5016],{},[1493,66064,3633],{},[1528,66066,66067],{"encoding":1530},"P_0\\,B\\,A",[1035,66069,66071],{"className":66070},[1480],[1482,66072,66073],{"xmlns":1484},[1487,66074,66075,66097],{},[1490,66076,66077,66079,66081,66083,66085,66087,66089,66091,66093,66095],{},[1493,66078,11353],{},[1506,66080,1508],{},[1506,66082,14314],{"stretchy":1552},[1680,66084,1871],{},[1506,66086,1559],{"separator":1041},[1493,66088,3712],{},[1506,66090,1553],{"stretchy":1552},[1680,66092,1871],{},[1506,66094,1564],{"stretchy":1552},[1506,66096,14323],{"stretchy":1552},[1528,66098,66099],{"encoding":1530},"B = [0, D(0)]",[1035,66101,66103],{"className":66102},[1480],[1482,66104,66105],{"xmlns":1484},[1487,66106,66107,66131],{},[1490,66108,66109,66111,66113,66115,66121,66123,66129],{},[1493,66110,3633],{},[1506,66112,1508],{},[1506,66114,14314],{"stretchy":1552},[1497,66116,66117,66119],{},[1493,66118,1520],{},[1680,66120,1871],{},[1506,66122,1559],{"separator":1041},[1497,66124,66125,66127],{},[1493,66126,1501],{},[1680,66128,1871],{},[1506,66130,14323],{"stretchy":1552},[1528,66132,65547],{"encoding":1530},[1246,66134],{},[1065,66136,66138,66139,1564],{"id":66137},"přebytek-výrobce-psps","Přebytek výrobce (",[1035,66140,66142],{"className":66141},[1480],[1482,66143,66144],{"xmlns":1484},[1487,66145,66146,66152],{},[1490,66147,66148,66150],{},[1493,66149,1501],{},[1493,66151,2001],{},[1528,66153,59308],{"encoding":1530},[1304,66155,66157],{"id":66156},"definice-vzorec-215","Definice (vzorec 2.15)",[1030,66159,66160,66161,65682,66184,65700,66201,1274],{},"Analogicky — pro nabídku ",[1035,66162,66164],{"className":66163},[1480],[1482,66165,66166],{"xmlns":1484},[1487,66167,66168,66182],{},[1490,66169,66170,66172,66174,66176,66178,66180],{},[1493,66171,1501],{},[1506,66173,1508],{},[1493,66175,2001],{},[1506,66177,1553],{"stretchy":1552},[1493,66179,1520],{},[1506,66181,1564],{"stretchy":1552},[1528,66183,55723],{"encoding":1530},[1035,66185,66187],{"className":66186},[1480],[1482,66188,66189],{"xmlns":1484},[1487,66190,66191,66199],{},[1490,66192,66193],{},[1497,66194,66195,66197],{},[1493,66196,1520],{},[1680,66198,1871],{},[1528,66200,53236],{"encoding":1530},[1035,66202,66204],{"className":66203},[1480],[1482,66205,66206],{"xmlns":1484},[1487,66207,66208,66230],{},[1490,66209,66210,66216,66218,66220,66222,66228],{},[1497,66211,66212,66214],{},[1493,66213,1501],{},[1680,66215,1871],{},[1506,66217,1508],{},[1493,66219,2001],{},[1506,66221,1553],{"stretchy":1552},[1497,66223,66224,66226],{},[1493,66225,1520],{},[1680,66227,1871],{},[1506,66229,1564],{"stretchy":1552},[1528,66231,65421],{"encoding":1530},[1035,66233,66235],{"className":66234},[1480],[1482,66236,66237],{"xmlns":1484,"display":1485},[1487,66238,66239,66315],{},[19617,66240,66241],{"width":19619},[19621,66242,66243,66245,66309,66311],{},[19624,66244],{"width":19626},[19624,66246,66247],{},[1490,66248,66249,66251,66253,66255,66261,66263,66265,66271,66273,66279,66281,66293,66295,66297,66299,66301,66303,66305,66307],{},[1493,66250,1501],{},[1493,66252,2001],{},[1506,66254,1553],{"stretchy":1552},[1497,66256,66257,66259],{},[1493,66258,1520],{},[1680,66260,1871],{},[1506,66262,1564],{"stretchy":1552},[1506,66264,1508],{},[1497,66266,66267,66269],{},[1493,66268,1501],{},[1680,66270,1871],{},[1988,66272,5016],{},[1497,66274,66275,66277],{},[1493,66276,1520],{},[1680,66278,1871],{},[1506,66280,1888],{},[1697,66282,66283,66285,66287],{},[1506,66284,10857],{},[1680,66286,1871],{},[1497,66288,66289,66291],{},[1493,66290,1520],{},[1680,66292,1871],{},[1493,66294,2001],{},[1506,66296,1553],{"stretchy":1552},[1493,66298,1520],{},[1506,66300,1564],{"stretchy":1552},[1988,66302,5016],{},[1493,66304,3384],{},[1493,66306,1520],{},[1493,66308,2632],{"mathvariant":1516},[19624,66310],{"width":19626},[19624,66312,66313],{},[1988,66314,59508],{},[1528,66316,59511],{"encoding":1530},[1304,66318,17903],{"id":66319},"geometrická-interpretace-1",[1203,66321,66322,66370,66431],{},[1206,66323,66324,22970,66349,66352,66353,2632],{},[1035,66325,66327],{"className":66326},[1480],[1482,66328,66329],{"xmlns":1484},[1487,66330,66331,66347],{},[1490,66332,66333,66339,66341],{},[1497,66334,66335,66337],{},[1493,66336,1501],{},[1680,66338,1871],{},[1988,66340,5016],{},[1497,66342,66343,66345],{},[1493,66344,1520],{},[1680,66346,1871],{},[1528,66348,65940],{"encoding":1530},[1047,66350,66351],{},"tržba"," výrobce za prodané množství ",[1035,66354,66356],{"className":66355},[1480],[1482,66357,66358],{"xmlns":1484},[1487,66359,66360,66368],{},[1490,66361,66362],{},[1497,66363,66364,66366],{},[1493,66365,1520],{},[1680,66367,1871],{},[1528,66369,53236],{"encoding":1530},[1206,66371,66372,66412,66413,66430],{},[1035,66373,66375],{"className":66374},[1480],[1482,66376,66377],{"xmlns":1484},[1487,66378,66379,66409],{},[1490,66380,66381],{},[1869,66382,66383,66395,66397,66399,66401,66403,66405,66407],{"scriptlevel":1871,"displaystyle":1041},[1697,66384,66385,66387,66389],{},[1506,66386,10857],{},[1680,66388,1871],{},[1497,66390,66391,66393],{},[1493,66392,1520],{},[1680,66394,1871],{},[1493,66396,2001],{},[1506,66398,1553],{"stretchy":1552},[1493,66400,1520],{},[1506,66402,1564],{"stretchy":1552},[1988,66404,5016],{},[1493,66406,3384],{},[1493,66408,1520],{},[1528,66410,66411],{"encoding":1530},"\\displaystyle \\int_0^{Q_0} S(Q)\\,dQ"," — plocha pod křivkou nabídky; minimální částka, za kterou by byl výrobce ochoten ",[1035,66414,66416],{"className":66415},[1480],[1482,66417,66418],{"xmlns":1484},[1487,66419,66420,66428],{},[1490,66421,66422],{},[1497,66423,66424,66426],{},[1493,66425,1520],{},[1680,66427,1871],{},[1528,66429,53236],{"encoding":1530}," jednotek dodat (souvisí s mezními náklady).",[1206,66432,66433,66448,66449,66470,66471,2632],{},[1035,66434,66436],{"className":66435},[1480],[1482,66437,66438],{"xmlns":1484},[1487,66439,66440,66446],{},[1490,66441,66442,66444],{},[1493,66443,1501],{},[1493,66445,2001],{},[1528,66447,59308],{"encoding":1530}," je plocha mezi vodorovnou přímkou ",[1035,66450,66452],{"className":66451},[1480],[1482,66453,66454],{"xmlns":1484},[1487,66455,66456,66468],{},[1490,66457,66458,66460,66462],{},[1493,66459,1501],{},[1506,66461,1508],{},[1497,66463,66464,66466],{},[1493,66465,1501],{},[1680,66467,1871],{},[1528,66469,66014],{"encoding":1530}," a křivkou nabídky v pásu ",[1035,66472,66474],{"className":66473},[1480],[1482,66475,66476],{"xmlns":1484},[1487,66477,66478,66494],{},[1490,66479,66480,66482,66484,66486,66492],{},[1506,66481,14314],{"stretchy":1552},[1680,66483,1871],{},[1506,66485,1559],{"separator":1041},[1497,66487,66488,66490],{},[1493,66489,1520],{},[1680,66491,1871],{},[1506,66493,14323],{"stretchy":1552},[1528,66495,65889],{"encoding":1530},[1246,66497],{},[1023,66499,66501,66508],{"className":66500,"dataCallout":1443},[1026,1442],[1030,66502,66504,66507],{"className":66503},[1033],[1035,66505],{"className":66506,"ariaHidden":1041},[1038,1450,1040],"Postup výpočtu CS a PS",[1276,66509,66510,66641,66751,66780,66914],{},[1206,66511,66512,66513,66530,66531,66562,66563,66594,66595,2632],{},"Zjisti (nebo si zvol) množství ",[1035,66514,66516],{"className":66515},[1480],[1482,66517,66518],{"xmlns":1484},[1487,66519,66520,66528],{},[1490,66521,66522],{},[1497,66523,66524,66526],{},[1493,66525,1520],{},[1680,66527,1871],{},[1528,66529,53236],{"encoding":1530}," a odpovídající cenu ",[1035,66532,66534],{"className":66533},[1480],[1482,66535,66536],{"xmlns":1484},[1487,66537,66538,66560],{},[1490,66539,66540,66546,66548,66550,66552,66558],{},[1497,66541,66542,66544],{},[1493,66543,1501],{},[1680,66545,1871],{},[1506,66547,1508],{},[1493,66549,3712],{},[1506,66551,1553],{"stretchy":1552},[1497,66553,66554,66556],{},[1493,66555,1520],{},[1680,66557,1871],{},[1506,66559,1564],{"stretchy":1552},[1528,66561,65389],{"encoding":1530}," resp. ",[1035,66564,66566],{"className":66565},[1480],[1482,66567,66568],{"xmlns":1484},[1487,66569,66570,66592],{},[1490,66571,66572,66578,66580,66582,66584,66590],{},[1497,66573,66574,66576],{},[1493,66575,1501],{},[1680,66577,1871],{},[1506,66579,1508],{},[1493,66581,2001],{},[1506,66583,1553],{"stretchy":1552},[1497,66585,66586,66588],{},[1493,66587,1520],{},[1680,66589,1871],{},[1506,66591,1564],{"stretchy":1552},[1528,66593,65421],{"encoding":1530},". V rovnováze platí ",[1035,66596,66598],{"className":66597},[1480],[1482,66599,66600],{"xmlns":1484},[1487,66601,66602,66638],{},[1490,66603,66604,66606,66608,66614,66616,66618,66620,66622,66628,66630,66632],{},[1493,66605,3712],{},[1506,66607,1553],{"stretchy":1552},[2315,66609,66610,66612],{},[1493,66611,1520],{},[1493,66613,2711],{},[1506,66615,1564],{"stretchy":1552},[1506,66617,1508],{},[1493,66619,2001],{},[1506,66621,1553],{"stretchy":1552},[2315,66623,66624,66626],{},[1493,66625,1520],{},[1493,66627,2711],{},[1506,66629,1564],{"stretchy":1552},[1506,66631,1508],{},[2315,66633,66634,66636],{},[1493,66635,1501],{},[1493,66637,2711],{},[1528,66639,66640],{"encoding":1530},"D(Q^E) = S(Q^E) = P^E",[1206,66642,66643,66644,35853,66682,66697,66698,35853,66736,16623],{},"Spočti určitý integrál ",[1035,66645,66647],{"className":66646},[1480],[1482,66648,66649],{"xmlns":1484},[1487,66650,66651,66679],{},[1490,66652,66653,66665,66667,66669,66671,66673,66675,66677],{},[1697,66654,66655,66657,66659],{},[1506,66656,10857],{},[1680,66658,1871],{},[1497,66660,66661,66663],{},[1493,66662,1520],{},[1680,66664,1871],{},[1493,66666,3712],{},[1506,66668,1553],{"stretchy":1552},[1493,66670,1520],{},[1506,66672,1564],{"stretchy":1552},[1988,66674,5016],{},[1493,66676,3384],{},[1493,66678,1520],{},[1528,66680,66681],{"encoding":1530},"\\int_0^{Q_0} D(Q)\\,dQ",[1035,66683,66685],{"className":66684},[1480],[1482,66686,66687],{"xmlns":1484},[1487,66688,66689,66695],{},[1490,66690,66691,66693],{},[1493,66692,1998],{},[1493,66694,2001],{},[1528,66696,59289],{"encoding":1530},") nebo ",[1035,66699,66701],{"className":66700},[1480],[1482,66702,66703],{"xmlns":1484},[1487,66704,66705,66733],{},[1490,66706,66707,66719,66721,66723,66725,66727,66729,66731],{},[1697,66708,66709,66711,66713],{},[1506,66710,10857],{},[1680,66712,1871],{},[1497,66714,66715,66717],{},[1493,66716,1520],{},[1680,66718,1871],{},[1493,66720,2001],{},[1506,66722,1553],{"stretchy":1552},[1493,66724,1520],{},[1506,66726,1564],{"stretchy":1552},[1988,66728,5016],{},[1493,66730,3384],{},[1493,66732,1520],{},[1528,66734,66735],{"encoding":1530},"\\int_0^{Q_0} S(Q)\\,dQ",[1035,66737,66739],{"className":66738},[1480],[1482,66740,66741],{"xmlns":1484},[1487,66742,66743,66749],{},[1490,66744,66745,66747],{},[1493,66746,1501],{},[1493,66748,2001],{},[1528,66750,59308],{"encoding":1530},[1206,66752,66753,66754,2632],{},"Sestav obdélník ",[1035,66755,66757],{"className":66756},[1480],[1482,66758,66759],{"xmlns":1484},[1487,66760,66761,66777],{},[1490,66762,66763,66769,66771],{},[1497,66764,66765,66767],{},[1493,66766,1501],{},[1680,66768,1871],{},[1506,66770,1714],{},[1497,66772,66773,66775],{},[1493,66774,1520],{},[1680,66776,1871],{},[1528,66778,66779],{"encoding":1530},"P_0 \\cdot Q_0",[1206,66781,66782,66783],{},"Dosaď:\n",[1203,66784,66785,66850],{},[1206,66786,66787,66845,66846,66849],{},[1035,66788,66790],{"className":66789},[1480],[1482,66791,66792],{"xmlns":1484},[1487,66793,66794,66842],{},[1490,66795,66796,66798,66800,66802,66814,66816,66818,66820,66822,66824,66826,66828,66830,66836],{},[1493,66797,1998],{},[1493,66799,2001],{},[1506,66801,1508],{},[1697,66803,66804,66806,66808],{},[1506,66805,10857],{},[1680,66807,1871],{},[1497,66809,66810,66812],{},[1493,66811,1520],{},[1680,66813,1871],{},[1493,66815,3712],{},[1506,66817,1553],{"stretchy":1552},[1493,66819,1520],{},[1506,66821,1564],{"stretchy":1552},[1988,66823,5016],{},[1493,66825,3384],{},[1493,66827,1520],{},[1506,66829,1888],{},[1497,66831,66832,66834],{},[1493,66833,1501],{},[1680,66835,1871],{},[1497,66837,66838,66840],{},[1493,66839,1520],{},[1680,66841,1871],{},[1528,66843,66844],{"encoding":1530},"CS = \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0"," (integrál ",[1047,66847,66848],{},"mínus"," obdélník)",[1206,66851,66852,66910,66911,66913],{},[1035,66853,66855],{"className":66854},[1480],[1482,66856,66857],{"xmlns":1484},[1487,66858,66859,66907],{},[1490,66860,66861,66863,66865,66867,66873,66879,66881,66893,66895,66897,66899,66901,66903,66905],{},[1493,66862,1501],{},[1493,66864,2001],{},[1506,66866,1508],{},[1497,66868,66869,66871],{},[1493,66870,1501],{},[1680,66872,1871],{},[1497,66874,66875,66877],{},[1493,66876,1520],{},[1680,66878,1871],{},[1506,66880,1888],{},[1697,66882,66883,66885,66887],{},[1506,66884,10857],{},[1680,66886,1871],{},[1497,66888,66889,66891],{},[1493,66890,1520],{},[1680,66892,1871],{},[1493,66894,2001],{},[1506,66896,1553],{"stretchy":1552},[1493,66898,1520],{},[1506,66900,1564],{"stretchy":1552},[1988,66902,5016],{},[1493,66904,3384],{},[1493,66906,1520],{},[1528,66908,66909],{"encoding":1530},"PS = P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ"," (obdélník ",[1047,66912,66848],{}," integrál)",[1206,66915,66916,66917,66920],{},"Kontrola znaménka: obě hodnoty musí být ",[1047,66918,66919],{},"kladné",". Pokud vyjde záporná, máš prohozené pořadí.",[1246,66922],{},[1065,66924,66926],{"id":66925},"příklady","Příklady",[1304,66928,66930],{"id":66929},"příklad-211-komparativní-statika-pro-rovnovážné-množství","Příklad 2.11 — komparativní statika pro rovnovážné množství",[1023,66932,66936,66943],{"className":66933,"dataCallout":66935},[1026,66934],"callout-example","example",[1030,66937,66939,16474],{"className":66938},[1033],[1035,66940],{"className":66941,"ariaHidden":1041},[1038,66942,1040],"i-lucide:flask-conical",[1030,66944,66945,66946,62056,66969,66992,66993,1732,67013,1732,67030,1732,67047,67064,67065,67141,67142,67159,67160,67173],{},"Jsou dány poptávka ",[1035,66947,66949],{"className":66948},[1480],[1482,66950,66951],{"xmlns":1484},[1487,66952,66953,66967],{},[1490,66954,66955,66957,66959,66961,66963,66965],{},[1493,66956,1501],{},[1506,66958,1508],{},[1493,66960,1052],{},[1493,66962,1520],{},[1506,66964,2162],{},[1493,66966,2394],{},[1528,66968,52158],{"encoding":1530},[1035,66970,66972],{"className":66971},[1480],[1482,66973,66974],{"xmlns":1484},[1487,66975,66976,66990],{},[1490,66977,66978,66980,66982,66984,66986,66988],{},[1493,66979,1501],{},[1506,66981,1508],{},[1493,66983,8730],{},[1493,66985,1520],{},[1506,66987,2162],{},[1493,66989,3384],{},[1528,66991,55008],{"encoding":1530}," s hodnotami ",[1035,66994,66996],{"className":66995},[1480],[1482,66997,66998],{"xmlns":1484},[1487,66999,67000,67010],{},[1490,67001,67002,67004,67006,67008],{},[1493,67003,1052],{},[1506,67005,1508],{},[1506,67007,1888],{},[1680,67009,3201],{},[1528,67011,67012],{"encoding":1530},"a = -3",[1035,67014,67016],{"className":67015},[1480],[1482,67017,67018],{"xmlns":1484},[1487,67019,67020,67028],{},[1490,67021,67022,67024,67026],{},[1493,67023,2394],{},[1506,67025,1508],{},[1680,67027,7380],{},[1528,67029,62980],{"encoding":1530},[1035,67031,67033],{"className":67032},[1480],[1482,67034,67035],{"xmlns":1484},[1487,67036,67037,67045],{},[1490,67038,67039,67041,67043],{},[1493,67040,8730],{},[1506,67042,1508],{},[1680,67044,3687],{},[1528,67046,62998],{"encoding":1530},[1035,67048,67050],{"className":67049},[1480],[1482,67051,67052],{"xmlns":1484},[1487,67053,67054,67062],{},[1490,67055,67056,67058,67060],{},[1493,67057,3384],{},[1506,67059,1508],{},[1680,67061,1775],{},[1528,67063,63016],{"encoding":1530},".\nRovnovážné množství:\n",[1035,67066,67068],{"className":67067},[1480],[1482,67069,67070],{"xmlns":1484},[1487,67071,67072,67138],{},[1490,67073,67074,67080,67082,67100,67102,67126,67128,67134,67136],{},[2315,67075,67076,67078],{},[1493,67077,1520],{},[1493,67079,2711],{},[1506,67081,1508],{},[1510,67083,67084,67092],{},[1490,67085,67086,67088,67090],{},[1493,67087,2394],{},[1506,67089,1888],{},[1493,67091,3384],{},[1490,67093,67094,67096,67098],{},[1493,67095,8730],{},[1506,67097,1888],{},[1493,67099,1052],{},[1506,67101,1508],{},[1510,67103,67104,67112],{},[1490,67105,67106,67108,67110],{},[1680,67107,7380],{},[1506,67109,1888],{},[1680,67111,1775],{},[1490,67113,67114,67116,67118,67120,67122,67124],{},[1680,67115,3687],{},[1506,67117,1888],{},[1506,67119,1553],{"stretchy":1552},[1506,67121,1888],{},[1680,67123,3201],{},[1506,67125,1564],{"stretchy":1552},[1506,67127,1508],{},[1510,67129,67130,67132],{},[1680,67131,6956],{},[1680,67133,58792],{},[1506,67135,21771],{},[1680,67137,58797],{},[1528,67139,67140],{"encoding":1530},"Q^E = \\frac{b - d}{c - a} = \\frac{40 - 10}{0{,}5 - (-3)} = \\frac{30}{3{,}5} \\doteq 8{,}571.","\nZjistěte změnu ",[1035,67143,67145],{"className":67144},[1480],[1482,67146,67147],{"xmlns":1484},[1487,67148,67149,67157],{},[1490,67150,67151],{},[2315,67152,67153,67155],{},[1493,67154,1520],{},[1493,67156,2711],{},[1528,67158,14059],{"encoding":1530}," (a) při změně samotného parametru ",[1035,67161,67163],{"className":67162},[1480],[1482,67164,67165],{"xmlns":1484},[1487,67166,67167,67171],{},[1490,67168,67169],{},[1493,67170,8730],{},[1528,67172,8730],{"encoding":1530},", (b) při současné změně všech čtyř parametrů.",[1030,67175,67176],{},[1047,67177,67178,67179,18125,67192,18139,67205,25524],{},"Řešení (a) — změna ",[1035,67180,67182],{"className":67181},[1480],[1482,67183,67184],{"xmlns":1484},[1487,67185,67186,67190],{},[1490,67187,67188],{},[1493,67189,8730],{},[1528,67191,8730],{"encoding":1530},[1035,67193,67195],{"className":67194},[1480],[1482,67196,67197],{"xmlns":1484},[1487,67198,67199,67203],{},[1490,67200,67201],{},[1680,67202,3687],{},[1528,67204,58832],{"encoding":1530},[1035,67206,67208],{"className":67207},[1480],[1482,67209,67210],{"xmlns":1484},[1487,67211,67212,67216],{},[1490,67213,67214],{},[1680,67215,3332],{},[1528,67217,58846],{"encoding":1530},[1030,67219,67220,67221,67285,67286,1274],{},"Pomocí vzorce (2.13) pro ",[1035,67222,67224],{"className":67223},[1480],[1482,67225,67226],{"xmlns":1484},[1487,67227,67228,67282],{},[1490,67229,67230,67250,67252,67254],{},[1869,67231,67232],{"scriptlevel":1871,"displaystyle":1041},[1510,67233,67234,67244],{},[1490,67235,67236,67238],{},[1493,67237,1517],{"mathvariant":1516},[2315,67239,67240,67242],{},[1493,67241,1520],{},[1493,67243,2711],{},[1490,67245,67246,67248],{},[1493,67247,1517],{"mathvariant":1516},[1493,67249,8730],{},[1506,67251,1508],{},[1506,67253,1888],{},[1869,67255,67256],{"scriptlevel":1871,"displaystyle":1041},[1510,67257,67258,67266],{},[1490,67259,67260,67262,67264],{},[1493,67261,2394],{},[1506,67263,1888],{},[1493,67265,3384],{},[1490,67267,67268,67270,67272,67274,67276],{},[1506,67269,1553],{"stretchy":1552},[1493,67271,8730],{},[1506,67273,1888],{},[1493,67275,1052],{},[2315,67277,67278,67280],{},[1506,67279,1564],{"stretchy":1552},[1680,67281,1691],{},[1528,67283,67284],{"encoding":1530},"\\dfrac{\\partial Q^E}{\\partial c} = -\\dfrac{b-d}{(c-a)^2}",", resp. ekvivalentně ",[1035,67287,67289],{"className":67288},[1480],[1482,67290,67291],{"xmlns":1484},[1487,67292,67293,67315],{},[1490,67294,67295,67297],{},[1506,67296,1888],{},[1869,67298,67299],{"scriptlevel":1871,"displaystyle":1041},[1510,67300,67301,67307],{},[2315,67302,67303,67305],{},[1493,67304,1520],{},[1493,67306,2711],{},[1490,67308,67309,67311,67313],{},[1493,67310,8730],{},[1506,67312,1888],{},[1493,67314,1052],{},[1528,67316,67317],{"encoding":1530},"-\\dfrac{Q^E}{c-a}",[1035,67319,67321],{"className":67320},[1480],[1482,67322,67323],{"xmlns":1484,"display":1485},[1487,67324,67325,67381],{},[1490,67326,67327,67329,67335,67337,67339,67355,67357,67359,67361,67363,67365,67371,67373,67375,67377,67379],{},[1493,67328,3384],{},[2315,67330,67331,67333],{},[1493,67332,1520],{},[1493,67334,2711],{},[1506,67336,1508],{},[1506,67338,1888],{},[1510,67340,67341,67347],{},[2315,67342,67343,67345],{},[1493,67344,1520],{},[1493,67346,2711],{},[1490,67348,67349,67351,67353],{},[1493,67350,8730],{},[1506,67352,1888],{},[1493,67354,1052],{},[1988,67356,5016],{},[1493,67358,3384],{},[1493,67360,8730],{},[1506,67362,1508],{},[1506,67364,1888],{},[1510,67366,67367,67369],{},[1680,67368,58959],{},[1680,67370,58792],{},[1506,67372,1714],{},[1680,67374,13237],{},[1506,67376,21771],{},[1506,67378,1888],{},[1680,67380,58931],{},[1528,67382,67383],{"encoding":1530},"dQ^E = -\\frac{Q^E}{c - a}\\,dc = -\\frac{8{,}571}{3{,}5}\\cdot 0{,}1 \\doteq -0{,}245.",[1030,67385,67386],{},"Nové rovnovážné množství:",[1035,67388,67390],{"className":67389},[1480],[1482,67391,67392],{"xmlns":1484,"display":1485},[1487,67393,67394,67417],{},[1490,67395,67396,67404,67406,67408,67410,67412,67414],{},[1697,67397,67398,67400,67402],{},[1493,67399,1520],{},[1680,67401,1682],{},[1493,67403,2711],{},[1506,67405,2343],{},[1680,67407,58959],{},[1506,67409,1888],{},[1680,67411,58964],{},[1506,67413,1508],{},[1680,67415,67416],{},"8,326.",[1528,67418,67419],{"encoding":1530},"Q_1^E \\approx 8{,}571 - 0{,}245 = 8{,}326.",[1030,67421,67422,1656,67425,1732,67451,1732,67473,1732,67495,21352,67517,1732,67536,1732,67557,1732,67576,2632],{},[1047,67423,67424],{},"Řešení (b) — současná změna všech parametrů:",[1035,67426,67428],{"className":67427},[1480],[1482,67429,67430],{"xmlns":1484},[1487,67431,67432,67448],{},[1490,67433,67434,67436,67438,67440,67442,67444,67446],{},[1493,67435,1052],{},[1506,67437,1274],{},[1506,67439,1888],{},[1680,67441,3201],{},[1506,67443,6380],{},[1506,67445,1888],{},[1680,67447,13279],{},[1528,67449,67450],{"encoding":1530},"a: -3 \\to -2{,}5",[1035,67452,67454],{"className":67453},[1480],[1482,67455,67456],{"xmlns":1484},[1487,67457,67458,67470],{},[1490,67459,67460,67462,67464,67466,67468],{},[1493,67461,2394],{},[1506,67463,1274],{},[1680,67465,7380],{},[1506,67467,6380],{},[1680,67469,5603],{},[1528,67471,67472],{"encoding":1530},"b: 40 \\to 35",[1035,67474,67476],{"className":67475},[1480],[1482,67477,67478],{"xmlns":1484},[1487,67479,67480,67492],{},[1490,67481,67482,67484,67486,67488,67490],{},[1493,67483,8730],{},[1506,67485,1274],{},[1680,67487,3687],{},[1506,67489,6380],{},[1680,67491,3332],{},[1528,67493,67494],{"encoding":1530},"c: 0{,}5 \\to 0{,}6",[1035,67496,67498],{"className":67497},[1480],[1482,67499,67500],{"xmlns":1484},[1487,67501,67502,67514],{},[1490,67503,67504,67506,67508,67510,67512],{},[1493,67505,3384],{},[1506,67507,1274],{},[1680,67509,1775],{},[1506,67511,6380],{},[1680,67513,8542],{},[1528,67515,67516],{"encoding":1530},"d: 10 \\to 11",[1035,67518,67520],{"className":67519},[1480],[1482,67521,67522],{"xmlns":1484},[1487,67523,67524,67534],{},[1490,67525,67526,67528,67530,67532],{},[1493,67527,3384],{},[1493,67529,1052],{},[1506,67531,1508],{},[1680,67533,3687],{},[1528,67535,58997],{"encoding":1530},[1035,67537,67539],{"className":67538},[1480],[1482,67540,67541],{"xmlns":1484},[1487,67542,67543,67555],{},[1490,67544,67545,67547,67549,67551,67553],{},[1493,67546,3384],{},[1493,67548,2394],{},[1506,67550,1508],{},[1506,67552,1888],{},[1680,67554,1752],{},[1528,67556,59019],{"encoding":1530},[1035,67558,67560],{"className":67559},[1480],[1482,67561,67562],{"xmlns":1484},[1487,67563,67564,67574],{},[1490,67565,67566,67568,67570,67572],{},[1493,67567,3384],{},[1493,67569,8730],{},[1506,67571,1508],{},[1680,67573,13237],{},[1528,67575,59039],{"encoding":1530},[1035,67577,67579],{"className":67578},[1480],[1482,67580,67581],{"xmlns":1484},[1487,67582,67583,67593],{},[1490,67584,67585,67587,67589,67591],{},[1493,67586,3384],{},[1493,67588,3384],{},[1506,67590,1508],{},[1680,67592,1682],{},[1528,67594,59059],{"encoding":1530},[1030,67596,67597,67598,67656],{},"Totální diferenciál ",[1035,67599,67601],{"className":67600},[1480],[1482,67602,67603],{"xmlns":1484},[1487,67604,67605,67653],{},[1490,67606,67607,67613,67615,67617,67619,67621,67623,67625,67627,67629,67631,67633],{},[2315,67608,67609,67611],{},[1493,67610,1520],{},[1493,67612,2711],{},[1506,67614,1553],{"stretchy":1552},[1493,67616,1052],{},[1506,67618,1559],{"separator":1041},[1493,67620,2394],{},[1506,67622,1559],{"separator":1041},[1493,67624,8730],{},[1506,67626,1559],{"separator":1041},[1493,67628,3384],{},[1506,67630,1564],{"stretchy":1552},[1506,67632,1508],{},[1869,67634,67635],{"scriptlevel":1871,"displaystyle":1041},[1510,67636,67637,67645],{},[1490,67638,67639,67641,67643],{},[1493,67640,2394],{},[1506,67642,1888],{},[1493,67644,3384],{},[1490,67646,67647,67649,67651],{},[1493,67648,8730],{},[1506,67650,1888],{},[1493,67652,1052],{},[1528,67654,67655],{"encoding":1530},"Q^E(a, b, c, d) = \\dfrac{b - d}{c - a}"," podle (2.11) a (2.12):",[1035,67658,67660],{"className":67659},[1480],[1482,67661,67662],{"xmlns":1484,"display":1485},[1487,67663,67664,67784],{},[1490,67665,67666,67668,67674,67676,67702,67704,67706,67708,67710,67722,67724,67726,67728,67730,67756,67758,67760,67762,67764,67776,67778,67780,67782],{},[1493,67667,3384],{},[2315,67669,67670,67672],{},[1493,67671,1520],{},[1493,67673,2711],{},[1506,67675,1508],{},[1510,67677,67678,67686],{},[1490,67679,67680,67682,67684],{},[1493,67681,2394],{},[1506,67683,1888],{},[1493,67685,3384],{},[1490,67687,67688,67690,67692,67694,67696],{},[1506,67689,1553],{"stretchy":1552},[1493,67691,8730],{},[1506,67693,1888],{},[1493,67695,1052],{},[2315,67697,67698,67700],{},[1506,67699,1564],{"stretchy":1552},[1680,67701,1691],{},[1988,67703,5016],{},[1493,67705,3384],{},[1493,67707,1052],{},[1506,67709,2162],{},[1510,67711,67712,67714],{},[1680,67713,1682],{},[1490,67715,67716,67718,67720],{},[1493,67717,8730],{},[1506,67719,1888],{},[1493,67721,1052],{},[1988,67723,5016],{},[1493,67725,3384],{},[1493,67727,2394],{},[1506,67729,1888],{},[1510,67731,67732,67740],{},[1490,67733,67734,67736,67738],{},[1493,67735,2394],{},[1506,67737,1888],{},[1493,67739,3384],{},[1490,67741,67742,67744,67746,67748,67750],{},[1506,67743,1553],{"stretchy":1552},[1493,67745,8730],{},[1506,67747,1888],{},[1493,67749,1052],{},[2315,67751,67752,67754],{},[1506,67753,1564],{"stretchy":1552},[1680,67755,1691],{},[1988,67757,5016],{},[1493,67759,3384],{},[1493,67761,8730],{},[1506,67763,1888],{},[1510,67765,67766,67768],{},[1680,67767,1682],{},[1490,67769,67770,67772,67774],{},[1493,67771,8730],{},[1506,67773,1888],{},[1493,67775,1052],{},[1988,67777,5016],{},[1493,67779,3384],{},[1493,67781,3384],{},[1493,67783,2632],{"mathvariant":1516},[1528,67785,67786],{"encoding":1530},"dQ^E = \\frac{b-d}{(c-a)^2}\\,da + \\frac{1}{c-a}\\,db - \\frac{b-d}{(c-a)^2}\\,dc - \\frac{1}{c-a}\\,dd.",[1030,67788,67789,67790,1732,67812,1732,67843,18579],{},"Dosazením číselných hodnot (",[1035,67791,67793],{"className":67792},[1480],[1482,67794,67795],{"xmlns":1484},[1487,67796,67797,67809],{},[1490,67798,67799,67801,67803,67805,67807],{},[1493,67800,8730],{},[1506,67802,1888],{},[1493,67804,1052],{},[1506,67806,1508],{},[1680,67808,58792],{},[1528,67810,67811],{"encoding":1530},"c - a = 3{,}5",[1035,67813,67815],{"className":67814},[1480],[1482,67816,67817],{"xmlns":1484},[1487,67818,67819,67840],{},[1490,67820,67821,67823,67825,67827,67829,67835,67837],{},[1506,67822,1553],{"stretchy":1552},[1493,67824,8730],{},[1506,67826,1888],{},[1493,67828,1052],{},[2315,67830,67831,67833],{},[1506,67832,1564],{"stretchy":1552},[1680,67834,1691],{},[1506,67836,1508],{},[1680,67838,67839],{},"12,25",[1528,67841,67842],{"encoding":1530},"(c-a)^2 = 12{,}25",[1035,67844,67846],{"className":67845},[1480],[1482,67847,67848],{"xmlns":1484},[1487,67849,67850,67862],{},[1490,67851,67852,67854,67856,67858,67860],{},[1493,67853,2394],{},[1506,67855,1888],{},[1493,67857,3384],{},[1506,67859,1508],{},[1680,67861,6956],{},[1528,67863,67864],{"encoding":1530},"b - d = 30",[1035,67866,67868],{"className":67867},[1480],[1482,67869,67870],{"xmlns":1484,"display":1485},[1487,67871,67872,67973],{},[1490,67873,67874,67876,67882,67884,67892,67894,67896,67898,67900,67908,67910,67912,67914,67916,67918,67926,67928,67930,67932,67934,67942,67944,67946,67948,67950,67953,67955,67958,67960,67962,67964,67967,67969,67971],{},[1493,67875,3384],{},[2315,67877,67878,67880],{},[1493,67879,1520],{},[1493,67881,2711],{},[1506,67883,2343],{},[1869,67885,67886],{"scriptlevel":1871,"displaystyle":1552},[1510,67887,67888,67890],{},[1680,67889,6956],{},[1680,67891,67839],{},[1506,67893,1553],{"stretchy":1552},[1680,67895,3687],{},[1506,67897,1564],{"stretchy":1552},[1506,67899,2162],{},[1869,67901,67902],{"scriptlevel":1871,"displaystyle":1552},[1510,67903,67904,67906],{},[1680,67905,1682],{},[1680,67907,58792],{},[1506,67909,1553],{"stretchy":1552},[1506,67911,1888],{},[1680,67913,1752],{},[1506,67915,1564],{"stretchy":1552},[1506,67917,1888],{},[1869,67919,67920],{"scriptlevel":1871,"displaystyle":1552},[1510,67921,67922,67924],{},[1680,67923,6956],{},[1680,67925,67839],{},[1506,67927,1553],{"stretchy":1552},[1680,67929,13237],{},[1506,67931,1564],{"stretchy":1552},[1506,67933,1888],{},[1869,67935,67936],{"scriptlevel":1871,"displaystyle":1552},[1510,67937,67938,67940],{},[1680,67939,1682],{},[1680,67941,58792],{},[1506,67943,1553],{"stretchy":1552},[1680,67945,1682],{},[1506,67947,1564],{"stretchy":1552},[1506,67949,21771],{},[1680,67951,67952],{},"1,224",[1506,67954,1888],{},[1680,67956,67957],{},"1,429",[1506,67959,1888],{},[1680,67961,58964],{},[1506,67963,1888],{},[1680,67965,67966],{},"0,286",[1506,67968,21771],{},[1506,67970,1888],{},[1680,67972,59210],{},[1528,67974,67975],{"encoding":1530},"dQ^E \\approx \\tfrac{30}{12{,}25}(0{,}5) + \\tfrac{1}{3{,}5}(-5) - \\tfrac{30}{12{,}25}(0{,}1) - \\tfrac{1}{3{,}5}(1) \\doteq 1{,}224 - 1{,}429 - 0{,}245 - 0{,}286 \\doteq -0{,}735.",[1030,67977,45390,67978,2632],{},[1035,67979,67981],{"className":67980},[1480],[1482,67982,67983],{"xmlns":1484},[1487,67984,67985,68007],{},[1490,67986,67987,67995,67997,67999,68001,68003,68005],{},[1697,67988,67989,67991,67993],{},[1493,67990,1520],{},[1680,67992,1682],{},[1493,67994,2711],{},[1506,67996,2343],{},[1680,67998,58959],{},[1506,68000,1888],{},[1680,68002,59241],{},[1506,68004,21771],{},[1680,68006,59246],{},[1528,68008,68009],{"encoding":1530},"Q_1^E \\approx 8{,}571 - 0{,}735 \\doteq 7{,}836",[1030,68011,68012,68013,68016],{},"Totální diferenciál je pouze ",[1047,68014,68015],{},"lineární aproximací",". Přesná hodnota ze změněného vzorce",[1035,68018,68020],{"className":68019},[1480],[1482,68021,68022],{"xmlns":1484,"display":1485},[1487,68023,68024,68110],{},[1490,68025,68026,68034,68036,68070,68072,68096,68098,68105,68107],{},[1697,68027,68028,68030,68032],{},[1493,68029,1520],{},[1680,68031,1682],{},[1493,68033,2711],{},[1506,68035,1508],{},[1510,68037,68038,68054],{},[1490,68039,68040,68046,68048],{},[2315,68041,68042,68044],{},[1493,68043,2394],{},[1506,68045,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,68047,1888],{},[2315,68049,68050,68052],{},[1493,68051,3384],{},[1506,68053,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1490,68055,68056,68062,68064],{},[2315,68057,68058,68060],{},[1493,68059,8730],{},[1506,68061,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,68063,1888],{},[2315,68065,68066,68068],{},[1493,68067,1052],{},[1506,68069,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,68071,1508],{},[1510,68073,68074,68082],{},[1490,68075,68076,68078,68080],{},[1680,68077,5603],{},[1506,68079,1888],{},[1680,68081,8542],{},[1490,68083,68084,68086,68088,68090,68092,68094],{},[1680,68085,3332],{},[1506,68087,1888],{},[1506,68089,1553],{"stretchy":1552},[1506,68091,1888],{},[1680,68093,13279],{},[1506,68095,1564],{"stretchy":1552},[1506,68097,1508],{},[1510,68099,68100,68102],{},[1680,68101,7201],{},[1680,68103,68104],{},"3,1",[1506,68106,21771],{},[1680,68108,68109],{},"7,742",[1528,68111,68112],{"encoding":1530},"Q_1^E = \\frac{b' - d'}{c' - a'} = \\frac{35 - 11}{0{,}6 - (-2{,}5)} = \\frac{24}{3{,}1} \\doteq 7{,}742",[1030,68114,68115,68116,68139,68140,2632],{},"dává skutečnou změnu ",[1035,68117,68119],{"className":68118},[1480],[1482,68120,68121],{"xmlns":1484},[1487,68122,68123,68136],{},[1490,68124,68125,68127,68129,68131,68133],{},[1493,68126,2976],{"mathvariant":1516},[1493,68128,1520],{},[1506,68130,21771],{},[1506,68132,1888],{},[1680,68134,68135],{},"0,829",[1528,68137,68138],{"encoding":1530},"\\Delta Q \\doteq -0{,}829",", dobře konzistentní s diferenciálovou aproximací ",[1035,68141,68143],{"className":68142},[1480],[1482,68144,68145],{"xmlns":1484},[1487,68146,68147,68153],{},[1490,68148,68149,68151],{},[1506,68150,1888],{},[1680,68152,59241],{},[1528,68154,68155],{"encoding":1530},"-0{,}735",[1304,68157,68159,68160],{"id":68158},"příklad-213-numerický-výpočet-psps","Příklad 2.13 — numerický výpočet ",[1035,68161,68163],{"className":68162},[1480],[1482,68164,68165],{"xmlns":1484},[1487,68166,68167,68173],{},[1490,68168,68169,68171],{},[1493,68170,1501],{},[1493,68172,2001],{},[1528,68174,59308],{"encoding":1530},[1023,68176,68178,68184],{"className":68177,"dataCallout":66935},[1026,66934],[1030,68179,68181,16474],{"className":68180},[1033],[1035,68182],{"className":68183,"ariaHidden":1041},[1038,66942,1040],[1030,68185,68186,68187,68221,68222,68244],{},"Pro nabídku ",[1035,68188,68190],{"className":68189},[1480],[1482,68191,68192],{"xmlns":1484},[1487,68193,68194,68218],{},[1490,68195,68196,68198,68200,68202,68204,68206,68208,68210,68212,68214,68216],{},[1493,68197,1501],{},[1506,68199,1508],{},[1493,68201,2001],{},[1506,68203,1553],{"stretchy":1552},[1493,68205,1520],{},[1506,68207,1564],{"stretchy":1552},[1506,68209,1508],{},[1680,68211,1775],{},[1506,68213,2162],{},[1680,68215,1691],{},[1493,68217,1520],{},[1528,68219,68220],{"encoding":1530},"P = S(Q) = 10 + 2Q"," a množství ",[1035,68223,68225],{"className":68224},[1480],[1482,68226,68227],{"xmlns":1484},[1487,68228,68229,68241],{},[1490,68230,68231,68237,68239],{},[1497,68232,68233,68235],{},[1493,68234,1520],{},[1680,68236,1871],{},[1506,68238,1508],{},[1680,68240,1775],{},[1528,68242,68243],{"encoding":1530},"Q_0 = 10"," vypočítejte přebytek výrobce.",[1030,68246,68247],{},[1047,68248,38365],{},[1030,68250,68251],{},"Odpovídající cena:",[1035,68253,68255],{"className":68254},[1480],[1482,68256,68257],{"xmlns":1484,"display":1485},[1487,68258,68259,68294],{},[1490,68260,68261,68267,68269,68271,68273,68275,68277,68279,68281,68283,68285,68287,68289,68291],{},[1497,68262,68263,68265],{},[1493,68264,1501],{},[1680,68266,1871],{},[1506,68268,1508],{},[1493,68270,2001],{},[1506,68272,1553],{"stretchy":1552},[1680,68274,1775],{},[1506,68276,1564],{"stretchy":1552},[1506,68278,1508],{},[1680,68280,1775],{},[1506,68282,2162],{},[1680,68284,1691],{},[1506,68286,1714],{},[1680,68288,1775],{},[1506,68290,1508],{},[1680,68292,68293],{},"30.",[1528,68295,68296],{"encoding":1530},"P_0 = S(10) = 10 + 2\\cdot 10 = 30.",[1030,68298,68299],{},"Dle vzorce (2.15):",[1035,68301,68303],{"className":68302},[1480],[1482,68304,68305],{"xmlns":1484,"display":1485},[1487,68306,68307,68414],{},[1490,68308,68309,68311,68313,68315,68317,68319,68321,68327,68333,68335,68343,68345,68347,68349,68351,68353,68355,68357,68359,68361,68363,68365,68367,68369,68371,68374,68376,68378,68380,68386,68394,68396,68398,68400,68402,68404,68406,68408,68410,68412],{},[1493,68310,1501],{},[1493,68312,2001],{},[1506,68314,1553],{"stretchy":1552},[1680,68316,1775],{},[1506,68318,1564],{"stretchy":1552},[1506,68320,1508],{},[1497,68322,68323,68325],{},[1493,68324,1501],{},[1680,68326,1871],{},[1497,68328,68329,68331],{},[1493,68330,1520],{},[1680,68332,1871],{},[1506,68334,1888],{},[1697,68336,68337,68339,68341],{},[1506,68338,10857],{},[1680,68340,1871],{},[1680,68342,1775],{},[1506,68344,1553],{"stretchy":1552},[1680,68346,1775],{},[1506,68348,2162],{},[1680,68350,1691],{},[1493,68352,1520],{},[1506,68354,1564],{"stretchy":1552},[1988,68356,5016],{},[1493,68358,3384],{},[1493,68360,1520],{},[1506,68362,1508],{},[1680,68364,1775],{},[1506,68366,1714],{},[1680,68368,6956],{},[1506,68370,1888],{},[1506,68372,14314],{"fence":1552,"stretchy":1041,"minsize":68373,"maxsize":68373},"1.8em",[1680,68375,1775],{},[1493,68377,1520],{},[1506,68379,2162],{},[2315,68381,68382,68384],{},[1493,68383,1520],{},[1680,68385,1691],{},[1697,68387,68388,68390,68392],{},[1506,68389,14323],{"fence":1552,"stretchy":1041,"minsize":68373,"maxsize":68373},[1680,68391,1871],{},[1680,68393,1775],{},[1506,68395,1508],{},[1680,68397,5231],{},[1506,68399,1888],{},[1506,68401,1553],{"stretchy":1552},[1680,68403,2916],{},[1506,68405,2162],{},[1680,68407,2916],{},[1506,68409,1564],{"stretchy":1552},[1506,68411,1508],{},[1680,68413,19791],{},[1528,68415,68416],{"encoding":1530},"PS(10) = P_0 Q_0 - \\int_0^{10}(10 + 2Q)\\,dQ = 10 \\cdot 30 - \\Big[10Q + Q^2\\Big]_0^{10} = 300 - (100 + 100) = 100.",[1030,68418,68419,68420,68441,68442,68462],{},"Přebytek výrobce při množství ",[1035,68421,68423],{"className":68422},[1480],[1482,68424,68425],{"xmlns":1484},[1487,68426,68427,68439],{},[1490,68428,68429,68435,68437],{},[1497,68430,68431,68433],{},[1493,68432,1520],{},[1680,68434,1871],{},[1506,68436,1508],{},[1680,68438,1775],{},[1528,68440,68243],{"encoding":1530}," je tedy ",[1035,68443,68445],{"className":68444},[1480],[1482,68446,68447],{"xmlns":1484},[1487,68448,68449,68459],{},[1490,68450,68451,68453,68455,68457],{},[1493,68452,1501],{},[1493,68454,2001],{},[1506,68456,1508],{},[1680,68458,2916],{},[1528,68460,68461],{"encoding":1530},"PS = 100"," (peněžních jednotek).",[1246,68464],{},[1065,68466,68468],{"id":68467},"cheat-sheet","Cheat sheet",[1073,68470,68471,68483],{},[1076,68472,68473],{},[1079,68474,68475,68478,68480],{},[1082,68476,68477],{},"Veličina",[1082,68479,17053],{},[1082,68481,68482],{},"Geometrie",[1092,68484,68485,68603,68717,68785],{},[1079,68486,68487,68515,68571],{},[1097,68488,68489],{},[1035,68490,68492],{"className":68491},[1480],[1482,68493,68494],{"xmlns":1484},[1487,68495,68496,68512],{},[1490,68497,68498,68500,68502,68504,68510],{},[1493,68499,1998],{},[1493,68501,2001],{},[1506,68503,1553],{"stretchy":1552},[1497,68505,68506,68508],{},[1493,68507,1520],{},[1680,68509,1871],{},[1506,68511,1564],{"stretchy":1552},[1528,68513,68514],{"encoding":1530},"CS(Q_0)",[1097,68516,68517],{},[1035,68518,68520],{"className":68519},[1480],[1482,68521,68522],{"xmlns":1484},[1487,68523,68524,68568],{},[1490,68525,68526],{},[1869,68527,68528,68540,68542,68544,68546,68548,68550,68552,68554,68556,68562],{"scriptlevel":1871,"displaystyle":1041},[1697,68529,68530,68532,68534],{},[1506,68531,10857],{},[1680,68533,1871],{},[1497,68535,68536,68538],{},[1493,68537,1520],{},[1680,68539,1871],{},[1493,68541,3712],{},[1506,68543,1553],{"stretchy":1552},[1493,68545,1520],{},[1506,68547,1564],{"stretchy":1552},[1988,68549,5016],{},[1493,68551,3384],{},[1493,68553,1520],{},[1506,68555,1888],{},[1497,68557,68558,68560],{},[1493,68559,1501],{},[1680,68561,1871],{},[1497,68563,68564,68566],{},[1493,68565,1520],{},[1680,68567,1871],{},[1528,68569,68570],{"encoding":1530},"\\displaystyle \\int_0^{Q_0} D(Q)\\,dQ - P_0 Q_0",[1097,68572,68573,68574,68577,68578,68581,68582],{},"plocha ",[1047,68575,68576],{},"pod"," křivkou poptávky, ",[1047,68579,68580],{},"nad"," čárou ",[1035,68583,68585],{"className":68584},[1480],[1482,68586,68587],{"xmlns":1484},[1487,68588,68589,68601],{},[1490,68590,68591,68593,68595],{},[1493,68592,1501],{},[1506,68594,1508],{},[1497,68596,68597,68599],{},[1493,68598,1501],{},[1680,68600,1871],{},[1528,68602,66014],{"encoding":1530},[1079,68604,68605,68633,68689],{},[1097,68606,68607],{},[1035,68608,68610],{"className":68609},[1480],[1482,68611,68612],{"xmlns":1484},[1487,68613,68614,68630],{},[1490,68615,68616,68618,68620,68622,68628],{},[1493,68617,1501],{},[1493,68619,2001],{},[1506,68621,1553],{"stretchy":1552},[1497,68623,68624,68626],{},[1493,68625,1520],{},[1680,68627,1871],{},[1506,68629,1564],{"stretchy":1552},[1528,68631,68632],{"encoding":1530},"PS(Q_0)",[1097,68634,68635],{},[1035,68636,68638],{"className":68637},[1480],[1482,68639,68640],{"xmlns":1484},[1487,68641,68642,68686],{},[1490,68643,68644],{},[1869,68645,68646,68652,68658,68660,68672,68674,68676,68678,68680,68682,68684],{"scriptlevel":1871,"displaystyle":1041},[1497,68647,68648,68650],{},[1493,68649,1501],{},[1680,68651,1871],{},[1497,68653,68654,68656],{},[1493,68655,1520],{},[1680,68657,1871],{},[1506,68659,1888],{},[1697,68661,68662,68664,68666],{},[1506,68663,10857],{},[1680,68665,1871],{},[1497,68667,68668,68670],{},[1493,68669,1520],{},[1680,68671,1871],{},[1493,68673,2001],{},[1506,68675,1553],{"stretchy":1552},[1493,68677,1520],{},[1506,68679,1564],{"stretchy":1552},[1988,68681,5016],{},[1493,68683,3384],{},[1493,68685,1520],{},[1528,68687,68688],{"encoding":1530},"\\displaystyle P_0 Q_0 - \\int_0^{Q_0} S(Q)\\,dQ",[1097,68690,68573,68691,68693,68694,68581,68696],{},[1047,68692,68580],{}," křivkou nabídky, ",[1047,68695,68576],{},[1035,68697,68699],{"className":68698},[1480],[1482,68700,68701],{"xmlns":1484},[1487,68702,68703,68715],{},[1490,68704,68705,68707,68709],{},[1493,68706,1501],{},[1506,68708,1508],{},[1497,68710,68711,68713],{},[1493,68712,1501],{},[1680,68714,1871],{},[1528,68716,66014],{"encoding":1530},[1079,68718,68719,68722,68749],{},[1097,68720,68721],{},"Výdaje \u002F tržby",[1097,68723,68724],{},[1035,68725,68727],{"className":68726},[1480],[1482,68728,68729],{"xmlns":1484},[1487,68730,68731,68747],{},[1490,68732,68733,68739,68741],{},[1497,68734,68735,68737],{},[1493,68736,1501],{},[1680,68738,1871],{},[1506,68740,1714],{},[1497,68742,68743,68745],{},[1493,68744,1520],{},[1680,68746,1871],{},[1528,68748,66779],{"encoding":1530},[1097,68750,68751,68752],{},"obdélník ",[1035,68753,68755],{"className":68754},[1480],[1482,68756,68757],{"xmlns":1484},[1487,68758,68759,68783],{},[1490,68760,68761,68763,68765,68771,68773,68775,68777],{},[1680,68762,1871],{},[1988,68764,5016],{},[1497,68766,68767,68769],{},[1493,68768,1520],{},[1680,68770,1871],{},[1988,68772,5016],{},[1493,68774,3633],{},[1988,68776,5016],{},[1497,68778,68779,68781],{},[1493,68780,1501],{},[1680,68782,1871],{},[1528,68784,65491],{"encoding":1530},[1079,68786,68787,68790,68813],{},[1097,68788,68789],{},"Celkový přebytek",[1097,68791,68792],{},[1035,68793,68795],{"className":68794},[1480],[1482,68796,68797],{"xmlns":1484},[1487,68798,68799,68811],{},[1490,68800,68801,68803,68805,68807,68809],{},[1493,68802,1998],{},[1493,68804,2001],{},[1506,68806,2162],{},[1493,68808,1501],{},[1493,68810,2001],{},[1528,68812,65228],{"encoding":1530},[1097,68814,68815],{},"součet obou ploch v rovnováze",[1246,68817],{},[1065,68819,31885],{"id":31884},[1203,68821,68822,68844,68866,68910,68954,69017,69045],{},[1206,68823,68824,7606,68826,1732,68841,68843],{},[1047,68825,59273],{},[1035,68827,68829],{"className":68828},[1480],[1482,68830,68831],{"xmlns":1484},[1487,68832,68833,68839],{},[1490,68834,68835,68837],{},[1493,68836,1998],{},[1493,68838,2001],{},[1528,68840,59289],{"encoding":1530},[1176,68842,59327],{},") — rozdíl mezi ochotou platit a skutečnou platbou, vzorec (2.14).",[1206,68845,68846,7606,68848,1732,68863,68865],{},[1047,68847,59420],{},[1035,68849,68851],{"className":68850},[1480],[1482,68852,68853],{"xmlns":1484},[1487,68854,68855,68861],{},[1490,68856,68857,68859],{},[1493,68858,1501],{},[1493,68860,2001],{},[1528,68862,59308],{"encoding":1530},[1176,68864,59423],{},") — rozdíl mezi tržbou a minimální cenou dle nabídky, vzorec (2.15).",[1206,68867,68868,22970,68871,2632],{},[1047,68869,68870],{},"Ochota platit",[1035,68872,68874],{"className":68873},[1480],[1482,68875,68876],{"xmlns":1484},[1487,68877,68878,68908],{},[1490,68879,68880],{},[1869,68881,68882,68894,68896,68898,68900,68902,68904,68906],{"scriptlevel":1871,"displaystyle":1041},[1697,68883,68884,68886,68888],{},[1506,68885,10857],{},[1680,68887,1871],{},[1497,68889,68890,68892],{},[1493,68891,1520],{},[1680,68893,1871],{},[1493,68895,3712],{},[1506,68897,1553],{"stretchy":1552},[1493,68899,1520],{},[1506,68901,1564],{"stretchy":1552},[1988,68903,5016],{},[1493,68905,3384],{},[1493,68907,1520],{},[1528,68909,65862],{"encoding":1530},[1206,68911,68912,22970,68915,2632],{},[1047,68913,68914],{},"Minimální cena výrobce",[1035,68916,68918],{"className":68917},[1480],[1482,68919,68920],{"xmlns":1484},[1487,68921,68922,68952],{},[1490,68923,68924],{},[1869,68925,68926,68938,68940,68942,68944,68946,68948,68950],{"scriptlevel":1871,"displaystyle":1041},[1697,68927,68928,68930,68932],{},[1506,68929,10857],{},[1680,68931,1871],{},[1497,68933,68934,68936],{},[1493,68935,1520],{},[1680,68937,1871],{},[1493,68939,2001],{},[1506,68941,1553],{"stretchy":1552},[1493,68943,1520],{},[1506,68945,1564],{"stretchy":1552},[1988,68947,5016],{},[1493,68949,3384],{},[1493,68951,1520],{},[1528,68953,66411],{"encoding":1530},[1206,68955,68956,22970,68959,66910,68984,16623],{},[1047,68957,68958],{},"Výdaje spotřebitele \u002F tržby výrobce",[1035,68960,68962],{"className":68961},[1480],[1482,68963,68964],{"xmlns":1484},[1487,68965,68966,68982],{},[1490,68967,68968,68974,68976],{},[1497,68969,68970,68972],{},[1493,68971,1501],{},[1680,68973,1871],{},[1988,68975,5016],{},[1497,68977,68978,68980],{},[1493,68979,1520],{},[1680,68981,1871],{},[1528,68983,65940],{"encoding":1530},[1035,68985,68987],{"className":68986},[1480],[1482,68988,68989],{"xmlns":1484},[1487,68990,68991,69015],{},[1490,68992,68993,68995,68997,69003,69005,69007,69009],{},[1680,68994,1871],{},[1988,68996,5016],{},[1497,68998,68999,69001],{},[1493,69000,1520],{},[1680,69002,1871],{},[1988,69004,5016],{},[1493,69006,3633],{},[1988,69008,5016],{},[1497,69010,69011,69013],{},[1493,69012,1501],{},[1680,69014,1871],{},[1528,69016,65491],{"encoding":1530},[1206,69018,69019,69022,69023,69044],{},[1047,69020,69021],{},"Celkový přebytek trhu"," — součet ",[1035,69024,69026],{"className":69025},[1480],[1482,69027,69028],{"xmlns":1484},[1487,69029,69030,69042],{},[1490,69031,69032,69034,69036,69038,69040],{},[1493,69033,1998],{},[1493,69035,2001],{},[1506,69037,2162],{},[1493,69039,1501],{},[1493,69041,2001],{},[1528,69043,65228],{"encoding":1530}," v rovnovážném bodě.",[1206,69046,69047,69049,69050,1732,69063,69076,69077,2632],{},[1047,69048,17903],{}," — plochy ohraničené křivkami ",[1035,69051,69053],{"className":69052},[1480],[1482,69054,69055],{"xmlns":1484},[1487,69056,69057,69061],{},[1490,69058,69059],{},[1493,69060,3712],{},[1528,69062,3712],{"encoding":1530},[1035,69064,69066],{"className":69065},[1480],[1482,69067,69068],{"xmlns":1484},[1487,69069,69070,69074],{},[1490,69071,69072],{},[1493,69073,2001],{},[1528,69075,2001],{"encoding":1530}," a přímkou ",[1035,69078,69080],{"className":69079},[1480],[1482,69081,69082],{"xmlns":1484},[1487,69083,69084,69096],{},[1490,69085,69086,69088,69090],{},[1493,69087,1501],{},[1506,69089,1508],{},[1497,69091,69092,69094],{},[1493,69093,1501],{},[1680,69095,1871],{},[1528,69097,66014],{"encoding":1530},[1246,69099],{},[1065,69101,69103],{"id":69102},"dopad-daně-na-přebytky-a-mrtvá-ztráta","Dopad daně na přebytky a mrtvá ztráta",[1030,69105,69106,69107,69120,69121,69138],{},"Uvalení jednotkové daně ",[1035,69108,69110],{"className":69109},[1480],[1482,69111,69112],{"xmlns":1484},[1487,69113,69114,69118],{},[1490,69115,69116],{},[1493,69117,5289],{},[1528,69119,5289],{"encoding":1530}," na trh posouvá rovnovážné množství pod ",[1035,69122,69124],{"className":69123},[1480],[1482,69125,69126],{"xmlns":1484},[1487,69127,69128,69136],{},[1490,69129,69130],{},[2315,69131,69132,69134],{},[1493,69133,1520],{},[1493,69135,2711],{},[1528,69137,14059],{"encoding":1530}," a rozkládá původní plochu přebytků na nové části.",[1030,69140,69141],{},[18014,69142],{"alt":69143,"className":69144,"src":69145},"imek-prebytky-s-dani-deadweight",[1055,18018],"\u002Fwiki-assets\u002Fimek-prebytky-s-dani-deadweight.jpeg",[1030,69147,69148,69149,69164,69165,69180,69181,66910,69184,69208,69209,7606,69212,69215,69216,2632],{},"Přebytek spotřebitele ",[1035,69150,69152],{"className":69151},[1480],[1482,69153,69154],{"xmlns":1484},[1487,69155,69156,69162],{},[1490,69157,69158,69160],{},[1493,69159,1998],{},[1493,69161,2001],{},[1528,69163,59289],{"encoding":1530}," se zmenší (spotřebitelé platí víc a nakupují méně), přebytek výrobce ",[1035,69166,69168],{"className":69167},[1480],[1482,69169,69170],{"xmlns":1484},[1487,69171,69172,69178],{},[1490,69173,69174,69176],{},[1493,69175,1501],{},[1493,69177,2001],{},[1528,69179,59308],{"encoding":1530}," se rovněž zmenší (výrobci obdrží po odvodu méně). Stát získává ",[1047,69182,69183],{},"daňový příjem",[1035,69185,69187],{"className":69186},[1480],[1482,69188,69189],{"xmlns":1484},[1487,69190,69191,69205],{},[1490,69192,69193,69195,69197],{},[1493,69194,5289],{},[1506,69196,1714],{},[1697,69198,69199,69201,69203],{},[1493,69200,1520],{},[1680,69202,1682],{},[1493,69204,2711],{},[1528,69206,69207],{"encoding":1530},"T \\cdot Q_1^E","). Zbývající část původních přebytků — ",[1047,69210,69211],{},"mrtvá ztráta",[1176,69213,69214],{},"deadweight loss",", DWL) — je čistým úbytkem blahobytu, který nikdo neinkasuje, a je důsledkem transakcí, které se kvůli dani vůbec neuskuteční. Detailní rozbor viz ",[1052,69217,57168],{"className":69218,"dataFsResolvedFilePath":57271,"href":57272},[1055],[1246,69220],{},[1065,69222,17159],{"id":17158},[1203,69224,69225,69232,69244,69251,69258],{},[1206,69226,69227,1656,69229],{},[1047,69228,32384],{},[1052,69230,3489],{"className":69231,"dataFsResolvedFilePath":3487,"href":3488},[1055],[1206,69233,69234,1656,69236,69239,69240,69243],{},[1047,69235,17249],{},[1052,69237,17258],{"className":69238,"dataFsResolvedFilePath":17256,"href":17257},[1055]," (určitý integrál, plocha pod křivkou), ",[1052,69241,3506],{"className":69242,"dataFsResolvedFilePath":16621,"href":16622},[1055]," (monotonie křivek)",[1206,69245,69246,1656,69248],{},[1047,69247,32393],{},[1052,69249,1301],{"className":69250,"dataFsResolvedFilePath":1299,"href":1300},[1055],[1206,69252,69253,1656,69255],{},[1047,69254,65092],{},[1052,69256,17190],{"className":69257,"dataFsResolvedFilePath":17188,"href":17189},[1055],[1206,69259,69260,1656,69262],{},[1047,69261,17176],{},[1052,69263,1058],{"className":69264,"dataFsResolvedFilePath":1056,"href":1057},[1055],{"title":17269,"searchDepth":141,"depth":141,"links":69266},[69267,69268,69273,69278,69283,69284,69285,69286],{"id":65287,"depth":141,"text":65288},{"id":65635,"depth":141,"text":69269,"children":69270},"Přebytek spotřebitele (CSCS)",[69271,69272],{"id":65654,"depth":96,"text":65655},{"id":17902,"depth":96,"text":17903},{"id":66137,"depth":141,"text":69274,"children":69275},"Přebytek výrobce (PSPS)",[69276,69277],{"id":66156,"depth":96,"text":66157},{"id":66319,"depth":96,"text":17903},{"id":66925,"depth":141,"text":66926,"children":69279},[69280,69281],{"id":66929,"depth":96,"text":66930},{"id":68158,"depth":96,"text":69282},"Příklad 2.13 — numerický výpočet PSPS",{"id":68467,"depth":141,"text":68468},{"id":31884,"depth":141,"text":31885},{"id":69102,"depth":141,"text":69103},{"id":17158,"depth":141,"text":17159},{},"\u002Ftopics\u002Fprebytek-spotrebitele-vyrobce",{"title":28281,"description":17269},[26098,19272],"topics\u002Fprebytek-spotrebitele-vyrobce",[9,281,428,846,110,132,323,978],"jONhpG6oF8BpA5aEYpZ7APxTRQrRsrZHafDSEzGT5X0",{"id":69295,"title":69296,"body":69297,"course":9,"courses":17424,"created":26093,"description":17269,"extension":17426,"meta":86813,"navigation":17428,"path":86814,"seo":86815,"sources":86816,"stem":86817,"tags":86818,"type":19275,"updated":26102,"__hash__":86819},"topics\u002Ftopics\u002Fprijem-naklady-zisk.md","Příjem, náklady, zisk a nabídka firmy",{"type":1016,"value":69298,"toc":86777},[69299,69302,69490,69492,69583,69588,69913,69917,69924,69928,69973,70040,70071,70121,70156,70160,70219,70224,70290,70406,70410,70433,70511,70561,70565,70594,70661,70667,70786,70790,70870,70907,70959,71157,71221,71308,71312,71315,71394,71397,71515,71534,71599,71603,71694,71762,71803,71857,71925,71962,71966,72024,72054,72264,72336,72368,72372,72376,72413,72478,72533,72537,72560,72649,72753,72822,72826,72922,73035,73091,73145,73148,73184,73249,73279,73509,73513,73540,73619,73738,73759,73838,73840,73946,73950,74088,74410,74414,74417,74421,74470,74474,74728,74880,74887,74892,75236,75240,75263,75265,75286,75345,75359,75408,75550,75624,75718,75833,75931,76054,76058,76127,76132,76244,76389,76440,76552,76594,76598,76618,76679,76711,76773,76777,76799,76868,77148,77161,77191,77198,77202,77280,77285,77361,77364,77452,77528,77592,77641,77744,77817,77938,77942,77945,77952,77955,77991,78050,78064,78213,78440,78444,78507,78686,78778,78833,78837,78893,78963,79015,79036,79117,79120,79194,79238,79242,79283,79326,79352,79356,79427,79523,79585,79637,79740,79818,79841,79870,79874,80040,80157,80229,80546,80550,80601,80663,80698,80728,80828,80870,81039,81044,81140,81144,81262,81563,81565,81600,81604,81608,81736,81868,82190,82377,82455,82459,82764,82877,83022,83207,83313,83545,83660,83742,83861,83959,84000,84004,84059,84202,84356,84514,84607,84801,85112,85242,85370,85374,85445,85487,85538,85540,86736,86738],[1019,69300,69296],{"id":69301},"příjem-náklady-zisk-a-nabídka-firmy",[1023,69303,69305,69311],{"className":69304,"dataCallout":1028},[1026,1027],[1030,69306,69308,1042],{"className":69307},[1033],[1035,69309],{"className":69310,"ariaHidden":1041},[1038,1039,1040],[1030,69312,69313,1656,69316,69331,69332,1656,69335,69350,69351,1656,69353,69380,69381,69403,69404,69428,69429,69450,69451,69454,69455,69471,69472,2632],{},[1047,69314,69315],{},"Příjem",[1035,69317,69319],{"className":69318},[1480],[1482,69320,69321],{"xmlns":1484},[1487,69322,69323,69329],{},[1490,69324,69325,69327],{},[1493,69326,5289],{},[1493,69328,1995],{},[1528,69330,16491],{"encoding":1530}," je to, co firma inkasuje (cena krát množství), ",[1047,69333,69334],{},"náklady",[1035,69336,69338],{"className":69337},[1480],[1482,69339,69340],{"xmlns":1484},[1487,69341,69342,69348],{},[1490,69343,69344,69346],{},[1493,69345,5289],{},[1493,69347,1998],{},[1528,69349,18668],{"encoding":1530}," to, co vynaloží (fixní plus variabilní), a ",[1047,69352,1008],{},[1035,69354,69356],{"className":69355},[1480],[1482,69357,69358],{"xmlns":1484},[1487,69359,69360,69378],{},[1490,69361,69362,69364,69366,69368,69370,69372,69374,69376],{},[1493,69363,1501],{},[1493,69365,1995],{},[1506,69367,1508],{},[1493,69369,5289],{},[1493,69371,1995],{},[1506,69373,1888],{},[1493,69375,5289],{},[1493,69377,1998],{},[1528,69379,9401],{"encoding":1530}," jejich rozdíl. Kapitola pro každou ze tří veličin zavádí celkovou, průměrnou a mezní podobu, ukáže jejich grafický průběh (pro lineární poptávku a kubické náklady) a odvodí tři klíčové optimalizační principy: ",[1035,69382,69384],{"className":69383},[1480],[1482,69385,69386],{"xmlns":1484},[1487,69387,69388,69400],{},[1490,69389,69390,69392,69394,69396,69398],{},[1493,69391,3633],{},[1493,69393,1998],{},[1506,69395,1508],{},[1493,69397,1495],{},[1493,69399,1998],{},[1528,69401,69402],{"encoding":1530},"AC = MC"," v minimu průměrných nákladů, ",[1035,69405,69407],{"className":69406},[1480],[1482,69408,69409],{"xmlns":1484},[1487,69410,69411,69425],{},[1490,69412,69413,69415,69417,69419,69421,69423],{},[1493,69414,3633],{},[1493,69416,55105],{},[1493,69418,1998],{},[1506,69420,1508],{},[1493,69422,1495],{},[1493,69424,1998],{},[1528,69426,69427],{"encoding":1530},"AVC = MC"," v minimu průměrných variabilních nákladů a ",[1035,69430,69432],{"className":69431},[1480],[1482,69433,69434],{"xmlns":1484},[1487,69435,69436,69448],{},[1490,69437,69438,69440,69442,69444,69446],{},[1493,69439,1495],{},[1493,69441,1995],{},[1506,69443,1508],{},[1493,69445,1495],{},[1493,69447,1998],{},[1528,69449,11390],{"encoding":1530}," v maximu zisku. Na závěr se sestaví ",[1047,69452,69453],{},"funkce nabídky firmy"," jako rostoucí část křivky ",[1035,69456,69458],{"className":69457},[1480],[1482,69459,69460],{"xmlns":1484},[1487,69461,69462,69468],{},[1490,69463,69464,69466],{},[1493,69465,1495],{},[1493,69467,1998],{},[1528,69469,69470],{"encoding":1530},"MC"," nad bodem minima ",[1035,69473,69475],{"className":69474},[1480],[1482,69476,69477],{"xmlns":1484},[1487,69478,69479,69487],{},[1490,69480,69481,69483,69485],{},[1493,69482,3633],{},[1493,69484,55105],{},[1493,69486,1998],{},[1528,69488,69489],{"encoding":1530},"AVC",[1065,69491,65288],{"id":65287},[1030,69493,69494,69495,69498,69499,69501,69502,1732,69505,1732,69508,69510,69511,69514,69515,69518,69519,69522,69523,18125,69538,16846,69553,18125,69568,16623],{},"Kapitola 3 se zabývá dvěma základními veličinami popisujícími ekonomickou aktivitu firmy — ",[1047,69496,69497],{},"příjmem"," (revenue) a ",[1047,69500,69334],{}," (cost) — v jejich třech standardních podobách: celkové, průměrné a mezní. Navazuje analýzou ",[1047,69503,69504],{},"zisku",[1047,69506,69507],{},"bodů zvratu",[1047,69509,17463],{}," a konstrukcí ",[1047,69512,69513],{},"nabídkové křivky firmy",". Klíčovými matematickými nástroji jsou ",[1052,69516,102],{"className":69517,"dataFsResolvedFilePath":16621,"href":16622},[1055]," (pro mezní veličiny) a diferenciál (pro odhad přírůstků); v několika úlohách se využívá také ",[1052,69520,27641],{"className":69521,"dataFsResolvedFilePath":17256,"href":17257},[1055]," (pro zpětnou rekonstrukci ",[1035,69524,69526],{"className":69525},[1480],[1482,69527,69528],{"xmlns":1484},[1487,69529,69530,69536],{},[1490,69531,69532,69534],{},[1493,69533,5289],{},[1493,69535,1995],{},[1528,69537,16491],{"encoding":1530},[1035,69539,69541],{"className":69540},[1480],[1482,69542,69543],{"xmlns":1484},[1487,69544,69545,69551],{},[1490,69546,69547,69549],{},[1493,69548,1495],{},[1493,69550,1995],{},[1528,69552,6258],{"encoding":1530},[1035,69554,69556],{"className":69555},[1480],[1482,69557,69558],{"xmlns":1484},[1487,69559,69560,69566],{},[1490,69561,69562,69564],{},[1493,69563,5289],{},[1493,69565,1998],{},[1528,69567,18668],{"encoding":1530},[1035,69569,69571],{"className":69570},[1480],[1482,69572,69573],{"xmlns":1484},[1487,69574,69575,69581],{},[1490,69576,69577,69579],{},[1493,69578,1495],{},[1493,69580,1998],{},[1528,69582,69470],{"encoding":1530},[1030,69584,69585],{},[1047,69586,69587],{},"Cílové znalosti:",[1203,69589,69590,69753,69756,69759,69852,69899,69906],{},[1206,69591,69592,69593,1732,69608,1732,69624,1586,69639,1732,69654,1732,69670,1732,69688,1732,69706,1732,69723,1732,69738,6065],{},"odvodit a interpretovat funkce ",[1035,69594,69596],{"className":69595},[1480],[1482,69597,69598],{"xmlns":1484},[1487,69599,69600,69606],{},[1490,69601,69602,69604],{},[1493,69603,5289],{},[1493,69605,1995],{},[1528,69607,16491],{"encoding":1530},[1035,69609,69611],{"className":69610},[1480],[1482,69612,69613],{"xmlns":1484},[1487,69614,69615,69621],{},[1490,69616,69617,69619],{},[1493,69618,3633],{},[1493,69620,1995],{},[1528,69622,69623],{"encoding":1530},"AR",[1035,69625,69627],{"className":69626},[1480],[1482,69628,69629],{"xmlns":1484},[1487,69630,69631,69637],{},[1490,69632,69633,69635],{},[1493,69634,1495],{},[1493,69636,1995],{},[1528,69638,6258],{"encoding":1530},[1035,69640,69642],{"className":69641},[1480],[1482,69643,69644],{"xmlns":1484},[1487,69645,69646,69652],{},[1490,69647,69648,69650],{},[1493,69649,5289],{},[1493,69651,1998],{},[1528,69653,18668],{"encoding":1530},[1035,69655,69657],{"className":69656},[1480],[1482,69658,69659],{"xmlns":1484},[1487,69660,69661,69667],{},[1490,69662,69663,69665],{},[1493,69664,10790],{},[1493,69666,1998],{},[1528,69668,69669],{"encoding":1530},"FC",[1035,69671,69673],{"className":69672},[1480],[1482,69674,69675],{"xmlns":1484},[1487,69676,69677,69685],{},[1490,69678,69679,69681,69683],{},[1493,69680,5289],{},[1493,69682,55105],{},[1493,69684,1998],{},[1528,69686,69687],{"encoding":1530},"TVC",[1035,69689,69691],{"className":69690},[1480],[1482,69692,69693],{"xmlns":1484},[1487,69694,69695,69703],{},[1490,69696,69697,69699,69701],{},[1493,69698,3633],{},[1493,69700,10790],{},[1493,69702,1998],{},[1528,69704,69705],{"encoding":1530},"AFC",[1035,69707,69709],{"className":69708},[1480],[1482,69710,69711],{"xmlns":1484},[1487,69712,69713,69721],{},[1490,69714,69715,69717,69719],{},[1493,69716,3633],{},[1493,69718,55105],{},[1493,69720,1998],{},[1528,69722,69489],{"encoding":1530},[1035,69724,69726],{"className":69725},[1480],[1482,69727,69728],{"xmlns":1484},[1487,69729,69730,69736],{},[1490,69731,69732,69734],{},[1493,69733,3633],{},[1493,69735,1998],{},[1528,69737,16523],{"encoding":1530},[1035,69739,69741],{"className":69740},[1480],[1482,69742,69743],{"xmlns":1484},[1487,69744,69745,69751],{},[1490,69746,69747,69749],{},[1493,69748,1495],{},[1493,69750,1998],{},[1528,69752,69470],{"encoding":1530},[1206,69754,69755],{},"porozumět vzájemným vztahům mezi průměrnou a mezní veličinou, zvláště pro lineární poptávku;",[1206,69757,69758],{},"pomocí diferenciálu odhadovat změny celkových veličin;",[1206,69760,69761,69762,69765,69766,56364,69808,6065],{},"osvojit si ",[1047,69763,69764],{},"princip minimalizace průměrných (variabilních) nákladů"," — podmínku ",[1035,69767,69769],{"className":69768},[1480],[1482,69770,69771],{"xmlns":1484},[1487,69772,69773,69805],{},[1490,69774,69775,69777,69779,69781,69787,69789,69791,69793,69795,69797,69803],{},[1493,69776,3633],{},[1493,69778,1998],{},[1506,69780,1553],{"stretchy":1552},[1497,69782,69783,69785],{},[1493,69784,1520],{},[1680,69786,1871],{},[1506,69788,1564],{"stretchy":1552},[1506,69790,1508],{},[1493,69792,1495],{},[1493,69794,1998],{},[1506,69796,1553],{"stretchy":1552},[1497,69798,69799,69801],{},[1493,69800,1520],{},[1680,69802,1871],{},[1506,69804,1564],{"stretchy":1552},[1528,69806,69807],{"encoding":1530},"AC(Q_0)=MC(Q_0)",[1035,69809,69811],{"className":69810},[1480],[1482,69812,69813],{"xmlns":1484},[1487,69814,69815,69849],{},[1490,69816,69817,69819,69821,69823,69825,69831,69833,69835,69837,69839,69841,69847],{},[1493,69818,3633],{},[1493,69820,55105],{},[1493,69822,1998],{},[1506,69824,1553],{"stretchy":1552},[1497,69826,69827,69829],{},[1493,69828,1520],{},[1680,69830,1871],{},[1506,69832,1564],{"stretchy":1552},[1506,69834,1508],{},[1493,69836,1495],{},[1493,69838,1998],{},[1506,69840,1553],{"stretchy":1552},[1497,69842,69843,69845],{},[1493,69844,1520],{},[1680,69846,1871],{},[1506,69848,1564],{"stretchy":1552},[1528,69850,69851],{"encoding":1530},"AVC(Q_0)=MC(Q_0)",[1206,69853,69761,69854,69765,69857,6065],{},[1047,69855,69856],{},"princip maximalizace zisku",[1035,69858,69860],{"className":69859},[1480],[1482,69861,69862],{"xmlns":1484},[1487,69863,69864,69896],{},[1490,69865,69866,69868,69870,69872,69878,69880,69882,69884,69886,69888,69894],{},[1493,69867,1495],{},[1493,69869,1995],{},[1506,69871,1553],{"stretchy":1552},[1497,69873,69874,69876],{},[1493,69875,1520],{},[1680,69877,1871],{},[1506,69879,1564],{"stretchy":1552},[1506,69881,1508],{},[1493,69883,1495],{},[1493,69885,1998],{},[1506,69887,1553],{"stretchy":1552},[1497,69889,69890,69892],{},[1493,69891,1520],{},[1680,69893,1871],{},[1506,69895,1564],{"stretchy":1552},[1528,69897,69898],{"encoding":1530},"MR(Q_0)=MC(Q_0)",[1206,69900,69901,69902,69905],{},"stanovit ",[1047,69903,69904],{},"body zvratu"," a interval zisku;",[1206,69907,69908,69909,69912],{},"zkonstruovat ",[1047,69910,69911],{},"funkci nabídky firmy"," na základě nákladových charakteristik.",[1065,69914,69916],{"id":69915},"příjem-firmy","Příjem firmy",[1030,69918,69919],{},[18014,69920],{"alt":69921,"className":69922,"src":69923},"imek-ar-mr-dvojnasobny-sklon",[1055,18018],"\u002Fwiki-assets\u002Fimek-ar-mr-dvojnasobny-sklon.jpeg",[1304,69925,69927],{"id":69926},"celkový-příjem","Celkový příjem",[1030,69929,69930,69931,7606,69946,69949,69950,45271],{},"Celkový příjem ",[1035,69932,69934],{"className":69933},[1480],[1482,69935,69936],{"xmlns":1484},[1487,69937,69938,69944],{},[1490,69939,69940,69942],{},[1493,69941,5289],{},[1493,69943,1995],{},[1528,69945,16491],{"encoding":1530},[1047,69947,69948],{},"total revenue",") je součin ceny a prodaného množství. Při poptávce ",[1035,69951,69953],{"className":69952},[1480],[1482,69954,69955],{"xmlns":1484},[1487,69956,69957,69971],{},[1490,69958,69959,69961,69963,69965,69967,69969],{},[1493,69960,1501],{},[1506,69962,1508],{},[1493,69964,3712],{},[1506,69966,1553],{"stretchy":1552},[1493,69968,1520],{},[1506,69970,1564],{"stretchy":1552},[1528,69972,20356],{"encoding":1530},[1035,69974,69976],{"className":69975},[1480],[1482,69977,69978],{"xmlns":1484,"display":1485},[1487,69979,69980,70037],{},[19617,69981,69982],{"width":19619},[19621,69983,69984,69986,70030,70032],{},[19624,69985],{"width":19626},[19624,69987,69988],{},[1490,69989,69990,69992,69994,69996,69998,70000,70002,70004,70006,70008,70010,70012,70014,70016,70018,70020,70022,70024,70026,70028],{},[1493,69991,5289],{},[1493,69993,1995],{},[1506,69995,1508],{},[1493,69997,5289],{},[1493,69999,1995],{},[1506,70001,1553],{"stretchy":1552},[1493,70003,1520],{},[1506,70005,1564],{"stretchy":1552},[1506,70007,1508],{},[1493,70009,1501],{},[1506,70011,1714],{},[1493,70013,1520],{},[1506,70015,1508],{},[1493,70017,3712],{},[1506,70019,1553],{"stretchy":1552},[1493,70021,1520],{},[1506,70023,1564],{"stretchy":1552},[1506,70025,1714],{},[1493,70027,1520],{},[1493,70029,2632],{"mathvariant":1516},[19624,70031],{"width":19626},[19624,70033,70034],{},[1988,70035,70036],{},"(3.1)",[1528,70038,70039],{"encoding":1530},"TR = TR(Q) = P \\cdot Q = D(Q) \\cdot Q.\n\\tag{3.1}",[1030,70041,70042,70043,70046,70047,70070],{},"Graf funkce se nazývá ",[1047,70044,70045],{},"křivka celkového příjmu"," (total revenue curve). Za předpokladu linearity poptávky, tj. ",[1035,70048,70050],{"className":70049},[1480],[1482,70051,70052],{"xmlns":1484},[1487,70053,70054,70068],{},[1490,70055,70056,70058,70060,70062,70064,70066],{},[1493,70057,1501],{},[1506,70059,1508],{},[1493,70061,1052],{},[1493,70063,1520],{},[1506,70065,2162],{},[1493,70067,2394],{},[1528,70069,52158],{"encoding":1530},", je celkový příjem kvadratickou funkcí, neboť",[1035,70072,70074],{"className":70073},[1480],[1482,70075,70076],{"xmlns":1484,"display":1485},[1487,70077,70078,70118],{},[1490,70079,70080,70082,70084,70086,70088,70090,70092,70094,70096,70098,70100,70102,70104,70110,70112,70114,70116],{},[1493,70081,5289],{},[1493,70083,1995],{},[1506,70085,1508],{},[1493,70087,1520],{},[1506,70089,1553],{"stretchy":1552},[1493,70091,1052],{},[1493,70093,1520],{},[1506,70095,2162],{},[1493,70097,2394],{},[1506,70099,1564],{"stretchy":1552},[1506,70101,1508],{},[1493,70103,1052],{},[2315,70105,70106,70108],{},[1493,70107,1520],{},[1680,70109,1691],{},[1506,70111,2162],{},[1493,70113,2394],{},[1493,70115,1520],{},[1506,70117,1559],{"separator":1041},[1528,70119,70120],{"encoding":1530},"TR = Q(aQ + b) = aQ^2 + bQ,",[1030,70122,70123,70124,70137,70138,70155],{},"a křivka celkového příjmu je parabola tvaru obráceného ",[1035,70125,70127],{"className":70126},[1480],[1482,70128,70129],{"xmlns":1484},[1487,70130,70131,70135],{},[1490,70132,70133],{},[1493,70134,1668],{},[1528,70136,1668],{"encoding":1530}," (jelikož ",[1035,70139,70141],{"className":70140},[1480],[1482,70142,70143],{"xmlns":1484},[1487,70144,70145,70153],{},[1490,70146,70147,70149,70151],{},[1493,70148,1052],{},[1506,70150,3961],{},[1680,70152,1871],{},[1528,70154,57642],{"encoding":1530},") procházející počátkem.",[52452,70157,70159],{"id":70158},"příklad-31","Příklad 3.1",[1030,70161,70162,70165,70166,70202,70203,70218],{},[1047,70163,70164],{},"Zadání."," Pro poptávku ",[1035,70167,70169],{"className":70168},[1480],[1482,70170,70171],{"xmlns":1484},[1487,70172,70173,70199],{},[1490,70174,70175,70177,70179,70181,70183,70185,70187,70189,70191,70193,70195,70197],{},[1493,70176,1501],{},[1506,70178,1508],{},[1493,70180,3712],{},[1506,70182,1553],{"stretchy":1552},[1493,70184,1520],{},[1506,70186,1564],{"stretchy":1552},[1506,70188,1508],{},[1506,70190,1888],{},[1680,70192,1691],{},[1493,70194,1520],{},[1506,70196,2162],{},[1680,70198,2916],{},[1528,70200,70201],{"encoding":1530},"P = D(Q) = -2Q + 100"," určete ",[1035,70204,70206],{"className":70205},[1480],[1482,70207,70208],{"xmlns":1484},[1487,70209,70210,70216],{},[1490,70211,70212,70214],{},[1493,70213,5289],{},[1493,70215,1995],{},[1528,70217,16491],{"encoding":1530}," a charakterizujte jeho křivku.",[1030,70220,70221,70223],{},[1047,70222,38365],{}," Celkový příjem je",[1035,70225,70227],{"className":70226},[1480],[1482,70228,70229],{"xmlns":1484,"display":1485},[1487,70230,70231,70287],{},[1490,70232,70233,70235,70237,70239,70241,70243,70245,70247,70249,70251,70253,70255,70257,70259,70261,70263,70265,70267,70269,70271,70273,70279,70281,70283,70285],{},[1493,70234,5289],{},[1493,70236,1995],{},[1506,70238,1508],{},[1493,70240,5289],{},[1493,70242,1995],{},[1506,70244,1553],{"stretchy":1552},[1493,70246,1520],{},[1506,70248,1564],{"stretchy":1552},[1506,70250,1508],{},[1493,70252,1520],{},[1506,70254,1553],{"stretchy":1552},[1506,70256,1888],{},[1680,70258,1691],{},[1493,70260,1520],{},[1506,70262,2162],{},[1680,70264,2916],{},[1506,70266,1564],{"stretchy":1552},[1506,70268,1508],{},[1506,70270,1888],{},[1680,70272,1691],{},[2315,70274,70275,70277],{},[1493,70276,1520],{},[1680,70278,1691],{},[1506,70280,2162],{},[1680,70282,2916],{},[1493,70284,1520],{},[1493,70286,2632],{"mathvariant":1516},[1528,70288,70289],{"encoding":1530},"TR = TR(Q) = Q(-2Q + 100) = -2Q^2 + 100Q.",[1030,70291,70292,70293,1586,70315,70337,70338,70356,70357,2632],{},"Křivkou je parabola s nulami v ",[1035,70294,70296],{"className":70295},[1480],[1482,70297,70298],{"xmlns":1484},[1487,70299,70300,70312],{},[1490,70301,70302,70308,70310],{},[1497,70303,70304,70306],{},[1493,70305,1520],{},[1680,70307,1682],{},[1506,70309,1508],{},[1680,70311,1871],{},[1528,70313,70314],{"encoding":1530},"Q_1 = 0",[1035,70316,70318],{"className":70317},[1480],[1482,70319,70320],{"xmlns":1484},[1487,70321,70322,70334],{},[1490,70323,70324,70330,70332],{},[1497,70325,70326,70328],{},[1493,70327,1520],{},[1680,70329,1691],{},[1506,70331,1508],{},[1680,70333,2292],{},[1528,70335,70336],{"encoding":1530},"Q_2 = 50",". Maxima dosahuje při ",[1035,70339,70341],{"className":70340},[1480],[1482,70342,70343],{"xmlns":1484},[1487,70344,70345,70353],{},[1490,70346,70347,70349,70351],{},[1493,70348,1520],{},[1506,70350,1508],{},[1680,70352,2309],{},[1528,70354,70355],{"encoding":1530},"Q = 25"," ve výši ",[1035,70358,70360],{"className":70359},[1480],[1482,70361,70362],{"xmlns":1484},[1487,70363,70364,70403],{},[1490,70365,70366,70368,70376,70378,70380,70382,70384,70387,70389,70391,70393,70395,70397,70399,70401],{},[1493,70367,5289],{},[1497,70369,70370,70372,70374],{},[1493,70371,1995],{},[1493,70373,7571],{},[1506,70375,7574],{},[1506,70377,1508],{},[1506,70379,1888],{},[1680,70381,1691],{},[1506,70383,1714],{},[1680,70385,70386],{},"625",[1506,70388,2162],{},[1680,70390,2916],{},[1506,70392,1714],{},[1680,70394,2309],{},[1506,70396,1508],{},[1680,70398,1682],{},[1988,70400,5016],{},[1680,70402,8140],{},[1528,70404,70405],{"encoding":1530},"TR_{\\max} = -2 \\cdot 625 + 100 \\cdot 25 = 1\\,250",[1304,70407,70409],{"id":70408},"průměrný-příjem","Průměrný příjem",[1030,70411,70412,1656,70414,7606,70429,70432],{},[1047,70413,70409],{},[1035,70415,70417],{"className":70416},[1480],[1482,70418,70419],{"xmlns":1484},[1487,70420,70421,70427],{},[1490,70422,70423,70425],{},[1493,70424,3633],{},[1493,70426,1995],{},[1528,70428,69623],{"encoding":1530},[1047,70430,70431],{},"average revenue",") je podíl celkového příjmu a množství. Z (3.1) plyne",[1035,70434,70436],{"className":70435},[1480],[1482,70437,70438],{"xmlns":1484,"display":1485},[1487,70439,70440,70508],{},[1490,70441,70442,70444,70446,70448,70450,70452,70454,70456,70458,70460,70476,70478,70496,70498,70500,70502,70504,70506],{},[1493,70443,3633],{},[1493,70445,1995],{},[1506,70447,1508],{},[1493,70449,3633],{},[1493,70451,1995],{},[1506,70453,1553],{"stretchy":1552},[1493,70455,1520],{},[1506,70457,1564],{"stretchy":1552},[1506,70459,1508],{},[1510,70461,70462,70474],{},[1490,70463,70464,70466,70468,70470,70472],{},[1493,70465,5289],{},[1493,70467,1995],{},[1506,70469,1553],{"stretchy":1552},[1493,70471,1520],{},[1506,70473,1564],{"stretchy":1552},[1493,70475,1520],{},[1506,70477,1508],{},[1510,70479,70480,70494],{},[1490,70481,70482,70484,70486,70488,70490,70492],{},[1493,70483,1520],{},[1988,70485,5016],{},[1493,70487,3712],{},[1506,70489,1553],{"stretchy":1552},[1493,70491,1520],{},[1506,70493,1564],{"stretchy":1552},[1493,70495,1520],{},[1506,70497,1508],{},[1493,70499,3712],{},[1506,70501,1553],{"stretchy":1552},[1493,70503,1520],{},[1506,70505,1564],{"stretchy":1552},[1493,70507,2632],{"mathvariant":1516},[1528,70509,70510],{"encoding":1530},"AR = AR(Q) = \\frac{TR(Q)}{Q} = \\frac{Q \\, D(Q)}{Q} = D(Q).",[1023,70512,70516,70524],{"className":70513,"dataCallout":70515},[1026,70514],"callout-note","note",[1030,70517,70519,70523],{"className":70518},[1033],[1035,70520],{"className":70521,"ariaHidden":1041},[1038,70522,1040],"i-lucide:pencil","Klíčové pozorování",[1030,70525,70526,1732,70529,2632],{},[1047,70527,70528],{},"Průměrný příjem se vždy rovná poptávkové funkci",[1035,70530,70532],{"className":70531},[1480],[1482,70533,70534],{"xmlns":1484},[1487,70535,70536,70558],{},[1490,70537,70538,70540,70542,70544,70546,70548,70550,70552,70554,70556],{},[1493,70539,3633],{},[1493,70541,1995],{},[1506,70543,1553],{"stretchy":1552},[1493,70545,1520],{},[1506,70547,1564],{"stretchy":1552},[1506,70549,1508],{},[1493,70551,3712],{},[1506,70553,1553],{"stretchy":1552},[1493,70555,1520],{},[1506,70557,1564],{"stretchy":1552},[1528,70559,70560],{"encoding":1530},"AR(Q) = D(Q)",[1304,70562,70564],{"id":70563},"mezní-příjem","Mezní příjem",[1030,70566,70567,70568,1656,70571,7606,70586,70589,70590,70593],{},"Pro zkoumání dynamiky změn celkového příjmu zavádíme ",[1047,70569,70570],{},"mezní příjem",[1035,70572,70574],{"className":70573},[1480],[1482,70575,70576],{"xmlns":1484},[1487,70577,70578,70584],{},[1490,70579,70580,70582],{},[1493,70581,1495],{},[1493,70583,1995],{},[1528,70585,6258],{"encoding":1530},[1047,70587,70588],{},"marginal revenue","), definovaný jako ",[1052,70591,102],{"className":70592,"dataFsResolvedFilePath":16621,"href":16622},[1055]," celkového příjmu podle množství:",[1035,70595,70597],{"className":70596},[1480],[1482,70598,70599],{"xmlns":1484,"display":1485},[1487,70600,70601,70658],{},[19617,70602,70603],{"width":19619},[19621,70604,70605,70607,70651,70653],{},[19624,70606],{"width":19626},[19624,70608,70609],{},[1490,70610,70611,70613,70615,70617,70633,70635,70637,70643,70645,70647,70649],{},[1493,70612,1495],{},[1493,70614,1995],{},[1506,70616,1508],{},[1510,70618,70619,70627],{},[1490,70620,70621,70623,70625],{},[1493,70622,3384],{"mathvariant":1516},[1493,70624,5289],{},[1493,70626,1995],{},[1490,70628,70629,70631],{},[1493,70630,3384],{"mathvariant":1516},[1493,70632,1520],{},[1506,70634,1508],{},[1493,70636,5289],{},[2315,70638,70639,70641],{},[1493,70640,1995],{},[1506,70642,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,70644,1553],{"stretchy":1552},[1493,70646,1520],{},[1506,70648,1564],{"stretchy":1552},[1493,70650,2632],{"mathvariant":1516},[19624,70652],{"width":19626},[19624,70654,70655],{},[1988,70656,70657],{},"(3.2)",[1528,70659,70660],{"encoding":1530},"MR = \\frac{\\mathrm{d}TR}{\\mathrm{d}Q} = TR'(Q).\n\\tag{3.2}",[1030,70662,70663,70664,70666],{},"Mezní příjem udává ",[1047,70665,18051],{}," celkového příjmu vzhledem k množství.",[1023,70668,70670,70677],{"className":70669,"dataCallout":582},[1026,1186],[1030,70671,70673,70676],{"className":70672},[1033],[1035,70674],{"className":70675,"ariaHidden":1041},[1038,1193,1040],"Intuice — „kolik vyděláš za další kus\"",[1030,70678,21886,70679,70705,70706,70723,70724,2632],{},[1035,70680,70682],{"className":70681},[1480],[1482,70683,70684],{"xmlns":1484},[1487,70685,70686,70702],{},[1490,70687,70688,70690,70692,70694,70700],{},[1493,70689,1495],{},[1493,70691,1995],{},[1506,70693,1553],{"stretchy":1552},[2315,70695,70696,70698],{},[1493,70697,1520],{},[1506,70699,2287],{},[1506,70701,1564],{"stretchy":1552},[1528,70703,70704],{"encoding":1530},"MR(Q^*)"," je přibližně to, o kolik se zvýší celkový příjem, prodá-li firma jednu další jednotku nad aktuální úroveň ",[1035,70707,70709],{"className":70708},[1480],[1482,70710,70711],{"xmlns":1484},[1487,70712,70713,70721],{},[1490,70714,70715],{},[2315,70716,70717,70719],{},[1493,70718,1520],{},[1506,70720,2287],{},[1528,70722,14097],{"encoding":1530},". Jinak řečeno: ",[1035,70725,70727],{"className":70726},[1480],[1482,70728,70729],{"xmlns":1484},[1487,70730,70731,70783],{},[1490,70732,70733,70735,70737,70739,70745,70747,70749,70751,70753,70755,70761,70763,70765,70767,70769,70771,70773,70775,70781],{},[1493,70734,1495],{},[1493,70736,1995],{},[1506,70738,1553],{"stretchy":1552},[2315,70740,70741,70743],{},[1493,70742,1520],{},[1506,70744,2287],{},[1506,70746,1564],{"stretchy":1552},[1506,70748,2343],{},[1493,70750,5289],{},[1493,70752,1995],{},[1506,70754,1553],{"stretchy":1552},[2315,70756,70757,70759],{},[1493,70758,1520],{},[1506,70760,2287],{},[1506,70762,2162],{},[1680,70764,1682],{},[1506,70766,1564],{"stretchy":1552},[1506,70768,1888],{},[1493,70770,5289],{},[1493,70772,1995],{},[1506,70774,1553],{"stretchy":1552},[2315,70776,70777,70779],{},[1493,70778,1520],{},[1506,70780,2287],{},[1506,70782,1564],{"stretchy":1552},[1528,70784,70785],{"encoding":1530},"MR(Q^*) \\approx TR(Q^* + 1) - TR(Q^*)",[52452,70787,70789],{"id":70788},"příklad-32","Příklad 3.2",[1030,70791,70792,70165,70794,70202,70828,70843,70844,2632],{},[1047,70793,70164],{},[1035,70795,70797],{"className":70796},[1480],[1482,70798,70799],{"xmlns":1484},[1487,70800,70801,70825],{},[1490,70802,70803,70805,70807,70809,70811,70813,70815,70817,70819,70821,70823],{},[1493,70804,1501],{},[1506,70806,1508],{},[1493,70808,3712],{},[1506,70810,1553],{"stretchy":1552},[1493,70812,1520],{},[1506,70814,1564],{"stretchy":1552},[1506,70816,1508],{},[1680,70818,2916],{},[1506,70820,1888],{},[1680,70822,1691],{},[1493,70824,1520],{},[1528,70826,70827],{"encoding":1530},"P = D(Q) = 100 - 2Q",[1035,70829,70831],{"className":70830},[1480],[1482,70832,70833],{"xmlns":1484},[1487,70834,70835,70841],{},[1490,70836,70837,70839],{},[1493,70838,1495],{},[1493,70840,1995],{},[1528,70842,6258],{"encoding":1530}," a interpretujte jeho hodnoty pro ",[1035,70845,70847],{"className":70846},[1480],[1482,70848,70849],{"xmlns":1484},[1487,70850,70851,70867],{},[1490,70852,70853,70855,70857,70859,70861,70863,70865],{},[1493,70854,1520],{},[1506,70856,1508],{},[1680,70858,9787],{},[1506,70860,1559],{"separator":1041},[1680,70862,9961],{},[1506,70864,1559],{"separator":1041},[1680,70866,8436],{},[1528,70868,70869],{"encoding":1530},"Q = 15, 16, 20",[1030,70871,70872,1656,70874,70906],{},[1047,70873,38365],{},[1035,70875,70877],{"className":70876},[1480],[1482,70878,70879],{"xmlns":1484},[1487,70880,70881,70903],{},[1490,70882,70883,70885,70887,70889,70891,70893,70895,70897],{},[1493,70884,5289],{},[1493,70886,1995],{},[1506,70888,1508],{},[1680,70890,2916],{},[1493,70892,1520],{},[1506,70894,1888],{},[1680,70896,1691],{},[2315,70898,70899,70901],{},[1493,70900,1520],{},[1680,70902,1691],{},[1528,70904,70905],{"encoding":1530},"TR = 100Q - 2Q^2",", tedy",[1035,70908,70910],{"className":70909},[1480],[1482,70911,70912],{"xmlns":1484,"display":1485},[1487,70913,70914,70956],{},[1490,70915,70916,70918,70920,70922,70924,70926,70928,70930,70932,70938,70944,70946,70948,70950,70952,70954],{},[1493,70917,1495],{},[1493,70919,1995],{},[1506,70921,1508],{},[1506,70923,1553],{"stretchy":1552},[1680,70925,2916],{},[1493,70927,1520],{},[1506,70929,1888],{},[1680,70931,1691],{},[2315,70933,70934,70936],{},[1493,70935,1520],{},[1680,70937,1691],{},[2315,70939,70940,70942],{},[1506,70941,1564],{"stretchy":1552},[1506,70943,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,70945,1508],{},[1680,70947,2916],{},[1506,70949,1888],{},[1680,70951,4007],{},[1493,70953,1520],{},[1493,70955,2632],{"mathvariant":1516},[1528,70957,70958],{"encoding":1530},"MR = (100Q - 2Q^2)' = 100 - 4Q.",[1030,70960,2364,70961,8994,70979,71005,71006,3397,71019,71034,71035,71048,71049,37016,71062,3397,71075,71090,71091,71104,71105,71136,71137,71156],{},[1035,70962,70964],{"className":70963},[1480],[1482,70965,70966],{"xmlns":1484},[1487,70967,70968,70976],{},[1490,70969,70970,70972,70974],{},[1493,70971,1520],{},[1506,70973,1508],{},[1680,70975,9787],{},[1528,70977,70978],{"encoding":1530},"Q = 15",[1035,70980,70982],{"className":70981},[1480],[1482,70983,70984],{"xmlns":1484},[1487,70985,70986,71002],{},[1490,70987,70988,70990,70992,70994,70996,70998,71000],{},[1493,70989,1495],{},[1493,70991,1995],{},[1506,70993,1553],{"stretchy":1552},[1680,70995,9787],{},[1506,70997,1564],{"stretchy":1552},[1506,70999,1508],{},[1680,71001,7380],{},[1528,71003,71004],{"encoding":1530},"MR(15) = 40",": při množství ",[1035,71007,71009],{"className":71008},[1480],[1482,71010,71011],{"xmlns":1484},[1487,71012,71013,71017],{},[1490,71014,71015],{},[1680,71016,9787],{},[1528,71018,9787],{"encoding":1530},[1035,71020,71022],{"className":71021},[1480],[1482,71023,71024],{"xmlns":1484},[1487,71025,71026,71032],{},[1490,71027,71028,71030],{},[1493,71029,5289],{},[1493,71031,1995],{},[1528,71033,16491],{"encoding":1530}," mění asi ",[1035,71036,71038],{"className":71037},[1480],[1482,71039,71040],{"xmlns":1484},[1487,71041,71042,71046],{},[1490,71043,71044],{},[1680,71045,7380],{},[1528,71047,7380],{"encoding":1530},"-krát rychleji než množství; s růstem ",[1035,71050,71052],{"className":71051},[1480],[1482,71053,71054],{"xmlns":1484},[1487,71055,71056,71060],{},[1490,71057,71058],{},[1493,71059,1520],{},[1528,71061,1520],{"encoding":1530},[1035,71063,71065],{"className":71064},[1480],[1482,71066,71067],{"xmlns":1484},[1487,71068,71069,71073],{},[1490,71070,71071],{},[1680,71072,1682],{},[1528,71074,1682],{"encoding":1530},[1035,71076,71078],{"className":71077},[1480],[1482,71079,71080],{"xmlns":1484},[1487,71081,71082,71088],{},[1490,71083,71084,71086],{},[1493,71085,5289],{},[1493,71087,1995],{},[1528,71089,16491],{"encoding":1530}," zvýší přibližně o ",[1035,71092,71094],{"className":71093},[1480],[1482,71095,71096],{"xmlns":1484},[1487,71097,71098,71102],{},[1490,71099,71100],{},[1680,71101,7380],{},[1528,71103,7380],{"encoding":1530},", tj. ze skutečné hodnoty ",[1035,71106,71108],{"className":71107},[1480],[1482,71109,71110],{"xmlns":1484},[1487,71111,71112,71133],{},[1490,71113,71114,71116,71118,71120,71122,71124,71126,71128,71130],{},[1493,71115,5289],{},[1493,71117,1995],{},[1506,71119,1553],{"stretchy":1552},[1680,71121,9787],{},[1506,71123,1564],{"stretchy":1552},[1506,71125,1508],{},[1680,71127,1682],{},[1988,71129,5016],{},[1680,71131,71132],{},"050",[1528,71134,71135],{"encoding":1530},"TR(15) = 1\\,050"," na přibližně ",[1035,71138,71140],{"className":71139},[1480],[1482,71141,71142],{"xmlns":1484},[1487,71143,71144,71153],{},[1490,71145,71146,71148,71150],{},[1680,71147,1682],{},[1988,71149,5016],{},[1680,71151,71152],{},"090",[1528,71154,71155],{"encoding":1530},"1\\,090",". Skutečná změna je",[1035,71158,71160],{"className":71159},[1480],[1482,71161,71162],{"xmlns":1484,"display":1485},[1487,71163,71164,71218],{},[1490,71165,71166,71168,71170,71172,71174,71176,71178,71180,71182,71184,71186,71188,71190,71192,71194,71196,71198,71200,71202,71205,71207,71209,71211,71213,71215],{},[1493,71167,2976],{"mathvariant":1516},[1493,71169,5289],{},[1493,71171,1995],{},[1506,71173,1508],{},[1493,71175,5289],{},[1493,71177,1995],{},[1506,71179,1553],{"stretchy":1552},[1680,71181,9961],{},[1506,71183,1564],{"stretchy":1552},[1506,71185,1888],{},[1493,71187,5289],{},[1493,71189,1995],{},[1506,71191,1553],{"stretchy":1552},[1680,71193,9787],{},[1506,71195,1564],{"stretchy":1552},[1506,71197,1508],{},[1680,71199,1682],{},[1988,71201,5016],{},[1680,71203,71204],{},"088",[1506,71206,1888],{},[1680,71208,1682],{},[1988,71210,5016],{},[1680,71212,71132],{},[1506,71214,1508],{},[1680,71216,71217],{},"38.",[1528,71219,71220],{"encoding":1530},"\\Delta TR = TR(16) - TR(15) = 1\\,088 - 1\\,050 = 38.",[1030,71222,71223,71224,1732,71250,18367,71276,71291,71292,71307],{},"Podobně ",[1035,71225,71227],{"className":71226},[1480],[1482,71228,71229],{"xmlns":1484},[1487,71230,71231,71247],{},[1490,71232,71233,71235,71237,71239,71241,71243,71245],{},[1493,71234,1495],{},[1493,71236,1995],{},[1506,71238,1553],{"stretchy":1552},[1680,71240,9961],{},[1506,71242,1564],{"stretchy":1552},[1506,71244,1508],{},[1680,71246,14846],{},[1528,71248,71249],{"encoding":1530},"MR(16) = 36",[1035,71251,71253],{"className":71252},[1480],[1482,71254,71255],{"xmlns":1484},[1487,71256,71257,71273],{},[1490,71258,71259,71261,71263,71265,71267,71269,71271],{},[1493,71260,1495],{},[1493,71262,1995],{},[1506,71264,1553],{"stretchy":1552},[1680,71266,8436],{},[1506,71268,1564],{"stretchy":1552},[1506,71270,1508],{},[1680,71272,8436],{},[1528,71274,71275],{"encoding":1530},"MR(20) = 20",[1035,71277,71279],{"className":71278},[1480],[1482,71280,71281],{"xmlns":1484},[1487,71282,71283,71289],{},[1490,71284,71285,71287],{},[1493,71286,1495],{},[1493,71288,1995],{},[1528,71290,6258],{"encoding":1530}," je klesající funkce — rychlost změny ",[1035,71293,71295],{"className":71294},[1480],[1482,71296,71297],{"xmlns":1484},[1487,71298,71299,71305],{},[1490,71300,71301,71303],{},[1493,71302,5289],{},[1493,71304,1995],{},[1528,71306,16491],{"encoding":1530}," s růstem množství klesá.",[1304,71309,71311],{"id":71310},"odhad-změny-tr-pomocí-diferenciálu","Odhad změny TR pomocí diferenciálu",[1030,71313,71314],{},"Užitím mezního příjmu lze odhadnout změnu celkového příjmu jako odezvu na změnu množství:",[1035,71316,71318],{"className":71317},[1480],[1482,71319,71320],{"xmlns":1484,"display":1485},[1487,71321,71322,71391],{},[19617,71323,71324],{"width":19619},[19621,71325,71326,71328,71384,71386],{},[19624,71327],{"width":19626},[19624,71329,71330],{},[1490,71331,71332,71334,71336,71338,71340,71342,71344,71346,71348,71350,71352,71354,71356,71358,71364,71366,71368,71370,71372,71374,71376,71378,71380,71382],{},[1493,71333,2976],{"mathvariant":1516},[1493,71335,5289],{},[1493,71337,1995],{},[1988,71339,1990],{},[1506,71341,2343],{},[1988,71343,1990],{},[1493,71345,3384],{"mathvariant":1516},[1493,71347,5289],{},[1493,71349,1995],{},[1506,71351,1508],{},[1506,71353,1553],{"stretchy":1552},[1493,71355,5289],{},[1493,71357,1995],{},[2315,71359,71360,71362],{},[1506,71361,1564],{"stretchy":1552},[1506,71363,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1988,71365,5016],{},[1493,71367,3384],{"mathvariant":1516},[1493,71369,1520],{},[1506,71371,1508],{},[1493,71373,1495],{},[1493,71375,1995],{},[1988,71377,5016],{},[1493,71379,3384],{"mathvariant":1516},[1493,71381,1520],{},[1506,71383,1559],{"separator":1041},[19624,71385],{"width":19626},[19624,71387,71388],{},[1988,71389,71390],{},"(3.3)",[1528,71392,71393],{"encoding":1530},"\\Delta TR \\;\\approx\\; \\mathrm{d}TR = (TR)' \\, \\mathrm{d}Q = MR \\, \\mathrm{d}Q,\n\\tag{3.3}",[1030,71395,71396],{},"schematicky:",[1035,71398,71400],{"className":71399},[1480],[1482,71401,71402],{"xmlns":1484,"display":1485},[1487,71403,71404,71512],{},[1490,71405,71406,71444,71446,71448,71450,71479,71482,71510],{},[1490,71407,71408,71411,71417,71420,71426,71429,71435,71441],{},[1988,71409,71410],{},"zm",[2178,71412,71413,71415],{"accent":1041},[1988,71414,8584],{},[1506,71416,8576],{},[1988,71418,71419],{},"na celkov",[2178,71421,71422,71424],{"accent":1041},[1988,71423,8584],{},[1506,71425,3055],{},[1988,71427,71428],{},"ho p",[2178,71430,71431,71433],{"accent":1041},[1988,71432,7740],{},[1506,71434,8576],{},[2178,71436,71437,71439],{"accent":1041},[1988,71438,7095],{},[1506,71440,3055],{},[1988,71442,71443],{},"jmu",[1988,71445,1990],{},[1506,71447,2343],{},[1988,71449,1990],{},[1490,71451,71452,71455,71461,71464,71470,71476],{},[1988,71453,71454],{},"mezn",[2178,71456,71457,71459],{"accent":1041},[1988,71458,7095],{},[1506,71460,3055],{},[1988,71462,71463],{}," p",[2178,71465,71466,71468],{"accent":1041},[1988,71467,7740],{},[1506,71469,8576],{},[2178,71471,71472,71474],{"accent":1041},[1988,71473,7095],{},[1506,71475,3055],{},[1988,71477,71478],{},"jem",[1506,71480,71481],{},"×",[1490,71483,71484,71486,71492,71495,71501,71504],{},[1988,71485,71410],{},[2178,71487,71488,71490],{"accent":1041},[1988,71489,8584],{},[1506,71491,8576],{},[1988,71493,71494],{},"na mno",[2178,71496,71497,71499],{"accent":1041},[1988,71498,25931],{},[1506,71500,8576],{},[1988,71502,71503],{},"stv",[2178,71505,71506,71508],{"accent":1041},[1988,71507,7095],{},[1506,71509,3055],{},[1493,71511,2632],{"mathvariant":1516},[1528,71513,71514],{"encoding":1530},"\\text{změna celkového příjmu} \\;\\approx\\; \\text{mezní příjem} \\times \\text{změna množství}.",[1030,71516,71517,71518,71533],{},"Pro porovnání skutečná změna ",[1035,71519,71521],{"className":71520},[1480],[1482,71522,71523],{"xmlns":1484},[1487,71524,71525,71531],{},[1490,71526,71527,71529],{},[1493,71528,5289],{},[1493,71530,1995],{},[1528,71532,16491],{"encoding":1530}," je",[1035,71535,71537],{"className":71536},[1480],[1482,71538,71539],{"xmlns":1484,"display":1485},[1487,71540,71541,71596],{},[19617,71542,71543],{"width":19619},[19621,71544,71545,71547,71589,71591],{},[19624,71546],{"width":19626},[19624,71548,71549],{},[1490,71550,71551,71553,71555,71557,71559,71561,71563,71565,71567,71569,71571,71573,71575,71577,71579,71581,71583,71585,71587],{},[1493,71552,2976],{"mathvariant":1516},[1493,71554,5289],{},[1493,71556,1995],{},[1506,71558,1508],{},[1493,71560,5289],{},[1493,71562,1995],{},[1506,71564,1553],{"stretchy":1552},[1493,71566,1520],{},[1506,71568,2162],{},[1493,71570,3384],{"mathvariant":1516},[1493,71572,1520],{},[1506,71574,1564],{"stretchy":1552},[1506,71576,1888],{},[1493,71578,5289],{},[1493,71580,1995],{},[1506,71582,1553],{"stretchy":1552},[1493,71584,1520],{},[1506,71586,1564],{"stretchy":1552},[1493,71588,2632],{"mathvariant":1516},[19624,71590],{"width":19626},[19624,71592,71593],{},[1988,71594,71595],{},"(3.4)",[1528,71597,71598],{"encoding":1530},"\\Delta TR = TR(Q + \\mathrm{d}Q) - TR(Q).\n\\tag{3.4}",[52452,71600,71602],{"id":71601},"příklad-33","Příklad 3.3",[1030,71604,71605,8686,71607,71637,71638,18111,71653,18125,71666,18139,71679,71693],{},[1047,71606,70164],{},[1035,71608,71610],{"className":71609},[1480],[1482,71611,71612],{"xmlns":1484},[1487,71613,71614,71634],{},[1490,71615,71616,71618,71620,71622,71624,71626,71628],{},[1493,71617,5289],{},[1493,71619,1995],{},[1506,71621,1508],{},[1680,71623,2916],{},[1493,71625,1520],{},[1506,71627,1888],{},[2315,71629,71630,71632],{},[1493,71631,1520],{},[1680,71633,1691],{},[1528,71635,71636],{"encoding":1530},"TR = 100Q - Q^2"," odhadněte změnu ",[1035,71639,71641],{"className":71640},[1480],[1482,71642,71643],{"xmlns":1484},[1487,71644,71645,71651],{},[1490,71646,71647,71649],{},[1493,71648,5289],{},[1493,71650,1995],{},[1528,71652,16491],{"encoding":1530},[1035,71654,71656],{"className":71655},[1480],[1482,71657,71658],{"xmlns":1484},[1487,71659,71660,71664],{},[1490,71661,71662],{},[1493,71663,1520],{},[1528,71665,1520],{"encoding":1530},[1035,71667,71669],{"className":71668},[1480],[1482,71670,71671],{"xmlns":1484},[1487,71672,71673,71677],{},[1490,71674,71675],{},[1680,71676,4965],{},[1528,71678,4965],{"encoding":1530},[1035,71680,71682],{"className":71681},[1480],[1482,71683,71684],{"xmlns":1484},[1487,71685,71686,71691],{},[1490,71687,71688],{},[1680,71689,71690],{},"63",[1528,71692,71690],{"encoding":1530}," a porovnejte se skutečnou změnou.",[1030,71695,71696,1656,71698,71723,71724,1732,71742,1274],{},[1047,71697,38365],{},[1035,71699,71701],{"className":71700},[1480],[1482,71702,71703],{"xmlns":1484},[1487,71704,71705,71721],{},[1490,71706,71707,71709,71711,71713,71715,71717,71719],{},[1493,71708,1495],{},[1493,71710,1995],{},[1506,71712,1508],{},[1680,71714,2916],{},[1506,71716,1888],{},[1680,71718,1691],{},[1493,71720,1520],{},[1528,71722,27941],{"encoding":1530},", tedy při ",[1035,71725,71727],{"className":71726},[1480],[1482,71728,71729],{"xmlns":1484},[1487,71730,71731,71739],{},[1490,71732,71733,71735,71737],{},[1493,71734,1520],{},[1506,71736,1508],{},[1680,71738,4965],{},[1528,71740,71741],{"encoding":1530},"Q = 60",[1035,71743,71745],{"className":71744},[1480],[1482,71746,71747],{"xmlns":1484},[1487,71748,71749,71759],{},[1490,71750,71751,71753,71755,71757],{},[1493,71752,3384],{"mathvariant":1516},[1493,71754,1520],{},[1506,71756,1508],{},[1680,71758,3201],{},[1528,71760,71761],{"encoding":1530},"\\mathrm{d}Q = 3",[1035,71763,71765],{"className":71764},[1480],[1482,71766,71767],{"xmlns":1484,"display":1485},[1487,71768,71769,71800],{},[1490,71770,71771,71773,71775,71777,71779,71781,71783,71785,71787,71789,71791,71793,71795,71797],{},[1493,71772,3384],{"mathvariant":1516},[1493,71774,5289],{},[1493,71776,1995],{},[1506,71778,1508],{},[1506,71780,1553],{"stretchy":1552},[1680,71782,2916],{},[1506,71784,1888],{},[1680,71786,10797],{},[1506,71788,1564],{"stretchy":1552},[1506,71790,1714],{},[1680,71792,3201],{},[1506,71794,1508],{},[1506,71796,1888],{},[1680,71798,71799],{},"60.",[1528,71801,71802],{"encoding":1530},"\\mathrm{d}TR = (100 - 120) \\cdot 3 = -60.",[1030,71804,71805,71806,71836,71837,71856],{},"Celkový příjem klesne z ",[1035,71807,71809],{"className":71808},[1480],[1482,71810,71811],{"xmlns":1484},[1487,71812,71813,71833],{},[1490,71814,71815,71817,71819,71821,71823,71825,71827,71829,71831],{},[1493,71816,5289],{},[1493,71818,1995],{},[1506,71820,1553],{"stretchy":1552},[1680,71822,4965],{},[1506,71824,1564],{"stretchy":1552},[1506,71826,1508],{},[1680,71828,1691],{},[1988,71830,5016],{},[1680,71832,5765],{},[1528,71834,71835],{"encoding":1530},"TR(60) = 2\\,400"," přibližně na ",[1035,71838,71840],{"className":71839},[1480],[1482,71841,71842],{"xmlns":1484},[1487,71843,71844,71853],{},[1490,71845,71846,71848,71850],{},[1680,71847,1691],{},[1988,71849,5016],{},[1680,71851,71852],{},"340",[1528,71854,71855],{"encoding":1530},"2\\,340",". Skutečná změna dle (3.4):",[1035,71858,71860],{"className":71859},[1480],[1482,71861,71862],{"xmlns":1484,"display":1485},[1487,71863,71864,71922],{},[1490,71865,71866,71868,71870,71872,71874,71876,71878,71880,71882,71884,71886,71888,71890,71892,71894,71896,71898,71900,71902,71905,71907,71909,71911,71913,71915,71917,71920],{},[1493,71867,2976],{"mathvariant":1516},[1493,71869,5289],{},[1493,71871,1995],{},[1506,71873,1508],{},[1493,71875,5289],{},[1493,71877,1995],{},[1506,71879,1553],{"stretchy":1552},[1680,71881,71690],{},[1506,71883,1564],{"stretchy":1552},[1506,71885,1888],{},[1493,71887,5289],{},[1493,71889,1995],{},[1506,71891,1553],{"stretchy":1552},[1680,71893,4965],{},[1506,71895,1564],{"stretchy":1552},[1506,71897,1508],{},[1680,71899,1691],{},[1988,71901,5016],{},[1680,71903,71904],{},"331",[1506,71906,1888],{},[1680,71908,1691],{},[1988,71910,5016],{},[1680,71912,5765],{},[1506,71914,1508],{},[1506,71916,1888],{},[1680,71918,71919],{},"69",[1506,71921,1559],{"separator":1041},[1528,71923,71924],{"encoding":1530},"\\Delta TR = TR(63) - TR(60) = 2\\,331 - 2\\,400 = -69,",[1030,71926,71927,71928,71943,71944,2632],{},"tj. ",[1035,71929,71931],{"className":71930},[1480],[1482,71932,71933],{"xmlns":1484},[1487,71934,71935,71941],{},[1490,71936,71937,71939],{},[1493,71938,5289],{},[1493,71940,1995],{},[1528,71942,16491],{"encoding":1530}," klesne na ",[1035,71945,71947],{"className":71946},[1480],[1482,71948,71949],{"xmlns":1484},[1487,71950,71951,71959],{},[1490,71952,71953,71955,71957],{},[1680,71954,1691],{},[1988,71956,5016],{},[1680,71958,71904],{},[1528,71960,71961],{"encoding":1530},"2\\,331",[1304,71963,71965],{"id":71964},"vztah-ar-a-mr-pro-lineární-poptávku","Vztah AR a MR pro lineární poptávku",[1030,71967,71968,71969,26918,71992,46682],{},"Obecně pro lineární poptávku ",[1035,71970,71972],{"className":71971},[1480],[1482,71973,71974],{"xmlns":1484},[1487,71975,71976,71990],{},[1490,71977,71978,71980,71982,71984,71986,71988],{},[1493,71979,1501],{},[1506,71981,1508],{},[1493,71983,1052],{},[1493,71985,1520],{},[1506,71987,2162],{},[1493,71989,2394],{},[1528,71991,52158],{"encoding":1530},[1035,71993,71995],{"className":71994},[1480],[1482,71996,71997],{"xmlns":1484},[1487,71998,71999,72021],{},[1490,72000,72001,72003,72005,72007,72009,72015,72017,72019],{},[1493,72002,5289],{},[1493,72004,1995],{},[1506,72006,1508],{},[1493,72008,1052],{},[2315,72010,72011,72013],{},[1493,72012,1520],{},[1680,72014,1691],{},[1506,72016,2162],{},[1493,72018,2394],{},[1493,72020,1520],{},[1528,72022,72023],{"encoding":1530},"TR = aQ^2 + bQ",[1035,72025,72027],{"className":72026},[1480],[1482,72028,72029],{"xmlns":1484,"display":1485},[1487,72030,72031,72051],{},[1490,72032,72033,72035,72037,72039,72041,72043,72045,72047,72049],{},[1493,72034,1495],{},[1493,72036,1995],{},[1506,72038,1508],{},[1680,72040,1691],{},[1493,72042,1052],{},[1493,72044,1520],{},[1506,72046,2162],{},[1493,72048,2394],{},[1493,72050,2632],{"mathvariant":1516},[1528,72052,72053],{"encoding":1530},"MR = 2aQ + b.",[1030,72055,72056,72057,72072,72073,72088,72089,72102,72103,7606,72106,72122,72123,34272,72136,72151,72152,72167,72168,72183,72184,11713,72197,72227,72228,72247,72248,72263],{},"Křivky ",[1035,72058,72060],{"className":72059},[1480],[1482,72061,72062],{"xmlns":1484},[1487,72063,72064,72070],{},[1490,72065,72066,72068],{},[1493,72067,1495],{},[1493,72069,1995],{},[1528,72071,6258],{"encoding":1530}," a poptávky (resp. ",[1035,72074,72076],{"className":72075},[1480],[1482,72077,72078],{"xmlns":1484},[1487,72079,72080,72086],{},[1490,72081,72082,72084],{},[1493,72083,3633],{},[1493,72085,1995],{},[1528,72087,69623],{"encoding":1530},") jsou přímky protínající svislou osu v témže bodě ",[1035,72090,72092],{"className":72091},[1480],[1482,72093,72094],{"xmlns":1484},[1487,72095,72096,72100],{},[1490,72097,72098],{},[1493,72099,2394],{},[1528,72101,2394],{"encoding":1530},", přičemž ",[1047,72104,72105],{},"přímka mezního příjmu má sklon rovný dvojnásobku sklonu přímky poptávky",[1035,72107,72109],{"className":72108},[1480],[1482,72110,72111],{"xmlns":1484},[1487,72112,72113,72119],{},[1490,72114,72115,72117],{},[1680,72116,1691],{},[1493,72118,1052],{},[1528,72120,72121],{"encoding":1530},"2a"," vs. ",[1035,72124,72126],{"className":72125},[1480],[1482,72127,72128],{"xmlns":1484},[1487,72129,72130,72134],{},[1490,72131,72132],{},[1493,72133,1052],{},[1528,72135,1052],{"encoding":1530},[1035,72137,72139],{"className":72138},[1480],[1482,72140,72141],{"xmlns":1484},[1487,72142,72143,72149],{},[1490,72144,72145,72147],{},[1493,72146,1495],{},[1493,72148,1995],{},[1528,72150,6258],{"encoding":1530}," nabývá jak kladných, tak záporných hodnot; křivka ",[1035,72153,72155],{"className":72154},[1480],[1482,72156,72157],{"xmlns":1484},[1487,72158,72159,72165],{},[1490,72160,72161,72163],{},[1493,72162,5289],{},[1493,72164,1995],{},[1528,72166,16491],{"encoding":1530}," nejprve roste, v bodě maxima protíná ",[1035,72169,72171],{"className":72170},[1480],[1482,72172,72173],{"xmlns":1484},[1487,72174,72175,72181],{},[1490,72176,72177,72179],{},[1493,72178,1495],{},[1493,72180,1995],{},[1528,72182,6258],{"encoding":1530}," osu ",[1035,72185,72187],{"className":72186},[1480],[1482,72188,72189],{"xmlns":1484},[1487,72190,72191,72195],{},[1490,72192,72193],{},[1493,72194,1520],{},[1528,72196,1520],{"encoding":1530},[1035,72198,72200],{"className":72199},[1480],[1482,72201,72202],{"xmlns":1484},[1487,72203,72204,72224],{},[1490,72205,72206,72208,72210,72212],{},[1493,72207,1520],{},[1506,72209,1508],{},[1506,72211,1888],{},[1869,72213,72214],{"scriptlevel":1871,"displaystyle":1552},[1510,72215,72216,72218],{},[1493,72217,2394],{},[1490,72219,72220,72222],{},[1680,72221,1691],{},[1493,72223,1052],{},[1528,72225,72226],{"encoding":1530},"Q = -\\tfrac{b}{2a}"," hodnotou ",[1035,72229,72231],{"className":72230},[1480],[1482,72232,72233],{"xmlns":1484},[1487,72234,72235,72245],{},[1490,72236,72237,72239,72241,72243],{},[1493,72238,1495],{},[1493,72240,1995],{},[1506,72242,1508],{},[1680,72244,1871],{},[1528,72246,11073],{"encoding":1530},", a dále ",[1035,72249,72251],{"className":72250},[1480],[1482,72252,72253],{"xmlns":1484},[1487,72254,72255,72261],{},[1490,72256,72257,72259],{},[1493,72258,5289],{},[1493,72260,1995],{},[1528,72262,16491],{"encoding":1530}," klesá.",[1030,72265,72266,72267,72273,72274,72306,72307,72335],{},"V případě ",[1047,72268,72269],{},[1052,72270,72272],{"className":72271,"dataFsResolvedFilePath":3487,"href":3488},[1055],"dokonalé konkurence",", kdy poptávka ",[1035,72275,72277],{"className":72276},[1480],[1482,72278,72279],{"xmlns":1484},[1487,72280,72281,72303],{},[1490,72282,72283,72285,72287,72289,72291,72293,72295,72297],{},[1493,72284,1501],{},[1506,72286,1508],{},[1493,72288,3712],{},[1506,72290,1553],{"stretchy":1552},[1493,72292,1520],{},[1506,72294,1564],{"stretchy":1552},[1506,72296,1508],{},[2315,72298,72299,72301],{},[1493,72300,1501],{},[1506,72302,2287],{},[1528,72304,72305],{"encoding":1530},"P = D(Q) = P^*"," je pevná tržní cena, platí ",[1035,72308,72310],{"className":72309},[1480],[1482,72311,72312],{"xmlns":1484},[1487,72313,72314,72332],{},[1490,72315,72316,72318,72320,72322,72324,72326],{},[1493,72317,5289],{},[1493,72319,1995],{},[1506,72321,1508],{},[1493,72323,1520],{},[1506,72325,1714],{},[2315,72327,72328,72330],{},[1493,72329,1501],{},[1506,72331,2287],{},[1528,72333,72334],{"encoding":1530},"TR = Q \\cdot P^*"," a tedy",[1035,72337,72339],{"className":72338},[1480],[1482,72340,72341],{"xmlns":1484,"display":1485},[1487,72342,72343,72365],{},[1490,72344,72345,72347,72349,72351,72353,72355,72357,72363],{},[1493,72346,1495],{},[1493,72348,1995],{},[1506,72350,1508],{},[1493,72352,3633],{},[1493,72354,1995],{},[1506,72356,1508],{},[2315,72358,72359,72361],{},[1493,72360,1501],{},[1506,72362,2287],{},[1493,72364,2632],{"mathvariant":1516},[1528,72366,72367],{"encoding":1530},"MR = AR = P^*.",[1065,72369,72371],{"id":72370},"náklady-firmy","Náklady firmy",[1304,72373,72375],{"id":72374},"celkové-náklady","Celkové náklady",[1030,72377,72378,1656,72380,7606,72395,72398,72399,72412],{},[1047,72379,72375],{},[1035,72381,72383],{"className":72382},[1480],[1482,72384,72385],{"xmlns":1484},[1487,72386,72387,72393],{},[1490,72388,72389,72391],{},[1493,72390,5289],{},[1493,72392,1998],{},[1528,72394,18668],{"encoding":1530},[1047,72396,72397],{},"total cost",") jsou veškeré náklady na realizaci ",[1035,72400,72402],{"className":72401},[1480],[1482,72403,72404],{"xmlns":1484},[1487,72405,72406,72410],{},[1490,72407,72408],{},[1493,72409,1520],{},[1528,72411,1520],{"encoding":1530}," jednotek produkce:",[1035,72414,72416],{"className":72415},[1480],[1482,72417,72418],{"xmlns":1484,"display":1485},[1487,72419,72420,72475],{},[19617,72421,72422],{"width":19619},[19621,72423,72424,72426,72468,72470],{},[19624,72425],{"width":19626},[19624,72427,72428],{},[1490,72429,72430,72432,72434,72436,72438,72440,72442,72444,72446,72448,72450,72452,72454,72456,72458,72460,72462,72464,72466],{},[1493,72431,5289],{},[1493,72433,1998],{},[1506,72435,1508],{},[1493,72437,5289],{},[1493,72439,1998],{},[1506,72441,1553],{"stretchy":1552},[1493,72443,1520],{},[1506,72445,1564],{"stretchy":1552},[1506,72447,1508],{},[1493,72449,10790],{},[1493,72451,1998],{},[1506,72453,2162],{},[1493,72455,5289],{},[1493,72457,55105],{},[1493,72459,1998],{},[1506,72461,1553],{"stretchy":1552},[1493,72463,1520],{},[1506,72465,1564],{"stretchy":1552},[1506,72467,1559],{"separator":1041},[19624,72469],{"width":19626},[19624,72471,72472],{},[1988,72473,72474],{},"(3.5)",[1528,72476,72477],{"encoding":1530},"TC = TC(Q) = FC + TVC(Q),\n\\tag{3.5}",[1030,72479,20022,72480,72495,72496,7606,72499,28611,72502,72495,72526,7606,72529,72532],{},[1035,72481,72483],{"className":72482},[1480],[1482,72484,72485],{"xmlns":1484},[1487,72486,72487,72493],{},[1490,72488,72489,72491],{},[1493,72490,10790],{},[1493,72492,1998],{},[1528,72494,69669],{"encoding":1530}," jsou ",[1047,72497,72498],{},"fixní náklady",[1047,72500,72501],{},"fixed cost",[1035,72503,72505],{"className":72504},[1480],[1482,72506,72507],{"xmlns":1484},[1487,72508,72509,72523],{},[1490,72510,72511,72513,72515,72517,72519,72521],{},[1493,72512,5289],{},[1493,72514,55105],{},[1493,72516,1998],{},[1506,72518,1553],{"stretchy":1552},[1493,72520,1520],{},[1506,72522,1564],{"stretchy":1552},[1528,72524,72525],{"encoding":1530},"TVC(Q)",[1047,72527,72528],{},"celkové variabilní náklady",[1047,72530,72531],{},"total variable cost","). Celkové náklady jsou rostoucí, neboť růst množství objektivně vynutí jejich růst.",[1304,72534,72536],{"id":72535},"průměrné-náklady","Průměrné náklady",[1030,72538,72539,1656,72541,7606,72556,72559],{},[1047,72540,72536],{},[1035,72542,72544],{"className":72543},[1480],[1482,72545,72546],{"xmlns":1484},[1487,72547,72548,72554],{},[1490,72549,72550,72552],{},[1493,72551,3633],{},[1493,72553,1998],{},[1528,72555,16523],{"encoding":1530},[1047,72557,72558],{},"average cost",") jsou podíl celkových nákladů a množství. Z (3.5):",[1035,72561,72563],{"className":72562},[1480],[1482,72564,72565],{"xmlns":1484,"display":1485},[1487,72566,72567,72646],{},[19617,72568,72569],{"width":19619},[19621,72570,72571,72573,72639,72641],{},[19624,72572],{"width":19626},[19624,72574,72575],{},[1490,72576,72577,72579,72581,72583,72585,72587,72589,72591,72593,72595,72605,72607,72617,72619,72637],{},[1493,72578,3633],{},[1493,72580,1998],{},[1506,72582,1508],{},[1493,72584,3633],{},[1493,72586,1998],{},[1506,72588,1553],{"stretchy":1552},[1493,72590,1520],{},[1506,72592,1564],{"stretchy":1552},[1506,72594,1508],{},[1510,72596,72597,72603],{},[1490,72598,72599,72601],{},[1493,72600,5289],{},[1493,72602,1998],{},[1493,72604,1520],{},[1506,72606,1508],{},[1510,72608,72609,72615],{},[1490,72610,72611,72613],{},[1493,72612,10790],{},[1493,72614,1998],{},[1493,72616,1520],{},[1506,72618,2162],{},[1510,72620,72621,72635],{},[1490,72622,72623,72625,72627,72629,72631,72633],{},[1493,72624,5289],{},[1493,72626,55105],{},[1493,72628,1998],{},[1506,72630,1553],{"stretchy":1552},[1493,72632,1520],{},[1506,72634,1564],{"stretchy":1552},[1493,72636,1520],{},[1506,72638,1559],{"separator":1041},[19624,72640],{"width":19626},[19624,72642,72643],{},[1988,72644,72645],{},"(3.6)",[1528,72647,72648],{"encoding":1530},"AC = AC(Q) = \\frac{TC}{Q} = \\frac{FC}{Q} + \\frac{TVC(Q)}{Q},\n\\tag{3.6}",[1030,72650,20022,72651,72495,72675,1656,72678,7606,72695,28611,72698,72495,72730,1656,72733,7606,72750,18579],{},[1035,72652,72654],{"className":72653},[1480],[1482,72655,72656],{"xmlns":1484},[1487,72657,72658,72672],{},[1490,72659,72660],{},[1869,72661,72662],{"scriptlevel":1871,"displaystyle":1552},[1510,72663,72664,72670],{},[1490,72665,72666,72668],{},[1493,72667,10790],{},[1493,72669,1998],{},[1493,72671,1520],{},[1528,72673,72674],{"encoding":1530},"\\tfrac{FC}{Q}",[1047,72676,72677],{},"průměrné fixní náklady",[1035,72679,72681],{"className":72680},[1480],[1482,72682,72683],{"xmlns":1484},[1487,72684,72685,72693],{},[1490,72686,72687,72689,72691],{},[1493,72688,3633],{},[1493,72690,10790],{},[1493,72692,1998],{},[1528,72694,69705],{"encoding":1530},[1047,72696,72697],{},"average fixed cost",[1035,72699,72701],{"className":72700},[1480],[1482,72702,72703],{"xmlns":1484},[1487,72704,72705,72727],{},[1490,72706,72707],{},[1869,72708,72709],{"scriptlevel":1871,"displaystyle":1552},[1510,72710,72711,72725],{},[1490,72712,72713,72715,72717,72719,72721,72723],{},[1493,72714,5289],{},[1493,72716,55105],{},[1493,72718,1998],{},[1506,72720,1553],{"stretchy":1552},[1493,72722,1520],{},[1506,72724,1564],{"stretchy":1552},[1493,72726,1520],{},[1528,72728,72729],{"encoding":1530},"\\tfrac{TVC(Q)}{Q}",[1047,72731,72732],{},"průměrné variabilní náklady",[1035,72734,72736],{"className":72735},[1480],[1482,72737,72738],{"xmlns":1484},[1487,72739,72740,72748],{},[1490,72741,72742,72744,72746],{},[1493,72743,3633],{},[1493,72745,55105],{},[1493,72747,1998],{},[1528,72749,69489],{"encoding":1530},[1047,72751,72752],{},"average variable cost",[1035,72754,72756],{"className":72755},[1480],[1482,72757,72758],{"xmlns":1484,"display":1485},[1487,72759,72760,72819],{},[19617,72761,72762],{"width":19619},[19621,72763,72764,72766,72812,72814],{},[19624,72765],{"width":19626},[19624,72767,72768],{},[1490,72769,72770,72772,72774,72776,72778,72780,72782,72784,72786,72788,72790,72792,72810],{},[1493,72771,3633],{},[1493,72773,55105],{},[1493,72775,1998],{},[1506,72777,1508],{},[1493,72779,3633],{},[1493,72781,55105],{},[1493,72783,1998],{},[1506,72785,1553],{"stretchy":1552},[1493,72787,1520],{},[1506,72789,1564],{"stretchy":1552},[1506,72791,1508],{},[1510,72793,72794,72808],{},[1490,72795,72796,72798,72800,72802,72804,72806],{},[1493,72797,5289],{},[1493,72799,55105],{},[1493,72801,1998],{},[1506,72803,1553],{"stretchy":1552},[1493,72805,1520],{},[1506,72807,1564],{"stretchy":1552},[1493,72809,1520],{},[1493,72811,2632],{"mathvariant":1516},[19624,72813],{"width":19626},[19624,72815,72816],{},[1988,72817,72818],{},"(3.7)",[1528,72820,72821],{"encoding":1530},"AVC = AVC(Q) = \\frac{TVC(Q)}{Q}.\n\\tag{3.7}",[52452,72823,72825],{"id":72824},"příklad-34","Příklad 3.4",[1030,72827,72828,8686,72830,1586,72854,70202,72878,1586,72893,72908,72909,2632],{},[1047,72829,70164],{},[1035,72831,72833],{"className":72832},[1480],[1482,72834,72835],{"xmlns":1484},[1487,72836,72837,72851],{},[1490,72838,72839,72841,72843,72845,72847,72849],{},[1493,72840,10790],{},[1493,72842,1998],{},[1506,72844,1508],{},[1680,72846,1682],{},[1988,72848,5016],{},[1680,72850,5608],{},[1528,72852,72853],{"encoding":1530},"FC = 1\\,000",[1035,72855,72857],{"className":72856},[1480],[1482,72858,72859],{"xmlns":1484},[1487,72860,72861,72875],{},[1490,72862,72863,72865,72867,72869,72871,72873],{},[1493,72864,5289],{},[1493,72866,55105],{},[1493,72868,1998],{},[1506,72870,1508],{},[1680,72872,4007],{},[1493,72874,1520],{},[1528,72876,72877],{"encoding":1530},"TVC = 4Q",[1035,72879,72881],{"className":72880},[1480],[1482,72882,72883],{"xmlns":1484},[1487,72884,72885,72891],{},[1490,72886,72887,72889],{},[1493,72888,5289],{},[1493,72890,1998],{},[1528,72892,18668],{"encoding":1530},[1035,72894,72896],{"className":72895},[1480],[1482,72897,72898],{"xmlns":1484},[1487,72899,72900,72906],{},[1490,72901,72902,72904],{},[1493,72903,3633],{},[1493,72905,1998],{},[1528,72907,16523],{"encoding":1530}," a jejich chování s rostoucím ",[1035,72910,72912],{"className":72911},[1480],[1482,72913,72914],{"xmlns":1484},[1487,72915,72916,72920],{},[1490,72917,72918],{},[1493,72919,1520],{},[1528,72921,1520],{"encoding":1530},[1030,72923,72924,1656,72926,1586,72956,72992,72993,3397,73006,73021,73022,1274],{},[1047,72925,38365],{},[1035,72927,72929],{"className":72928},[1480],[1482,72930,72931],{"xmlns":1484},[1487,72932,72933,72953],{},[1490,72934,72935,72937,72939,72941,72943,72945,72947,72949,72951],{},[1493,72936,5289],{},[1493,72938,1998],{},[1506,72940,1508],{},[1680,72942,1682],{},[1988,72944,5016],{},[1680,72946,5608],{},[1506,72948,2162],{},[1680,72950,4007],{},[1493,72952,1520],{},[1528,72954,72955],{"encoding":1530},"TC = 1\\,000 + 4Q",[1035,72957,72959],{"className":72958},[1480],[1482,72960,72961],{"xmlns":1484},[1487,72962,72963,72989],{},[1490,72964,72965,72967,72969,72971,72985,72987],{},[1493,72966,3633],{},[1493,72968,1998],{},[1506,72970,1508],{},[1869,72972,72973],{"scriptlevel":1871,"displaystyle":1552},[1510,72974,72975,72983],{},[1490,72976,72977,72979,72981],{},[1680,72978,1682],{},[1988,72980,5016],{},[1680,72982,5608],{},[1493,72984,1520],{},[1506,72986,2162],{},[1680,72988,4007],{},[1528,72990,72991],{"encoding":1530},"AC = \\tfrac{1\\,000}{Q} + 4",". S rostoucím ",[1035,72994,72996],{"className":72995},[1480],[1482,72997,72998],{"xmlns":1484},[1487,72999,73000,73004],{},[1490,73001,73002],{},[1493,73003,1520],{},[1528,73005,1520],{"encoding":1530},[1035,73007,73009],{"className":73008},[1480],[1482,73010,73011],{"xmlns":1484},[1487,73012,73013,73019],{},[1490,73014,73015,73017],{},[1493,73016,3633],{},[1493,73018,1998],{},[1528,73020,16523],{"encoding":1530}," blíží ",[1035,73023,73025],{"className":73024},[1480],[1482,73026,73027],{"xmlns":1484},[1487,73028,73029,73033],{},[1490,73030,73031],{},[1680,73032,4007],{},[1528,73034,4007],{"encoding":1530},[1035,73036,73038],{"className":73037},[1480],[1482,73039,73040],{"xmlns":1484,"display":1485},[1487,73041,73042,73088],{},[1490,73043,73044,73061,73083,73085],{},[3151,73045,73046,73053],{},[1490,73047,73048,73051],{},[1493,73049,73050],{},"lim",[1506,73052,7574],{},[1490,73054,73055,73057,73059],{},[1493,73056,1520],{},[1506,73058,6380],{},[1493,73060,6383],{"mathvariant":1516},[1490,73062,73063,73065,73077,73079,73081],{},[1506,73064,1553],{"fence":1041},[1510,73066,73067,73075],{},[1490,73068,73069,73071,73073],{},[1680,73070,1682],{},[1988,73072,5016],{},[1680,73074,5608],{},[1493,73076,1520],{},[1506,73078,2162],{},[1680,73080,4007],{},[1506,73082,1564],{"fence":1041},[1506,73084,1508],{},[1680,73086,73087],{},"4.",[1528,73089,73090],{"encoding":1530},"\\lim_{Q \\to \\infty} \\left( \\frac{1\\,000}{Q} + 4 \\right) = 4.",[1030,73092,73093,73131,73132,2632],{},[1035,73094,73096],{"className":73095},[1480],[1482,73097,73098],{"xmlns":1484},[1487,73099,73100,73128],{},[1490,73101,73102,73104,73106,73108,73110,73124,73126],{},[1493,73103,3633],{},[1493,73105,10790],{},[1493,73107,1998],{},[1506,73109,1508],{},[1869,73111,73112],{"scriptlevel":1871,"displaystyle":1552},[1510,73113,73114,73122],{},[1490,73115,73116,73118,73120],{},[1680,73117,1682],{},[1988,73119,5016],{},[1680,73121,5608],{},[1493,73123,1520],{},[1506,73125,6380],{},[1680,73127,1871],{},[1528,73129,73130],{"encoding":1530},"AFC = \\tfrac{1\\,000}{Q} \\to 0"," s rostoucím ",[1035,73133,73135],{"className":73134},[1480],[1482,73136,73137],{"xmlns":1484},[1487,73138,73139,73143],{},[1490,73140,73141],{},[1493,73142,1520],{},[1528,73144,1520],{"encoding":1530},[1030,73146,73147],{},"Celkové variabilní náklady lze často vyjádřit ve tvaru",[1035,73149,73151],{"className":73150},[1480],[1482,73152,73153],{"xmlns":1484,"display":1485},[1487,73154,73155,73181],{},[1490,73156,73157,73159,73161,73163,73165,73167,73169,73171,73173,73175,73177,73179],{},[1493,73158,5289],{},[1493,73160,55105],{},[1493,73162,1998],{},[1506,73164,1508],{},[1493,73166,1520],{},[1506,73168,1714],{},[1493,73170,55105],{},[1493,73172,1998],{},[1506,73174,1553],{"stretchy":1552},[1493,73176,1520],{},[1506,73178,1564],{"stretchy":1552},[1506,73180,1559],{"separator":1041},[1528,73182,73183],{"encoding":1530},"TVC = Q \\cdot VC(Q),",[1030,73185,20022,73186,72495,73214,73217,73218,73248],{},[1035,73187,73189],{"className":73188},[1480],[1482,73190,73191],{"xmlns":1484},[1487,73192,73193,73211],{},[1490,73194,73195,73197,73199,73201,73203,73205,73207,73209],{},[1493,73196,55105],{},[1493,73198,1998],{},[1506,73200,1508],{},[1493,73202,55105],{},[1493,73204,1998],{},[1506,73206,1553],{"stretchy":1552},[1493,73208,1520],{},[1506,73210,1564],{"stretchy":1552},[1528,73212,73213],{"encoding":1530},"VC = VC(Q)",[1047,73215,73216],{},"variabilní náklady na jednotku množství",". Jsou-li konstantní, ",[1035,73219,73221],{"className":73220},[1480],[1482,73222,73223],{"xmlns":1484},[1487,73224,73225,73245],{},[1490,73226,73227,73229,73231,73233,73235,73237,73239,73241,73243],{},[1493,73228,5289],{},[1493,73230,55105],{},[1493,73232,1998],{},[1506,73234,1553],{"stretchy":1552},[1493,73236,1520],{},[1506,73238,1564],{"stretchy":1552},[1506,73240,1508],{},[1493,73242,1052],{},[1493,73244,1520],{},[1528,73246,73247],{"encoding":1530},"TVC(Q) = aQ"," a nejjednodušší model nákladů má tvar",[1035,73250,73252],{"className":73251},[1480],[1482,73253,73254],{"xmlns":1484,"display":1485},[1487,73255,73256,73276],{},[1490,73257,73258,73260,73262,73264,73266,73268,73270,73272,73274],{},[1493,73259,5289],{},[1493,73261,1998],{},[1506,73263,1508],{},[1493,73265,10790],{},[1493,73267,1998],{},[1506,73269,2162],{},[1493,73271,1052],{},[1493,73273,1520],{},[1493,73275,2632],{"mathvariant":1516},[1528,73277,73278],{"encoding":1530},"TC = FC + aQ.",[1030,73280,73281,73282,73297,73298,73313,73314,73337,73338,73372,73373,73386,73387,73400,73401,1586,73449,73493,73494,2632],{},"Křivkou ",[1035,73283,73285],{"className":73284},[1480],[1482,73286,73287],{"xmlns":1484},[1487,73288,73289,73295],{},[1490,73290,73291,73293],{},[1493,73292,5289],{},[1493,73294,1998],{},[1528,73296,18668],{"encoding":1530}," je přímka se svislým průsečíkem ",[1035,73299,73301],{"className":73300},[1480],[1482,73302,73303],{"xmlns":1484},[1487,73304,73305,73311],{},[1490,73306,73307,73309],{},[1493,73308,10790],{},[1493,73310,1998],{},[1528,73312,69669],{"encoding":1530}," a sklonem ",[1035,73315,73317],{"className":73316},[1480],[1482,73318,73319],{"xmlns":1484},[1487,73320,73321,73334],{},[1490,73322,73323,73326,73328,73330,73332],{},[1493,73324,73325],{},"tan",[1506,73327,7574],{},[1493,73329,34997],{},[1506,73331,1508],{},[1493,73333,1052],{},[1528,73335,73336],{"encoding":1530},"\\tan\\alpha = a",". Průměrné náklady tvoří hyperbolu ",[1035,73339,73341],{"className":73340},[1480],[1482,73342,73343],{"xmlns":1484},[1487,73344,73345,73369],{},[1490,73346,73347,73349,73351,73353,73365,73367],{},[1493,73348,3633],{},[1493,73350,1998],{},[1506,73352,1508],{},[1869,73354,73355],{"scriptlevel":1871,"displaystyle":1552},[1510,73356,73357,73363],{},[1490,73358,73359,73361],{},[1493,73360,10790],{},[1493,73362,1998],{},[1493,73364,1520],{},[1506,73366,2162],{},[1493,73368,1052],{},[1528,73370,73371],{"encoding":1530},"AC = \\tfrac{FC}{Q} + a"," tvaru ",[1035,73374,73376],{"className":73375},[1480],[1482,73377,73378],{"xmlns":1484},[1487,73379,73380,73384],{},[1490,73381,73382],{},[1493,73383,1556],{},[1528,73385,1556],{"encoding":1530}," s vodorovnou asymptotou ",[1035,73388,73390],{"className":73389},[1480],[1482,73391,73392],{"xmlns":1484},[1487,73393,73394,73398],{},[1490,73395,73396],{},[1493,73397,1052],{},[1528,73399,1052],{"encoding":1530},". Limity ",[1035,73402,73404],{"className":73403},[1480],[1482,73405,73406],{"xmlns":1484},[1487,73407,73408,73446],{},[1490,73409,73410,73430,73442,73444],{},[1497,73411,73412,73418],{},[1490,73413,73414,73416],{},[1493,73415,73050],{},[1506,73417,7574],{},[1490,73419,73420,73422,73424],{},[1493,73421,1520],{},[1506,73423,6380],{},[2315,73425,73426,73428],{},[1680,73427,1871],{},[1506,73429,2162],{},[1869,73431,73432],{"scriptlevel":1871,"displaystyle":1552},[1510,73433,73434,73440],{},[1490,73435,73436,73438],{},[1493,73437,10790],{},[1493,73439,1998],{},[1493,73441,1520],{},[1506,73443,1508],{},[1493,73445,6383],{"mathvariant":1516},[1528,73447,73448],{"encoding":1530},"\\lim_{Q \\to 0^+} \\tfrac{FC}{Q} = \\infty",[1035,73450,73452],{"className":73451},[1480],[1482,73453,73454],{"xmlns":1484},[1487,73455,73456,73490],{},[1490,73457,73458,73474,73486,73488],{},[1497,73459,73460,73466],{},[1490,73461,73462,73464],{},[1493,73463,73050],{},[1506,73465,7574],{},[1490,73467,73468,73470,73472],{},[1493,73469,1520],{},[1506,73471,6380],{},[1493,73473,6383],{"mathvariant":1516},[1869,73475,73476],{"scriptlevel":1871,"displaystyle":1552},[1510,73477,73478,73484],{},[1490,73479,73480,73482],{},[1493,73481,10790],{},[1493,73483,1998],{},[1493,73485,1520],{},[1506,73487,1508],{},[1680,73489,1871],{},[1528,73491,73492],{"encoding":1530},"\\lim_{Q \\to \\infty} \\tfrac{FC}{Q} = 0"," vysvětlují, proč s rostoucí produkcí fixní náklady stále méně ovlivňují ",[1035,73495,73497],{"className":73496},[1480],[1482,73498,73499],{"xmlns":1484},[1487,73500,73501,73507],{},[1490,73502,73503,73505],{},[1493,73504,3633],{},[1493,73506,1998],{},[1528,73508,16523],{"encoding":1530},[1304,73510,73512],{"id":73511},"mezní-náklady","Mezní náklady",[1030,73514,73515,1656,73517,7606,73532,73535,73536,73539],{},[1047,73516,73512],{},[1035,73518,73520],{"className":73519},[1480],[1482,73521,73522],{"xmlns":1484},[1487,73523,73524,73530],{},[1490,73525,73526,73528],{},[1493,73527,1495],{},[1493,73529,1998],{},[1528,73531,69470],{"encoding":1530},[1047,73533,73534],{},"marginal cost",") jsou ",[1052,73537,102],{"className":73538,"dataFsResolvedFilePath":16621,"href":16622},[1055]," celkových nákladů podle množství:",[1035,73541,73543],{"className":73542},[1480],[1482,73544,73545],{"xmlns":1484,"display":1485},[1487,73546,73547,73616],{},[19617,73548,73549],{"width":19619},[19621,73550,73551,73553,73609,73611],{},[19624,73552],{"width":19626},[19624,73554,73555],{},[1490,73556,73557,73559,73561,73563,73565,73567,73569,73571,73573,73575,73591,73593,73595,73601,73603,73605,73607],{},[1493,73558,1495],{},[1493,73560,1998],{},[1506,73562,1508],{},[1493,73564,1495],{},[1493,73566,1998],{},[1506,73568,1553],{"stretchy":1552},[1493,73570,1520],{},[1506,73572,1564],{"stretchy":1552},[1506,73574,1508],{},[1510,73576,73577,73585],{},[1490,73578,73579,73581,73583],{},[1493,73580,3384],{"mathvariant":1516},[1493,73582,5289],{},[1493,73584,1998],{},[1490,73586,73587,73589],{},[1493,73588,3384],{"mathvariant":1516},[1493,73590,1520],{},[1506,73592,1508],{},[1493,73594,5289],{},[2315,73596,73597,73599],{},[1493,73598,1998],{},[1506,73600,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,73602,1553],{"stretchy":1552},[1493,73604,1520],{},[1506,73606,1564],{"stretchy":1552},[1493,73608,2632],{"mathvariant":1516},[19624,73610],{"width":19626},[19624,73612,73613],{},[1988,73614,73615],{},"(3.8)",[1528,73617,73618],{"encoding":1530},"MC = MC(Q) = \\frac{\\mathrm{d}TC}{\\mathrm{d}Q} = TC'(Q).\n\\tag{3.8}",[1023,73620,73622,73629],{"className":73621,"dataCallout":582},[1026,1186],[1030,73623,73625,73628],{"className":73624},[1033],[1035,73626],{"className":73627,"ariaHidden":1041},[1038,1193,1040],"Intuice — „kolik stojí další kus\"",[1030,73630,73631,73657,73658,73675,73676,2632],{},[1035,73632,73634],{"className":73633},[1480],[1482,73635,73636],{"xmlns":1484},[1487,73637,73638,73654],{},[1490,73639,73640,73642,73644,73646,73652],{},[1493,73641,1495],{},[1493,73643,1998],{},[1506,73645,1553],{"stretchy":1552},[2315,73647,73648,73650],{},[1493,73649,1520],{},[1506,73651,2287],{},[1506,73653,1564],{"stretchy":1552},[1528,73655,73656],{"encoding":1530},"MC(Q^*)"," udává přibližné náklady na výrobu jedné další jednotky, když firma aktuálně produkuje ",[1035,73659,73661],{"className":73660},[1480],[1482,73662,73663],{"xmlns":1484},[1487,73664,73665,73673],{},[1490,73666,73667],{},[2315,73668,73669,73671],{},[1493,73670,1520],{},[1506,73672,2287],{},[1528,73674,14097],{"encoding":1530},". Formálně ",[1035,73677,73679],{"className":73678},[1480],[1482,73680,73681],{"xmlns":1484},[1487,73682,73683,73735],{},[1490,73684,73685,73687,73689,73691,73697,73699,73701,73703,73705,73707,73713,73715,73717,73719,73721,73723,73725,73727,73733],{},[1493,73686,1495],{},[1493,73688,1998],{},[1506,73690,1553],{"stretchy":1552},[2315,73692,73693,73695],{},[1493,73694,1520],{},[1506,73696,2287],{},[1506,73698,1564],{"stretchy":1552},[1506,73700,2343],{},[1493,73702,5289],{},[1493,73704,1998],{},[1506,73706,1553],{"stretchy":1552},[2315,73708,73709,73711],{},[1493,73710,1520],{},[1506,73712,2287],{},[1506,73714,2162],{},[1680,73716,1682],{},[1506,73718,1564],{"stretchy":1552},[1506,73720,1888],{},[1493,73722,5289],{},[1493,73724,1998],{},[1506,73726,1553],{"stretchy":1552},[2315,73728,73729,73731],{},[1493,73730,1520],{},[1506,73732,2287],{},[1506,73734,1564],{"stretchy":1552},[1528,73736,73737],{"encoding":1530},"MC(Q^*) \\approx TC(Q^* + 1) - TC(Q^*)",[1030,73739,73740,73741,1274],{},"Analogicky ke vztahu (3.3) platí pro odhad změny ",[1035,73742,73744],{"className":73743},[1480],[1482,73745,73746],{"xmlns":1484},[1487,73747,73748,73756],{},[1490,73749,73750,73752,73754],{},[1493,73751,2976],{"mathvariant":1516},[1493,73753,5289],{},[1493,73755,1998],{},[1528,73757,73758],{"encoding":1530},"\\Delta TC",[1035,73760,73762],{"className":73761},[1480],[1482,73763,73764],{"xmlns":1484,"display":1485},[1487,73765,73766,73835],{},[19617,73767,73768],{"width":19619},[19621,73769,73770,73772,73828,73830],{},[19624,73771],{"width":19626},[19624,73773,73774],{},[1490,73775,73776,73778,73780,73782,73784,73786,73788,73790,73792,73794,73796,73798,73800,73802,73808,73810,73812,73814,73816,73818,73820,73822,73824,73826],{},[1493,73777,2976],{"mathvariant":1516},[1493,73779,5289],{},[1493,73781,1998],{},[1988,73783,1990],{},[1506,73785,2343],{},[1988,73787,1990],{},[1493,73789,3384],{"mathvariant":1516},[1493,73791,5289],{},[1493,73793,1998],{},[1506,73795,1508],{},[1506,73797,1553],{"stretchy":1552},[1493,73799,5289],{},[1493,73801,1998],{},[2315,73803,73804,73806],{},[1506,73805,1564],{"stretchy":1552},[1506,73807,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1988,73809,5016],{},[1493,73811,3384],{"mathvariant":1516},[1493,73813,1520],{},[1506,73815,1508],{},[1493,73817,1495],{},[1493,73819,1998],{},[1988,73821,5016],{},[1493,73823,3384],{"mathvariant":1516},[1493,73825,1520],{},[1506,73827,1559],{"separator":1041},[19624,73829],{"width":19626},[19624,73831,73832],{},[1988,73833,73834],{},"(3.9)",[1528,73836,73837],{"encoding":1530},"\\Delta TC \\;\\approx\\; \\mathrm{d}TC = (TC)' \\, \\mathrm{d}Q = MC \\, \\mathrm{d}Q,\n\\tag{3.9}",[1030,73839,71396],{},[1035,73841,73843],{"className":73842},[1480],[1482,73844,73845],{"xmlns":1484,"display":1485},[1487,73846,73847,73943],{},[1490,73848,73849,73885,73887,73889,73891,73913,73915,73941],{},[1490,73850,73851,73853,73859,73861,73867,73870,73876,73879],{},[1988,73852,71410],{},[2178,73854,73855,73857],{"accent":1041},[1988,73856,8584],{},[1506,73858,8576],{},[1988,73860,71419],{},[2178,73862,73863,73865],{"accent":1041},[1988,73864,3052],{},[1506,73866,3055],{},[1988,73868,73869],{},"ch n",[2178,73871,73872,73874],{"accent":1041},[1988,73873,1052],{},[1506,73875,3055],{},[1988,73877,73878],{},"klad",[2178,73880,73881,73883],{"accent":1041},[1988,73882,7105],{},[1506,73884,7108],{},[1988,73886,1990],{},[1506,73888,2343],{},[1988,73890,1990],{},[1490,73892,73893,73895,73901,73904,73910],{},[1988,73894,71454],{},[2178,73896,73897,73899],{"accent":1041},[1988,73898,7095],{},[1506,73900,3055],{},[1988,73902,73903],{}," n",[2178,73905,73906,73908],{"accent":1041},[1988,73907,1052],{},[1506,73909,3055],{},[1988,73911,73912],{},"klady",[1506,73914,71481],{},[1490,73916,73917,73919,73925,73927,73933,73935],{},[1988,73918,71410],{},[2178,73920,73921,73923],{"accent":1041},[1988,73922,8584],{},[1506,73924,8576],{},[1988,73926,71494],{},[2178,73928,73929,73931],{"accent":1041},[1988,73930,25931],{},[1506,73932,8576],{},[1988,73934,71503],{},[2178,73936,73937,73939],{"accent":1041},[1988,73938,7095],{},[1506,73940,3055],{},[1493,73942,2632],{"mathvariant":1516},[1528,73944,73945],{"encoding":1530},"\\text{změna celkových nákladů} \\;\\approx\\; \\text{mezní náklady} \\times \\text{změna množství}.",[52452,73947,73949],{"id":73948},"příklad-35","Příklad 3.5",[1030,73951,73952,8686,73954,70202,73990,74005,74006,74021,74022,18125,74035,18139,74048,74061,74062,18139,74075,2632],{},[1047,73953,70164],{},[1035,73955,73957],{"className":73956},[1480],[1482,73958,73959],{"xmlns":1484},[1487,73960,73961,73987],{},[1490,73962,73963,73965,73967,73969,73971,73973,73975,73977,73979,73981],{},[1493,73964,5289],{},[1493,73966,1998],{},[1506,73968,1508],{},[1680,73970,5263],{},[1506,73972,2162],{},[1680,73974,7508],{},[1493,73976,1520],{},[1506,73978,2162],{},[1680,73980,1691],{},[2315,73982,73983,73985],{},[1493,73984,1520],{},[1680,73986,1691],{},[1528,73988,73989],{"encoding":1530},"TC = 200 + 6Q + 2Q^2",[1035,73991,73993],{"className":73992},[1480],[1482,73994,73995],{"xmlns":1484},[1487,73996,73997,74003],{},[1490,73998,73999,74001],{},[1493,74000,1495],{},[1493,74002,1998],{},[1528,74004,69470],{"encoding":1530}," a odhadněte změny ",[1035,74007,74009],{"className":74008},[1480],[1482,74010,74011],{"xmlns":1484},[1487,74012,74013,74019],{},[1490,74014,74015,74017],{},[1493,74016,5289],{},[1493,74018,1998],{},[1528,74020,18668],{"encoding":1530}," při změnách ",[1035,74023,74025],{"className":74024},[1480],[1482,74026,74027],{"xmlns":1484},[1487,74028,74029,74033],{},[1490,74030,74031],{},[1493,74032,1520],{},[1528,74034,1520],{"encoding":1530},[1035,74036,74038],{"className":74037},[1480],[1482,74039,74040],{"xmlns":1484},[1487,74041,74042,74046],{},[1490,74043,74044],{},[1680,74045,9787],{},[1528,74047,9787],{"encoding":1530},[1035,74049,74051],{"className":74050},[1480],[1482,74052,74053],{"xmlns":1484},[1487,74054,74055,74059],{},[1490,74056,74057],{},[1680,74058,9961],{},[1528,74060,9961],{"encoding":1530}," a z ",[1035,74063,74065],{"className":74064},[1480],[1482,74066,74067],{"xmlns":1484},[1487,74068,74069,74073],{},[1490,74070,74071],{},[1680,74072,9787],{},[1528,74074,9787],{"encoding":1530},[1035,74076,74078],{"className":74077},[1480],[1482,74079,74080],{"xmlns":1484},[1487,74081,74082,74086],{},[1490,74083,74084],{},[1680,74085,6797],{},[1528,74087,6797],{"encoding":1530},[1030,74089,74090,1656,74092,18367,74118,1732,74145,74172,74173,74188,74189,74204,74205,74232,74233,74253,74254,36253,74275,74331,74332,18125,74345,18139,74358,8994,74371,2632],{},[1047,74091,38365],{},[1035,74093,74095],{"className":74094},[1480],[1482,74096,74097],{"xmlns":1484},[1487,74098,74099,74115],{},[1490,74100,74101,74103,74105,74107,74109,74111,74113],{},[1493,74102,1495],{},[1493,74104,1998],{},[1506,74106,1508],{},[1680,74108,7508],{},[1506,74110,2162],{},[1680,74112,4007],{},[1493,74114,1520],{},[1528,74116,74117],{"encoding":1530},"MC = 6 + 4Q",[1035,74119,74121],{"className":74120},[1480],[1482,74122,74123],{"xmlns":1484},[1487,74124,74125,74142],{},[1490,74126,74127,74129,74131,74133,74135,74137,74139],{},[1493,74128,1495],{},[1493,74130,1998],{},[1506,74132,1553],{"stretchy":1552},[1680,74134,9787],{},[1506,74136,1564],{"stretchy":1552},[1506,74138,1508],{},[1680,74140,74141],{},"66",[1528,74143,74144],{"encoding":1530},"MC(15) = 66",[1035,74146,74148],{"className":74147},[1480],[1482,74149,74150],{"xmlns":1484},[1487,74151,74152,74169],{},[1490,74153,74154,74156,74158,74160,74162,74164,74166],{},[1493,74155,1495],{},[1493,74157,1998],{},[1506,74159,1553],{"stretchy":1552},[1680,74161,8436],{},[1506,74163,1564],{"stretchy":1552},[1506,74165,1508],{},[1680,74167,74168],{},"86",[1528,74170,74171],{"encoding":1530},"MC(20) = 86",": s růstem množství se rychlost změny ",[1035,74174,74176],{"className":74175},[1480],[1482,74177,74178],{"xmlns":1484},[1487,74179,74180,74186],{},[1490,74181,74182,74184],{},[1493,74183,5289],{},[1493,74185,1998],{},[1528,74187,18668],{"encoding":1530}," zvyšuje (",[1035,74190,74192],{"className":74191},[1480],[1482,74193,74194],{"xmlns":1484},[1487,74195,74196,74202],{},[1490,74197,74198,74200],{},[1493,74199,1495],{},[1493,74201,1998],{},[1528,74203,69470],{"encoding":1530}," je rostoucí). Z ",[1035,74206,74208],{"className":74207},[1480],[1482,74209,74210],{"xmlns":1484},[1487,74211,74212,74229],{},[1490,74213,74214,74216,74218,74220,74222,74224,74226],{},[1493,74215,5289],{},[1493,74217,1998],{},[1506,74219,1553],{"stretchy":1552},[1680,74221,9787],{},[1506,74223,1564],{"stretchy":1552},[1506,74225,1508],{},[1680,74227,74228],{},"740",[1528,74230,74231],{"encoding":1530},"TC(15) = 740"," se po přírůstku ",[1035,74234,74236],{"className":74235},[1480],[1482,74237,74238],{"xmlns":1484},[1487,74239,74240,74250],{},[1490,74241,74242,74244,74246,74248],{},[1493,74243,3384],{"mathvariant":1516},[1493,74245,1520],{},[1506,74247,1508],{},[1680,74249,1682],{},[1528,74251,74252],{"encoding":1530},"\\mathrm{d}Q = 1"," předpokládá ",[1035,74255,74257],{"className":74256},[1480],[1482,74258,74259],{"xmlns":1484},[1487,74260,74261,74272],{},[1490,74262,74263,74265,74267,74269],{},[1493,74264,5289],{},[1493,74266,1998],{},[1506,74268,2343],{},[1680,74270,74271],{},"806",[1528,74273,74274],{"encoding":1530},"TC \\approx 806",[1035,74276,74278],{"className":74277},[1480],[1482,74279,74280],{"xmlns":1484},[1487,74281,74282,74328],{},[1490,74283,74284,74286,74288,74290,74292,74294,74296,74298,74300,74302,74304,74306,74308,74310,74312,74314,74316,74319,74321,74323,74325],{},[1493,74285,2976],{"mathvariant":1516},[1493,74287,5289],{},[1493,74289,1998],{},[1506,74291,1508],{},[1493,74293,5289],{},[1493,74295,1998],{},[1506,74297,1553],{"stretchy":1552},[1680,74299,9961],{},[1506,74301,1564],{"stretchy":1552},[1506,74303,1888],{},[1493,74305,5289],{},[1493,74307,1998],{},[1506,74309,1553],{"stretchy":1552},[1680,74311,9787],{},[1506,74313,1564],{"stretchy":1552},[1506,74315,1508],{},[1680,74317,74318],{},"808",[1506,74320,1888],{},[1680,74322,74228],{},[1506,74324,1508],{},[1680,74326,74327],{},"68",[1528,74329,74330],{"encoding":1530},"\\Delta TC = TC(16) - TC(15) = 808 - 740 = 68",". Při poklesu ",[1035,74333,74335],{"className":74334},[1480],[1482,74336,74337],{"xmlns":1484},[1487,74338,74339,74343],{},[1490,74340,74341],{},[1493,74342,1520],{},[1528,74344,1520],{"encoding":1530},[1035,74346,74348],{"className":74347},[1480],[1482,74349,74350],{"xmlns":1484},[1487,74351,74352,74356],{},[1490,74353,74354],{},[1680,74355,9787],{},[1528,74357,9787],{"encoding":1530},[1035,74359,74361],{"className":74360},[1480],[1482,74362,74363],{"xmlns":1484},[1487,74364,74365,74369],{},[1490,74366,74367],{},[1680,74368,6797],{},[1528,74370,6797],{"encoding":1530},[1035,74372,74374],{"className":74373},[1480],[1482,74375,74376],{"xmlns":1484},[1487,74377,74378,74407],{},[1490,74379,74380,74382,74384,74386,74388,74390,74392,74394,74396,74398,74400,74402,74404],{},[1493,74381,2976],{"mathvariant":1516},[1493,74383,5289],{},[1493,74385,1998],{},[1506,74387,2343],{},[1680,74389,74141],{},[1506,74391,1714],{},[1506,74393,1553],{"stretchy":1552},[1506,74395,1888],{},[1680,74397,3201],{},[1506,74399,1564],{"stretchy":1552},[1506,74401,1508],{},[1506,74403,1888],{},[1680,74405,74406],{},"198",[1528,74408,74409],{"encoding":1530},"\\Delta TC \\approx 66 \\cdot (-3) = -198",[1304,74411,74413],{"id":74412},"kubická-nákladová-funkce","Kubická nákladová funkce",[1030,74415,74416],{},"V ekonomicky reálných situacích mají křivky nákladů charakteristické vazby a tvary.",[52452,74418,74420],{"id":74419},"příklad-36","Příklad 3.6",[1030,74422,74423,8686,74425,74469],{},[1047,74424,70164],{},[1035,74426,74428],{"className":74427},[1480],[1482,74429,74430],{"xmlns":1484},[1487,74431,74432,74466],{},[1490,74433,74434,74436,74438,74440,74442,74444,74446,74448,74450,74452,74458,74460],{},[1493,74435,5289],{},[1493,74437,1998],{},[1506,74439,1508],{},[1680,74441,2916],{},[1506,74443,2162],{},[1680,74445,2309],{},[1493,74447,1520],{},[1506,74449,1888],{},[1680,74451,1752],{},[2315,74453,74454,74456],{},[1493,74455,1520],{},[1680,74457,1691],{},[1506,74459,2162],{},[2315,74461,74462,74464],{},[1493,74463,1520],{},[1680,74465,3201],{},[1528,74467,74468],{"encoding":1530},"TC = 100 + 25Q - 5Q^2 + Q^3"," odvoďte všechny nákladové charakteristiky.",[1030,74471,74472],{},[1047,74473,38365],{},[1035,74475,74477],{"className":74476},[1480],[1482,74478,74479],{"xmlns":1484,"display":1485},[1487,74480,74481,74725],{},[19617,74482,74483,74509,74557,74591,74633,74683],{"rowspacing":36473,"columnalign":36474,"columnspacing":6926},[19621,74484,74485,74495],{},[19624,74486,74487],{},[1869,74488,74489],{"scriptlevel":1871,"displaystyle":1041},[1490,74490,74491,74493],{},[1493,74492,10790],{},[1493,74494,1998],{},[19624,74496,74497],{},[1869,74498,74499],{"scriptlevel":1871,"displaystyle":1041},[1490,74500,74501,74503,74505,74507],{},[1490,74502],{},[1506,74504,1508],{},[1680,74506,2916],{},[1506,74508,1559],{"separator":1041},[19621,74510,74511,74523],{},[19624,74512,74513],{},[1869,74514,74515],{"scriptlevel":1871,"displaystyle":1041},[1490,74516,74517,74519,74521],{},[1493,74518,5289],{},[1493,74520,55105],{},[1493,74522,1998],{},[19624,74524,74525],{},[1869,74526,74527],{"scriptlevel":1871,"displaystyle":1041},[1490,74528,74529,74531,74533,74535,74537,74539,74541,74547,74549,74555],{},[1490,74530],{},[1506,74532,1508],{},[1680,74534,2309],{},[1493,74536,1520],{},[1506,74538,1888],{},[1680,74540,1752],{},[2315,74542,74543,74545],{},[1493,74544,1520],{},[1680,74546,1691],{},[1506,74548,2162],{},[2315,74550,74551,74553],{},[1493,74552,1520],{},[1680,74554,3201],{},[1506,74556,1559],{"separator":1041},[19621,74558,74559,74571],{},[19624,74560,74561],{},[1869,74562,74563],{"scriptlevel":1871,"displaystyle":1041},[1490,74564,74565,74567,74569],{},[1493,74566,3633],{},[1493,74568,10790],{},[1493,74570,1998],{},[19624,74572,74573],{},[1869,74574,74575],{"scriptlevel":1871,"displaystyle":1041},[1490,74576,74577,74579,74581,74589],{},[1490,74578],{},[1506,74580,1508],{},[1869,74582,74583],{"scriptlevel":1871,"displaystyle":1552},[1510,74584,74585,74587],{},[1680,74586,2916],{},[1493,74588,1520],{},[1506,74590,1559],{"separator":1041},[19621,74592,74593,74605],{},[19624,74594,74595],{},[1869,74596,74597],{"scriptlevel":1871,"displaystyle":1041},[1490,74598,74599,74601,74603],{},[1493,74600,3633],{},[1493,74602,55105],{},[1493,74604,1998],{},[19624,74606,74607],{},[1869,74608,74609],{"scriptlevel":1871,"displaystyle":1041},[1490,74610,74611,74613,74615,74617,74619,74621,74623,74625,74631],{},[1490,74612],{},[1506,74614,1508],{},[1680,74616,2309],{},[1506,74618,1888],{},[1680,74620,1752],{},[1493,74622,1520],{},[1506,74624,2162],{},[2315,74626,74627,74629],{},[1493,74628,1520],{},[1680,74630,1691],{},[1506,74632,1559],{"separator":1041},[19621,74634,74635,74645],{},[19624,74636,74637],{},[1869,74638,74639],{"scriptlevel":1871,"displaystyle":1041},[1490,74640,74641,74643],{},[1493,74642,3633],{},[1493,74644,1998],{},[19624,74646,74647],{},[1869,74648,74649],{"scriptlevel":1871,"displaystyle":1041},[1490,74650,74651,74653,74655,74663,74665,74667,74669,74671,74673,74675,74681],{},[1490,74652],{},[1506,74654,1508],{},[1869,74656,74657],{"scriptlevel":1871,"displaystyle":1552},[1510,74658,74659,74661],{},[1680,74660,2916],{},[1493,74662,1520],{},[1506,74664,2162],{},[1680,74666,2309],{},[1506,74668,1888],{},[1680,74670,1752],{},[1493,74672,1520],{},[1506,74674,2162],{},[2315,74676,74677,74679],{},[1493,74678,1520],{},[1680,74680,1691],{},[1506,74682,1559],{"separator":1041},[19621,74684,74685,74695],{},[19624,74686,74687],{},[1869,74688,74689],{"scriptlevel":1871,"displaystyle":1041},[1490,74690,74691,74693],{},[1493,74692,1495],{},[1493,74694,1998],{},[19624,74696,74697],{},[1869,74698,74699],{"scriptlevel":1871,"displaystyle":1041},[1490,74700,74701,74703,74705,74707,74709,74711,74713,74715,74717,74723],{},[1490,74702],{},[1506,74704,1508],{},[1680,74706,2309],{},[1506,74708,1888],{},[1680,74710,1775],{},[1493,74712,1520],{},[1506,74714,2162],{},[1680,74716,3201],{},[2315,74718,74719,74721],{},[1493,74720,1520],{},[1680,74722,1691],{},[1493,74724,2632],{"mathvariant":1516},[1528,74726,74727],{"encoding":1530},"\\begin{aligned}\nFC &= 100, \\\\\nTVC &= 25Q - 5Q^2 + Q^3, \\\\\nAFC &= \\tfrac{100}{Q}, \\\\\nAVC &= 25 - 5Q + Q^2, \\\\\nAC  &= \\tfrac{100}{Q} + 25 - 5Q + Q^2, \\\\\nMC  &= 25 - 10Q + 3Q^2.\n\\end{aligned}",[1030,74729,74730,74731,16351,74746,16351,74761,74776,74777,74792,74793,1732,74811,74792,74828,1732,74846,74792,74861,74879],{},"Význačné body ",[1035,74732,74734],{"className":74733},[1480],[1482,74735,74736],{"xmlns":1484},[1487,74737,74738,74743],{},[1490,74739,74740],{},[1680,74741,74742],{},"1,67",[1528,74744,74745],{"encoding":1530},"1{,}67",[1035,74747,74749],{"className":74748},[1480],[1482,74750,74751],{"xmlns":1484},[1487,74752,74753,74758],{},[1490,74754,74755],{},[1680,74756,74757],{},"2,50",[1528,74759,74760],{"encoding":1530},"2{,}50",[1035,74762,74764],{"className":74763},[1480],[1482,74765,74766],{"xmlns":1484},[1487,74767,74768,74773],{},[1490,74769,74770],{},[1680,74771,74772],{},"4,73",[1528,74774,74775],{"encoding":1530},"4{,}73"," odpovídají: ",[1035,74778,74780],{"className":74779},[1480],[1482,74781,74782],{"xmlns":1484},[1487,74783,74784,74790],{},[1490,74785,74786,74788],{},[1493,74787,1495],{},[1493,74789,1998],{},[1528,74791,69470],{"encoding":1530}," minimum v ",[1035,74794,74796],{"className":74795},[1480],[1482,74797,74798],{"xmlns":1484},[1487,74799,74800,74808],{},[1490,74801,74802,74804,74806],{},[1493,74803,1520],{},[1506,74805,21771],{},[1680,74807,74742],{},[1528,74809,74810],{"encoding":1530},"Q \\doteq 1{,}67",[1035,74812,74814],{"className":74813},[1480],[1482,74815,74816],{"xmlns":1484},[1487,74817,74818,74826],{},[1490,74819,74820,74822,74824],{},[1493,74821,3633],{},[1493,74823,55105],{},[1493,74825,1998],{},[1528,74827,69489],{"encoding":1530},[1035,74829,74831],{"className":74830},[1480],[1482,74832,74833],{"xmlns":1484},[1487,74834,74835,74843],{},[1490,74836,74837,74839,74841],{},[1493,74838,1520],{},[1506,74840,1508],{},[1680,74842,74757],{},[1528,74844,74845],{"encoding":1530},"Q = 2{,}50",[1035,74847,74849],{"className":74848},[1480],[1482,74850,74851],{"xmlns":1484},[1487,74852,74853,74859],{},[1490,74854,74855,74857],{},[1493,74856,3633],{},[1493,74858,1998],{},[1528,74860,16523],{"encoding":1530},[1035,74862,74864],{"className":74863},[1480],[1482,74865,74866],{"xmlns":1484},[1487,74867,74868,74876],{},[1490,74869,74870,74872,74874],{},[1493,74871,1520],{},[1506,74873,21771],{},[1680,74875,74772],{},[1528,74877,74878],{"encoding":1530},"Q \\doteq 4{,}73"," (téma úlohy 3.11).",[1030,74881,74882],{},[18014,74883],{"alt":74884,"className":74885,"src":74886},"imek-ac-avc-mc",[1055,18018],"\u002Fwiki-assets\u002Fimek-ac-avc-mc.jpeg",[1030,74888,74889],{},[1047,74890,74891],{},"Standardní vlastnosti:",[1203,74893,74894,74929,74993,75061,75112,75132],{},[1206,74895,74896,1586,74911,74928],{},[1035,74897,74899],{"className":74898},[1480],[1482,74900,74901],{"xmlns":1484},[1487,74902,74903,74909],{},[1490,74904,74905,74907],{},[1493,74906,5289],{},[1493,74908,1998],{},[1528,74910,18668],{"encoding":1530},[1035,74912,74914],{"className":74913},[1480],[1482,74915,74916],{"xmlns":1484},[1487,74917,74918,74926],{},[1490,74919,74920,74922,74924],{},[1493,74921,5289],{},[1493,74923,55105],{},[1493,74925,1998],{},[1528,74927,69687],{"encoding":1530}," jsou kubické funkce;",[1206,74930,74931,1732,74946,1732,74963,74978,74979,74992],{},[1035,74932,74934],{"className":74933},[1480],[1482,74935,74936],{"xmlns":1484},[1487,74937,74938,74944],{},[1490,74939,74940,74942],{},[1493,74941,3633],{},[1493,74943,1998],{},[1528,74945,16523],{"encoding":1530},[1035,74947,74949],{"className":74948},[1480],[1482,74950,74951],{"xmlns":1484},[1487,74952,74953,74961],{},[1490,74954,74955,74957,74959],{},[1493,74956,3633],{},[1493,74958,55105],{},[1493,74960,1998],{},[1528,74962,69489],{"encoding":1530},[1035,74964,74966],{"className":74965},[1480],[1482,74967,74968],{"xmlns":1484},[1487,74969,74970,74976],{},[1490,74971,74972,74974],{},[1493,74973,1495],{},[1493,74975,1998],{},[1528,74977,69470],{"encoding":1530}," jsou křivky tvaru ",[1035,74980,74982],{"className":74981},[1480],[1482,74983,74984],{"xmlns":1484},[1487,74985,74986,74990],{},[1490,74987,74988],{},[1493,74989,1668],{},[1528,74991,1668],{"encoding":1530}," (nejprve klesají, po minimu rostou);",[1206,74994,74995,75010,75011,1732,75028,75045,75046,6065],{},[1035,74996,74998],{"className":74997},[1480],[1482,74999,75000],{"xmlns":1484},[1487,75001,75002,75008],{},[1490,75003,75004,75006],{},[1493,75005,1495],{},[1493,75007,1998],{},[1528,75009,69470],{"encoding":1530}," nabývá minima před ",[1035,75012,75014],{"className":75013},[1480],[1482,75015,75016],{"xmlns":1484},[1487,75017,75018,75026],{},[1490,75019,75020,75022,75024],{},[1493,75021,3633],{},[1493,75023,55105],{},[1493,75025,1998],{},[1528,75027,69489],{"encoding":1530},[1035,75029,75031],{"className":75030},[1480],[1482,75032,75033],{"xmlns":1484},[1487,75034,75035,75043],{},[1490,75036,75037,75039,75041],{},[1493,75038,3633],{},[1493,75040,55105],{},[1493,75042,1998],{},[1528,75044,69489],{"encoding":1530}," před ",[1035,75047,75049],{"className":75048},[1480],[1482,75050,75051],{"xmlns":1484},[1487,75052,75053,75059],{},[1490,75054,75055,75057],{},[1493,75056,3633],{},[1493,75058,1998],{},[1528,75060,16523],{"encoding":1530},[1206,75062,75063,75078,75079,1586,75094,75111],{},[1035,75064,75066],{"className":75065},[1480],[1482,75067,75068],{"xmlns":1484},[1487,75069,75070,75076],{},[1490,75071,75072,75074],{},[1493,75073,1495],{},[1493,75075,1998],{},[1528,75077,69470],{"encoding":1530}," protíná ",[1035,75080,75082],{"className":75081},[1480],[1482,75083,75084],{"xmlns":1484},[1487,75085,75086,75092],{},[1490,75087,75088,75090],{},[1493,75089,3633],{},[1493,75091,1998],{},[1528,75093,16523],{"encoding":1530},[1035,75095,75097],{"className":75096},[1480],[1482,75098,75099],{"xmlns":1484},[1487,75100,75101,75109],{},[1490,75102,75103,75105,75107],{},[1493,75104,3633],{},[1493,75106,55105],{},[1493,75108,1998],{},[1528,75110,69489],{"encoding":1530}," zdola právě v jejich minimech;",[1206,75113,75114,75131],{},[1035,75115,75117],{"className":75116},[1480],[1482,75118,75119],{"xmlns":1484},[1487,75120,75121,75129],{},[1490,75122,75123,75125,75127],{},[1493,75124,3633],{},[1493,75126,10790],{},[1493,75128,1998],{},[1528,75130,69705],{"encoding":1530}," je hyperbola, stále klesající;",[1206,75133,75134,75166,75167,1586,75182,75199,75200,75213,75214,16623],{},[1035,75135,75137],{"className":75136},[1480],[1482,75138,75139],{"xmlns":1484},[1487,75140,75141,75163],{},[1490,75142,75143,75145,75147,75149,75151,75153,75155,75157,75159,75161],{},[1493,75144,3633],{},[1493,75146,1998],{},[1506,75148,1508],{},[1493,75150,3633],{},[1493,75152,10790],{},[1493,75154,1998],{},[1506,75156,2162],{},[1493,75158,3633],{},[1493,75160,55105],{},[1493,75162,1998],{},[1528,75164,75165],{"encoding":1530},"AC = AFC + AVC","; vzdálenost mezi ",[1035,75168,75170],{"className":75169},[1480],[1482,75171,75172],{"xmlns":1484},[1487,75173,75174,75180],{},[1490,75175,75176,75178],{},[1493,75177,3633],{},[1493,75179,1998],{},[1528,75181,16523],{"encoding":1530},[1035,75183,75185],{"className":75184},[1480],[1482,75186,75187],{"xmlns":1484},[1487,75188,75189,75197],{},[1490,75190,75191,75193,75195],{},[1493,75192,3633],{},[1493,75194,55105],{},[1493,75196,1998],{},[1528,75198,69489],{"encoding":1530}," klesá s rostoucím ",[1035,75201,75203],{"className":75202},[1480],[1482,75204,75205],{"xmlns":1484},[1487,75206,75207,75211],{},[1490,75208,75209],{},[1493,75210,1520],{},[1528,75212,1520],{"encoding":1530}," (protože ",[1035,75215,75217],{"className":75216},[1480],[1482,75218,75219],{"xmlns":1484},[1487,75220,75221,75233],{},[1490,75222,75223,75225,75227,75229,75231],{},[1493,75224,3633],{},[1493,75226,10790],{},[1493,75228,1998],{},[1506,75230,6380],{},[1680,75232,1871],{},[1528,75234,75235],{"encoding":1530},"AFC \\to 0",[1065,75237,75239],{"id":75238},"princip-minimalizace-průměrných-nákladů","Princip minimalizace průměrných nákladů",[1030,75241,75242,75243,75246,75247,75262],{},"Častou optimalizační úlohou je ",[1047,75244,75245],{},"minimalizace průměrných nákladů"," — stanovení produkce, pro niž je ",[1035,75248,75250],{"className":75249},[1480],[1482,75251,75252],{"xmlns":1484},[1487,75253,75254,75260],{},[1490,75255,75256,75258],{},[1493,75257,3633],{},[1493,75259,1998],{},[1528,75261,16523],{"encoding":1530}," minimální.",[1304,75264,32569],{"id":32568},[1030,75266,75267,75268,75285],{},"Mají-li průměrné náklady minimum v bodě ",[1035,75269,75271],{"className":75270},[1480],[1482,75272,75273],{"xmlns":1484},[1487,75274,75275,75283],{},[1490,75276,75277],{},[1497,75278,75279,75281],{},[1493,75280,1520],{},[1680,75282,1871],{},[1528,75284,53236],{"encoding":1530},", pak platí",[1035,75287,75289],{"className":75288},[1480],[1482,75290,75291],{"xmlns":1484,"display":1485},[1487,75292,75293,75342],{},[19617,75294,75295],{"width":19619},[19621,75296,75297,75299,75335,75337],{},[19624,75298],{"width":19626},[19624,75300,75301],{},[1490,75302,75303,75305,75307,75309,75315,75317,75319,75321,75323,75325,75331,75333],{},[1493,75304,3633],{},[1493,75306,1998],{},[1506,75308,1553],{"stretchy":1552},[1497,75310,75311,75313],{},[1493,75312,1520],{},[1680,75314,1871],{},[1506,75316,1564],{"stretchy":1552},[1506,75318,1508],{},[1493,75320,1495],{},[1493,75322,1998],{},[1506,75324,1553],{"stretchy":1552},[1497,75326,75327,75329],{},[1493,75328,1520],{},[1680,75330,1871],{},[1506,75332,1564],{"stretchy":1552},[1493,75334,2632],{"mathvariant":1516},[19624,75336],{"width":19626},[19624,75338,75339],{},[1988,75340,75341],{},"(3.10)",[1528,75343,75344],{"encoding":1530},"AC(Q_0) = MC(Q_0).\n\\tag{3.10}",[1023,75346,75348,75354],{"className":75347,"dataCallout":70515},[1026,70514],[1030,75349,75351,32569],{"className":75350},[1033],[1035,75352],{"className":75353,"ariaHidden":1041},[1038,70522,1040],[1030,75355,75356],{},[1047,75357,75358],{},"V bodě minima průměrných nákladů se průměrné náklady rovnají mezním nákladům.",[1030,75360,75361,75364,75365,75407],{},[1047,75362,75363],{},"Odvození."," Z ",[1035,75366,75368],{"className":75367},[1480],[1482,75369,75370],{"xmlns":1484},[1487,75371,75372,75404],{},[1490,75373,75374,75376,75378,75380,75382,75384,75386],{},[1493,75375,3633],{},[1493,75377,1998],{},[1506,75379,1553],{"stretchy":1552},[1493,75381,1520],{},[1506,75383,1564],{"stretchy":1552},[1506,75385,1508],{},[1869,75387,75388],{"scriptlevel":1871,"displaystyle":1552},[1510,75389,75390,75402],{},[1490,75391,75392,75394,75396,75398,75400],{},[1493,75393,5289],{},[1493,75395,1998],{},[1506,75397,1553],{"stretchy":1552},[1493,75399,1520],{},[1506,75401,1564],{"stretchy":1552},[1493,75403,1520],{},[1528,75405,75406],{"encoding":1530},"AC(Q) = \\tfrac{TC(Q)}{Q}"," derivací podílu plyne",[1035,75409,75411],{"className":75410},[1480],[1482,75412,75413],{"xmlns":1484,"display":1485},[1487,75414,75415,75547],{},[1490,75416,75417,75419,75425,75427,75429,75431,75433,75473,75475,75515,75517,75545],{},[1493,75418,3633],{},[2315,75420,75421,75423],{},[1493,75422,1998],{},[1506,75424,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,75426,1553],{"stretchy":1552},[1493,75428,1520],{},[1506,75430,1564],{"stretchy":1552},[1506,75432,1508],{},[1510,75434,75435,75467],{},[1490,75436,75437,75439,75445,75447,75449,75451,75453,75455,75457,75459,75461,75463,75465],{},[1493,75438,5289],{},[2315,75440,75441,75443],{},[1493,75442,1998],{},[1506,75444,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,75446,1553],{"stretchy":1552},[1493,75448,1520],{},[1506,75450,1564],{"stretchy":1552},[1506,75452,1714],{},[1493,75454,1520],{},[1506,75456,1888],{},[1493,75458,5289],{},[1493,75460,1998],{},[1506,75462,1553],{"stretchy":1552},[1493,75464,1520],{},[1506,75466,1564],{"stretchy":1552},[2315,75468,75469,75471],{},[1493,75470,1520],{},[1680,75472,1691],{},[1506,75474,1508],{},[1510,75476,75477,75509],{},[1490,75478,75479,75481,75483,75485,75487,75489,75491,75493,75495,75497,75499,75501,75503,75505,75507],{},[1493,75480,1495],{},[1493,75482,1998],{},[1506,75484,1553],{"stretchy":1552},[1493,75486,1520],{},[1506,75488,1564],{"stretchy":1552},[1506,75490,1714],{},[1493,75492,1520],{},[1506,75494,1888],{},[1493,75496,3633],{},[1493,75498,1998],{},[1506,75500,1553],{"stretchy":1552},[1493,75502,1520],{},[1506,75504,1564],{"stretchy":1552},[1506,75506,1714],{},[1493,75508,1520],{},[2315,75510,75511,75513],{},[1493,75512,1520],{},[1680,75514,1691],{},[1506,75516,1508],{},[1510,75518,75519,75543],{},[1490,75520,75521,75523,75525,75527,75529,75531,75533,75535,75537,75539,75541],{},[1493,75522,1495],{},[1493,75524,1998],{},[1506,75526,1553],{"stretchy":1552},[1493,75528,1520],{},[1506,75530,1564],{"stretchy":1552},[1506,75532,1888],{},[1493,75534,3633],{},[1493,75536,1998],{},[1506,75538,1553],{"stretchy":1552},[1493,75540,1520],{},[1506,75542,1564],{"stretchy":1552},[1493,75544,1520],{},[1493,75546,2632],{"mathvariant":1516},[1528,75548,75549],{"encoding":1530},"AC'(Q) = \\frac{TC'(Q) \\cdot Q - TC(Q)}{Q^2} = \\frac{MC(Q) \\cdot Q - AC(Q) \\cdot Q}{Q^2} = \\frac{MC(Q) - AC(Q)}{Q}.",[1030,75551,75552,75553,11713,75568,8994,75590,70906],{},"Nutnou podmínkou minima ",[1035,75554,75556],{"className":75555},[1480],[1482,75557,75558],{"xmlns":1484},[1487,75559,75560,75566],{},[1490,75561,75562,75564],{},[1493,75563,3633],{},[1493,75565,1998],{},[1528,75567,16523],{"encoding":1530},[1035,75569,75571],{"className":75570},[1480],[1482,75572,75573],{"xmlns":1484},[1487,75574,75575,75587],{},[1490,75576,75577,75583,75585],{},[1497,75578,75579,75581],{},[1493,75580,1520],{},[1680,75582,1871],{},[1506,75584,2796],{},[1680,75586,1871],{},[1528,75588,75589],{"encoding":1530},"Q_0 > 0",[1035,75591,75593],{"className":75592},[1480],[1482,75594,75595],{"xmlns":1484},[1487,75596,75597,75621],{},[1490,75598,75599,75601,75607,75609,75615,75617,75619],{},[1493,75600,3633],{},[2315,75602,75603,75605],{},[1493,75604,1998],{},[1506,75606,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,75608,1553],{"stretchy":1552},[1497,75610,75611,75613],{},[1493,75612,1520],{},[1680,75614,1871],{},[1506,75616,1564],{"stretchy":1552},[1506,75618,1508],{},[1680,75620,1871],{},[1528,75622,75623],{"encoding":1530},"AC'(Q_0) = 0",[1035,75625,75627],{"className":75626},[1480],[1482,75628,75629],{"xmlns":1484,"display":1485},[1487,75630,75631,75715],{},[1490,75632,75633,75673,75675,75677,75679,75681,75683,75685,75687,75689,75695,75697,75699,75701,75703,75705,75711,75713],{},[1510,75634,75635,75667],{},[1490,75636,75637,75639,75641,75643,75649,75651,75653,75655,75657,75659,75665],{},[1493,75638,1495],{},[1493,75640,1998],{},[1506,75642,1553],{"stretchy":1552},[1497,75644,75645,75647],{},[1493,75646,1520],{},[1680,75648,1871],{},[1506,75650,1564],{"stretchy":1552},[1506,75652,1888],{},[1493,75654,3633],{},[1493,75656,1998],{},[1506,75658,1553],{"stretchy":1552},[1497,75660,75661,75663],{},[1493,75662,1520],{},[1680,75664,1871],{},[1506,75666,1564],{"stretchy":1552},[1497,75668,75669,75671],{},[1493,75670,1520],{},[1680,75672,1871],{},[1506,75674,1508],{},[1680,75676,1871],{},[1912,75678],{"width":2108},[1506,75680,11263],{},[1912,75682],{"width":2108},[1493,75684,1495],{},[1493,75686,1998],{},[1506,75688,1553],{"stretchy":1552},[1497,75690,75691,75693],{},[1493,75692,1520],{},[1680,75694,1871],{},[1506,75696,1564],{"stretchy":1552},[1506,75698,1508],{},[1493,75700,3633],{},[1493,75702,1998],{},[1506,75704,1553],{"stretchy":1552},[1497,75706,75707,75709],{},[1493,75708,1520],{},[1680,75710,1871],{},[1506,75712,1564],{"stretchy":1552},[1493,75714,2632],{"mathvariant":1516},[1528,75716,75717],{"encoding":1530},"\\frac{MC(Q_0) - AC(Q_0)}{Q_0} = 0 \\quad\\Longleftrightarrow\\quad MC(Q_0) = AC(Q_0).",[1030,75719,75720,1656,75723,75078,75738,75753,75754,75769,75770,8994,75787,75809,75810,75832],{},[1047,75721,75722],{},"Geometrická interpretace.",[1035,75724,75726],{"className":75725},[1480],[1482,75727,75728],{"xmlns":1484},[1487,75729,75730,75736],{},[1490,75731,75732,75734],{},[1493,75733,1495],{},[1493,75735,1998],{},[1528,75737,69470],{"encoding":1530},[1035,75739,75741],{"className":75740},[1480],[1482,75742,75743],{"xmlns":1484},[1487,75744,75745,75751],{},[1490,75746,75747,75749],{},[1493,75748,3633],{},[1493,75750,1998],{},[1528,75752,16523],{"encoding":1530}," právě v bodě minima ",[1035,75755,75757],{"className":75756},[1480],[1482,75758,75759],{"xmlns":1484},[1487,75760,75761,75767],{},[1490,75762,75763,75765],{},[1493,75764,3633],{},[1493,75766,1998],{},[1528,75768,16523],{"encoding":1530},"; nalevo od ",[1035,75771,75773],{"className":75772},[1480],[1482,75774,75775],{"xmlns":1484},[1487,75776,75777,75785],{},[1490,75778,75779],{},[1497,75780,75781,75783],{},[1493,75782,1520],{},[1680,75784,1871],{},[1528,75786,53236],{"encoding":1530},[1035,75788,75790],{"className":75789},[1480],[1482,75791,75792],{"xmlns":1484},[1487,75793,75794,75806],{},[1490,75795,75796,75798,75800,75802,75804],{},[1493,75797,1495],{},[1493,75799,1998],{},[1506,75801,3961],{},[1493,75803,3633],{},[1493,75805,1998],{},[1528,75807,75808],{"encoding":1530},"MC \u003C AC"," (průměrné náklady klesají), napravo ",[1035,75811,75813],{"className":75812},[1480],[1482,75814,75815],{"xmlns":1484},[1487,75816,75817,75829],{},[1490,75818,75819,75821,75823,75825,75827],{},[1493,75820,1495],{},[1493,75822,1998],{},[1506,75824,2796],{},[1493,75826,3633],{},[1493,75828,1998],{},[1528,75830,75831],{"encoding":1530},"MC > AC"," (průměrné náklady rostou).",[1030,75834,75835,75836,75878,75879,75896,75897,2632],{},"Za obvyklých ekonomických podmínek platí i obrácené tvrzení — jestliže ",[1035,75837,75839],{"className":75838},[1480],[1482,75840,75841],{"xmlns":1484},[1487,75842,75843,75875],{},[1490,75844,75845,75847,75849,75851,75857,75859,75861,75863,75865,75867,75873],{},[1493,75846,3633],{},[1493,75848,1998],{},[1506,75850,1553],{"stretchy":1552},[1497,75852,75853,75855],{},[1493,75854,1520],{},[1680,75856,1871],{},[1506,75858,1564],{"stretchy":1552},[1506,75860,1508],{},[1493,75862,1495],{},[1493,75864,1998],{},[1506,75866,1553],{"stretchy":1552},[1497,75868,75869,75871],{},[1493,75870,1520],{},[1680,75872,1871],{},[1506,75874,1564],{"stretchy":1552},[1528,75876,75877],{"encoding":1530},"AC(Q_0) = MC(Q_0)",", pak ",[1035,75880,75882],{"className":75881},[1480],[1482,75883,75884],{"xmlns":1484},[1487,75885,75886,75894],{},[1490,75887,75888],{},[1497,75889,75890,75892],{},[1493,75891,1520],{},[1680,75893,1871],{},[1528,75895,53236],{"encoding":1530}," je bod minima. V praktických úlohách tedy postačí řešit rovnici ",[1035,75898,75900],{"className":75899},[1480],[1482,75901,75902],{"xmlns":1484},[1487,75903,75904,75928],{},[1490,75905,75906,75908,75910,75912,75914,75916,75918,75920,75922,75924,75926],{},[1493,75907,3633],{},[1493,75909,1998],{},[1506,75911,1553],{"stretchy":1552},[1493,75913,1520],{},[1506,75915,1564],{"stretchy":1552},[1506,75917,1508],{},[1493,75919,1495],{},[1493,75921,1998],{},[1506,75923,1553],{"stretchy":1552},[1493,75925,1520],{},[1506,75927,1564],{"stretchy":1552},[1528,75929,75930],{"encoding":1530},"AC(Q) = MC(Q)",[1023,75932,75934,75941],{"className":75933,"dataCallout":1155},[1026,1154],[1030,75935,75937,75940],{"className":75936},[1033],[1035,75938],{"className":75939,"ariaHidden":1041},[1038,1162,1040],"Pozor — neplést s principem maxima zisku",[1030,75942,2364,75943,26918,75961,75982,75983,26918,75986,76007,76008,76023,76024,72122,76039,16623],{},[1047,75944,75945,75946],{},"minimum ",[1035,75947,75949],{"className":75948},[1480],[1482,75950,75951],{"xmlns":1484},[1487,75952,75953,75959],{},[1490,75954,75955,75957],{},[1493,75956,3633],{},[1493,75958,1998],{},[1528,75960,16523],{"encoding":1530},[1035,75962,75964],{"className":75963},[1480],[1482,75965,75966],{"xmlns":1484},[1487,75967,75968,75980],{},[1490,75969,75970,75972,75974,75976,75978],{},[1493,75971,3633],{},[1493,75973,1998],{},[1506,75975,1508],{},[1493,75977,1495],{},[1493,75979,1998],{},[1528,75981,69402],{"encoding":1530},", pro ",[1047,75984,75985],{},"maximum zisku",[1035,75987,75989],{"className":75988},[1480],[1482,75990,75991],{"xmlns":1484},[1487,75992,75993,76005],{},[1490,75994,75995,75997,75999,76001,76003],{},[1493,75996,1495],{},[1493,75998,1995],{},[1506,76000,1508],{},[1493,76002,1495],{},[1493,76004,1998],{},[1528,76006,11390],{"encoding":1530},". Obě podmínky využívají ",[1035,76009,76011],{"className":76010},[1480],[1482,76012,76013],{"xmlns":1484},[1487,76014,76015,76021],{},[1490,76016,76017,76019],{},[1493,76018,1495],{},[1493,76020,1998],{},[1528,76022,69470],{"encoding":1530},", ale rovnají ho rozdílným veličinám (",[1035,76025,76027],{"className":76026},[1480],[1482,76028,76029],{"xmlns":1484},[1487,76030,76031,76037],{},[1490,76032,76033,76035],{},[1493,76034,3633],{},[1493,76036,1998],{},[1528,76038,16523],{"encoding":1530},[1035,76040,76042],{"className":76041},[1480],[1482,76043,76044],{"xmlns":1484},[1487,76045,76046,76052],{},[1490,76047,76048,76050],{},[1493,76049,1495],{},[1493,76051,1995],{},[1528,76053,6258],{"encoding":1530},[52452,76055,76057],{"id":76056},"příklad-37","Příklad 3.7",[1030,76059,76060,8686,76062,76096,76097,76110,76111,76126],{},[1047,76061,70164],{},[1035,76063,76065],{"className":76064},[1480],[1482,76066,76067],{"xmlns":1484},[1487,76068,76069,76093],{},[1490,76070,76071,76073,76075,76077,76083,76085,76087,76089,76091],{},[1493,76072,5289],{},[1493,76074,1998],{},[1506,76076,1508],{},[2315,76078,76079,76081],{},[1493,76080,1520],{},[1680,76082,1691],{},[1506,76084,2162],{},[1680,76086,3201],{},[1493,76088,1520],{},[1506,76090,2162],{},[1680,76092,14846],{},[1528,76094,76095],{"encoding":1530},"TC = Q^2 + 3Q + 36"," najděte ",[1035,76098,76100],{"className":76099},[1480],[1482,76101,76102],{"xmlns":1484},[1487,76103,76104,76108],{},[1490,76105,76106],{},[1493,76107,1520],{},[1528,76109,1520],{"encoding":1530}," minimalizující ",[1035,76112,76114],{"className":76113},[1480],[1482,76115,76116],{"xmlns":1484},[1487,76117,76118,76124],{},[1490,76119,76120,76122],{},[1493,76121,3633],{},[1493,76123,1998],{},[1528,76125,16523],{"encoding":1530}," a ověřte princip (3.10).",[1030,76128,76129,76131],{},[1047,76130,38365],{}," Přímý výpočet:",[1035,76133,76135],{"className":76134},[1480],[1482,76136,76137],{"xmlns":1484,"display":1485},[1487,76138,76139,76241],{},[1490,76140,76141,76143,76145,76147,76169,76171,76173,76175,76177,76179,76185,76187,76189,76191,76193,76195,76201,76203,76205,76207,76217,76219,76239],{},[1493,76142,3633],{},[1493,76144,1998],{},[1506,76146,1508],{},[1510,76148,76149,76167],{},[1490,76150,76151,76157,76159,76161,76163,76165],{},[2315,76152,76153,76155],{},[1493,76154,1520],{},[1680,76156,1691],{},[1506,76158,2162],{},[1680,76160,3201],{},[1493,76162,1520],{},[1506,76164,2162],{},[1680,76166,14846],{},[1493,76168,1520],{},[1506,76170,1508],{},[1493,76172,1520],{},[1506,76174,2162],{},[1680,76176,3201],{},[1506,76178,2162],{},[1510,76180,76181,76183],{},[1680,76182,14846],{},[1493,76184,1520],{},[1506,76186,1559],{"separator":1041},[1912,76188],{"width":1914},[1506,76190,1553],{"stretchy":1552},[1493,76192,3633],{},[1493,76194,1998],{},[2315,76196,76197,76199],{},[1506,76198,1564],{"stretchy":1552},[1506,76200,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,76202,1508],{},[1680,76204,1682],{},[1506,76206,1888],{},[1510,76208,76209,76211],{},[1680,76210,14846],{},[2315,76212,76213,76215],{},[1493,76214,1520],{},[1680,76216,1691],{},[1506,76218,1508],{},[1510,76220,76221,76233],{},[1490,76222,76223,76229,76231],{},[2315,76224,76225,76227],{},[1493,76226,1520],{},[1680,76228,1691],{},[1506,76230,1888],{},[1680,76232,14846],{},[2315,76234,76235,76237],{},[1493,76236,1520],{},[1680,76238,1691],{},[1493,76240,2632],{"mathvariant":1516},[1528,76242,76243],{"encoding":1530},"AC = \\frac{Q^2 + 3Q + 36}{Q} = Q + 3 + \\frac{36}{Q}, \\qquad (AC)' = 1 - \\frac{36}{Q^2} = \\frac{Q^2 - 36}{Q^2}.",[1030,76245,76246,76286,76287,76311,76312,76362,76363,2632],{},[1035,76247,76249],{"className":76248},[1480],[1482,76250,76251],{"xmlns":1484},[1487,76252,76253,76283],{},[1490,76254,76255,76257,76259,76261,76267,76269,76271,76273,76279,76281],{},[1506,76256,1553],{"stretchy":1552},[1493,76258,3633],{},[1493,76260,1998],{},[2315,76262,76263,76265],{},[1506,76264,1564],{"stretchy":1552},[1506,76266,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,76268,1508],{},[1680,76270,1871],{},[1506,76272,2183],{},[1497,76274,76275,76277],{},[1493,76276,1520],{},[1680,76278,1682],{},[1506,76280,1508],{},[1680,76282,7508],{},[1528,76284,76285],{"encoding":1530},"(AC)' = 0 \\Rightarrow Q_1 = 6"," (smysluplné), ",[1035,76288,76290],{"className":76289},[1480],[1482,76291,76292],{"xmlns":1484},[1487,76293,76294,76308],{},[1490,76295,76296,76302,76304,76306],{},[1497,76297,76298,76300],{},[1493,76299,1520],{},[1680,76301,1691],{},[1506,76303,1508],{},[1506,76305,1888],{},[1680,76307,7508],{},[1528,76309,76310],{"encoding":1530},"Q_2 = -6"," (vyloučeno). ",[1035,76313,76315],{"className":76314},[1480],[1482,76316,76317],{"xmlns":1484},[1487,76318,76319,76359],{},[1490,76320,76321,76323,76325,76327,76337,76339,76341,76343,76345,76353,76355,76357],{},[1506,76322,1553],{"stretchy":1552},[1493,76324,3633],{},[1493,76326,1998],{},[2315,76328,76329,76331],{},[1506,76330,1564],{"stretchy":1552},[1490,76332,76333,76335],{},[1506,76334,6927],{"mathvariant":1516},[1506,76336,6927],{"mathvariant":1516},[1506,76338,1553],{"stretchy":1552},[1680,76340,7508],{},[1506,76342,1564],{"stretchy":1552},[1506,76344,1508],{},[1869,76346,76347],{"scriptlevel":1871,"displaystyle":1552},[1510,76348,76349,76351],{},[1680,76350,1682],{},[1680,76352,3201],{},[1506,76354,2796],{},[1680,76356,1871],{},[1506,76358,2183],{},[1528,76360,76361],{"encoding":1530},"(AC)''(6) = \\tfrac{1}{3} > 0 \\Rightarrow"," minimum. ",[1035,76364,76366],{"className":76365},[1480],[1482,76367,76368],{"xmlns":1484},[1487,76369,76370,76386],{},[1490,76371,76372,76374,76376,76378,76380,76382,76384],{},[1493,76373,3633],{},[1493,76375,1998],{},[1506,76377,1553],{"stretchy":1552},[1680,76379,7508],{},[1506,76381,1564],{"stretchy":1552},[1506,76383,1508],{},[1680,76385,9787],{},[1528,76387,76388],{"encoding":1530},"AC(6) = 15",[1030,76390,76391,76392,76418,76419,1274],{},"Pomocí principu: ",[1035,76393,76395],{"className":76394},[1480],[1482,76396,76397],{"xmlns":1484},[1487,76398,76399,76415],{},[1490,76400,76401,76403,76405,76407,76409,76411,76413],{},[1493,76402,1495],{},[1493,76404,1998],{},[1506,76406,1508],{},[1680,76408,1691],{},[1493,76410,1520],{},[1506,76412,2162],{},[1680,76414,3201],{},[1528,76416,76417],{"encoding":1530},"MC = 2Q + 3",", rovnice ",[1035,76420,76422],{"className":76421},[1480],[1482,76423,76424],{"xmlns":1484},[1487,76425,76426,76438],{},[1490,76427,76428,76430,76432,76434,76436],{},[1493,76429,3633],{},[1493,76431,1998],{},[1506,76433,1508],{},[1493,76435,1495],{},[1493,76437,1998],{},[1528,76439,69402],{"encoding":1530},[1035,76441,76443],{"className":76442},[1480],[1482,76444,76445],{"xmlns":1484,"display":1485},[1487,76446,76447,76549],{},[1490,76448,76449,76471,76473,76475,76477,76479,76481,76483,76485,76487,76493,76495,76497,76499,76501,76503,76505,76507,76513,76515,76517,76519,76521,76523,76525,76531,76533,76535,76537,76539,76541,76543,76545,76547],{},[1510,76450,76451,76469],{},[1490,76452,76453,76459,76461,76463,76465,76467],{},[2315,76454,76455,76457],{},[1493,76456,1520],{},[1680,76458,1691],{},[1506,76460,2162],{},[1680,76462,3201],{},[1493,76464,1520],{},[1506,76466,2162],{},[1680,76468,14846],{},[1493,76470,1520],{},[1506,76472,1508],{},[1680,76474,1691],{},[1493,76476,1520],{},[1506,76478,2162],{},[1680,76480,3201],{},[1988,76482,1990],{},[1506,76484,2183],{},[1988,76486,1990],{},[2315,76488,76489,76491],{},[1493,76490,1520],{},[1680,76492,1691],{},[1506,76494,2162],{},[1680,76496,3201],{},[1493,76498,1520],{},[1506,76500,2162],{},[1680,76502,14846],{},[1506,76504,1508],{},[1680,76506,1691],{},[2315,76508,76509,76511],{},[1493,76510,1520],{},[1680,76512,1691],{},[1506,76514,2162],{},[1680,76516,3201],{},[1493,76518,1520],{},[1988,76520,1990],{},[1506,76522,2183],{},[1988,76524,1990],{},[2315,76526,76527,76529],{},[1493,76528,1520],{},[1680,76530,1691],{},[1506,76532,1508],{},[1680,76534,14846],{},[1988,76536,1990],{},[1506,76538,2183],{},[1988,76540,1990],{},[1493,76542,1520],{},[1506,76544,1508],{},[1680,76546,7508],{},[1506,76548,1559],{"separator":1041},[1528,76550,76551],{"encoding":1530},"\\frac{Q^2 + 3Q + 36}{Q} = 2Q + 3 \\;\\Rightarrow\\; Q^2 + 3Q + 36 = 2Q^2 + 3Q \\;\\Rightarrow\\; Q^2 = 36 \\;\\Rightarrow\\; Q = 6,",[1030,76553,76554,76555,76593],{},"a ",[1035,76556,76558],{"className":76557},[1480],[1482,76559,76560],{"xmlns":1484},[1487,76561,76562,76590],{},[1490,76563,76564,76566,76568,76570,76572,76574,76576,76578,76580,76582,76584,76586,76588],{},[1493,76565,3633],{},[1493,76567,1998],{},[1506,76569,1553],{"stretchy":1552},[1680,76571,7508],{},[1506,76573,1564],{"stretchy":1552},[1506,76575,1508],{},[1493,76577,1495],{},[1493,76579,1998],{},[1506,76581,1553],{"stretchy":1552},[1680,76583,7508],{},[1506,76585,1564],{"stretchy":1552},[1506,76587,1508],{},[1680,76589,9787],{},[1528,76591,76592],{"encoding":1530},"AC(6) = MC(6) = 15",". Oba postupy dávají stejný výsledek.",[1304,76595,76597],{"id":76596},"princip-minimalizace-průměrných-variabilních-nákladů","Princip minimalizace průměrných variabilních nákladů",[1030,76599,76600,76601,1274],{},"Analogicky pro ",[1035,76602,76604],{"className":76603},[1480],[1482,76605,76606],{"xmlns":1484},[1487,76607,76608,76616],{},[1490,76609,76610,76612,76614],{},[1493,76611,3633],{},[1493,76613,55105],{},[1493,76615,1998],{},[1528,76617,69489],{"encoding":1530},[1035,76619,76621],{"className":76620},[1480],[1482,76622,76623],{"xmlns":1484,"display":1485},[1487,76624,76625,76676],{},[19617,76626,76627],{"width":19619},[19621,76628,76629,76631,76669,76671],{},[19624,76630],{"width":19626},[19624,76632,76633],{},[1490,76634,76635,76637,76639,76641,76643,76649,76651,76653,76655,76657,76659,76665,76667],{},[1493,76636,3633],{},[1493,76638,55105],{},[1493,76640,1998],{},[1506,76642,1553],{"stretchy":1552},[1497,76644,76645,76647],{},[1493,76646,1520],{},[1680,76648,1871],{},[1506,76650,1564],{"stretchy":1552},[1506,76652,1508],{},[1493,76654,1495],{},[1493,76656,1998],{},[1506,76658,1553],{"stretchy":1552},[1497,76660,76661,76663],{},[1493,76662,1520],{},[1680,76664,1871],{},[1506,76666,1564],{"stretchy":1552},[1493,76668,2632],{"mathvariant":1516},[19624,76670],{"width":19626},[19624,76672,76673],{},[1988,76674,76675],{},"(3.11)",[1528,76677,76678],{"encoding":1530},"AVC(Q_0) = MC(Q_0).\n\\tag{3.11}",[1023,76680,76682,76688],{"className":76681,"dataCallout":70515},[1026,70514],[1030,76683,76685,32569],{"className":76684},[1033],[1035,76686],{"className":76687,"ariaHidden":1041},[1038,70522,1040],[1030,76689,76690],{},[1047,76691,76692,76693,76710],{},"V bodě minima průměrných variabilních nákladů se ",[1035,76694,76696],{"className":76695},[1480],[1482,76697,76698],{"xmlns":1484},[1487,76699,76700,76708],{},[1490,76701,76702,76704,76706],{},[1493,76703,3633],{},[1493,76705,55105],{},[1493,76707,1998],{},[1528,76709,69489],{"encoding":1530}," rovnají mezním nákladům.",[1030,76712,76713,76714,76736,76737,2632],{},"Odvození je analogické (úloha 3.14). Pro kubickou nákladovou funkci z příkladu 3.6 odpovídá ",[1035,76715,76717],{"className":76716},[1480],[1482,76718,76719],{"xmlns":1484},[1487,76720,76721,76733],{},[1490,76722,76723,76729,76731],{},[1497,76724,76725,76727],{},[1493,76726,1520],{},[1680,76728,1871],{},[1506,76730,1508],{},[1680,76732,13279],{},[1528,76734,76735],{"encoding":1530},"Q_0 = 2{,}5",". Za obvyklých podmínek platí i obrácené tvrzení — postačí řešit rovnici ",[1035,76738,76740],{"className":76739},[1480],[1482,76741,76742],{"xmlns":1484},[1487,76743,76744,76770],{},[1490,76745,76746,76748,76750,76752,76754,76756,76758,76760,76762,76764,76766,76768],{},[1493,76747,3633],{},[1493,76749,55105],{},[1493,76751,1998],{},[1506,76753,1553],{"stretchy":1552},[1493,76755,1520],{},[1506,76757,1564],{"stretchy":1552},[1506,76759,1508],{},[1493,76761,1495],{},[1493,76763,1998],{},[1506,76765,1553],{"stretchy":1552},[1493,76767,1520],{},[1506,76769,1564],{"stretchy":1552},[1528,76771,76772],{"encoding":1530},"AVC(Q) = MC(Q)",[1065,76774,76776],{"id":76775},"zisk-a-body-zvratu","Zisk a body zvratu",[1030,76778,76779,1656,76782,76798],{},[1047,76780,76781],{},"Zisk",[1035,76783,76785],{"className":76784},[1480],[1482,76786,76787],{"xmlns":1484},[1487,76788,76789,76795],{},[1490,76790,76791,76793],{},[1493,76792,1501],{},[1493,76794,1995],{},[1528,76796,76797],{"encoding":1530},"PR"," (profit) je rozdíl celkového příjmu a celkových nákladů:",[1035,76800,76802],{"className":76801},[1480],[1482,76803,76804],{"xmlns":1484,"display":1485},[1487,76805,76806,76865],{},[19617,76807,76808],{"width":19619},[19621,76809,76810,76812,76858,76860],{},[19624,76811],{"width":19626},[19624,76813,76814],{},[1490,76815,76816,76818,76820,76822,76824,76826,76828,76830,76832,76834,76836,76838,76840,76842,76844,76846,76848,76850,76852,76854,76856],{},[1493,76817,1501],{},[1493,76819,1995],{},[1506,76821,1508],{},[1493,76823,1501],{},[1493,76825,1995],{},[1506,76827,1553],{"stretchy":1552},[1493,76829,1520],{},[1506,76831,1564],{"stretchy":1552},[1506,76833,1508],{},[1493,76835,5289],{},[1493,76837,1995],{},[1506,76839,1553],{"stretchy":1552},[1493,76841,1520],{},[1506,76843,1564],{"stretchy":1552},[1506,76845,1888],{},[1493,76847,5289],{},[1493,76849,1998],{},[1506,76851,1553],{"stretchy":1552},[1493,76853,1520],{},[1506,76855,1564],{"stretchy":1552},[1493,76857,2632],{"mathvariant":1516},[19624,76859],{"width":19626},[19624,76861,76862],{},[1988,76863,76864],{},"(3.12)",[1528,76866,76867],{"encoding":1530},"PR = PR(Q) = TR(Q) - TC(Q).\n\\tag{3.12}",[1030,76869,76870,76871,1586,76886,58116,76901,76903,76904,76907,76908,76924,76925,76940,76941,76956,76957,1732,76970,76983,76984,1732,77002,77020,77021,7606,77024,77027,77028,16846,77050,8994,77072,77094,77095,8994,77125,77147],{},"Body rovnosti ",[1035,76872,76874],{"className":76873},[1480],[1482,76875,76876],{"xmlns":1484},[1487,76877,76878,76884],{},[1490,76879,76880,76882],{},[1493,76881,5289],{},[1493,76883,1995],{},[1528,76885,16491],{"encoding":1530},[1035,76887,76889],{"className":76888},[1480],[1482,76890,76891],{"xmlns":1484},[1487,76892,76893,76899],{},[1490,76894,76895,76897],{},[1493,76896,5289],{},[1493,76898,1998],{},[1528,76900,18668],{"encoding":1530},[1047,76902,69904],{}," (též vyrovnání, ",[1176,76905,76906],{},"break-even points","). V nejjednodušším modelu (lineární poptávka, konstantní ",[1035,76909,76911],{"className":76910},[1480],[1482,76912,76913],{"xmlns":1484},[1487,76914,76915,76921],{},[1490,76916,76917,76919],{},[1493,76918,55105],{},[1493,76920,1998],{},[1528,76922,76923],{"encoding":1530},"VC",") je ",[1035,76926,76928],{"className":76927},[1480],[1482,76929,76930],{"xmlns":1484},[1487,76931,76932,76938],{},[1490,76933,76934,76936],{},[1493,76935,5289],{},[1493,76937,1995],{},[1528,76939,16491],{"encoding":1530}," kvadratická a ",[1035,76942,76944],{"className":76943},[1480],[1482,76945,76946],{"xmlns":1484},[1487,76947,76948,76954],{},[1490,76949,76950,76952],{},[1493,76951,5289],{},[1493,76953,1998],{},[1528,76955,18668],{"encoding":1530}," lineární. Křivky se protínají v bodech ",[1035,76958,76960],{"className":76959},[1480],[1482,76961,76962],{"xmlns":1484},[1487,76963,76964,76968],{},[1490,76965,76966],{},[1493,76967,3633],{},[1528,76969,3633],{"encoding":1530},[1035,76971,76973],{"className":76972},[1480],[1482,76974,76975],{"xmlns":1484},[1487,76976,76977,76981],{},[1490,76978,76979],{},[1493,76980,11353],{},[1528,76982,11353],{"encoding":1530}," odpovídajících množstvím ",[1035,76985,76987],{"className":76986},[1480],[1482,76988,76989],{"xmlns":1484},[1487,76990,76991,76999],{},[1490,76992,76993],{},[1497,76994,76995,76997],{},[1493,76996,1520],{},[1493,76998,3633],{},[1528,77000,77001],{"encoding":1530},"Q_A",[1035,77003,77005],{"className":77004},[1480],[1482,77006,77007],{"xmlns":1484},[1487,77008,77009,77017],{},[1490,77010,77011],{},[1497,77012,77013,77015],{},[1493,77014,1520],{},[1493,77016,11353],{},[1528,77018,77019],{"encoding":1530},"Q_B"," — firma je na ",[1047,77022,77023],{},"prahu rentability",[1176,77025,77026],{},"break even","). Pro ",[1035,77029,77031],{"className":77030},[1480],[1482,77032,77033],{"xmlns":1484},[1487,77034,77035,77047],{},[1490,77036,77037,77039,77041],{},[1493,77038,1520],{},[1506,77040,3961],{},[1497,77042,77043,77045],{},[1493,77044,1520],{},[1493,77046,3633],{},[1528,77048,77049],{"encoding":1530},"Q \u003C Q_A",[1035,77051,77053],{"className":77052},[1480],[1482,77054,77055],{"xmlns":1484},[1487,77056,77057,77069],{},[1490,77058,77059,77061,77063],{},[1493,77060,1520],{},[1506,77062,2796],{},[1497,77064,77065,77067],{},[1493,77066,1520],{},[1493,77068,11353],{},[1528,77070,77071],{"encoding":1530},"Q > Q_B",[1035,77073,77075],{"className":77074},[1480],[1482,77076,77077],{"xmlns":1484},[1487,77078,77079,77091],{},[1490,77080,77081,77083,77085,77087,77089],{},[1493,77082,5289],{},[1493,77084,1998],{},[1506,77086,2796],{},[1493,77088,5289],{},[1493,77090,1995],{},[1528,77092,77093],{"encoding":1530},"TC > TR"," (ztráta); pro ",[1035,77096,77098],{"className":77097},[1480],[1482,77099,77100],{"xmlns":1484},[1487,77101,77102,77122],{},[1490,77103,77104,77110,77112,77114,77116],{},[1497,77105,77106,77108],{},[1493,77107,1520],{},[1493,77109,3633],{},[1506,77111,3961],{},[1493,77113,1520],{},[1506,77115,3961],{},[1497,77117,77118,77120],{},[1493,77119,1520],{},[1493,77121,11353],{},[1528,77123,77124],{"encoding":1530},"Q_A \u003C Q \u003C Q_B",[1035,77126,77128],{"className":77127},[1480],[1482,77129,77130],{"xmlns":1484},[1487,77131,77132,77144],{},[1490,77133,77134,77136,77138,77140,77142],{},[1493,77135,5289],{},[1493,77137,1995],{},[1506,77139,2796],{},[1493,77141,5289],{},[1493,77143,1998],{},[1528,77145,77146],{"encoding":1530},"TR > TC"," (zisk).",[1023,77149,77151,77158],{"className":77150,"dataCallout":582},[1026,1186],[1030,77152,77154,77157],{"className":77153},[1033],[1035,77155],{"className":77156,"ariaHidden":1041},[1038,1193,1040],"Intuice — body zvratu",[1030,77159,77160],{},"Body zvratu jsou hranice „prodělečné\" a „ziskové\" zóny. Mezi nimi firma vydělává, za nimi prodělává. Maximum zisku leží uvnitř tohoto intervalu — typicky v jeho středu, je-li zisk kvadratický.",[1030,77162,77163,77164,77190],{},"Body zvratu jsou řešení rovnice ",[1035,77165,77167],{"className":77166},[1480],[1482,77168,77169],{"xmlns":1484},[1487,77170,77171,77187],{},[1490,77172,77173,77175,77177,77179,77181,77183,77185],{},[1493,77174,1501],{},[1493,77176,1995],{},[1506,77178,1553],{"stretchy":1552},[1493,77180,1520],{},[1506,77182,1564],{"stretchy":1552},[1506,77184,1508],{},[1680,77186,1871],{},[1528,77188,77189],{"encoding":1530},"PR(Q) = 0",". Pro vyšší stupně polynomu může být nutné použít software či numerický odhad. Maximum zisku se stanoví jako extrém funkce zisku.",[1030,77192,77193],{},[18014,77194],{"alt":77195,"className":77196,"src":77197},"imek-tr-tc-body-zvratu",[1055,18018],"\u002Fwiki-assets\u002Fimek-tr-tc-body-zvratu.jpeg",[52452,77199,77201],{"id":77200},"příklad-38","Příklad 3.8",[1030,77203,77204,77206,77207,1732,77227,1732,77253,77279],{},[1047,77205,70164],{}," Dáno ",[1035,77208,77210],{"className":77209},[1480],[1482,77211,77212],{"xmlns":1484},[1487,77213,77214,77224],{},[1490,77215,77216,77218,77220,77222],{},[1493,77217,10790],{},[1493,77219,1998],{},[1506,77221,1508],{},[1680,77223,4007],{},[1528,77225,77226],{"encoding":1530},"FC = 4",[1035,77228,77230],{"className":77229},[1480],[1482,77231,77232],{"xmlns":1484},[1487,77233,77234,77250],{},[1490,77235,77236,77238,77240,77242,77244],{},[1493,77237,5289],{},[1493,77239,55105],{},[1493,77241,1998],{},[1506,77243,1508],{},[2315,77245,77246,77248],{},[1493,77247,1520],{},[1680,77249,1691],{},[1528,77251,77252],{"encoding":1530},"TVC = Q^2",[1035,77254,77256],{"className":77255},[1480],[1482,77257,77258],{"xmlns":1484},[1487,77259,77260,77276],{},[1490,77261,77262,77264,77266,77268,77270,77272,77274],{},[1493,77263,1501],{},[1506,77265,1508],{},[1506,77267,1888],{},[1680,77269,1691],{},[1493,77271,1520],{},[1506,77273,2162],{},[1680,77275,14365],{},[1528,77277,77278],{"encoding":1530},"P = -2Q + 9",". Určete zisk, body zvratu a bod maxima zisku.",[1030,77281,77282,77284],{},[1047,77283,38365],{}," Celkové náklady a příjem:",[1035,77286,77288],{"className":77287},[1480],[1482,77289,77290],{"xmlns":1484,"display":1485},[1487,77291,77292,77358],{},[1490,77293,77294,77296,77298,77300,77302,77304,77310,77312,77314,77316,77318,77320,77322,77324,77326,77328,77330,77332,77334,77336,77338,77340,77342,77344,77350,77352,77354,77356],{},[1493,77295,5289],{},[1493,77297,1998],{},[1506,77299,1508],{},[1680,77301,4007],{},[1506,77303,2162],{},[2315,77305,77306,77308],{},[1493,77307,1520],{},[1680,77309,1691],{},[1506,77311,1559],{"separator":1041},[1912,77313],{"width":1914},[1493,77315,5289],{},[1493,77317,1995],{},[1506,77319,1508],{},[1493,77321,1520],{},[1506,77323,1714],{},[1506,77325,1553],{"stretchy":1552},[1506,77327,1888],{},[1680,77329,1691],{},[1493,77331,1520],{},[1506,77333,2162],{},[1680,77335,14365],{},[1506,77337,1564],{"stretchy":1552},[1506,77339,1508],{},[1506,77341,1888],{},[1680,77343,1691],{},[2315,77345,77346,77348],{},[1493,77347,1520],{},[1680,77349,1691],{},[1506,77351,2162],{},[1680,77353,14365],{},[1493,77355,1520],{},[1493,77357,2632],{"mathvariant":1516},[1528,77359,77360],{"encoding":1530},"TC = 4 + Q^2, \\qquad TR = Q \\cdot (-2Q + 9) = -2Q^2 + 9Q.",[1030,77362,77363],{},"Zisk dle (3.12):",[1035,77365,77367],{"className":77366},[1480],[1482,77368,77369],{"xmlns":1484,"display":1485},[1487,77370,77371,77449],{},[1490,77372,77373,77375,77377,77379,77381,77383,77385,77387,77389,77391,77393,77395,77397,77403,77405,77407,77409,77411,77413,77415,77417,77419,77425,77427,77429,77431,77433,77439,77441,77443,77445,77447],{},[1493,77374,1501],{},[1493,77376,1995],{},[1506,77378,1508],{},[1493,77380,5289],{},[1493,77382,1995],{},[1506,77384,1888],{},[1493,77386,5289],{},[1493,77388,1998],{},[1506,77390,1508],{},[1506,77392,1553],{"stretchy":1552},[1506,77394,1888],{},[1680,77396,1691],{},[2315,77398,77399,77401],{},[1493,77400,1520],{},[1680,77402,1691],{},[1506,77404,2162],{},[1680,77406,14365],{},[1493,77408,1520],{},[1506,77410,1564],{"stretchy":1552},[1506,77412,1888],{},[1506,77414,1553],{"stretchy":1552},[1680,77416,4007],{},[1506,77418,2162],{},[2315,77420,77421,77423],{},[1493,77422,1520],{},[1680,77424,1691],{},[1506,77426,1564],{"stretchy":1552},[1506,77428,1508],{},[1506,77430,1888],{},[1680,77432,3201],{},[2315,77434,77435,77437],{},[1493,77436,1520],{},[1680,77438,1691],{},[1506,77440,2162],{},[1680,77442,14365],{},[1493,77444,1520],{},[1506,77446,1888],{},[1680,77448,73087],{},[1528,77450,77451],{"encoding":1530},"PR = TR - TC = (-2Q^2 + 9Q) - (4 + Q^2) = -3Q^2 + 9Q - 4.",[1030,77453,77454,77457,77458,33723,77494,1274],{},[1047,77455,77456],{},"Body zvratu"," jsou kořeny rovnice ",[1035,77459,77461],{"className":77460},[1480],[1482,77462,77463],{"xmlns":1484},[1487,77464,77465,77491],{},[1490,77466,77467,77469,77471,77477,77479,77481,77483,77485,77487,77489],{},[1506,77468,1888],{},[1680,77470,3201],{},[2315,77472,77473,77475],{},[1493,77474,1520],{},[1680,77476,1691],{},[1506,77478,2162],{},[1680,77480,14365],{},[1493,77482,1520],{},[1506,77484,1888],{},[1680,77486,4007],{},[1506,77488,1508],{},[1680,77490,1871],{},[1528,77492,77493],{"encoding":1530},"-3Q^2 + 9Q - 4 = 0",[1035,77495,77497],{"className":77496},[1480],[1482,77498,77499],{"xmlns":1484},[1487,77500,77501,77525],{},[1490,77502,77503,77505,77511,77513,77515,77517,77519,77521,77523],{},[1680,77504,3201],{},[2315,77506,77507,77509],{},[1493,77508,1520],{},[1680,77510,1691],{},[1506,77512,1888],{},[1680,77514,14365],{},[1493,77516,1520],{},[1506,77518,2162],{},[1680,77520,4007],{},[1506,77522,1508],{},[1680,77524,1871],{},[1528,77526,77527],{"encoding":1530},"3Q^2 - 9Q + 4 = 0",[1035,77529,77531],{"className":77530},[1480],[1482,77532,77533],{"xmlns":1484,"display":1485},[1487,77534,77535,77589],{},[1490,77536,77537,77549,77551,77571,77573,77587],{},[1497,77538,77539,77541],{},[1493,77540,1520],{},[1490,77542,77543,77545,77547],{},[1680,77544,1682],{},[1506,77546,1559],{"separator":1041},[1680,77548,1691],{},[1506,77550,1508],{},[1510,77552,77553,77569],{},[1490,77554,77555,77557,77559],{},[1680,77556,14365],{},[1506,77558,11304],{},[2324,77560,77561],{},[1490,77562,77563,77565,77567],{},[1680,77564,14703],{},[1506,77566,1888],{},[1680,77568,10052],{},[1680,77570,7508],{},[1506,77572,1508],{},[1510,77574,77575,77585],{},[1490,77576,77577,77579,77581],{},[1680,77578,14365],{},[1506,77580,11304],{},[2324,77582,77583],{},[1680,77584,6057],{},[1680,77586,7508],{},[1506,77588,1559],{"separator":1041},[1528,77590,77591],{"encoding":1530},"Q_{1,2} = \\frac{9 \\pm \\sqrt{81 - 48}}{6} = \\frac{9 \\pm \\sqrt{33}}{6},",[1030,77593,77594,77595,1586,77618,2632],{},"numericky ",[1035,77596,77598],{"className":77597},[1480],[1482,77599,77600],{"xmlns":1484},[1487,77601,77602,77615],{},[1490,77603,77604,77610,77612],{},[1497,77605,77606,77608],{},[1493,77607,1520],{},[1680,77609,1682],{},[1506,77611,21771],{},[1680,77613,77614],{},"0,543",[1528,77616,77617],{"encoding":1530},"Q_1 \\doteq 0{,}543",[1035,77619,77621],{"className":77620},[1480],[1482,77622,77623],{"xmlns":1484},[1487,77624,77625,77638],{},[1490,77626,77627,77633,77635],{},[1497,77628,77629,77631],{},[1493,77630,1520],{},[1680,77632,1691],{},[1506,77634,21771],{},[1680,77636,77637],{},"2,457",[1528,77639,77640],{"encoding":1530},"Q_2 \\doteq 2{,}457",[1030,77642,77643,1656,77646,23505,77691,33723,77725,77743],{},[1047,77644,77645],{},"Maximum zisku.",[1035,77647,77649],{"className":77648},[1480],[1482,77650,77651],{"xmlns":1484},[1487,77652,77653,77688],{},[1490,77654,77655,77657,77663,77665,77667,77669,77671,77673,77675,77677,77679,77681,77683,77685],{},[1493,77656,1501],{},[2315,77658,77659,77661],{},[1493,77660,1995],{},[1506,77662,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,77664,1508],{},[1506,77666,1888],{},[1680,77668,7508],{},[1493,77670,1520],{},[1506,77672,2162],{},[1680,77674,14365],{},[1506,77676,1508],{},[1680,77678,1871],{},[1506,77680,2183],{},[1493,77682,1520],{},[1506,77684,1508],{},[1680,77686,77687],{},"1,5",[1528,77689,77690],{"encoding":1530},"PR' = -6Q + 9 = 0 \\Rightarrow Q = 1{,}5",[1035,77692,77694],{"className":77693},[1480],[1482,77695,77696],{"xmlns":1484},[1487,77697,77698,77722],{},[1490,77699,77700,77702,77712,77714,77716,77718,77720],{},[1493,77701,1501],{},[2315,77703,77704,77706],{},[1493,77705,1995],{},[1490,77707,77708,77710],{},[1506,77709,6927],{"mathvariant":1516},[1506,77711,6927],{"mathvariant":1516},[1506,77713,1508],{},[1506,77715,1888],{},[1680,77717,7508],{},[1506,77719,3961],{},[1680,77721,1871],{},[1528,77723,77724],{"encoding":1530},"PR'' = -6 \u003C 0",[1035,77726,77728],{"className":77727},[1480],[1482,77729,77730],{"xmlns":1484},[1487,77731,77732,77740],{},[1490,77733,77734,77736,77738],{},[1493,77735,1520],{},[1506,77737,1508],{},[1680,77739,77687],{},[1528,77741,77742],{"encoding":1530},"Q = 1{,}5"," je bod maxima s hodnotou",[1035,77745,77747],{"className":77746},[1480],[1482,77748,77749],{"xmlns":1484,"display":1485},[1487,77750,77751,77814],{},[1490,77752,77753,77755,77757,77759,77761,77763,77765,77767,77769,77771,77773,77775,77781,77783,77785,77787,77789,77791,77793,77795,77797,77800,77802,77805,77807,77809,77811],{},[1493,77754,1501],{},[1493,77756,1995],{},[1506,77758,1553],{"stretchy":1552},[1680,77760,77687],{},[1506,77762,1564],{"stretchy":1552},[1506,77764,1508],{},[1506,77766,1888],{},[1680,77768,3201],{},[1506,77770,1714],{},[1506,77772,1553],{"stretchy":1552},[1680,77774,77687],{},[2315,77776,77777,77779],{},[1506,77778,1564],{"stretchy":1552},[1680,77780,1691],{},[1506,77782,2162],{},[1680,77784,14365],{},[1506,77786,1714],{},[1680,77788,77687],{},[1506,77790,1888],{},[1680,77792,4007],{},[1506,77794,1508],{},[1506,77796,1888],{},[1680,77798,77799],{},"6,75",[1506,77801,2162],{},[1680,77803,77804],{},"13,5",[1506,77806,1888],{},[1680,77808,4007],{},[1506,77810,1508],{},[1680,77812,77813],{},"2,75.",[1528,77815,77816],{"encoding":1530},"PR(1{,}5) = -3 \\cdot (1{,}5)^2 + 9 \\cdot 1{,}5 - 4 = -6{,}75 + 13{,}5 - 4 = 2{,}75.",[1030,77818,77819,77820,1732,77865,77918,77919,77937],{},"Pro srovnání maximum celkového příjmu (bez ohledu na náklady): ",[1035,77821,77823],{"className":77822},[1480],[1482,77824,77825],{"xmlns":1484},[1487,77826,77827,77862],{},[1490,77828,77829,77831,77837,77839,77841,77843,77845,77847,77849,77851,77853,77855,77857,77859],{},[1493,77830,5289],{},[2315,77832,77833,77835],{},[1493,77834,1995],{},[1506,77836,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,77838,1508],{},[1506,77840,1888],{},[1680,77842,4007],{},[1493,77844,1520],{},[1506,77846,2162],{},[1680,77848,14365],{},[1506,77850,1508],{},[1680,77852,1871],{},[1506,77854,2183],{},[1493,77856,1520],{},[1506,77858,1508],{},[1680,77860,77861],{},"2,25",[1528,77863,77864],{"encoding":1530},"TR' = -4Q + 9 = 0 \\Rightarrow Q = 2{,}25",[1035,77866,77868],{"className":77867},[1480],[1482,77869,77870],{"xmlns":1484},[1487,77871,77872,77915],{},[1490,77873,77874,77876,77884,77886,77888,77890,77892,77894,77896,77902,77904,77906,77908,77910,77912],{},[1493,77875,5289],{},[1497,77877,77878,77880,77882],{},[1493,77879,1995],{},[1493,77881,7571],{},[1506,77883,7574],{},[1506,77885,1508],{},[1506,77887,1888],{},[1680,77889,1691],{},[1506,77891,1714],{},[1506,77893,1553],{"stretchy":1552},[1680,77895,77861],{},[2315,77897,77898,77900],{},[1506,77899,1564],{"stretchy":1552},[1680,77901,1691],{},[1506,77903,2162],{},[1680,77905,14365],{},[1506,77907,1714],{},[1680,77909,77861],{},[1506,77911,1508],{},[1680,77913,77914],{},"10,125",[1528,77916,77917],{"encoding":1530},"TR_{\\max} = -2 \\cdot (2{,}25)^2 + 9 \\cdot 2{,}25 = 10{,}125",". Leží vpravo od bodu maxima zisku, protože při ",[1035,77920,77922],{"className":77921},[1480],[1482,77923,77924],{"xmlns":1484},[1487,77925,77926,77934],{},[1490,77927,77928,77930,77932],{},[1493,77929,1520],{},[1506,77931,1508],{},[1680,77933,77861],{},[1528,77935,77936],{"encoding":1530},"Q = 2{,}25"," rostou už náklady rychleji než příjem.",[1065,77939,77941],{"id":77940},"princip-maximalizace-zisku","Princip maximalizace zisku",[1030,77943,77944],{},"Kromě standardního hledání extrému lze využít následující princip.",[1030,77946,77947],{},[18014,77948],{"alt":77949,"className":77950,"src":77951},"imek-max-zisku-dva-pohledy",[1055,18018],"\u002Fwiki-assets\u002Fimek-max-zisku-dva-pohledy.jpeg",[1304,77953,32569],{"id":77954},"princip-1",[1030,77956,77957,77958,11713,77973,77990],{},"Má-li zisk ",[1035,77959,77961],{"className":77960},[1480],[1482,77962,77963],{"xmlns":1484},[1487,77964,77965,77971],{},[1490,77966,77967,77969],{},[1493,77968,1501],{},[1493,77970,1995],{},[1528,77972,76797],{"encoding":1530},[1035,77974,77976],{"className":77975},[1480],[1482,77977,77978],{"xmlns":1484},[1487,77979,77980,77988],{},[1490,77981,77982],{},[1497,77983,77984,77986],{},[1493,77985,1520],{},[1680,77987,1871],{},[1528,77989,53236],{"encoding":1530}," maximum, pak platí",[1035,77992,77994],{"className":77993},[1480],[1482,77995,77996],{"xmlns":1484,"display":1485},[1487,77997,77998,78047],{},[19617,77999,78000],{"width":19619},[19621,78001,78002,78004,78040,78042],{},[19624,78003],{"width":19626},[19624,78005,78006],{},[1490,78007,78008,78010,78012,78014,78020,78022,78024,78026,78028,78030,78036,78038],{},[1493,78009,1495],{},[1493,78011,1995],{},[1506,78013,1553],{"stretchy":1552},[1497,78015,78016,78018],{},[1493,78017,1520],{},[1680,78019,1871],{},[1506,78021,1564],{"stretchy":1552},[1506,78023,1508],{},[1493,78025,1495],{},[1493,78027,1998],{},[1506,78029,1553],{"stretchy":1552},[1497,78031,78032,78034],{},[1493,78033,1520],{},[1680,78035,1871],{},[1506,78037,1564],{"stretchy":1552},[1493,78039,2632],{"mathvariant":1516},[19624,78041],{"width":19626},[19624,78043,78044],{},[1988,78045,78046],{},"(3.13)",[1528,78048,78049],{"encoding":1530},"MR(Q_0) = MC(Q_0).\n\\tag{3.13}",[1023,78051,78053,78059],{"className":78052,"dataCallout":70515},[1026,70514],[1030,78054,78056,32569],{"className":78055},[1033],[1035,78057],{"className":78058,"ariaHidden":1041},[1038,70522,1040],[1030,78060,78061],{},[1047,78062,78063],{},"V bodě maxima zisku se mezní příjem rovná mezním nákladům.",[1030,78065,78066,78069,78070,8994,78097,33723,78171,2632],{},[1047,78067,78068],{},"Odvození"," (úloha 3.21): nutnou podmínkou maxima ",[1035,78071,78073],{"className":78072},[1480],[1482,78074,78075],{"xmlns":1484},[1487,78076,78077,78095],{},[1490,78078,78079,78081,78083,78085,78087,78089,78091,78093],{},[1493,78080,1501],{},[1493,78082,1995],{},[1506,78084,1508],{},[1493,78086,5289],{},[1493,78088,1995],{},[1506,78090,1888],{},[1493,78092,5289],{},[1493,78094,1998],{},[1528,78096,9401],{"encoding":1530},[1035,78098,78100],{"className":78099},[1480],[1482,78101,78102],{"xmlns":1484},[1487,78103,78104,78168],{},[1490,78105,78106,78108,78114,78116,78122,78124,78126,78128,78134,78136,78142,78144,78146,78148,78154,78156,78162,78164,78166],{},[1493,78107,1501],{},[2315,78109,78110,78112],{},[1493,78111,1995],{},[1506,78113,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,78115,1553],{"stretchy":1552},[1497,78117,78118,78120],{},[1493,78119,1520],{},[1680,78121,1871],{},[1506,78123,1564],{"stretchy":1552},[1506,78125,1508],{},[1493,78127,5289],{},[2315,78129,78130,78132],{},[1493,78131,1995],{},[1506,78133,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,78135,1553],{"stretchy":1552},[1497,78137,78138,78140],{},[1493,78139,1520],{},[1680,78141,1871],{},[1506,78143,1564],{"stretchy":1552},[1506,78145,1888],{},[1493,78147,5289],{},[2315,78149,78150,78152],{},[1493,78151,1998],{},[1506,78153,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,78155,1553],{"stretchy":1552},[1497,78157,78158,78160],{},[1493,78159,1520],{},[1680,78161,1871],{},[1506,78163,1564],{"stretchy":1552},[1506,78165,1508],{},[1680,78167,1871],{},[1528,78169,78170],{"encoding":1530},"PR'(Q_0) = TR'(Q_0) - TC'(Q_0) = 0",[1035,78172,78174],{"className":78173},[1480],[1482,78175,78176],{"xmlns":1484},[1487,78177,78178,78210],{},[1490,78179,78180,78182,78184,78186,78192,78194,78196,78198,78200,78202,78208],{},[1493,78181,1495],{},[1493,78183,1995],{},[1506,78185,1553],{"stretchy":1552},[1497,78187,78188,78190],{},[1493,78189,1520],{},[1680,78191,1871],{},[1506,78193,1564],{"stretchy":1552},[1506,78195,1508],{},[1493,78197,1495],{},[1493,78199,1998],{},[1506,78201,1553],{"stretchy":1552},[1497,78203,78204,78206],{},[1493,78205,1520],{},[1680,78207,1871],{},[1506,78209,1564],{"stretchy":1552},[1528,78211,78212],{"encoding":1530},"MR(Q_0) = MC(Q_0)",[1023,78214,78216,78223],{"className":78215,"dataCallout":1443},[1026,1442],[1030,78217,78219,78222],{"className":78218},[1033],[1035,78220],{"className":78221,"ariaHidden":1041},[1038,1450,1040],"Postup — jak najít maximum zisku",[1276,78224,78225,78289,78344,78381,78409],{},[1206,78226,78227,78228,1586,78243,78258,78259,16623],{},"Sestavte ",[1035,78229,78231],{"className":78230},[1480],[1482,78232,78233],{"xmlns":1484},[1487,78234,78235,78241],{},[1490,78236,78237,78239],{},[1493,78238,5289],{},[1493,78240,1995],{},[1528,78242,16491],{"encoding":1530},[1035,78244,78246],{"className":78245},[1480],[1482,78247,78248],{"xmlns":1484},[1487,78249,78250,78256],{},[1490,78251,78252,78254],{},[1493,78253,5289],{},[1493,78255,1998],{},[1528,78257,18668],{"encoding":1530}," ze zadání (typicky ",[1035,78260,78262],{"className":78261},[1480],[1482,78263,78264],{"xmlns":1484},[1487,78265,78266,78286],{},[1490,78267,78268,78270,78272,78274,78276,78278,78280,78282,78284],{},[1493,78269,5289],{},[1493,78271,1995],{},[1506,78273,1508],{},[1493,78275,1501],{},[1506,78277,1553],{"stretchy":1552},[1493,78279,1520],{},[1506,78281,1564],{"stretchy":1552},[1506,78283,1714],{},[1493,78285,1520],{},[1528,78287,78288],{"encoding":1530},"TR = P(Q) \\cdot Q",[1206,78290,78291,78292,1586,78318,2632],{},"Vypočtěte ",[1035,78293,78295],{"className":78294},[1480],[1482,78296,78297],{"xmlns":1484},[1487,78298,78299,78315],{},[1490,78300,78301,78303,78305,78307,78309],{},[1493,78302,1495],{},[1493,78304,1995],{},[1506,78306,1508],{},[1493,78308,5289],{},[2315,78310,78311,78313],{},[1493,78312,1995],{},[1506,78314,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,78316,78317],{"encoding":1530},"MR = TR'",[1035,78319,78321],{"className":78320},[1480],[1482,78322,78323],{"xmlns":1484},[1487,78324,78325,78341],{},[1490,78326,78327,78329,78331,78333,78335],{},[1493,78328,1495],{},[1493,78330,1998],{},[1506,78332,1508],{},[1493,78334,5289],{},[2315,78336,78337,78339],{},[1493,78338,1998],{},[1506,78340,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,78342,78343],{"encoding":1530},"MC = TC'",[1206,78345,78346,78347,2632],{},"Řešte rovnici ",[1035,78348,78350],{"className":78349},[1480],[1482,78351,78352],{"xmlns":1484},[1487,78353,78354,78378],{},[1490,78355,78356,78358,78360,78362,78364,78366,78368,78370,78372,78374,78376],{},[1493,78357,1495],{},[1493,78359,1995],{},[1506,78361,1553],{"stretchy":1552},[1493,78363,1520],{},[1506,78365,1564],{"stretchy":1552},[1506,78367,1508],{},[1493,78369,1495],{},[1493,78371,1998],{},[1506,78373,1553],{"stretchy":1552},[1493,78375,1520],{},[1506,78377,1564],{"stretchy":1552},[1528,78379,78380],{"encoding":1530},"MR(Q) = MC(Q)",[1206,78382,78383,78384,78408],{},"Ověřte druhou derivaci ",[1035,78385,78387],{"className":78386},[1480],[1482,78388,78389],{"xmlns":1484},[1487,78390,78391,78405],{},[1490,78392,78393,78395],{},[1493,78394,1501],{},[2315,78396,78397,78399],{},[1493,78398,1995],{},[1490,78400,78401,78403],{},[1506,78402,6927],{"mathvariant":1516},[1506,78404,6927],{"mathvariant":1516},[1528,78406,78407],{"encoding":1530},"PR''"," (nebo že má rovnice jediný ekonomicky smysluplný kořen).",[1206,78410,78411,78412,78439],{},"Dosaďte do ",[1035,78413,78415],{"className":78414},[1480],[1482,78416,78417],{"xmlns":1484},[1487,78418,78419,78437],{},[1490,78420,78421,78423,78425,78427,78429,78431,78433,78435],{},[1493,78422,1501],{},[1493,78424,1995],{},[1506,78426,1508],{},[1493,78428,5289],{},[1493,78430,1995],{},[1506,78432,1888],{},[1493,78434,5289],{},[1493,78436,1998],{},[1528,78438,9401],{"encoding":1530}," pro hodnotu maxima.",[52452,78441,78443],{"id":78442},"příklad-39","Příklad 3.9",[1030,78445,78446,70165,78448,1586,78470,78506],{},[1047,78447,70164],{},[1035,78449,78451],{"className":78450},[1480],[1482,78452,78453],{"xmlns":1484},[1487,78454,78455,78467],{},[1490,78456,78457,78459,78461,78463,78465],{},[1493,78458,1501],{},[1506,78460,1508],{},[1680,78462,6956],{},[1506,78464,1888],{},[1493,78466,1520],{},[1528,78468,78469],{"encoding":1530},"P = 30 - Q",[1035,78471,78473],{"className":78472},[1480],[1482,78474,78475],{"xmlns":1484},[1487,78476,78477,78503],{},[1490,78478,78479,78481,78483,78485,78487,78493,78495,78497,78499,78501],{},[1493,78480,5289],{},[1493,78482,1998],{},[1506,78484,1508],{},[1680,78486,3687],{},[2315,78488,78489,78491],{},[1493,78490,1520],{},[1680,78492,1691],{},[1506,78494,2162],{},[1680,78496,7508],{},[1493,78498,1520],{},[1506,78500,2162],{},[1680,78502,16580],{},[1528,78504,78505],{"encoding":1530},"TC = 0{,}5Q^2 + 6Q + 7"," stanovte produkci maximalizující zisk.",[1030,78508,78509,1656,78511,1732,78541,78579,78580,16351,78624,78658,78659,2632],{},[1047,78510,38365],{},[1035,78512,78514],{"className":78513},[1480],[1482,78515,78516],{"xmlns":1484},[1487,78517,78518,78538],{},[1490,78519,78520,78522,78524,78526,78528,78530,78532],{},[1493,78521,5289],{},[1493,78523,1995],{},[1506,78525,1508],{},[1680,78527,6956],{},[1493,78529,1520],{},[1506,78531,1888],{},[2315,78533,78534,78536],{},[1493,78535,1520],{},[1680,78537,1691],{},[1528,78539,78540],{"encoding":1530},"TR = 30Q - Q^2",[1035,78542,78544],{"className":78543},[1480],[1482,78545,78546],{"xmlns":1484},[1487,78547,78548,78576],{},[1490,78549,78550,78552,78554,78556,78558,78560,78566,78568,78570,78572,78574],{},[1493,78551,1501],{},[1493,78553,1995],{},[1506,78555,1508],{},[1506,78557,1888],{},[1680,78559,77687],{},[2315,78561,78562,78564],{},[1493,78563,1520],{},[1680,78565,1691],{},[1506,78567,2162],{},[1680,78569,7201],{},[1493,78571,1520],{},[1506,78573,1888],{},[1680,78575,16580],{},[1528,78577,78578],{"encoding":1530},"PR = -1{,}5Q^2 + 24Q - 7",". Extrém: ",[1035,78581,78583],{"className":78582},[1480],[1482,78584,78585],{"xmlns":1484},[1487,78586,78587,78621],{},[1490,78588,78589,78591,78597,78599,78601,78603,78605,78607,78609,78611,78613,78615,78617,78619],{},[1493,78590,1501],{},[2315,78592,78593,78595],{},[1493,78594,1995],{},[1506,78596,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,78598,1508],{},[1506,78600,1888],{},[1680,78602,3201],{},[1493,78604,1520],{},[1506,78606,2162],{},[1680,78608,7201],{},[1506,78610,1508],{},[1680,78612,1871],{},[1506,78614,2183],{},[1493,78616,1520],{},[1506,78618,1508],{},[1680,78620,6138],{},[1528,78622,78623],{"encoding":1530},"PR' = -3Q + 24 = 0 \\Rightarrow Q = 8",[1035,78625,78627],{"className":78626},[1480],[1482,78628,78629],{"xmlns":1484},[1487,78630,78631,78655],{},[1490,78632,78633,78635,78645,78647,78649,78651,78653],{},[1493,78634,1501],{},[2315,78636,78637,78639],{},[1493,78638,1995],{},[1490,78640,78641,78643],{},[1506,78642,6927],{"mathvariant":1516},[1506,78644,6927],{"mathvariant":1516},[1506,78646,1508],{},[1506,78648,1888],{},[1680,78650,3201],{},[1506,78652,3961],{},[1680,78654,1871],{},[1528,78656,78657],{"encoding":1530},"PR'' = -3 \u003C 0"," (maximum); ",[1035,78660,78662],{"className":78661},[1480],[1482,78663,78664],{"xmlns":1484},[1487,78665,78666,78683],{},[1490,78667,78668,78670,78672,78674,78676,78678,78680],{},[1493,78669,1501],{},[1493,78671,1995],{},[1506,78673,1553],{"stretchy":1552},[1680,78675,6138],{},[1506,78677,1564],{"stretchy":1552},[1506,78679,1508],{},[1680,78681,78682],{},"89",[1528,78684,78685],{"encoding":1530},"PR(8) = 89",[1030,78687,78688,78689,1732,78715,16351,78739,78777],{},"Ověření principu: ",[1035,78690,78692],{"className":78691},[1480],[1482,78693,78694],{"xmlns":1484},[1487,78695,78696,78712],{},[1490,78697,78698,78700,78702,78704,78706,78708,78710],{},[1493,78699,1495],{},[1493,78701,1995],{},[1506,78703,1508],{},[1680,78705,6956],{},[1506,78707,1888],{},[1680,78709,1691],{},[1493,78711,1520],{},[1528,78713,78714],{"encoding":1530},"MR = 30 - 2Q",[1035,78716,78718],{"className":78717},[1480],[1482,78719,78720],{"xmlns":1484},[1487,78721,78722,78736],{},[1490,78723,78724,78726,78728,78730,78732,78734],{},[1493,78725,1495],{},[1493,78727,1998],{},[1506,78729,1508],{},[1493,78731,1520],{},[1506,78733,2162],{},[1680,78735,7508],{},[1528,78737,78738],{"encoding":1530},"MC = Q + 6",[1035,78740,78742],{"className":78741},[1480],[1482,78743,78744],{"xmlns":1484},[1487,78745,78746,78774],{},[1490,78747,78748,78750,78752,78754,78756,78758,78760,78762,78764,78766,78768,78770,78772],{},[1493,78749,1495],{},[1493,78751,1995],{},[1506,78753,1553],{"stretchy":1552},[1680,78755,6138],{},[1506,78757,1564],{"stretchy":1552},[1506,78759,1508],{},[1680,78761,38539],{},[1506,78763,1508],{},[1493,78765,1495],{},[1493,78767,1998],{},[1506,78769,1553],{"stretchy":1552},[1680,78771,6138],{},[1506,78773,1564],{"stretchy":1552},[1528,78775,78776],{"encoding":1530},"MR(8) = 14 = MC(8)",", tj. platí (3.13).",[1030,78779,78780,78781,78814,78815,78832],{},"V řadě případů — má-li rovnice ",[1035,78782,78784],{"className":78783},[1480],[1482,78785,78786],{"xmlns":1484},[1487,78787,78788,78812],{},[1490,78789,78790,78792,78794,78796,78798,78800,78802,78804,78806,78808,78810],{},[1493,78791,1495],{},[1493,78793,1995],{},[1506,78795,1553],{"stretchy":1552},[1493,78797,1520],{},[1506,78799,1564],{"stretchy":1552},[1506,78801,1508],{},[1493,78803,1495],{},[1493,78805,1998],{},[1506,78807,1553],{"stretchy":1552},[1493,78809,1520],{},[1506,78811,1564],{"stretchy":1552},[1528,78813,78380],{"encoding":1530}," jediné ekonomicky smysluplné řešení ",[1035,78816,78818],{"className":78817},[1480],[1482,78819,78820],{"xmlns":1484},[1487,78821,78822,78830],{},[1490,78823,78824],{},[1497,78825,78826,78828],{},[1493,78827,1520],{},[1680,78829,1871],{},[1528,78831,53236],{"encoding":1530}," — není třeba provádět test druhé derivace.",[52452,78834,78836],{"id":78835},"příklad-310","Příklad 3.10",[1030,78838,78839,78841,78842,78846,78847,78860,78861,78892],{},[1047,78840,70164],{}," Firma vyrábí minipočítače v ",[1052,78843,78845],{"className":78844,"dataFsResolvedFilePath":3487,"href":3488},[1055],"dokonalé konkurenci",", produkuje 30 výrobků denně za ",[1035,78848,78850],{"className":78849},[1480],[1482,78851,78852],{"xmlns":1484},[1487,78853,78854,78858],{},[1490,78855,78856],{},[1680,78857,7032],{},[1528,78859,7032],{"encoding":1530}," EUR\u002Fks. ",[1035,78862,78864],{"className":78863},[1480],[1482,78865,78866],{"xmlns":1484},[1487,78867,78868,78889],{},[1490,78869,78870,78872,78874,78876,78878,78880,78883],{},[1493,78871,5289],{},[1493,78873,1998],{},[1506,78875,1508],{},[1680,78877,2292],{},[1506,78879,2162],{},[1680,78881,78882],{},"28",[2315,78884,78885,78887],{},[1493,78886,1520],{},[1680,78888,1691],{},[1528,78890,78891],{"encoding":1530},"TC = 50 + 28Q^2",". Určete optimální denní produkci a zisk.",[1030,78894,78895,1656,78897,1732,78919,1732,78939,78962],{},[1047,78896,38365],{},[1035,78898,78900],{"className":78899},[1480],[1482,78901,78902],{"xmlns":1484},[1487,78903,78904,78916],{},[1490,78905,78906,78908,78910,78912,78914],{},[1493,78907,5289],{},[1493,78909,1995],{},[1506,78911,1508],{},[1680,78913,7032],{},[1493,78915,1520],{},[1528,78917,78918],{"encoding":1530},"TR = 900Q",[1035,78920,78922],{"className":78921},[1480],[1482,78923,78924],{"xmlns":1484},[1487,78925,78926,78936],{},[1490,78927,78928,78930,78932,78934],{},[1493,78929,1495],{},[1493,78931,1995],{},[1506,78933,1508],{},[1680,78935,7032],{},[1528,78937,78938],{"encoding":1530},"MR = 900",[1035,78940,78942],{"className":78941},[1480],[1482,78943,78944],{"xmlns":1484},[1487,78945,78946,78959],{},[1490,78947,78948,78950,78952,78954,78957],{},[1493,78949,1495],{},[1493,78951,1998],{},[1506,78953,1508],{},[1680,78955,78956],{},"56",[1493,78958,1520],{},[1528,78960,78961],{"encoding":1530},"MC = 56Q",". Z principu:",[1035,78964,78966],{"className":78965},[1480],[1482,78967,78968],{"xmlns":1484,"display":1485},[1487,78969,78970,79012],{},[1490,78971,78972,78974,78976,78978,78980,78982,78984,78986,78988,78990,78998,79000,79003,79005,79007,79009],{},[1680,78973,7032],{},[1506,78975,1508],{},[1680,78977,78956],{},[1493,78979,1520],{},[1988,78981,1990],{},[1506,78983,2183],{},[1988,78985,1990],{},[1493,78987,1520],{},[1506,78989,1508],{},[1869,78991,78992],{"scriptlevel":1871,"displaystyle":1552},[1510,78993,78994,78996],{},[1680,78995,7032],{},[1680,78997,78956],{},[1506,78999,21771],{},[1680,79001,79002],{},"16,07",[1988,79004,1990],{},[1506,79006,2343],{},[1988,79008,1990],{},[1680,79010,79011],{},"16.",[1528,79013,79014],{"encoding":1530},"900 = 56Q \\;\\Rightarrow\\; Q = \\tfrac{900}{56} \\doteq 16{,}07 \\;\\approx\\; 16.",[1030,79016,79017,79018,1274],{},"Zisk při ",[1035,79019,79021],{"className":79020},[1480],[1482,79022,79023],{"xmlns":1484},[1487,79024,79025,79033],{},[1490,79026,79027,79029,79031],{},[1493,79028,1520],{},[1506,79030,1508],{},[1680,79032,9961],{},[1528,79034,79035],{"encoding":1530},"Q = 16",[1035,79037,79039],{"className":79038},[1480],[1482,79040,79041],{"xmlns":1484,"display":1485},[1487,79042,79043,79114],{},[1490,79044,79045,79047,79049,79051,79053,79055,79057,79059,79061,79063,79065,79067,79069,79071,79073,79075,79081,79083,79085,79087,79089,79091,79093,79095,79097,79100,79102,79104,79106,79109,79112],{},[1493,79046,1501],{},[1493,79048,1995],{},[1506,79050,1553],{"stretchy":1552},[1680,79052,9961],{},[1506,79054,1564],{"stretchy":1552},[1506,79056,1508],{},[1680,79058,7032],{},[1506,79060,1714],{},[1680,79062,9961],{},[1506,79064,1888],{},[1506,79066,1553],{"stretchy":1552},[1680,79068,2292],{},[1506,79070,2162],{},[1680,79072,78882],{},[1506,79074,1714],{},[2315,79076,79077,79079],{},[1680,79078,9961],{},[1680,79080,1691],{},[1506,79082,1564],{"stretchy":1552},[1506,79084,1508],{},[1680,79086,38539],{},[1988,79088,5016],{},[1680,79090,5765],{},[1506,79092,1888],{},[1680,79094,16580],{},[1988,79096,5016],{},[1680,79098,79099],{},"218",[1506,79101,1508],{},[1680,79103,16580],{},[1988,79105,5016],{},[1680,79107,79108],{},"182",[1988,79110,79111],{}," EUR",[1493,79113,2632],{"mathvariant":1516},[1528,79115,79116],{"encoding":1530},"PR(16) = 900 \\cdot 16 - (50 + 28 \\cdot 16^2) = 14\\,400 - 7\\,218 = 7\\,182 \\text{ EUR}.",[1030,79118,79119],{},"Pro srovnání při původních 30 ks:",[1035,79121,79123],{"className":79122},[1480],[1482,79124,79125],{"xmlns":1484,"display":1485},[1487,79126,79127,79191],{},[1490,79128,79129,79131,79133,79135,79137,79139,79141,79143,79145,79147,79149,79151,79153,79155,79157,79159,79161,79163,79165,79167,79169,79171,79173,79175,79177,79179,79181,79183,79185,79187,79189],{},[1493,79130,1501],{},[1493,79132,1995],{},[1506,79134,1553],{"stretchy":1552},[1680,79136,6956],{},[1506,79138,1564],{"stretchy":1552},[1506,79140,1508],{},[1680,79142,7032],{},[1506,79144,1714],{},[1680,79146,6956],{},[1506,79148,1888],{},[1506,79150,1553],{"stretchy":1552},[1680,79152,2292],{},[1506,79154,2162],{},[1680,79156,78882],{},[1506,79158,1714],{},[1680,79160,7032],{},[1506,79162,1564],{"stretchy":1552},[1506,79164,1508],{},[1680,79166,15165],{},[1988,79168,5016],{},[1680,79170,5608],{},[1506,79172,1888],{},[1680,79174,2309],{},[1988,79176,5016],{},[1680,79178,8140],{},[1506,79180,1508],{},[1680,79182,1682],{},[1988,79184,5016],{},[1680,79186,39328],{},[1988,79188,79111],{},[1493,79190,2632],{"mathvariant":1516},[1528,79192,79193],{"encoding":1530},"PR(30) = 900 \\cdot 30 - (50 + 28 \\cdot 900) = 27\\,000 - 25\\,250 = 1\\,750 \\text{ EUR}.",[1030,79195,79196,79199,79200,79218,79219,79237],{},[1047,79197,79198],{},"Doporučení:"," vyrábět 16 ks\u002Fden se ziskem ",[1035,79201,79203],{"className":79202},[1480],[1482,79204,79205],{"xmlns":1484},[1487,79206,79207,79215],{},[1490,79208,79209,79211,79213],{},[1680,79210,16580],{},[1988,79212,5016],{},[1680,79214,79108],{},[1528,79216,79217],{"encoding":1530},"7\\,182"," EUR namísto původních ",[1035,79220,79222],{"className":79221},[1480],[1482,79223,79224],{"xmlns":1484},[1487,79225,79226,79234],{},[1490,79227,79228,79230,79232],{},[1680,79229,1682],{},[1988,79231,5016],{},[1680,79233,39328],{},[1528,79235,79236],{"encoding":1530},"1\\,750"," EUR.",[1304,79239,79241],{"id":79240},"speciální-tvar-pro-pevnou-cenu","Speciální tvar pro pevnou cenu",[1030,79243,79244,79245,75878,79258,79282],{},"Předpokládáme-li, že výrobce prodává za pevnou cenu ",[1035,79246,79248],{"className":79247},[1480],[1482,79249,79250],{"xmlns":1484},[1487,79251,79252,79256],{},[1490,79253,79254],{},[1493,79255,1501],{},[1528,79257,1501],{"encoding":1530},[1035,79259,79261],{"className":79260},[1480],[1482,79262,79263],{"xmlns":1484},[1487,79264,79265,79279],{},[1490,79266,79267,79269,79271,79273,79275,79277],{},[1493,79268,5289],{},[1493,79270,1995],{},[1506,79272,1508],{},[1493,79274,1501],{},[1506,79276,1714],{},[1493,79278,1520],{},[1528,79280,79281],{"encoding":1530},"TR = P \\cdot Q"," a z (3.13) speciálně:",[1035,79284,79286],{"className":79285},[1480],[1482,79287,79288],{"xmlns":1484,"display":1485},[1487,79289,79290,79323],{},[19617,79291,79292],{"width":19619},[19621,79293,79294,79296,79316,79318],{},[19624,79295],{"width":19626},[19624,79297,79298],{},[1490,79299,79300,79302,79304,79306,79308,79310,79312,79314],{},[1493,79301,1501],{},[1506,79303,1508],{},[1493,79305,1495],{},[1493,79307,1998],{},[1506,79309,1553],{"stretchy":1552},[1493,79311,1520],{},[1506,79313,1564],{"stretchy":1552},[1493,79315,2632],{"mathvariant":1516},[19624,79317],{"width":19626},[19624,79319,79320],{},[1988,79321,79322],{},"(3.14)",[1528,79324,79325],{"encoding":1530},"P = MC(Q).\n\\tag{3.14}",[1030,79327,79328,79329,2632],{},"Výrobce musí nastavit nabízené množství tak, aby se mezní náklady rovnaly ceně. Má-li rovnice (3.14) více řešení, rozhoduje znaménko ",[1035,79330,79332],{"className":79331},[1480],[1482,79333,79334],{"xmlns":1484},[1487,79335,79336,79350],{},[1490,79337,79338,79340],{},[1493,79339,1501],{},[2315,79341,79342,79344],{},[1493,79343,1995],{},[1490,79345,79346,79348],{},[1506,79347,6927],{"mathvariant":1516},[1506,79349,6927],{"mathvariant":1516},[1528,79351,78407],{"encoding":1530},[52452,79353,79355],{"id":79354},"příklad-311","Příklad 3.11",[1030,79357,79358,8686,79360,79407,79408,79426],{},[1047,79359,70164],{},[1035,79361,79363],{"className":79362},[1480],[1482,79364,79365],{"xmlns":1484},[1487,79366,79367,79404],{},[1490,79368,79369,79371,79373,79375,79378,79384,79386,79388,79394,79396,79398,79400,79402],{},[1493,79370,5289],{},[1493,79372,1998],{},[1506,79374,1508],{},[1680,79376,79377],{},"0,04",[2315,79379,79380,79382],{},[1493,79381,1520],{},[1680,79383,3201],{},[1506,79385,1888],{},[1680,79387,13364],{},[2315,79389,79390,79392],{},[1493,79391,1520],{},[1680,79393,1691],{},[1506,79395,2162],{},[1680,79397,1775],{},[1493,79399,1520],{},[1506,79401,2162],{},[1680,79403,1752],{},[1528,79405,79406],{"encoding":1530},"TC = 0{,}04Q^3 - 0{,}9Q^2 + 10Q + 5"," a pevnou cenu ",[1035,79409,79411],{"className":79410},[1480],[1482,79412,79413],{"xmlns":1484},[1487,79414,79415,79423],{},[1490,79416,79417,79419,79421],{},[1493,79418,1501],{},[1506,79420,1508],{},[1680,79422,4007],{},[1528,79424,79425],{"encoding":1530},"P = 4"," stanovte optimální produkci.",[1030,79428,79429,79431,79432,33723,79474,79508,79509,1274],{},[1047,79430,38365],{}," Z (3.14): ",[1035,79433,79435],{"className":79434},[1480],[1482,79436,79437],{"xmlns":1484},[1487,79438,79439,79471],{},[1490,79440,79441,79443,79445,79447,79450,79456,79458,79461,79463,79465,79467,79469],{},[1493,79442,1495],{},[1493,79444,1998],{},[1506,79446,1508],{},[1680,79448,79449],{},"0,12",[2315,79451,79452,79454],{},[1493,79453,1520],{},[1680,79455,1691],{},[1506,79457,1888],{},[1680,79459,79460],{},"1,8",[1493,79462,1520],{},[1506,79464,2162],{},[1680,79466,1775],{},[1506,79468,1508],{},[1680,79470,4007],{},[1528,79472,79473],{"encoding":1530},"MC = 0{,}12Q^2 - 1{,}8Q + 10 = 4",[1035,79475,79477],{"className":79476},[1480],[1482,79478,79479],{"xmlns":1484},[1487,79480,79481,79505],{},[1490,79482,79483,79485,79491,79493,79495,79497,79499,79501,79503],{},[1680,79484,79449],{},[2315,79486,79487,79489],{},[1493,79488,1520],{},[1680,79490,1691],{},[1506,79492,1888],{},[1680,79494,79460],{},[1493,79496,1520],{},[1506,79498,2162],{},[1680,79500,7508],{},[1506,79502,1508],{},[1680,79504,1871],{},[1528,79506,79507],{"encoding":1530},"0{,}12Q^2 - 1{,}8Q + 6 = 0",", po vydělení ",[1035,79510,79512],{"className":79511},[1480],[1482,79513,79514],{"xmlns":1484},[1487,79515,79516,79520],{},[1490,79517,79518],{},[1680,79519,79449],{},[1528,79521,79522],{"encoding":1530},"0{,}12",[1035,79524,79526],{"className":79525},[1480],[1482,79527,79528],{"xmlns":1484,"display":1485},[1487,79529,79530,79582],{},[1490,79531,79532,79538,79540,79542,79544,79546,79548,79550,79552,79554,79556,79558,79564,79566,79568,79570,79572,79578,79580],{},[2315,79533,79534,79536],{},[1493,79535,1520],{},[1680,79537,1691],{},[1506,79539,1888],{},[1680,79541,9787],{},[1493,79543,1520],{},[1506,79545,2162],{},[1680,79547,2292],{},[1506,79549,1508],{},[1680,79551,1871],{},[1988,79553,1990],{},[1506,79555,2183],{},[1988,79557,1990],{},[1497,79559,79560,79562],{},[1493,79561,1520],{},[1680,79563,1682],{},[1506,79565,1508],{},[1680,79567,1752],{},[1506,79569,1559],{"separator":1041},[1988,79571,1990],{},[1497,79573,79574,79576],{},[1493,79575,1520],{},[1680,79577,1691],{},[1506,79579,1508],{},[1680,79581,35212],{},[1528,79583,79584],{"encoding":1530},"Q^2 - 15Q + 50 = 0 \\;\\Rightarrow\\; Q_1 = 5, \\; Q_2 = 10.",[1030,79586,79587,79588,1274],{},"Dále ",[1035,79589,79591],{"className":79590},[1480],[1482,79592,79593],{"xmlns":1484},[1487,79594,79595,79634],{},[1490,79596,79597,79599,79609,79611,79613,79615,79621,79623,79625,79628,79630,79632],{},[1493,79598,1501],{},[2315,79600,79601,79603],{},[1493,79602,1995],{},[1490,79604,79605,79607],{},[1506,79606,6927],{"mathvariant":1516},[1506,79608,6927],{"mathvariant":1516},[1506,79610,1508],{},[1506,79612,1888],{},[1493,79614,1495],{},[2315,79616,79617,79619],{},[1493,79618,1998],{},[1506,79620,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,79622,1508],{},[1506,79624,1888],{},[1680,79626,79627],{},"0,24",[1493,79629,1520],{},[1506,79631,2162],{},[1680,79633,79460],{},[1528,79635,79636],{"encoding":1530},"PR'' = -MC' = -0{,}24Q + 1{,}8",[1203,79638,79639,79689],{},[1206,79640,79641,79685,79686,79688],{},[1035,79642,79644],{"className":79643},[1480],[1482,79645,79646],{"xmlns":1484},[1487,79647,79648,79682],{},[1490,79649,79650,79652,79662,79664,79666,79668,79670,79672,79674,79676,79678,79680],{},[1493,79651,1501],{},[2315,79653,79654,79656],{},[1493,79655,1995],{},[1490,79657,79658,79660],{},[1506,79659,6927],{"mathvariant":1516},[1506,79661,6927],{"mathvariant":1516},[1506,79663,1553],{"stretchy":1552},[1680,79665,1752],{},[1506,79667,1564],{"stretchy":1552},[1506,79669,1508],{},[1680,79671,3332],{},[1506,79673,2796],{},[1680,79675,1871],{},[1988,79677,1990],{},[1506,79679,2183],{},[1988,79681,1990],{},[1528,79683,79684],{"encoding":1530},"PR''(5) = 0{,}6 > 0 \\;\\Rightarrow\\;"," lokální ",[1047,79687,19195],{}," zisku (minimalizace ztráty);",[1206,79690,79691,79685,79737,79739],{},[1035,79692,79694],{"className":79693},[1480],[1482,79695,79696],{"xmlns":1484},[1487,79697,79698,79734],{},[1490,79699,79700,79702,79712,79714,79716,79718,79720,79722,79724,79726,79728,79730,79732],{},[1493,79701,1501],{},[2315,79703,79704,79706],{},[1493,79705,1995],{},[1490,79707,79708,79710],{},[1506,79709,6927],{"mathvariant":1516},[1506,79711,6927],{"mathvariant":1516},[1506,79713,1553],{"stretchy":1552},[1680,79715,1775],{},[1506,79717,1564],{"stretchy":1552},[1506,79719,1508],{},[1506,79721,1888],{},[1680,79723,3332],{},[1506,79725,3961],{},[1680,79727,1871],{},[1988,79729,1990],{},[1506,79731,2183],{},[1988,79733,1990],{},[1528,79735,79736],{"encoding":1530},"PR''(10) = -0{,}6 \u003C 0 \\;\\Rightarrow\\;",[1047,79738,9982],{}," zisku, avšak",[1035,79741,79743],{"className":79742},[1480],[1482,79744,79745],{"xmlns":1484,"display":1485},[1487,79746,79747,79815],{},[1490,79748,79749,79751,79753,79755,79757,79759,79761,79763,79765,79767,79769,79771,79773,79775,79777,79779,79781,79783,79785,79787,79789,79791,79793,79795,79797,79799,79801,79803,79805,79807,79809,79811,79813],{},[1493,79750,1501],{},[1493,79752,1995],{},[1506,79754,1553],{"stretchy":1552},[1680,79756,1775],{},[1506,79758,1564],{"stretchy":1552},[1506,79760,1508],{},[1680,79762,4007],{},[1506,79764,1714],{},[1680,79766,1775],{},[1506,79768,1888],{},[1506,79770,1553],{"stretchy":1552},[1680,79772,79377],{},[1506,79774,1714],{},[1680,79776,1682],{},[1988,79778,5016],{},[1680,79780,5608],{},[1506,79782,1888],{},[1680,79784,13364],{},[1506,79786,1714],{},[1680,79788,2916],{},[1506,79790,2162],{},[1680,79792,2916],{},[1506,79794,2162],{},[1680,79796,1752],{},[1506,79798,1564],{"stretchy":1552},[1506,79800,1508],{},[1680,79802,7380],{},[1506,79804,1888],{},[1680,79806,36891],{},[1506,79808,1508],{},[1506,79810,1888],{},[1680,79812,9787],{},[1506,79814,1559],{"separator":1041},[1528,79816,79817],{"encoding":1530},"PR(10) = 4 \\cdot 10 - (0{,}04 \\cdot 1\\,000 - 0{,}9 \\cdot 100 + 100 + 5) = 40 - 55 = -15,",[1030,79819,79820,79821,2632],{},"tj. ztráta větší než ",[1035,79822,79824],{"className":79823},[1480],[1482,79825,79826],{"xmlns":1484},[1487,79827,79828,79838],{},[1490,79829,79830,79832,79834,79836],{},[1493,79831,10790],{},[1493,79833,1998],{},[1506,79835,1508],{},[1680,79837,1752],{},[1528,79839,79840],{"encoding":1530},"FC = 5",[1030,79842,79843,79846,79847,79850,79851,2632],{},[1047,79844,79845],{},"Závěr:"," firma by měla ",[1047,79848,79849],{},"zastavit výrobu"," — i vypnutí provozu způsobí menší ztrátu, a to pouze ve výši ",[1035,79852,79854],{"className":79853},[1480],[1482,79855,79856],{"xmlns":1484},[1487,79857,79858,79868],{},[1490,79859,79860,79862,79864,79866],{},[1493,79861,10790],{},[1493,79863,1998],{},[1506,79865,1508],{},[1680,79867,1752],{},[1528,79869,79840],{"encoding":1530},[1065,79871,79873],{"id":79872},"konstrukce-křivky-nabídky-firmy","Konstrukce křivky nabídky firmy",[1030,79875,79876,79877,79879,79880,79895,79896,79909,79910,79936,79937,79950,79951,79968,79969,11713,79986,79989,79990,80010,80011,80026,80027,1274],{},"Důležitým završením analýzy je konstrukce ",[1047,79878,69453],{},". S nabízeným množstvím rostou mezní náklady ",[1035,79881,79883],{"className":79882},[1480],[1482,79884,79885],{"xmlns":1484},[1487,79886,79887,79893],{},[1490,79888,79889,79891],{},[1493,79890,1495],{},[1493,79892,1998],{},[1528,79894,69470],{"encoding":1530}," a tyto určují cenu ",[1035,79897,79899],{"className":79898},[1480],[1482,79900,79901],{"xmlns":1484},[1487,79902,79903,79907],{},[1490,79904,79905],{},[1493,79906,1501],{},[1528,79908,1501],{"encoding":1530},", za kterou je firma ochotna toto množství realizovat. Proto platí ",[1035,79911,79913],{"className":79912},[1480],[1482,79914,79915],{"xmlns":1484},[1487,79916,79917,79933],{},[1490,79918,79919,79921,79923,79925,79927,79929,79931],{},[1493,79920,1501],{},[1506,79922,1508],{},[1493,79924,1495],{},[1493,79926,1998],{},[1506,79928,1553],{"stretchy":1552},[1493,79930,1520],{},[1506,79932,1564],{"stretchy":1552},[1528,79934,79935],{"encoding":1530},"P = MC(Q)",". Cena ",[1035,79938,79940],{"className":79939},[1480],[1482,79941,79942],{"xmlns":1484},[1487,79943,79944,79948],{},[1490,79945,79946],{},[1493,79947,1501],{},[1528,79949,1501],{"encoding":1530}," však nemůže být nižší než ",[1035,79952,79954],{"className":79953},[1480],[1482,79955,79956],{"xmlns":1484},[1487,79957,79958,79966],{},[1490,79959,79960],{},[2315,79961,79962,79964],{},[1493,79963,1501],{},[1506,79965,2287],{},[1528,79967,20114],{"encoding":1530}," odpovídající množství ",[1035,79970,79972],{"className":79971},[1480],[1482,79973,79974],{"xmlns":1484},[1487,79975,79976,79984],{},[1490,79977,79978],{},[2315,79979,79980,79982],{},[1493,79981,1520],{},[1506,79983,2287],{},[1528,79985,14097],{"encoding":1530},[1047,79987,79988],{},"minima průměrných variabilních nákladů"," (fixní náklady nelze při optimalizaci zahrnout — jsou konstantní součástí nákladů i zisku). Křivka nabídky se tedy skládá z úsečky ",[1035,79991,79993],{"className":79992},[1480],[1482,79994,79995],{"xmlns":1484},[1487,79996,79997,80007],{},[1490,79998,79999,80001],{},[1680,80000,1871],{},[2315,80002,80003,80005],{},[1493,80004,1520],{},[1506,80006,2287],{},[1528,80008,80009],{"encoding":1530},"0Q^*"," (kde firma nenabízí nic) a rostoucí části ",[1035,80012,80014],{"className":80013},[1480],[1482,80015,80016],{"xmlns":1484},[1487,80017,80018,80024],{},[1490,80019,80020,80022],{},[1493,80021,1495],{},[1493,80023,1998],{},[1528,80025,69470],{"encoding":1530}," nad bodem ",[1035,80028,80030],{"className":80029},[1480],[1482,80031,80032],{"xmlns":1484},[1487,80033,80034,80038],{},[1490,80035,80036],{},[1493,80037,3633],{},[1528,80039,3633],{"encoding":1530},[1035,80041,80043],{"className":80042},[1480],[1482,80044,80045],{"xmlns":1484,"display":1485},[1487,80046,80047,80154],{},[19617,80048,80049],{"width":19619},[19621,80050,80051,80053,80147,80149],{},[19624,80052],{"width":19626},[19624,80054,80055],{},[1490,80056,80057,80059,80061,80063,80065,80067,80069,80071],{},[1493,80058,1501],{},[1506,80060,1508],{},[1493,80062,2001],{},[1506,80064,1553],{"stretchy":1552},[1493,80066,1520],{},[1506,80068,1564],{"stretchy":1552},[1506,80070,1508],{},[1490,80072,80073,80076],{},[1506,80074,80075],{"fence":1041},"{",[19617,80077,80080,80119],{"rowspacing":80078,"columnalign":80079,"columnspacing":2108},"0.36em","left left",[19621,80081,80082,80098],{},[19624,80083,80084],{},[1869,80085,80086],{"scriptlevel":1871,"displaystyle":1552},[1490,80087,80088,80090,80092,80094,80096],{},[1493,80089,1495],{},[1493,80091,1998],{},[1506,80093,1553],{"stretchy":1552},[1493,80095,1520],{},[1506,80097,1564],{"stretchy":1552},[19624,80099,80100],{},[1869,80101,80102],{"scriptlevel":1871,"displaystyle":1552},[1490,80103,80104,80107,80109,80111,80117],{},[1988,80105,80106],{},"pro ",[1493,80108,1520],{},[1506,80110,20200],{},[2315,80112,80113,80115],{},[1493,80114,1520],{},[1506,80116,2287],{},[1506,80118,1559],{"separator":1041},[19621,80120,80121,80127],{},[19624,80122,80123],{},[1869,80124,80125],{"scriptlevel":1871,"displaystyle":1552},[1680,80126,1871],{},[19624,80128,80129],{},[1869,80130,80131],{"scriptlevel":1871,"displaystyle":1552},[1490,80132,80133,80135,80137,80139,80145],{},[1988,80134,80106],{},[1493,80136,1520],{},[1506,80138,3961],{},[2315,80140,80141,80143],{},[1493,80142,1520],{},[1506,80144,2287],{},[1506,80146,1559],{"separator":1041},[19624,80148],{"width":19626},[19624,80150,80151],{},[1988,80152,80153],{},"(3.15)",[1528,80155,80156],{"encoding":1530},"P = S(Q) = \\begin{cases} MC(Q) & \\text{pro } Q \\geq Q^*, \\\\ 0 & \\text{pro } Q \u003C Q^*, \\end{cases}\n\\tag{3.15}",[1030,80158,20022,80159,80176,80177,80194,80195,56135,80225,80228],{},[1035,80160,80162],{"className":80161},[1480],[1482,80163,80164],{"xmlns":1484},[1487,80165,80166,80174],{},[1490,80167,80168],{},[2315,80169,80170,80172],{},[1493,80171,1520],{},[1506,80173,2287],{},[1528,80175,14097],{"encoding":1530}," je bod minima ",[1035,80178,80180],{"className":80179},[1480],[1482,80181,80182],{"xmlns":1484},[1487,80183,80184,80192],{},[1490,80185,80186,80188,80190],{},[1493,80187,3633],{},[1493,80189,55105],{},[1493,80191,1998],{},[1528,80193,69489],{"encoding":1530},". Bod ",[1035,80196,80198],{"className":80197},[1480],[1482,80199,80200],{"xmlns":1484},[1487,80201,80202,80222],{},[1490,80203,80204,80206,80212,80214,80220],{},[1506,80205,1553],{"stretchy":1552},[2315,80207,80208,80210],{},[1493,80209,1520],{},[1506,80211,2287],{},[1506,80213,1559],{"separator":1041},[2315,80215,80216,80218],{},[1493,80217,1501],{},[1506,80219,2287],{},[1506,80221,1564],{"stretchy":1552},[1528,80223,80224],{"encoding":1530},"(Q^*, P^*)",[1047,80226,80227],{},"shutdown point"," — pod ním se firmě nevyplatí produkovat.",[1023,80230,80232,80239],{"className":80231,"dataCallout":1443},[1026,1442],[1030,80233,80235,80238],{"className":80234},[1033],[1035,80236],{"className":80237,"ariaHidden":1041},[1038,1450,1040],"Postup — jak odvodit nabídku firmy",[1276,80240,80241,80289,80384,80439,80510],{},[1206,80242,80243,80244,1586,80265,2632],{},"Ze zadaných nákladů určete ",[1035,80245,80247],{"className":80246},[1480],[1482,80248,80249],{"xmlns":1484},[1487,80250,80251,80263],{},[1490,80252,80253,80255,80257,80259,80261],{},[1493,80254,1495],{},[1493,80256,1998],{},[1506,80258,1553],{"stretchy":1552},[1493,80260,1520],{},[1506,80262,1564],{"stretchy":1552},[1528,80264,11736],{"encoding":1530},[1035,80266,80268],{"className":80267},[1480],[1482,80269,80270],{"xmlns":1484},[1487,80271,80272,80286],{},[1490,80273,80274,80276,80278,80280,80282,80284],{},[1493,80275,3633],{},[1493,80277,55105],{},[1493,80279,1998],{},[1506,80281,1553],{"stretchy":1552},[1493,80283,1520],{},[1506,80285,1564],{"stretchy":1552},[1528,80287,80288],{"encoding":1530},"AVC(Q)",[1206,80290,80291,80292,80309,80310,80327,80328,80360,80361,16623],{},"Najděte ",[1035,80293,80295],{"className":80294},[1480],[1482,80296,80297],{"xmlns":1484},[1487,80298,80299,80307],{},[1490,80300,80301],{},[2315,80302,80303,80305],{},[1493,80304,1520],{},[1506,80306,2287],{},[1528,80308,14097],{"encoding":1530}," jako bod minima ",[1035,80311,80313],{"className":80312},[1480],[1482,80314,80315],{"xmlns":1484},[1487,80316,80317,80325],{},[1490,80318,80319,80321,80323],{},[1493,80320,3633],{},[1493,80322,55105],{},[1493,80324,1998],{},[1528,80326,69489],{"encoding":1530}," (řešením ",[1035,80329,80331],{"className":80330},[1480],[1482,80332,80333],{"xmlns":1484},[1487,80334,80335,80357],{},[1490,80336,80337,80339,80341,80347,80349,80351,80353,80355],{},[1493,80338,3633],{},[1493,80340,55105],{},[2315,80342,80343,80345],{},[1493,80344,1998],{},[1506,80346,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,80348,1553],{"stretchy":1552},[1493,80350,1520],{},[1506,80352,1564],{"stretchy":1552},[1506,80354,1508],{},[1680,80356,1871],{},[1528,80358,80359],{"encoding":1530},"AVC'(Q) = 0",", případně rovnice ",[1035,80362,80364],{"className":80363},[1480],[1482,80365,80366],{"xmlns":1484},[1487,80367,80368,80382],{},[1490,80369,80370,80372,80374,80376,80378,80380],{},[1493,80371,3633],{},[1493,80373,55105],{},[1493,80375,1998],{},[1506,80377,1508],{},[1493,80379,1495],{},[1493,80381,1998],{},[1528,80383,69427],{"encoding":1530},[1206,80385,78291,80386,80438],{},[1035,80387,80389],{"className":80388},[1480],[1482,80390,80391],{"xmlns":1484},[1487,80392,80393,80435],{},[1490,80394,80395,80401,80403,80405,80407,80409,80415,80417,80419,80421,80423,80425,80427,80433],{},[2315,80396,80397,80399],{},[1493,80398,1501],{},[1506,80400,2287],{},[1506,80402,1508],{},[1493,80404,1495],{},[1493,80406,1998],{},[1506,80408,1553],{"stretchy":1552},[2315,80410,80411,80413],{},[1493,80412,1520],{},[1506,80414,2287],{},[1506,80416,1564],{"stretchy":1552},[1506,80418,1508],{},[1493,80420,3633],{},[1493,80422,55105],{},[1493,80424,1998],{},[1506,80426,1553],{"stretchy":1552},[2315,80428,80429,80431],{},[1493,80430,1520],{},[1506,80432,2287],{},[1506,80434,1564],{"stretchy":1552},[1528,80436,80437],{"encoding":1530},"P^* = MC(Q^*) = AVC(Q^*)"," — minimální cenu nabídky.",[1206,80440,80441,80442,22345,80474,80496,80497,2632],{},"Zapište nabídku: ",[1035,80443,80445],{"className":80444},[1480],[1482,80446,80447],{"xmlns":1484},[1487,80448,80449,80471],{},[1490,80450,80451,80453,80455,80457,80459,80461,80463,80465,80467,80469],{},[1493,80452,2001],{},[1506,80454,1553],{"stretchy":1552},[1493,80456,1520],{},[1506,80458,1564],{"stretchy":1552},[1506,80460,1508],{},[1493,80462,1495],{},[1493,80464,1998],{},[1506,80466,1553],{"stretchy":1552},[1493,80468,1520],{},[1506,80470,1564],{"stretchy":1552},[1528,80472,80473],{"encoding":1530},"S(Q) = MC(Q)",[1035,80475,80477],{"className":80476},[1480],[1482,80478,80479],{"xmlns":1484},[1487,80480,80481,80493],{},[1490,80482,80483,80485,80487],{},[1493,80484,1520],{},[1506,80486,20200],{},[2315,80488,80489,80491],{},[1493,80490,1520],{},[1506,80492,2287],{},[1528,80494,80495],{"encoding":1530},"Q \\geq Q^*",", jinak ",[1035,80498,80500],{"className":80499},[1480],[1482,80501,80502],{"xmlns":1484},[1487,80503,80504,80508],{},[1490,80505,80506],{},[1680,80507,1871],{},[1528,80509,1871],{"encoding":1530},[1206,80511,80512,80513,80545],{},"V případě potřeby vyjádřete inverzi ",[1035,80514,80516],{"className":80515},[1480],[1482,80517,80518],{"xmlns":1484},[1487,80519,80520,80542],{},[1490,80521,80522,80524,80526,80536,80538,80540],{},[1493,80523,1520],{},[1506,80525,1508],{},[2315,80527,80528,80530],{},[1493,80529,2001],{},[1490,80531,80532,80534],{},[1506,80533,1888],{},[1680,80535,1682],{},[1506,80537,1553],{"stretchy":1552},[1493,80539,1501],{},[1506,80541,1564],{"stretchy":1552},[1528,80543,80544],{"encoding":1530},"Q = S^{-1}(P)"," doplněním na čtverec.",[52452,80547,80549],{"id":80548},"příklad-312","Příklad 3.12",[1030,80551,80552,8686,80554,80600],{},[1047,80553,70164],{},[1035,80555,80557],{"className":80556},[1480],[1482,80558,80559],{"xmlns":1484},[1487,80560,80561,80597],{},[1490,80562,80563,80565,80567,80569,80571,80577,80579,80581,80587,80589,80591,80593,80595],{},[1493,80564,5289],{},[1493,80566,1998],{},[1506,80568,1508],{},[1680,80570,13237],{},[2315,80572,80573,80575],{},[1493,80574,1520],{},[1680,80576,3201],{},[1506,80578,1888],{},[1680,80580,1691],{},[2315,80582,80583,80585],{},[1493,80584,1520],{},[1680,80586,1691],{},[1506,80588,2162],{},[1680,80590,9787],{},[1493,80592,1520],{},[1506,80594,2162],{},[1680,80596,1775],{},[1528,80598,80599],{"encoding":1530},"TC = 0{,}1Q^3 - 2Q^2 + 15Q + 10"," odvoďte funkci nabídky firmy.",[1030,80602,80603,1656,80605,80642,80643,1274],{},[1047,80604,38365],{},[1035,80606,80608],{"className":80607},[1480],[1482,80609,80610],{"xmlns":1484},[1487,80611,80612,80639],{},[1490,80613,80614,80616,80618,80620,80623,80629,80631,80633,80635,80637],{},[1493,80615,1495],{},[1493,80617,1998],{},[1506,80619,1508],{},[1680,80621,80622],{},"0,3",[2315,80624,80625,80627],{},[1493,80626,1520],{},[1680,80628,1691],{},[1506,80630,1888],{},[1680,80632,4007],{},[1493,80634,1520],{},[1506,80636,2162],{},[1680,80638,9787],{},[1528,80640,80641],{"encoding":1530},"MC = 0{,}3Q^2 - 4Q + 15",", takže z ",[1035,80644,80646],{"className":80645},[1480],[1482,80647,80648],{"xmlns":1484},[1487,80649,80650,80660],{},[1490,80651,80652,80654,80656,80658],{},[1493,80653,1501],{},[1506,80655,1508],{},[1493,80657,1495],{},[1493,80659,1998],{},[1528,80661,80662],{"encoding":1530},"P = MC",[1035,80664,80666],{"className":80665},[1480],[1482,80667,80668],{"xmlns":1484,"display":1485},[1487,80669,80670,80695],{},[1490,80671,80672,80674,80676,80678,80684,80686,80688,80690,80692],{},[1493,80673,1501],{},[1506,80675,1508],{},[1680,80677,80622],{},[2315,80679,80680,80682],{},[1493,80681,1520],{},[1680,80683,1691],{},[1506,80685,1888],{},[1680,80687,4007],{},[1493,80689,1520],{},[1506,80691,2162],{},[1680,80693,80694],{},"15.",[1528,80696,80697],{"encoding":1530},"P = 0{,}3Q^2 - 4Q + 15.",[1030,80699,80700,80701,21092,80714,80727],{},"Vyjádření ",[1035,80702,80704],{"className":80703},[1480],[1482,80705,80706],{"xmlns":1484},[1487,80707,80708,80712],{},[1490,80709,80710],{},[1493,80711,1520],{},[1528,80713,1520],{"encoding":1530},[1035,80715,80717],{"className":80716},[1480],[1482,80718,80719],{"xmlns":1484},[1487,80720,80721,80725],{},[1490,80722,80723],{},[1493,80724,1501],{},[1528,80726,1501],{"encoding":1530}," doplněním na čtverec:",[1035,80729,80731],{"className":80730},[1480],[1482,80732,80733],{"xmlns":1484,"display":1485},[1487,80734,80735,80825],{},[1490,80736,80737,80739,80741,80743,80781,80783,80785,80807,80809,80823],{},[1493,80738,1501],{},[1506,80740,1508],{},[1680,80742,80622],{},[1490,80744,80745,80747,80769,80771,80779],{},[1506,80746,1553],{"fence":1041},[2315,80748,80749,80767],{},[1490,80750,80751,80753,80755,80757,80765],{},[1506,80752,1553],{"fence":1041},[1493,80754,1520],{},[1506,80756,1888],{},[1869,80758,80759],{"scriptlevel":1871,"displaystyle":1552},[1510,80760,80761,80763],{},[1680,80762,8436],{},[1680,80764,3201],{},[1506,80766,1564],{"fence":1041},[1680,80768,1691],{},[1506,80770,2162],{},[1869,80772,80773],{"scriptlevel":1871,"displaystyle":1552},[1510,80774,80775,80777],{},[1680,80776,2292],{},[1680,80778,14365],{},[1506,80780,1564],{"fence":1041},[1506,80782,1559],{"separator":1041},[1912,80784],{"width":1914},[2315,80786,80787,80805],{},[1490,80788,80789,80791,80793,80795,80803],{},[1506,80790,1553],{"fence":1041},[1493,80792,1520],{},[1506,80794,1888],{},[1869,80796,80797],{"scriptlevel":1871,"displaystyle":1552},[1510,80798,80799,80801],{},[1680,80800,8436],{},[1680,80802,3201],{},[1506,80804,1564],{"fence":1041},[1680,80806,1691],{},[1506,80808,1508],{},[1510,80810,80811,80821],{},[1490,80812,80813,80815,80817,80819],{},[1680,80814,6956],{},[1493,80816,1501],{},[1506,80818,1888],{},[1680,80820,2292],{},[1680,80822,14365],{},[1506,80824,1559],{"separator":1041},[1528,80826,80827],{"encoding":1530},"P = 0{,}3\\left(\\left(Q - \\tfrac{20}{3}\\right)^2 + \\tfrac{50}{9}\\right), \\qquad \\left(Q - \\tfrac{20}{3}\\right)^2 = \\frac{30P - 50}{9},",[1035,80829,80831],{"className":80830},[1480],[1482,80832,80833],{"xmlns":1484,"display":1485},[1487,80834,80835,80867],{},[1490,80836,80837,80839,80841,80847,80849,80865],{},[1493,80838,1520],{},[1506,80840,1508],{},[1510,80842,80843,80845],{},[1680,80844,8436],{},[1680,80846,3201],{},[1506,80848,2162],{},[1510,80850,80851,80863],{},[2324,80852,80853],{},[1490,80854,80855,80857,80859,80861],{},[1680,80856,6956],{},[1493,80858,1501],{},[1506,80860,1888],{},[1680,80862,2292],{},[1680,80864,3201],{},[1493,80866,2632],{"mathvariant":1516},[1528,80868,80869],{"encoding":1530},"Q = \\frac{20}{3} + \\frac{\\sqrt{30P - 50}}{3}.",[1030,80871,79587,80872,1732,80910,1732,80958,80992,80993,2632],{},[1035,80873,80875],{"className":80874},[1480],[1482,80876,80877],{"xmlns":1484},[1487,80878,80879,80907],{},[1490,80880,80881,80883,80885,80887,80889,80891,80897,80899,80901,80903,80905],{},[1493,80882,3633],{},[1493,80884,55105],{},[1493,80886,1998],{},[1506,80888,1508],{},[1680,80890,13237],{},[2315,80892,80893,80895],{},[1493,80894,1520],{},[1680,80896,1691],{},[1506,80898,1888],{},[1680,80900,1691],{},[1493,80902,1520],{},[1506,80904,2162],{},[1680,80906,9787],{},[1528,80908,80909],{"encoding":1530},"AVC = 0{,}1Q^2 - 2Q + 15",[1035,80911,80913],{"className":80912},[1480],[1482,80914,80915],{"xmlns":1484},[1487,80916,80917,80955],{},[1490,80918,80919,80921,80923,80929,80931,80933,80935,80937,80939,80941,80943,80945,80951,80953],{},[1493,80920,3633],{},[1493,80922,55105],{},[2315,80924,80925,80927],{},[1493,80926,1998],{},[1506,80928,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,80930,1508],{},[1680,80932,2929],{},[1493,80934,1520],{},[1506,80936,1888],{},[1680,80938,1691],{},[1506,80940,1508],{},[1680,80942,1871],{},[1506,80944,2183],{},[2315,80946,80947,80949],{},[1493,80948,1520],{},[1506,80950,2287],{},[1506,80952,1508],{},[1680,80954,1775],{},[1528,80956,80957],{"encoding":1530},"AVC' = 0{,}2Q - 2 = 0 \\Rightarrow Q^* = 10",[1035,80959,80961],{"className":80960},[1480],[1482,80962,80963],{"xmlns":1484},[1487,80964,80965,80989],{},[1490,80966,80967,80969,80971,80981,80983,80985,80987],{},[1493,80968,3633],{},[1493,80970,55105],{},[2315,80972,80973,80975],{},[1493,80974,1998],{},[1490,80976,80977,80979],{},[1506,80978,6927],{"mathvariant":1516},[1506,80980,6927],{"mathvariant":1516},[1506,80982,1508],{},[1680,80984,2929],{},[1506,80986,2796],{},[1680,80988,1871],{},[1528,80990,80991],{"encoding":1530},"AVC'' = 0{,}2 > 0"," (minimum). Minimální cena nabídky ",[1035,80994,80996],{"className":80995},[1480],[1482,80997,80998],{"xmlns":1484},[1487,80999,81000,81036],{},[1490,81001,81002,81008,81010,81012,81014,81016,81018,81020,81022,81024,81026,81028,81030,81032,81034],{},[2315,81003,81004,81006],{},[1493,81005,1501],{},[1506,81007,2287],{},[1506,81009,1508],{},[1493,81011,1495],{},[1493,81013,1998],{},[1506,81015,1553],{"stretchy":1552},[1680,81017,1775],{},[1506,81019,1564],{"stretchy":1552},[1506,81021,1508],{},[1680,81023,6956],{},[1506,81025,1888],{},[1680,81027,7380],{},[1506,81029,2162],{},[1680,81031,9787],{},[1506,81033,1508],{},[1680,81035,1752],{},[1528,81037,81038],{"encoding":1530},"P^* = MC(10) = 30 - 40 + 15 = 5",[1030,81040,81041],{},[1047,81042,81043],{},"Závěr.",[1035,81045,81047],{"className":81046},[1480],[1482,81048,81049],{"xmlns":1484,"display":1485},[1487,81050,81051,81137],{},[1490,81052,81053,81055,81057,81059,81061,81063,81065,81067],{},[1493,81054,1501],{},[1506,81056,1508],{},[1493,81058,2001],{},[1506,81060,1553],{"stretchy":1552},[1493,81062,1520],{},[1506,81064,1564],{"stretchy":1552},[1506,81066,1508],{},[1490,81068,81069,81071],{},[1506,81070,80075],{"fence":1041},[19617,81072,81073,81115],{"rowspacing":80078,"columnalign":80079,"columnspacing":2108},[19621,81074,81075,81099],{},[19624,81076,81077],{},[1869,81078,81079],{"scriptlevel":1871,"displaystyle":1552},[1490,81080,81081,81083,81089,81091,81093,81095,81097],{},[1680,81082,80622],{},[2315,81084,81085,81087],{},[1493,81086,1520],{},[1680,81088,1691],{},[1506,81090,1888],{},[1680,81092,4007],{},[1493,81094,1520],{},[1506,81096,2162],{},[1680,81098,9787],{},[19624,81100,81101],{},[1869,81102,81103],{"scriptlevel":1871,"displaystyle":1552},[1490,81104,81105,81107,81109,81111,81113],{},[1988,81106,80106],{},[1493,81108,1520],{},[1506,81110,20200],{},[1680,81112,1775],{},[1506,81114,1559],{"separator":1041},[19621,81116,81117,81123],{},[19624,81118,81119],{},[1869,81120,81121],{"scriptlevel":1871,"displaystyle":1552},[1680,81122,1871],{},[19624,81124,81125],{},[1869,81126,81127],{"scriptlevel":1871,"displaystyle":1552},[1490,81128,81129,81131,81133,81135],{},[1988,81130,80106],{},[1493,81132,1520],{},[1506,81134,3961],{},[1680,81136,35212],{},[1528,81138,81139],{"encoding":1530},"P = S(Q) = \\begin{cases} 0{,}3Q^2 - 4Q + 15 & \\text{pro } Q \\geq 10, \\\\ 0 & \\text{pro } Q \u003C 10. \\end{cases}",[1065,81141,81143],{"id":81142},"shrnutí-kapitoly-3","Shrnutí kapitoly 3",[1030,81145,81146,81147,81151,81152,81167,81168,81188,81189,1586,81192,81195,81196,81198,81199,35675,81221,81223,81224,1586,81226,72495,81228,1656,81231,56364,81246,81261],{},"Celkový příjem je součin ceny a množství, kde cena je dána funkcí ",[1052,81148,81150],{"className":81149,"dataFsResolvedFilePath":3487,"href":3488},[1055],"poptávky",". Pro lineární poptávku je ",[1035,81153,81155],{"className":81154},[1480],[1482,81156,81157],{"xmlns":1484},[1487,81158,81159,81165],{},[1490,81160,81161,81163],{},[1493,81162,5289],{},[1493,81164,1995],{},[1528,81166,16491],{"encoding":1530}," kvadratická. Průměrný příjem je podíl ",[1035,81169,81171],{"className":81170},[1480],[1482,81172,81173],{"xmlns":1484},[1487,81174,81175,81185],{},[1490,81176,81177,81179,81181,81183],{},[1493,81178,5289],{},[1493,81180,1995],{},[1493,81182,1709],{"mathvariant":1516},[1493,81184,1520],{},[1528,81186,81187],{"encoding":1530},"TR\u002FQ"," a rovná se poptávkové funkci. Celkové náklady se skládají z ",[1047,81190,81191],{},"fixních",[1047,81193,81194],{},"celkových variabilních"," nákladů. Průměrné veličiny jsou jejich podíly s množstvím. ",[1047,81197,77456],{}," identifikují, kdy se firma nachází na prahu rentability. Rozdíl ",[1035,81200,81202],{"className":81201},[1480],[1482,81203,81204],{"xmlns":1484},[1487,81205,81206,81218],{},[1490,81207,81208,81210,81212,81214,81216],{},[1493,81209,5289],{},[1493,81211,1995],{},[1506,81213,1888],{},[1493,81215,5289],{},[1493,81217,1998],{},[1528,81219,81220],{"encoding":1530},"TR - TC",[1047,81222,1008],{},"; klíčový je výpočet produkce, která zisk maximalizuje. ",[1047,81225,70564],{},[1047,81227,16572],{},[1052,81229,102],{"className":81230,"dataFsResolvedFilePath":16621,"href":16622},[1055],[1035,81232,81234],{"className":81233},[1480],[1482,81235,81236],{"xmlns":1484},[1487,81237,81238,81244],{},[1490,81239,81240,81242],{},[1493,81241,5289],{},[1493,81243,1995],{},[1528,81245,16491],{"encoding":1530},[1035,81247,81249],{"className":81248},[1480],[1482,81250,81251],{"xmlns":1484},[1487,81252,81253,81259],{},[1490,81254,81255,81257],{},[1493,81256,5289],{},[1493,81258,1998],{},[1528,81260,18668],{"encoding":1530}," podle produkce; udávají rychlosti změn, resp. přibližné změny odpovídající jednotkové změně produkce.",[1203,81263,81264,81326,81392,81454],{},[1206,81265,81266,81269,81270,26918,81285,2632],{},[1047,81267,81268],{},"Princip minimalizace průměrných nákladů:"," v bodě minima ",[1035,81271,81273],{"className":81272},[1480],[1482,81274,81275],{"xmlns":1484},[1487,81276,81277,81283],{},[1490,81278,81279,81281],{},[1493,81280,3633],{},[1493,81282,1998],{},[1528,81284,16523],{"encoding":1530},[1035,81286,81288],{"className":81287},[1480],[1482,81289,81290],{"xmlns":1484},[1487,81291,81292,81324],{},[1490,81293,81294,81296,81298,81300,81306,81308,81310,81312,81314,81316,81322],{},[1493,81295,3633],{},[1493,81297,1998],{},[1506,81299,1553],{"stretchy":1552},[1497,81301,81302,81304],{},[1493,81303,1520],{},[1680,81305,1871],{},[1506,81307,1564],{"stretchy":1552},[1506,81309,1508],{},[1493,81311,1495],{},[1493,81313,1998],{},[1506,81315,1553],{"stretchy":1552},[1497,81317,81318,81320],{},[1493,81319,1520],{},[1680,81321,1871],{},[1506,81323,1564],{"stretchy":1552},[1528,81325,75877],{"encoding":1530},[1206,81327,81328,81269,81331,26918,81348,2632],{},[1047,81329,81330],{},"Princip minimalizace průměrných variabilních nákladů:",[1035,81332,81334],{"className":81333},[1480],[1482,81335,81336],{"xmlns":1484},[1487,81337,81338,81346],{},[1490,81339,81340,81342,81344],{},[1493,81341,3633],{},[1493,81343,55105],{},[1493,81345,1998],{},[1528,81347,69489],{"encoding":1530},[1035,81349,81351],{"className":81350},[1480],[1482,81352,81353],{"xmlns":1484},[1487,81354,81355,81389],{},[1490,81356,81357,81359,81361,81363,81365,81371,81373,81375,81377,81379,81381,81387],{},[1493,81358,3633],{},[1493,81360,55105],{},[1493,81362,1998],{},[1506,81364,1553],{"stretchy":1552},[1497,81366,81367,81369],{},[1493,81368,1520],{},[1680,81370,1871],{},[1506,81372,1564],{"stretchy":1552},[1506,81374,1508],{},[1493,81376,1495],{},[1493,81378,1998],{},[1506,81380,1553],{"stretchy":1552},[1497,81382,81383,81385],{},[1493,81384,1520],{},[1680,81386,1871],{},[1506,81388,1564],{"stretchy":1552},[1528,81390,81391],{"encoding":1530},"AVC(Q_0) = MC(Q_0)",[1206,81393,81394,81397,81398,26918,81413,2632],{},[1047,81395,81396],{},"Princip maximalizace zisku:"," v bodě maxima ",[1035,81399,81401],{"className":81400},[1480],[1482,81402,81403],{"xmlns":1484},[1487,81404,81405,81411],{},[1490,81406,81407,81409],{},[1493,81408,1501],{},[1493,81410,1995],{},[1528,81412,76797],{"encoding":1530},[1035,81414,81416],{"className":81415},[1480],[1482,81417,81418],{"xmlns":1484},[1487,81419,81420,81452],{},[1490,81421,81422,81424,81426,81428,81434,81436,81438,81440,81442,81444,81450],{},[1493,81423,1495],{},[1493,81425,1995],{},[1506,81427,1553],{"stretchy":1552},[1497,81429,81430,81432],{},[1493,81431,1520],{},[1680,81433,1871],{},[1506,81435,1564],{"stretchy":1552},[1506,81437,1508],{},[1493,81439,1495],{},[1493,81441,1998],{},[1506,81443,1553],{"stretchy":1552},[1497,81445,81446,81448],{},[1493,81447,1520],{},[1680,81449,1871],{},[1506,81451,1564],{"stretchy":1552},[1528,81453,78212],{"encoding":1530},[1206,81455,81456,1656,81459,22345,81495,80496,81516,37188,81529,80176,81546,2632],{},[1047,81457,81458],{},"Funkce nabídky firmy:",[1035,81460,81462],{"className":81461},[1480],[1482,81463,81464],{"xmlns":1484},[1487,81465,81466,81492],{},[1490,81467,81468,81470,81472,81474,81476,81478,81480,81482,81484,81486,81488,81490],{},[1493,81469,1501],{},[1506,81471,1508],{},[1493,81473,2001],{},[1506,81475,1553],{"stretchy":1552},[1493,81477,1520],{},[1506,81479,1564],{"stretchy":1552},[1506,81481,1508],{},[1493,81483,1495],{},[1493,81485,1998],{},[1506,81487,1553],{"stretchy":1552},[1493,81489,1520],{},[1506,81491,1564],{"stretchy":1552},[1528,81493,81494],{"encoding":1530},"P = S(Q) = MC(Q)",[1035,81496,81498],{"className":81497},[1480],[1482,81499,81500],{"xmlns":1484},[1487,81501,81502,81514],{},[1490,81503,81504,81506,81508],{},[1493,81505,1520],{},[1506,81507,20200],{},[2315,81509,81510,81512],{},[1493,81511,1520],{},[1506,81513,2287],{},[1528,81515,80495],{"encoding":1530},[1035,81517,81519],{"className":81518},[1480],[1482,81520,81521],{"xmlns":1484},[1487,81522,81523,81527],{},[1490,81524,81525],{},[1680,81526,1871],{},[1528,81528,1871],{"encoding":1530},[1035,81530,81532],{"className":81531},[1480],[1482,81533,81534],{"xmlns":1484},[1487,81535,81536,81544],{},[1490,81537,81538],{},[2315,81539,81540,81542],{},[1493,81541,1520],{},[1506,81543,2287],{},[1528,81545,14097],{"encoding":1530},[1035,81547,81549],{"className":81548},[1480],[1482,81550,81551],{"xmlns":1484},[1487,81552,81553,81561],{},[1490,81554,81555,81557,81559],{},[1493,81556,3633],{},[1493,81558,55105],{},[1493,81560,1998],{},[1528,81562,69489],{"encoding":1530},[1065,81564,64217],{"id":64216},[1276,81566,81567,81570,81573,81576,81579,81582,81585,81588,81591,81594,81597],{},[1206,81568,81569],{},"Jaký je vztah pro celkový příjem v podmínkách dokonalé konkurence?",[1206,81571,81572],{},"Jaký tvar má křivka celkového příjmu pro lineární poptávku?",[1206,81574,81575],{},"Jak se vypočte mezní příjem a co udává?",[1206,81577,81578],{},"Z jakých složek se skládají celkové náklady?",[1206,81580,81581],{},"Jak se stanoví celkové náklady, známe-li náklady mezní?",[1206,81583,81584],{},"Jaký je trend průměrných fixních nákladů a průměrných nákladů, roste-li produkce?",[1206,81586,81587],{},"Jak se stanoví přibližně změna celkových nákladů?",[1206,81589,81590],{},"Jak se vypočte zisk?",[1206,81592,81593],{},"Jaká vlastnost platí v bodě maxima zisku?",[1206,81595,81596],{},"Co jsou body zvratu? Jak se najdou?",[1206,81598,81599],{},"Z jakých nákladových charakteristik se vychází při konstrukci nabídky?",[1065,81601,81603],{"id":81602},"úlohy-31328","Úlohy 3.1–3.28",[1304,81605,81607],{"id":81606},"příjem-3135","Příjem (3.1–3.5)",[1030,81609,81610,59765,81613,81641,81642,81657,81658,81673,81674,81689,81690,1732,81705,1732,81720,81735],{},[1047,81611,81612],{},"3.1",[1035,81614,81616],{"className":81615},[1480],[1482,81617,81618],{"xmlns":1484},[1487,81619,81620,81638],{},[1490,81621,81622,81624,81626,81628,81630,81632,81634,81636],{},[1493,81623,1501],{},[1506,81625,1508],{},[1493,81627,3712],{},[1506,81629,1553],{"stretchy":1552},[1493,81631,1520],{},[1506,81633,1564],{"stretchy":1552},[1506,81635,1508],{},[1680,81637,2916],{},[1528,81639,81640],{"encoding":1530},"P = D(Q) = 100",". (a) Rozhodněte, v jakých podmínkách konkurence zadaná poptávka platí. (b) Najděte celkový příjem ",[1035,81643,81645],{"className":81644},[1480],[1482,81646,81647],{"xmlns":1484},[1487,81648,81649,81655],{},[1490,81650,81651,81653],{},[1493,81652,5289],{},[1493,81654,1995],{},[1528,81656,16491],{"encoding":1530},", průměrný příjem ",[1035,81659,81661],{"className":81660},[1480],[1482,81662,81663],{"xmlns":1484},[1487,81664,81665,81671],{},[1490,81666,81667,81669],{},[1493,81668,3633],{},[1493,81670,1995],{},[1528,81672,69623],{"encoding":1530}," a mezní příjem ",[1035,81675,81677],{"className":81676},[1480],[1482,81678,81679],{"xmlns":1484},[1487,81680,81681,81687],{},[1490,81682,81683,81685],{},[1493,81684,1495],{},[1493,81686,1995],{},[1528,81688,6258],{"encoding":1530},". (c) Vypočtěte ",[1035,81691,81693],{"className":81692},[1480],[1482,81694,81695],{"xmlns":1484},[1487,81696,81697,81703],{},[1490,81698,81699,81701],{},[1493,81700,5289],{},[1493,81702,1995],{},[1528,81704,16491],{"encoding":1530},[1035,81706,81708],{"className":81707},[1480],[1482,81709,81710],{"xmlns":1484},[1487,81711,81712,81718],{},[1490,81713,81714,81716],{},[1493,81715,3633],{},[1493,81717,1995],{},[1528,81719,69623],{"encoding":1530},[1035,81721,81723],{"className":81722},[1480],[1482,81724,81725],{"xmlns":1484},[1487,81726,81727,81733],{},[1490,81728,81729,81731],{},[1493,81730,1495],{},[1493,81732,1995],{},[1528,81734,6258],{"encoding":1530}," při množství 20. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[1030,81737,81738,59765,81741,81641,81777,81657,81792,81673,81807,81689,81822,1732,81837,1732,81852,81867],{},[1047,81739,81740],{},"3.2",[1035,81742,81744],{"className":81743},[1480],[1482,81745,81746],{"xmlns":1484},[1487,81747,81748,81774],{},[1490,81749,81750,81752,81754,81756,81758,81760,81762,81764,81766,81768,81770,81772],{},[1493,81751,1501],{},[1506,81753,1508],{},[1493,81755,3712],{},[1506,81757,1553],{"stretchy":1552},[1493,81759,1520],{},[1506,81761,1564],{"stretchy":1552},[1506,81763,1508],{},[1506,81765,1888],{},[1680,81767,3687],{},[1493,81769,1520],{},[1506,81771,2162],{},[1680,81773,8436],{},[1528,81775,81776],{"encoding":1530},"P = D(Q) = -0{,}5Q + 20",[1035,81778,81780],{"className":81779},[1480],[1482,81781,81782],{"xmlns":1484},[1487,81783,81784,81790],{},[1490,81785,81786,81788],{},[1493,81787,5289],{},[1493,81789,1995],{},[1528,81791,16491],{"encoding":1530},[1035,81793,81795],{"className":81794},[1480],[1482,81796,81797],{"xmlns":1484},[1487,81798,81799,81805],{},[1490,81800,81801,81803],{},[1493,81802,3633],{},[1493,81804,1995],{},[1528,81806,69623],{"encoding":1530},[1035,81808,81810],{"className":81809},[1480],[1482,81811,81812],{"xmlns":1484},[1487,81813,81814,81820],{},[1490,81815,81816,81818],{},[1493,81817,1495],{},[1493,81819,1995],{},[1528,81821,6258],{"encoding":1530},[1035,81823,81825],{"className":81824},[1480],[1482,81826,81827],{"xmlns":1484},[1487,81828,81829,81835],{},[1490,81830,81831,81833],{},[1493,81832,5289],{},[1493,81834,1995],{},[1528,81836,16491],{"encoding":1530},[1035,81838,81840],{"className":81839},[1480],[1482,81841,81842],{"xmlns":1484},[1487,81843,81844,81850],{},[1490,81845,81846,81848],{},[1493,81847,3633],{},[1493,81849,1995],{},[1528,81851,69623],{"encoding":1530},[1035,81853,81855],{"className":81854},[1480],[1482,81856,81857],{"xmlns":1484},[1487,81858,81859,81865],{},[1490,81860,81861,81863],{},[1493,81862,1495],{},[1493,81864,1995],{},[1528,81866,6258],{"encoding":1530}," při množství 10. (d) Načrtněte křivky poptávky, celkového příjmu, průměrného příjmu a mezního příjmu a charakterizujte je geometricky.",[1030,81869,81870,59765,81873,81910,81911,81657,81926,81673,81941,81956,81957,22345,81972,81998,81999,82014,82015,1732,82030,22345,82045,81998,82070,82085,82086,82099,82100,82115,82116,82131,82132,1732,82145,1732,82160,1732,82175,2632],{},[1047,81871,81872],{},"3.3",[1035,81874,81876],{"className":81875},[1480],[1482,81877,81878],{"xmlns":1484},[1487,81879,81880,81907],{},[1490,81881,81882,81884,81886,81888,81890,81892,81894,81896,81899,81901],{},[1493,81883,1501],{},[1506,81885,1508],{},[1493,81887,3712],{},[1506,81889,1553],{"stretchy":1552},[1493,81891,1520],{},[1506,81893,1564],{"stretchy":1552},[1506,81895,1508],{},[1680,81897,81898],{},"1200",[1506,81900,1888],{},[2315,81902,81903,81905],{},[1493,81904,1520],{},[1680,81906,1691],{},[1528,81908,81909],{"encoding":1530},"P = D(Q) = 1200 - Q^2",". (a) Najděte celkový příjem ",[1035,81912,81914],{"className":81913},[1480],[1482,81915,81916],{"xmlns":1484},[1487,81917,81918,81924],{},[1490,81919,81920,81922],{},[1493,81921,5289],{},[1493,81923,1995],{},[1528,81925,16491],{"encoding":1530},[1035,81927,81929],{"className":81928},[1480],[1482,81930,81931],{"xmlns":1484},[1487,81932,81933,81939],{},[1490,81934,81935,81937],{},[1493,81936,3633],{},[1493,81938,1995],{},[1528,81940,69623],{"encoding":1530},[1035,81942,81944],{"className":81943},[1480],[1482,81945,81946],{"xmlns":1484},[1487,81947,81948,81954],{},[1490,81949,81950,81952],{},[1493,81951,1495],{},[1493,81953,1995],{},[1528,81955,6258],{"encoding":1530},". (b) Vypočtěte ",[1035,81958,81960],{"className":81959},[1480],[1482,81961,81962],{"xmlns":1484},[1487,81963,81964,81970],{},[1490,81965,81966,81968],{},[1493,81967,5289],{},[1493,81969,1995],{},[1528,81971,16491],{"encoding":1530},[1035,81973,81975],{"className":81974},[1480],[1482,81976,81977],{"xmlns":1484},[1487,81978,81979,81995],{},[1490,81980,81981,81983,81985,81987,81989,81991,81993],{},[1493,81982,1520],{},[1506,81984,1508],{},[1680,81986,1775],{},[1506,81988,1559],{"separator":1041},[1680,81990,8436],{},[1506,81992,1559],{"separator":1041},[1680,81994,6956],{},[1528,81996,81997],{"encoding":1530},"Q = 10, 20, 30"," a rozhodněte, kdy ",[1035,82000,82002],{"className":82001},[1480],[1482,82003,82004],{"xmlns":1484},[1487,82005,82006,82012],{},[1490,82007,82008,82010],{},[1493,82009,5289],{},[1493,82011,1995],{},[1528,82013,16491],{"encoding":1530}," roste, resp. klesá. (c) Vypočtěte ",[1035,82016,82018],{"className":82017},[1480],[1482,82019,82020],{"xmlns":1484},[1487,82021,82022,82028],{},[1490,82023,82024,82026],{},[1493,82025,3633],{},[1493,82027,1995],{},[1528,82029,69623],{"encoding":1530},[1035,82031,82033],{"className":82032},[1480],[1482,82034,82035],{"xmlns":1484},[1487,82036,82037,82043],{},[1490,82038,82039,82041],{},[1493,82040,1495],{},[1493,82042,1995],{},[1528,82044,6258],{"encoding":1530},[1035,82046,82048],{"className":82047},[1480],[1482,82049,82050],{"xmlns":1484},[1487,82051,82052,82068],{},[1490,82053,82054,82056,82058,82060,82062,82064,82066],{},[1493,82055,1520],{},[1506,82057,1508],{},[1680,82059,1775],{},[1506,82061,1559],{"separator":1041},[1680,82063,8436],{},[1506,82065,1559],{"separator":1041},[1680,82067,6956],{},[1528,82069,81997],{"encoding":1530},[1035,82071,82073],{"className":82072},[1480],[1482,82074,82075],{"xmlns":1484},[1487,82076,82077,82083],{},[1490,82078,82079,82081],{},[1493,82080,1495],{},[1493,82082,1995],{},[1528,82084,6258],{"encoding":1530}," roste, resp. klesá. (d) Vypočtěte ",[1035,82087,82089],{"className":82088},[1480],[1482,82090,82091],{"xmlns":1484},[1487,82092,82093,82097],{},[1490,82094,82095],{},[1493,82096,1520],{},[1528,82098,1520],{"encoding":1530},", které maximalizuje ",[1035,82101,82103],{"className":82102},[1480],[1482,82104,82105],{"xmlns":1484},[1487,82106,82107,82113],{},[1490,82108,82109,82111],{},[1493,82110,5289],{},[1493,82112,1995],{},[1528,82114,16491],{"encoding":1530}," a stanovte příslušnou hodnotu maxima ",[1035,82117,82119],{"className":82118},[1480],[1482,82120,82121],{"xmlns":1484},[1487,82122,82123,82129],{},[1490,82124,82125,82127],{},[1493,82126,5289],{},[1493,82128,1995],{},[1528,82130,16491],{"encoding":1530},". (e) Určete (je užitečné vyšetřit i jejich průběhy). (f) Charakterizujte geometricky křivky ",[1035,82133,82135],{"className":82134},[1480],[1482,82136,82137],{"xmlns":1484},[1487,82138,82139,82143],{},[1490,82140,82141],{},[1493,82142,3712],{},[1528,82144,3712],{"encoding":1530},[1035,82146,82148],{"className":82147},[1480],[1482,82149,82150],{"xmlns":1484},[1487,82151,82152,82158],{},[1490,82153,82154,82156],{},[1493,82155,5289],{},[1493,82157,1995],{},[1528,82159,16491],{"encoding":1530},[1035,82161,82163],{"className":82162},[1480],[1482,82164,82165],{"xmlns":1484},[1487,82166,82167,82173],{},[1490,82168,82169,82171],{},[1493,82170,3633],{},[1493,82172,1995],{},[1528,82174,69623],{"encoding":1530},[1035,82176,82178],{"className":82177},[1480],[1482,82179,82180],{"xmlns":1484},[1487,82181,82182,82188],{},[1490,82183,82184,82186],{},[1493,82185,1495],{},[1493,82187,1995],{},[1528,82189,6258],{"encoding":1530},[1030,82191,82192,82195,82196,82226,82227,82242,82243,26683,82256,1732,82273,1732,82290,82308,82309,82331,82332,82347,82348,82361,82362,2632],{},[1047,82193,82194],{},"3.4"," Je dán celkový příjem ",[1035,82197,82199],{"className":82198},[1480],[1482,82200,82201],{"xmlns":1484},[1487,82202,82203,82223],{},[1490,82204,82205,82207,82209,82211,82213,82215,82217],{},[1493,82206,5289],{},[1493,82208,1995],{},[1506,82210,1508],{},[1680,82212,81898],{},[1493,82214,1520],{},[1506,82216,1888],{},[2315,82218,82219,82221],{},[1493,82220,1520],{},[1680,82222,3201],{},[1528,82224,82225],{"encoding":1530},"TR = 1200Q - Q^3",". (a) Určete, jak rychle se (přibližně) mění ",[1035,82228,82230],{"className":82229},[1480],[1482,82231,82232],{"xmlns":1484},[1487,82233,82234,82240],{},[1490,82235,82236,82238],{},[1493,82237,5289],{},[1493,82239,1995],{},[1528,82241,16491],{"encoding":1530}," vzhledem ke ",[1035,82244,82246],{"className":82245},[1480],[1482,82247,82248],{"xmlns":1484},[1487,82249,82250,82254],{},[1490,82251,82252],{},[1493,82253,1520],{},[1528,82255,1520],{"encoding":1530},[1035,82257,82259],{"className":82258},[1480],[1482,82260,82261],{"xmlns":1484},[1487,82262,82263,82271],{},[1490,82264,82265,82267,82269],{},[1493,82266,1520],{},[1506,82268,1508],{},[1680,82270,1752],{},[1528,82272,11731],{"encoding":1530},[1035,82274,82276],{"className":82275},[1480],[1482,82277,82278],{"xmlns":1484},[1487,82279,82280,82288],{},[1490,82281,82282,82284,82286],{},[1493,82283,1520],{},[1506,82285,1508],{},[1680,82287,6138],{},[1528,82289,21351],{"encoding":1530},[1035,82291,82293],{"className":82292},[1480],[1482,82294,82295],{"xmlns":1484},[1487,82296,82297,82305],{},[1490,82298,82299,82301,82303],{},[1493,82300,1520],{},[1506,82302,1508],{},[1680,82304,6797],{},[1528,82306,82307],{"encoding":1530},"Q = 12"," a charakterizujte dynamiku změn. (b) Vypočtěte a ekonomicky interpretujte ",[1035,82310,82312],{"className":82311},[1480],[1482,82313,82314],{"xmlns":1484},[1487,82315,82316,82328],{},[1490,82317,82318,82320,82322,82324,82326],{},[1493,82319,1495],{},[1493,82321,1995],{},[1506,82323,1553],{"stretchy":1552},[1680,82325,1775],{},[1506,82327,1564],{"stretchy":1552},[1528,82329,82330],{"encoding":1530},"MR(10)",". (c) Odhadněte, o kolik se přibližně změní ",[1035,82333,82335],{"className":82334},[1480],[1482,82336,82337],{"xmlns":1484},[1487,82338,82339,82345],{},[1490,82340,82341,82343],{},[1493,82342,5289],{},[1493,82344,1995],{},[1528,82346,16491],{"encoding":1530},", jestliže se ",[1035,82349,82351],{"className":82350},[1480],[1482,82352,82353],{"xmlns":1484},[1487,82354,82355,82359],{},[1490,82356,82357],{},[1493,82358,1520],{},[1528,82360,1520],{"encoding":1530}," změní z 10 na 12 a porovnejte se skutečnou změnou ",[1035,82363,82365],{"className":82364},[1480],[1482,82366,82367],{"xmlns":1484},[1487,82368,82369,82375],{},[1490,82370,82371,82373],{},[1493,82372,5289],{},[1493,82374,1995],{},[1528,82376,16491],{"encoding":1530},[1030,82378,82379,82382,82383,82409,82410,82425,82426,82347,82441,82454],{},[1047,82380,82381],{},"3.5"," Je dán mezní příjem ",[1035,82384,82386],{"className":82385},[1480],[1482,82387,82388],{"xmlns":1484},[1487,82389,82390,82406],{},[1490,82391,82392,82394,82396,82398,82400,82402,82404],{},[1493,82393,1495],{},[1493,82395,1995],{},[1506,82397,1508],{},[1506,82399,1888],{},[1493,82401,1520],{},[1506,82403,2162],{},[1680,82405,8436],{},[1528,82407,82408],{"encoding":1530},"MR = -Q + 20",". (a) Určete celkový příjem ",[1035,82411,82413],{"className":82412},[1480],[1482,82414,82415],{"xmlns":1484},[1487,82416,82417,82423],{},[1490,82418,82419,82421],{},[1493,82420,5289],{},[1493,82422,1995],{},[1528,82424,16491],{"encoding":1530},". (b) Vypočtěte změnu ",[1035,82427,82429],{"className":82428},[1480],[1482,82430,82431],{"xmlns":1484},[1487,82432,82433,82439],{},[1490,82434,82435,82437],{},[1493,82436,5289],{},[1493,82438,1995],{},[1528,82440,16491],{"encoding":1530},[1035,82442,82444],{"className":82443},[1480],[1482,82445,82446],{"xmlns":1484},[1487,82447,82448,82452],{},[1490,82449,82450],{},[1493,82451,1520],{},[1528,82453,1520],{"encoding":1530}," změní z 8 na 12.",[1304,82456,82458],{"id":82457},"náklady-36316","Náklady (3.6–3.16)",[1030,82460,82461,82464,82465,82505,82506,82521,82522,82539,82540,82557,82558,82573,82574,82589,82590,81956,82605,1732,82620,1732,82637,1732,82654,1732,82669,1732,82684,22345,82699,82717,82718,1732,82733,1732,82748,82763],{},[1047,82462,82463],{},"3.6"," Jsou dány celkové náklady ",[1035,82466,82468],{"className":82467},[1480],[1482,82469,82470],{"xmlns":1484},[1487,82471,82472,82502],{},[1490,82473,82474,82476,82478,82480,82482,82484,82486,82488,82490],{},[1493,82475,5289],{},[1493,82477,1998],{},[1506,82479,1508],{},[1680,82481,2916],{},[1506,82483,2162],{},[1680,82485,1691],{},[1493,82487,1520],{},[1506,82489,2162],{},[1869,82491,82492],{"scriptlevel":1871,"displaystyle":1552},[1510,82493,82494,82500],{},[2315,82495,82496,82498],{},[1493,82497,1520],{},[1680,82499,1691],{},[1680,82501,1775],{},[1528,82503,82504],{"encoding":1530},"TC = 100 + 2Q + \\tfrac{Q^2}{10}",". (a) Určete fixní náklady ",[1035,82507,82509],{"className":82508},[1480],[1482,82510,82511],{"xmlns":1484},[1487,82512,82513,82519],{},[1490,82514,82515,82517],{},[1493,82516,10790],{},[1493,82518,1998],{},[1528,82520,69669],{"encoding":1530},", celkové variabilní náklady ",[1035,82523,82525],{"className":82524},[1480],[1482,82526,82527],{"xmlns":1484},[1487,82528,82529,82537],{},[1490,82530,82531,82533,82535],{},[1493,82532,5289],{},[1493,82534,55105],{},[1493,82536,1998],{},[1528,82538,69687],{"encoding":1530},", průměrné variabilní náklady ",[1035,82541,82543],{"className":82542},[1480],[1482,82544,82545],{"xmlns":1484},[1487,82546,82547,82555],{},[1490,82548,82549,82551,82553],{},[1493,82550,3633],{},[1493,82552,55105],{},[1493,82554,1998],{},[1528,82556,69489],{"encoding":1530},", variabilní náklady na jednotku ",[1035,82559,82561],{"className":82560},[1480],[1482,82562,82563],{"xmlns":1484},[1487,82564,82565,82571],{},[1490,82566,82567,82569],{},[1493,82568,55105],{},[1493,82570,1998],{},[1528,82572,76923],{"encoding":1530},", průměrné náklady ",[1035,82575,82577],{"className":82576},[1480],[1482,82578,82579],{"xmlns":1484},[1487,82580,82581,82587],{},[1490,82582,82583,82585],{},[1493,82584,3633],{},[1493,82586,1998],{},[1528,82588,16523],{"encoding":1530}," a mezní náklady ",[1035,82591,82593],{"className":82592},[1480],[1482,82594,82595],{"xmlns":1484},[1487,82596,82597,82603],{},[1490,82598,82599,82601],{},[1493,82600,1495],{},[1493,82602,1998],{},[1528,82604,69470],{"encoding":1530},[1035,82606,82608],{"className":82607},[1480],[1482,82609,82610],{"xmlns":1484},[1487,82611,82612,82618],{},[1490,82613,82614,82616],{},[1493,82615,5289],{},[1493,82617,1998],{},[1528,82619,18668],{"encoding":1530},[1035,82621,82623],{"className":82622},[1480],[1482,82624,82625],{"xmlns":1484},[1487,82626,82627,82635],{},[1490,82628,82629,82631,82633],{},[1493,82630,5289],{},[1493,82632,55105],{},[1493,82634,1998],{},[1528,82636,69687],{"encoding":1530},[1035,82638,82640],{"className":82639},[1480],[1482,82641,82642],{"xmlns":1484},[1487,82643,82644,82652],{},[1490,82645,82646,82648,82650],{},[1493,82647,3633],{},[1493,82649,55105],{},[1493,82651,1998],{},[1528,82653,69489],{"encoding":1530},[1035,82655,82657],{"className":82656},[1480],[1482,82658,82659],{"xmlns":1484},[1487,82660,82661,82667],{},[1490,82662,82663,82665],{},[1493,82664,55105],{},[1493,82666,1998],{},[1528,82668,76923],{"encoding":1530},[1035,82670,82672],{"className":82671},[1480],[1482,82673,82674],{"xmlns":1484},[1487,82675,82676,82682],{},[1490,82677,82678,82680],{},[1493,82679,3633],{},[1493,82681,1998],{},[1528,82683,16523],{"encoding":1530},[1035,82685,82687],{"className":82686},[1480],[1482,82688,82689],{"xmlns":1484},[1487,82690,82691,82697],{},[1490,82692,82693,82695],{},[1493,82694,1495],{},[1493,82696,1998],{},[1528,82698,69470],{"encoding":1530},[1035,82700,82702],{"className":82701},[1480],[1482,82703,82704],{"xmlns":1484},[1487,82705,82706,82714],{},[1490,82707,82708,82710,82712],{},[1493,82709,1520],{},[1506,82711,1508],{},[1680,82713,2292],{},[1528,82715,82716],{"encoding":1530},"Q = 50",". (c) Rozhodněte, kdy ",[1035,82719,82721],{"className":82720},[1480],[1482,82722,82723],{"xmlns":1484},[1487,82724,82725,82731],{},[1490,82726,82727,82729],{},[1493,82728,5289],{},[1493,82730,1998],{},[1528,82732,18668],{"encoding":1530},[1035,82734,82736],{"className":82735},[1480],[1482,82737,82738],{"xmlns":1484},[1487,82739,82740,82746],{},[1490,82741,82742,82744],{},[1493,82743,3633],{},[1493,82745,1998],{},[1528,82747,16523],{"encoding":1530},[1035,82749,82751],{"className":82750},[1480],[1482,82752,82753],{"xmlns":1484},[1487,82754,82755,82761],{},[1490,82756,82757,82759],{},[1493,82758,1495],{},[1493,82760,1998],{},[1528,82762,69470],{"encoding":1530}," rostou, resp. klesají.",[1030,82765,82766,82769,82770,82589,82800,82815,82816,82831,82832,1732,82847,1732,82862,2632],{},[1047,82767,82768],{},"3.7"," Jsou dány průměrné náklady ",[1035,82771,82773],{"className":82772},[1480],[1482,82774,82775],{"xmlns":1484},[1487,82776,82777,82797],{},[1490,82778,82779,82781,82783,82785,82793,82795],{},[1493,82780,3633],{},[1493,82782,1998],{},[1506,82784,1508],{},[1869,82786,82787],{"scriptlevel":1871,"displaystyle":1552},[1510,82788,82789,82791],{},[1680,82790,2916],{},[1493,82792,1520],{},[1506,82794,2162],{},[1680,82796,8436],{},[1528,82798,82799],{"encoding":1530},"AC = \\tfrac{100}{Q} + 20",[1035,82801,82803],{"className":82802},[1480],[1482,82804,82805],{"xmlns":1484},[1487,82806,82807,82813],{},[1490,82808,82809,82811],{},[1493,82810,1495],{},[1493,82812,1998],{},[1528,82814,69470],{"encoding":1530},". (a) Určete celkové náklady ",[1035,82817,82819],{"className":82818},[1480],[1482,82820,82821],{"xmlns":1484},[1487,82822,82823,82829],{},[1490,82824,82825,82827],{},[1493,82826,5289],{},[1493,82828,1998],{},[1528,82830,18668],{"encoding":1530},". (b) Načrtněte a geometricky charakterizujte křivky ",[1035,82833,82835],{"className":82834},[1480],[1482,82836,82837],{"xmlns":1484},[1487,82838,82839,82845],{},[1490,82840,82841,82843],{},[1493,82842,3633],{},[1493,82844,1998],{},[1528,82846,16523],{"encoding":1530},[1035,82848,82850],{"className":82849},[1480],[1482,82851,82852],{"xmlns":1484},[1487,82853,82854,82860],{},[1490,82855,82856,82858],{},[1493,82857,5289],{},[1493,82859,1998],{},[1528,82861,18668],{"encoding":1530},[1035,82863,82865],{"className":82864},[1480],[1482,82866,82867],{"xmlns":1484},[1487,82868,82869,82875],{},[1490,82870,82871,82873],{},[1493,82872,1495],{},[1493,82874,1998],{},[1528,82876,69470],{"encoding":1530},[1030,82878,82879,82464,82882,1800,82926,1732,82943,1732,82958,1732,82975,1732,82990,1732,83007,2632],{},[1047,82880,82881],{},"3.8",[1035,82883,82885],{"className":82884},[1480],[1482,82886,82887],{"xmlns":1484},[1487,82888,82889,82923],{},[1490,82890,82891,82893,82895,82897,82899,82901,82903,82905,82907,82909,82915,82917],{},[1493,82892,5289],{},[1493,82894,1998],{},[1506,82896,1508],{},[1680,82898,11232],{},[1506,82900,2162],{},[1680,82902,6956],{},[1493,82904,1520],{},[1506,82906,1888],{},[1680,82908,7508],{},[2315,82910,82911,82913],{},[1493,82912,1520],{},[1680,82914,1691],{},[1506,82916,2162],{},[2315,82918,82919,82921],{},[1493,82920,1520],{},[1680,82922,3201],{},[1528,82924,82925],{"encoding":1530},"TC = 80 + 30Q - 6Q^2 + Q^3",[1035,82927,82929],{"className":82928},[1480],[1482,82930,82931],{"xmlns":1484},[1487,82932,82933,82941],{},[1490,82934,82935,82937,82939],{},[1493,82936,5289],{},[1493,82938,55105],{},[1493,82940,1998],{},[1528,82942,69687],{"encoding":1530},[1035,82944,82946],{"className":82945},[1480],[1482,82947,82948],{"xmlns":1484},[1487,82949,82950,82956],{},[1490,82951,82952,82954],{},[1493,82953,10790],{},[1493,82955,1998],{},[1528,82957,69669],{"encoding":1530},[1035,82959,82961],{"className":82960},[1480],[1482,82962,82963],{"xmlns":1484},[1487,82964,82965,82973],{},[1490,82966,82967,82969,82971],{},[1493,82968,3633],{},[1493,82970,55105],{},[1493,82972,1998],{},[1528,82974,69489],{"encoding":1530},[1035,82976,82978],{"className":82977},[1480],[1482,82979,82980],{"xmlns":1484},[1487,82981,82982,82988],{},[1490,82983,82984,82986],{},[1493,82985,3633],{},[1493,82987,1998],{},[1528,82989,16523],{"encoding":1530},[1035,82991,82993],{"className":82992},[1480],[1482,82994,82995],{"xmlns":1484},[1487,82996,82997,83005],{},[1490,82998,82999,83001,83003],{},[1493,83000,3633],{},[1493,83002,10790],{},[1493,83004,1998],{},[1528,83006,69705],{"encoding":1530},[1035,83008,83010],{"className":83009},[1480],[1482,83011,83012],{"xmlns":1484},[1487,83013,83014,83020],{},[1490,83015,83016,83018],{},[1493,83017,1495],{},[1493,83019,1998],{},[1528,83021,69470],{"encoding":1530},[1030,83023,83024,82464,83027,83057,83058,82242,83073,22345,83086,1732,83104,1732,83122,82308,83140,82331,83162,83177,83178,83191,83192,2632],{},[1047,83025,83026],{},"3.9",[1035,83028,83030],{"className":83029},[1480],[1482,83031,83032],{"xmlns":1484},[1487,83033,83034,83054],{},[1490,83035,83036,83038,83040,83042,83044,83046,83048],{},[1493,83037,5289],{},[1493,83039,1998],{},[1506,83041,1508],{},[1680,83043,1796],{},[1506,83045,2162],{},[1680,83047,3332],{},[2315,83049,83050,83052],{},[1493,83051,1520],{},[1680,83053,1691],{},[1528,83055,83056],{"encoding":1530},"TC = 500 + 0{,}6Q^2",". (a) Určete, jak rychle se přibližně mění ",[1035,83059,83061],{"className":83060},[1480],[1482,83062,83063],{"xmlns":1484},[1487,83064,83065,83071],{},[1490,83066,83067,83069],{},[1493,83068,5289],{},[1493,83070,1998],{},[1528,83072,18668],{"encoding":1530},[1035,83074,83076],{"className":83075},[1480],[1482,83077,83078],{"xmlns":1484},[1487,83079,83080,83084],{},[1490,83081,83082],{},[1493,83083,1520],{},[1528,83085,1520],{"encoding":1530},[1035,83087,83089],{"className":83088},[1480],[1482,83090,83091],{"xmlns":1484},[1487,83092,83093,83101],{},[1490,83094,83095,83097,83099],{},[1493,83096,1520],{},[1506,83098,1508],{},[1680,83100,1775],{},[1528,83102,83103],{"encoding":1530},"Q = 10",[1035,83105,83107],{"className":83106},[1480],[1482,83108,83109],{"xmlns":1484},[1487,83110,83111,83119],{},[1490,83112,83113,83115,83117],{},[1493,83114,1520],{},[1506,83116,1508],{},[1680,83118,8436],{},[1528,83120,83121],{"encoding":1530},"Q = 20",[1035,83123,83125],{"className":83124},[1480],[1482,83126,83127],{"xmlns":1484},[1487,83128,83129,83137],{},[1490,83130,83131,83133,83135],{},[1493,83132,1520],{},[1506,83134,1508],{},[1680,83136,6956],{},[1528,83138,83139],{"encoding":1530},"Q = 30",[1035,83141,83143],{"className":83142},[1480],[1482,83144,83145],{"xmlns":1484},[1487,83146,83147,83159],{},[1490,83148,83149,83151,83153,83155,83157],{},[1493,83150,1495],{},[1493,83152,1998],{},[1506,83154,1553],{"stretchy":1552},[1680,83156,9787],{},[1506,83158,1564],{"stretchy":1552},[1528,83160,83161],{"encoding":1530},"MC(15)",[1035,83163,83165],{"className":83164},[1480],[1482,83166,83167],{"xmlns":1484},[1487,83168,83169,83175],{},[1490,83170,83171,83173],{},[1493,83172,5289],{},[1493,83174,1998],{},[1528,83176,18668],{"encoding":1530}," v důsledku změny ",[1035,83179,83181],{"className":83180},[1480],[1482,83182,83183],{"xmlns":1484},[1487,83184,83185,83189],{},[1490,83186,83187],{},[1493,83188,1520],{},[1528,83190,1520],{"encoding":1530}," z 15 na 20 a porovnejte se skutečnou změnou ",[1035,83193,83195],{"className":83194},[1480],[1482,83196,83197],{"xmlns":1484},[1487,83198,83199,83205],{},[1490,83200,83201,83203],{},[1493,83202,5289],{},[1493,83204,1998],{},[1528,83206,18668],{"encoding":1530},[1030,83208,83209,83212,83213,82815,83249,83264,83265,82425,83284,83177,83299,83312],{},[1047,83210,83211],{},"3.10"," Jsou dány mezní náklady ",[1035,83214,83216],{"className":83215},[1480],[1482,83217,83218],{"xmlns":1484},[1487,83219,83220,83246],{},[1490,83221,83222,83224,83226,83228,83230,83232,83234,83236,83238,83240],{},[1493,83223,1495],{},[1493,83225,1998],{},[1506,83227,1508],{},[1680,83229,4965],{},[1506,83231,1888],{},[1680,83233,9961],{},[1493,83235,1520],{},[1506,83237,2162],{},[1680,83239,77687],{},[2315,83241,83242,83244],{},[1493,83243,1520],{},[1680,83245,1691],{},[1528,83247,83248],{"encoding":1530},"MC = 60 - 16Q + 1{,}5Q^2",[1035,83250,83252],{"className":83251},[1480],[1482,83253,83254],{"xmlns":1484},[1487,83255,83256,83262],{},[1490,83257,83258,83260],{},[1493,83259,5289],{},[1493,83261,1998],{},[1528,83263,18668],{"encoding":1530},", jestliže fixní náklady ",[1035,83266,83268],{"className":83267},[1480],[1482,83269,83270],{"xmlns":1484},[1487,83271,83272,83282],{},[1490,83273,83274,83276,83278,83280],{},[1493,83275,10790],{},[1493,83277,1998],{},[1506,83279,1508],{},[1680,83281,2916],{},[1528,83283,28133],{"encoding":1530},[1035,83285,83287],{"className":83286},[1480],[1482,83288,83289],{"xmlns":1484},[1487,83290,83291,83297],{},[1490,83292,83293,83295],{},[1493,83294,5289],{},[1493,83296,1998],{},[1528,83298,18668],{"encoding":1530},[1035,83300,83302],{"className":83301},[1480],[1482,83303,83304],{"xmlns":1484},[1487,83305,83306,83310],{},[1490,83307,83308],{},[1493,83309,1520],{},[1528,83311,1520],{"encoding":1530}," z 15 na 20.",[1030,83314,83315,82464,83318,83361,83362,83375,83376,83391,83392,83407,83408,83375,83421,83391,83438,83455,83456,83375,83469,83391,83484,83499,83500,83520,83521,83544],{},[1047,83316,83317],{},"3.11",[1035,83319,83321],{"className":83320},[1480],[1482,83322,83323],{"xmlns":1484},[1487,83324,83325,83359],{},[1490,83326,83327,83329,83331,83333,83335,83337,83339,83341,83343,83345,83351,83353],{},[1493,83328,5289],{},[1493,83330,1998],{},[1506,83332,1508],{},[1680,83334,2916],{},[1506,83336,2162],{},[1680,83338,2309],{},[1493,83340,1520],{},[1506,83342,1888],{},[1680,83344,1752],{},[2315,83346,83347,83349],{},[1493,83348,1520],{},[1680,83350,1691],{},[1506,83352,2162],{},[2315,83354,83355,83357],{},[1493,83356,1520],{},[1680,83358,3201],{},[1528,83360,74468],{"encoding":1530},". (a) Určete ",[1035,83363,83365],{"className":83364},[1480],[1482,83366,83367],{"xmlns":1484},[1487,83368,83369,83373],{},[1490,83370,83371],{},[1493,83372,1520],{},[1528,83374,1520],{"encoding":1530},", které minimalizuje ",[1035,83377,83379],{"className":83378},[1480],[1482,83380,83381],{"xmlns":1484},[1487,83382,83383,83389],{},[1490,83384,83385,83387],{},[1493,83386,1495],{},[1493,83388,1998],{},[1528,83390,69470],{"encoding":1530}," a stanovte příslušnou hodnotu minima ",[1035,83393,83395],{"className":83394},[1480],[1482,83396,83397],{"xmlns":1484},[1487,83398,83399,83405],{},[1490,83400,83401,83403],{},[1493,83402,1495],{},[1493,83404,1998],{},[1528,83406,69470],{"encoding":1530},". (b) Určete ",[1035,83409,83411],{"className":83410},[1480],[1482,83412,83413],{"xmlns":1484},[1487,83414,83415,83419],{},[1490,83416,83417],{},[1493,83418,1520],{},[1528,83420,1520],{"encoding":1530},[1035,83422,83424],{"className":83423},[1480],[1482,83425,83426],{"xmlns":1484},[1487,83427,83428,83436],{},[1490,83429,83430,83432,83434],{},[1493,83431,3633],{},[1493,83433,55105],{},[1493,83435,1998],{},[1528,83437,69489],{"encoding":1530},[1035,83439,83441],{"className":83440},[1480],[1482,83442,83443],{"xmlns":1484},[1487,83444,83445,83453],{},[1490,83446,83447,83449,83451],{},[1493,83448,3633],{},[1493,83450,55105],{},[1493,83452,1998],{},[1528,83454,69489],{"encoding":1530},". (c) Určete ",[1035,83457,83459],{"className":83458},[1480],[1482,83460,83461],{"xmlns":1484},[1487,83462,83463,83467],{},[1490,83464,83465],{},[1493,83466,1520],{},[1528,83468,1520],{"encoding":1530},[1035,83470,83472],{"className":83471},[1480],[1482,83473,83474],{"xmlns":1484},[1487,83475,83476,83482],{},[1490,83477,83478,83480],{},[1493,83479,3633],{},[1493,83481,1998],{},[1528,83483,16523],{"encoding":1530},[1035,83485,83487],{"className":83486},[1480],[1482,83488,83489],{"xmlns":1484},[1487,83490,83491,83497],{},[1490,83492,83493,83495],{},[1493,83494,3633],{},[1493,83496,1998],{},[1528,83498,16523],{"encoding":1530}," (rada: hledaný kořen ",[1035,83501,83503],{"className":83502},[1480],[1482,83504,83505],{"xmlns":1484},[1487,83506,83507,83517],{},[1490,83508,83509,83511],{},[1493,83510,3633],{},[2315,83512,83513,83515],{},[1493,83514,1998],{},[1506,83516,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,83518,83519],{"encoding":1530},"AC'"," určete přibližně, patří do ",[1035,83522,83524],{"className":83523},[1480],[1482,83525,83526],{"xmlns":1484},[1487,83527,83528,83541],{},[1490,83529,83530,83532,83535,83537,83539],{},[1506,83531,1553],{"stretchy":1552},[1680,83533,83534],{},"4,7",[1506,83536,6065],{"separator":1041},[1680,83538,20989],{},[1506,83540,1564],{"stretchy":1552},[1528,83542,83543],{"encoding":1530},"(4{,}7; 4{,}8)",", zpřesněte).",[1030,83546,83547,83550,83551,11713,83579,83596,83597,37188,83638,83659],{},[1047,83548,83549],{},"3.12"," Dokažte, že mají-li průměrné náklady ",[1035,83552,83554],{"className":83553},[1480],[1482,83555,83556],{"xmlns":1484},[1487,83557,83558,83576],{},[1490,83559,83560,83562,83564,83566,83568,83570,83572,83574],{},[1493,83561,3633],{},[1493,83563,1998],{},[1506,83565,1508],{},[1493,83567,3633],{},[1493,83569,1998],{},[1506,83571,1553],{"stretchy":1552},[1493,83573,1520],{},[1506,83575,1564],{"stretchy":1552},[1528,83577,83578],{"encoding":1530},"AC = AC(Q)",[1035,83580,83582],{"className":83581},[1480],[1482,83583,83584],{"xmlns":1484},[1487,83585,83586,83594],{},[1490,83587,83588],{},[1497,83589,83590,83592],{},[1493,83591,1520],{},[1680,83593,1871],{},[1528,83595,53236],{"encoding":1530}," minimum, pak platí ",[1035,83598,83600],{"className":83599},[1480],[1482,83601,83602],{"xmlns":1484},[1487,83603,83604,83636],{},[1490,83605,83606,83608,83610,83612,83618,83620,83622,83624,83626,83628,83634],{},[1493,83607,3633],{},[1493,83609,1998],{},[1506,83611,1553],{"stretchy":1552},[1497,83613,83614,83616],{},[1493,83615,1520],{},[1680,83617,1871],{},[1506,83619,1564],{"stretchy":1552},[1506,83621,1508],{},[1493,83623,1495],{},[1493,83625,1998],{},[1506,83627,1553],{"stretchy":1552},[1497,83629,83630,83632],{},[1493,83631,1520],{},[1680,83633,1871],{},[1506,83635,1564],{"stretchy":1552},[1528,83637,75877],{"encoding":1530},[1035,83639,83641],{"className":83640},[1480],[1482,83642,83643],{"xmlns":1484},[1487,83644,83645,83657],{},[1490,83646,83647,83649,83651,83653,83655],{},[1493,83648,1495],{},[1493,83650,1998],{},[1506,83652,1553],{"stretchy":1552},[1493,83654,1520],{},[1506,83656,1564],{"stretchy":1552},[1528,83658,11736],{"encoding":1530}," jsou mezní náklady.",[1030,83661,83662,82464,83665,1800,83699,83375,83712,83391,83727,2632],{},[1047,83663,83664],{},"3.13",[1035,83666,83668],{"className":83667},[1480],[1482,83669,83670],{"xmlns":1484},[1487,83671,83672,83696],{},[1490,83673,83674,83676,83678,83680,83686,83688,83690,83692,83694],{},[1493,83675,5289],{},[1493,83677,1998],{},[1506,83679,1508],{},[2315,83681,83682,83684],{},[1493,83683,1520],{},[1680,83685,1691],{},[1506,83687,2162],{},[1680,83689,1691],{},[1493,83691,1520],{},[1506,83693,2162],{},[1680,83695,2309],{},[1528,83697,83698],{"encoding":1530},"TC = Q^2 + 2Q + 25",[1035,83700,83702],{"className":83701},[1480],[1482,83703,83704],{"xmlns":1484},[1487,83705,83706,83710],{},[1490,83707,83708],{},[1493,83709,1520],{},[1528,83711,1520],{"encoding":1530},[1035,83713,83715],{"className":83714},[1480],[1482,83716,83717],{"xmlns":1484},[1487,83718,83719,83725],{},[1490,83720,83721,83723],{},[1493,83722,3633],{},[1493,83724,1998],{},[1528,83726,16523],{"encoding":1530},[1035,83728,83730],{"className":83729},[1480],[1482,83731,83732],{"xmlns":1484},[1487,83733,83734,83740],{},[1490,83735,83736,83738],{},[1493,83737,3633],{},[1493,83739,1998],{},[1528,83741,16523],{"encoding":1530},[1030,83743,83744,83747,83748,11713,83780,83596,83797,37188,83840,83659],{},[1047,83745,83746],{},"3.14"," Dokažte, že mají-li průměrné variabilní náklady ",[1035,83749,83751],{"className":83750},[1480],[1482,83752,83753],{"xmlns":1484},[1487,83754,83755,83777],{},[1490,83756,83757,83759,83761,83763,83765,83767,83769,83771,83773,83775],{},[1493,83758,3633],{},[1493,83760,55105],{},[1493,83762,1998],{},[1506,83764,1508],{},[1493,83766,3633],{},[1493,83768,55105],{},[1493,83770,1998],{},[1506,83772,1553],{"stretchy":1552},[1493,83774,1520],{},[1506,83776,1564],{"stretchy":1552},[1528,83778,83779],{"encoding":1530},"AVC = AVC(Q)",[1035,83781,83783],{"className":83782},[1480],[1482,83784,83785],{"xmlns":1484},[1487,83786,83787,83795],{},[1490,83788,83789],{},[1497,83790,83791,83793],{},[1493,83792,1520],{},[1680,83794,1871],{},[1528,83796,53236],{"encoding":1530},[1035,83798,83800],{"className":83799},[1480],[1482,83801,83802],{"xmlns":1484},[1487,83803,83804,83838],{},[1490,83805,83806,83808,83810,83812,83814,83820,83822,83824,83826,83828,83830,83836],{},[1493,83807,3633],{},[1493,83809,55105],{},[1493,83811,1998],{},[1506,83813,1553],{"stretchy":1552},[1497,83815,83816,83818],{},[1493,83817,1520],{},[1680,83819,1871],{},[1506,83821,1564],{"stretchy":1552},[1506,83823,1508],{},[1493,83825,1495],{},[1493,83827,1998],{},[1506,83829,1553],{"stretchy":1552},[1497,83831,83832,83834],{},[1493,83833,1520],{},[1680,83835,1871],{},[1506,83837,1564],{"stretchy":1552},[1528,83839,81391],{"encoding":1530},[1035,83841,83843],{"className":83842},[1480],[1482,83844,83845],{"xmlns":1484},[1487,83846,83847,83859],{},[1490,83848,83849,83851,83853,83855,83857],{},[1493,83850,1495],{},[1493,83852,1998],{},[1506,83854,1553],{"stretchy":1552},[1493,83856,1520],{},[1506,83858,1564],{"stretchy":1552},[1528,83860,11736],{"encoding":1530},[1030,83862,83863,82464,83866,1800,83912,83375,83925,83391,83942,2632],{},[1047,83864,83865],{},"3.15",[1035,83867,83869],{"className":83868},[1480],[1482,83870,83871],{"xmlns":1484},[1487,83872,83873,83909],{},[1490,83874,83875,83877,83879,83881,83883,83885,83887,83889,83891,83893,83899,83901,83903],{},[1493,83876,5289],{},[1493,83878,1998],{},[1506,83880,1508],{},[1680,83882,2292],{},[1506,83884,2162],{},[1680,83886,9787],{},[1493,83888,1520],{},[1506,83890,1888],{},[1680,83892,1691],{},[2315,83894,83895,83897],{},[1493,83896,1520],{},[1680,83898,1691],{},[1506,83900,2162],{},[1680,83902,2929],{},[2315,83904,83905,83907],{},[1493,83906,1520],{},[1680,83908,3201],{},[1528,83910,83911],{"encoding":1530},"TC = 50 + 15Q - 2Q^2 + 0{,}2Q^3",[1035,83913,83915],{"className":83914},[1480],[1482,83916,83917],{"xmlns":1484},[1487,83918,83919,83923],{},[1490,83920,83921],{},[1493,83922,1520],{},[1528,83924,1520],{"encoding":1530},[1035,83926,83928],{"className":83927},[1480],[1482,83929,83930],{"xmlns":1484},[1487,83931,83932,83940],{},[1490,83933,83934,83936,83938],{},[1493,83935,3633],{},[1493,83937,55105],{},[1493,83939,1998],{},[1528,83941,69489],{"encoding":1530},[1035,83943,83945],{"className":83944},[1480],[1482,83946,83947],{"xmlns":1484},[1487,83948,83949,83957],{},[1490,83950,83951,83953,83955],{},[1493,83952,3633],{},[1493,83954,55105],{},[1493,83956,1998],{},[1528,83958,69489],{"encoding":1530},[1030,83960,83961,83964,83965,83978,83979,83999],{},[1047,83962,83963],{},"3.16"," Celkové náklady na výstavbu domu o ",[1035,83966,83968],{"className":83967},[1480],[1482,83969,83970],{"xmlns":1484},[1487,83971,83972,83976],{},[1490,83973,83974],{},[1493,83975,17494],{},[1528,83977,17494],{"encoding":1530}," podlažích se skládají ze tří komponent (1), (2), (3): (1) 10 milionů Kč za pozemek, (2) 0,25 milionu Kč za každé podlaží, (3) zvláštní náklady ",[1035,83980,83982],{"className":83981},[1480],[1482,83983,83984],{"xmlns":1484},[1487,83985,83986,83996],{},[1490,83987,83988,83990,83992,83994],{},[1680,83989,1775],{},[1988,83991,5016],{},[1680,83993,5608],{},[1493,83995,17494],{},[1528,83997,83998],{"encoding":1530},"10\\,000 x"," Kč za podlaží. Určete počet podlaží, které minimalizuje průměrné náklady na jedno podlaží a stanovte příslušnou hodnotu minima průměrných nákladů.",[1304,84001,84003],{"id":84002},"zisk-body-zvratu-317325","Zisk, body zvratu (3.17–3.25)",[1030,84005,84006,84009,84010,1586,84032,84058],{},[1047,84007,84008],{},"3.17"," Jsou dány ",[1035,84011,84013],{"className":84012},[1480],[1482,84014,84015],{"xmlns":1484},[1487,84016,84017,84029],{},[1490,84018,84019,84021,84023,84025,84027],{},[1493,84020,5289],{},[1493,84022,1995],{},[1506,84024,1508],{},[1680,84026,1775],{},[1493,84028,1520],{},[1528,84030,84031],{"encoding":1530},"TR = 10Q",[1035,84033,84035],{"className":84034},[1480],[1482,84036,84037],{"xmlns":1484},[1487,84038,84039,84055],{},[1490,84040,84041,84043,84045,84047,84049,84051,84053],{},[1493,84042,5289],{},[1493,84044,1998],{},[1506,84046,1508],{},[1680,84048,2916],{},[1506,84050,2162],{},[1680,84052,1752],{},[1493,84054,1520],{},[1528,84056,84057],{"encoding":1530},"TC = 100 + 5Q",". Určete body zvratu a geometricky výsledek interpretujte.",[1030,84060,84061,84064,84065,22060,84080,84095,84096,1732,84118,37188,84144,84166,84167,84201],{},[1047,84062,84063],{},"3.18"," Odvoďte, že jestliže ",[1035,84066,84068],{"className":84067},[1480],[1482,84069,84070],{"xmlns":1484},[1487,84071,84072,84078],{},[1490,84073,84074,84076],{},[1493,84075,5289],{},[1493,84077,1995],{},[1528,84079,16491],{"encoding":1530},[1035,84081,84083],{"className":84082},[1480],[1482,84084,84085],{"xmlns":1484},[1487,84086,84087,84093],{},[1490,84088,84089,84091],{},[1493,84090,5289],{},[1493,84092,1998],{},[1528,84094,18668],{"encoding":1530}," jsou lineární tvaru ",[1035,84097,84099],{"className":84098},[1480],[1482,84100,84101],{"xmlns":1484},[1487,84102,84103,84115],{},[1490,84104,84105,84107,84109,84111,84113],{},[1493,84106,5289],{},[1493,84108,1995],{},[1506,84110,1508],{},[1493,84112,1030],{},[1493,84114,1520],{},[1528,84116,84117],{"encoding":1530},"TR = pQ",[1035,84119,84121],{"className":84120},[1480],[1482,84122,84123],{"xmlns":1484},[1487,84124,84125,84141],{},[1490,84126,84127,84129,84131,84133,84135,84137,84139],{},[1493,84128,5289],{},[1493,84130,1998],{},[1506,84132,1508],{},[1493,84134,7774],{},[1506,84136,2162],{},[1493,84138,7781],{},[1493,84140,1520],{},[1528,84142,84143],{"encoding":1530},"TC = m + nQ",[1035,84145,84147],{"className":84146},[1480],[1482,84148,84149],{"xmlns":1484},[1487,84150,84151,84163],{},[1490,84152,84153,84155,84157,84159,84161],{},[1493,84154,7774],{},[1506,84156,1559],{"separator":1041},[1493,84158,7781],{},[1506,84160,1559],{"separator":1041},[1493,84162,1030],{},[1528,84164,84165],{"encoding":1530},"m, n, p"," jsou pevně zadány, pak existuje jediný bod zvratu ",[1035,84168,84170],{"className":84169},[1480],[1482,84171,84172],{"xmlns":1484},[1487,84173,84174,84198],{},[1490,84175,84176,84182,84184],{},[2315,84177,84178,84180],{},[1493,84179,1520],{},[1506,84181,2287],{},[1506,84183,1508],{},[1869,84185,84186],{"scriptlevel":1871,"displaystyle":1552},[1510,84187,84188,84190],{},[1493,84189,7774],{},[1490,84191,84192,84194,84196],{},[1493,84193,1030],{},[1506,84195,1888],{},[1493,84197,7781],{},[1528,84199,84200],{"encoding":1530},"Q^* = \\tfrac{m}{p - n}"," a proveďte diskusi podmínek. Načrtněte obrázek.",[1030,84203,84204,84009,84207,1586,84241,83361,84267,84280,84281,82115,84296,84311,84312,82099,84325,82115,84340,84355],{},[1047,84205,84206],{},"3.19",[1035,84208,84210],{"className":84209},[1480],[1482,84211,84212],{"xmlns":1484},[1487,84213,84214,84238],{},[1490,84215,84216,84218,84220,84222,84224,84226,84232,84234,84236],{},[1493,84217,5289],{},[1493,84219,1995],{},[1506,84221,1508],{},[1506,84223,1888],{},[1680,84225,1691],{},[2315,84227,84228,84230],{},[1493,84229,1520],{},[1680,84231,1691],{},[1506,84233,2162],{},[1680,84235,38539],{},[1493,84237,1520],{},[1528,84239,84240],{"encoding":1530},"TR = -2Q^2 + 14Q",[1035,84242,84244],{"className":84243},[1480],[1482,84245,84246],{"xmlns":1484},[1487,84247,84248,84264],{},[1490,84249,84250,84252,84254,84256,84258,84260,84262],{},[1493,84251,5289],{},[1493,84253,1998],{},[1506,84255,1508],{},[1680,84257,1691],{},[1493,84259,1520],{},[1506,84261,2162],{},[1680,84263,1775],{},[1528,84265,84266],{"encoding":1530},"TC = 2Q + 10",[1035,84268,84270],{"className":84269},[1480],[1482,84271,84272],{"xmlns":1484},[1487,84273,84274,84278],{},[1490,84275,84276],{},[1493,84277,1520],{},[1528,84279,1520],{"encoding":1530},", které maximalizuje zisk ",[1035,84282,84284],{"className":84283},[1480],[1482,84285,84286],{"xmlns":1484},[1487,84287,84288,84294],{},[1490,84289,84290,84292],{},[1493,84291,1501],{},[1493,84293,1995],{},[1528,84295,76797],{"encoding":1530},[1035,84297,84299],{"className":84298},[1480],[1482,84300,84301],{"xmlns":1484},[1487,84302,84303,84309],{},[1490,84304,84305,84307],{},[1493,84306,1501],{},[1493,84308,1995],{},[1528,84310,76797],{"encoding":1530},". (b) Určete body zvratu a interval, ve kterém je firma v zisku. (c) Určete ",[1035,84313,84315],{"className":84314},[1480],[1482,84316,84317],{"xmlns":1484},[1487,84318,84319,84323],{},[1490,84320,84321],{},[1493,84322,1520],{},[1528,84324,1520],{"encoding":1530},[1035,84326,84328],{"className":84327},[1480],[1482,84329,84330],{"xmlns":1484},[1487,84331,84332,84338],{},[1490,84333,84334,84336],{},[1493,84335,5289],{},[1493,84337,1995],{},[1528,84339,16491],{"encoding":1530},[1035,84341,84343],{"className":84342},[1480],[1482,84344,84345],{"xmlns":1484},[1487,84346,84347,84353],{},[1490,84348,84349,84351],{},[1493,84350,5289],{},[1493,84352,1995],{},[1528,84354,16491],{"encoding":1530},". (d) Graficky interpretujte.",[1030,84357,84358,62019,84361,1732,84387,1732,84406,83361,84425,84280,84438,82115,84453,84468,84469,84491,84492,83544],{},[1047,84359,84360],{},"3.20",[1035,84362,84364],{"className":84363},[1480],[1482,84365,84366],{"xmlns":1484},[1487,84367,84368,84384],{},[1490,84369,84370,84372,84374,84376,84378],{},[1493,84371,1501],{},[1506,84373,1508],{},[1680,84375,5765],{},[1506,84377,1888],{},[2315,84379,84380,84382],{},[1493,84381,1520],{},[1680,84383,1691],{},[1528,84385,84386],{"encoding":1530},"P = 400 - Q^2",[1035,84388,84390],{"className":84389},[1480],[1482,84391,84392],{"xmlns":1484},[1487,84393,84394,84404],{},[1490,84395,84396,84398,84400,84402],{},[1493,84397,10790],{},[1493,84399,1998],{},[1506,84401,1508],{},[1680,84403,2916],{},[1528,84405,28133],{"encoding":1530},[1035,84407,84409],{"className":84408},[1480],[1482,84410,84411],{"xmlns":1484},[1487,84412,84413,84423],{},[1490,84414,84415,84417,84419,84421],{},[1493,84416,1495],{},[1493,84418,1998],{},[1506,84420,1508],{},[1680,84422,8436],{},[1528,84424,10778],{"encoding":1530},[1035,84426,84428],{"className":84427},[1480],[1482,84429,84430],{"xmlns":1484},[1487,84431,84432,84436],{},[1490,84433,84434],{},[1493,84435,1520],{},[1528,84437,1520],{"encoding":1530},[1035,84439,84441],{"className":84440},[1480],[1482,84442,84443],{"xmlns":1484},[1487,84444,84445,84451],{},[1490,84446,84447,84449],{},[1493,84448,1501],{},[1493,84450,1995],{},[1528,84452,76797],{"encoding":1530},[1035,84454,84456],{"className":84455},[1480],[1482,84457,84458],{"xmlns":1484},[1487,84459,84460,84466],{},[1490,84461,84462,84464],{},[1493,84463,1501],{},[1493,84465,1995],{},[1528,84467,76797],{"encoding":1530},". (b) Určete body zvratu a interval, ve kterém je firma v zisku (rada: jeden z bodů zvratu patří do ",[1035,84470,84472],{"className":84471},[1480],[1482,84473,84474],{"xmlns":1484},[1487,84475,84476,84488],{},[1490,84477,84478,84480,84482,84484,84486],{},[1506,84479,1553],{"stretchy":1552},[1680,84481,1871],{},[1506,84483,1559],{"separator":1041},[1680,84485,1682],{},[1506,84487,1564],{"stretchy":1552},[1528,84489,84490],{"encoding":1530},"(0, 1)",", druhý do ",[1035,84493,84495],{"className":84494},[1480],[1482,84496,84497],{"xmlns":1484},[1487,84498,84499,84511],{},[1490,84500,84501,84503,84505,84507,84509],{},[1506,84502,1553],{"stretchy":1552},[1680,84504,7499],{},[1506,84506,1559],{"separator":1041},[1680,84508,8436],{},[1506,84510,1564],{"stretchy":1552},[1528,84512,84513],{"encoding":1530},"(19, 20)",[1030,84515,84516,84519,84520,11713,84548,84565,84566,2632],{},[1047,84517,84518],{},"3.21"," Dokažte, že má-li zisk ",[1035,84521,84523],{"className":84522},[1480],[1482,84524,84525],{"xmlns":1484},[1487,84526,84527,84545],{},[1490,84528,84529,84531,84533,84535,84537,84539,84541,84543],{},[1493,84530,1501],{},[1493,84532,1995],{},[1506,84534,1508],{},[1493,84536,1501],{},[1493,84538,1995],{},[1506,84540,1553],{"stretchy":1552},[1493,84542,1520],{},[1506,84544,1564],{"stretchy":1552},[1528,84546,84547],{"encoding":1530},"PR = PR(Q)",[1035,84549,84551],{"className":84550},[1480],[1482,84552,84553],{"xmlns":1484},[1487,84554,84555,84563],{},[1490,84556,84557],{},[1497,84558,84559,84561],{},[1493,84560,1520],{},[1680,84562,1871],{},[1528,84564,53236],{"encoding":1530}," maximum, pak platí ",[1035,84567,84569],{"className":84568},[1480],[1482,84570,84571],{"xmlns":1484},[1487,84572,84573,84605],{},[1490,84574,84575,84577,84579,84581,84587,84589,84591,84593,84595,84597,84603],{},[1493,84576,1495],{},[1493,84578,1995],{},[1506,84580,1553],{"stretchy":1552},[1497,84582,84583,84585],{},[1493,84584,1520],{},[1680,84586,1871],{},[1506,84588,1564],{"stretchy":1552},[1506,84590,1508],{},[1493,84592,1495],{},[1493,84594,1998],{},[1506,84596,1553],{"stretchy":1552},[1497,84598,84599,84601],{},[1493,84600,1520],{},[1680,84602,1871],{},[1506,84604,1564],{"stretchy":1552},[1528,84606,78212],{"encoding":1530},[1030,84608,84609,84612,84613,1586,84628,70202,84643,84280,84656,84671,84672,1732,84699,84736,84737,1732,84764,2632],{},[1047,84610,84611],{},"3.22"," Pro zadané ",[1035,84614,84616],{"className":84615},[1480],[1482,84617,84618],{"xmlns":1484},[1487,84619,84620,84626],{},[1490,84621,84622,84624],{},[1493,84623,1495],{},[1493,84625,1995],{},[1528,84627,6258],{"encoding":1530},[1035,84629,84631],{"className":84630},[1480],[1482,84632,84633],{"xmlns":1484},[1487,84634,84635,84641],{},[1490,84636,84637,84639],{},[1493,84638,1495],{},[1493,84640,1998],{},[1528,84642,69470],{"encoding":1530},[1035,84644,84646],{"className":84645},[1480],[1482,84647,84648],{"xmlns":1484},[1487,84649,84650,84654],{},[1490,84651,84652],{},[1493,84653,1520],{},[1528,84655,1520],{"encoding":1530},[1035,84657,84659],{"className":84658},[1480],[1482,84660,84661],{"xmlns":1484},[1487,84662,84663,84669],{},[1490,84664,84665,84667],{},[1493,84666,1501],{},[1493,84668,1995],{},[1528,84670,76797],{"encoding":1530},". (a) ",[1035,84673,84675],{"className":84674},[1480],[1482,84676,84677],{"xmlns":1484},[1487,84678,84679,84696],{},[1490,84680,84681,84683,84685,84687,84690,84692,84694],{},[1493,84682,1495],{},[1493,84684,1995],{},[1506,84686,1508],{},[1680,84688,84689],{},"236",[1506,84691,1888],{},[1680,84693,9961],{},[1493,84695,1520],{},[1528,84697,84698],{"encoding":1530},"MR = 236 - 16Q",[1035,84700,84702],{"className":84701},[1480],[1482,84703,84704],{"xmlns":1484},[1487,84705,84706,84733],{},[1490,84707,84708,84710,84712,84714,84716,84722,84724,84727,84729,84731],{},[1493,84709,1495],{},[1493,84711,1998],{},[1506,84713,1508],{},[1680,84715,3201],{},[2315,84717,84718,84720],{},[1493,84719,1520],{},[1680,84721,1691],{},[1506,84723,1888],{},[1680,84725,84726],{},"32",[1493,84728,1520],{},[1506,84730,2162],{},[1680,84732,21619],{},[1528,84734,84735],{"encoding":1530},"MC = 3Q^2 - 32Q + 96",". (b) ",[1035,84738,84740],{"className":84739},[1480],[1482,84741,84742],{"xmlns":1484},[1487,84743,84744,84761],{},[1490,84745,84746,84748,84750,84752,84755,84757,84759],{},[1493,84747,1495],{},[1493,84749,1995],{},[1506,84751,1508],{},[1680,84753,84754],{},"280",[1506,84756,1888],{},[1680,84758,8436],{},[1493,84760,1520],{},[1528,84762,84763],{"encoding":1530},"MR = 280 - 20Q",[1035,84765,84767],{"className":84766},[1480],[1482,84768,84769],{"xmlns":1484},[1487,84770,84771,84798],{},[1490,84772,84773,84775,84777,84779,84782,84788,84790,84792,84794,84796],{},[1493,84774,1495],{},[1493,84776,1998],{},[1506,84778,1508],{},[1680,84780,84781],{},"1,6",[2315,84783,84784,84786],{},[1493,84785,1520],{},[1680,84787,1691],{},[1506,84789,1888],{},[1680,84791,9787],{},[1493,84793,1520],{},[1506,84795,2162],{},[1680,84797,4965],{},[1528,84799,84800],{"encoding":1530},"MC = 1{,}6Q^2 - 15Q + 60",[1030,84802,84803,84612,84806,1586,84821,70202,84836,82099,84849,82115,84864,84671,84879,1732,84909,84736,84945,1732,84977,85021,85022,1732,85054,2632],{},[1047,84804,84805],{},"3.23",[1035,84807,84809],{"className":84808},[1480],[1482,84810,84811],{"xmlns":1484},[1487,84812,84813,84819],{},[1490,84814,84815,84817],{},[1493,84816,5289],{},[1493,84818,1995],{},[1528,84820,16491],{"encoding":1530},[1035,84822,84824],{"className":84823},[1480],[1482,84825,84826],{"xmlns":1484},[1487,84827,84828,84834],{},[1490,84829,84830,84832],{},[1493,84831,5289],{},[1493,84833,1998],{},[1528,84835,18668],{"encoding":1530},[1035,84837,84839],{"className":84838},[1480],[1482,84840,84841],{"xmlns":1484},[1487,84842,84843,84847],{},[1490,84844,84845],{},[1493,84846,1520],{},[1528,84848,1520],{"encoding":1530},[1035,84850,84852],{"className":84851},[1480],[1482,84853,84854],{"xmlns":1484},[1487,84855,84856,84862],{},[1490,84857,84858,84860],{},[1493,84859,1501],{},[1493,84861,1995],{},[1528,84863,76797],{"encoding":1530},[1035,84865,84867],{"className":84866},[1480],[1482,84868,84869],{"xmlns":1484},[1487,84870,84871,84877],{},[1490,84872,84873,84875],{},[1493,84874,1501],{},[1493,84876,1995],{},[1528,84878,76797],{"encoding":1530},[1035,84880,84882],{"className":84881},[1480],[1482,84883,84884],{"xmlns":1484},[1487,84885,84886,84906],{},[1490,84887,84888,84890,84892,84894,84896,84898,84900],{},[1493,84889,5289],{},[1493,84891,1995],{},[1506,84893,1508],{},[1680,84895,3021],{},[1493,84897,1520],{},[1506,84899,1888],{},[2315,84901,84902,84904],{},[1493,84903,1520],{},[1680,84905,1691],{},[1528,84907,84908],{"encoding":1530},"TR = 125Q - Q^2",[1035,84910,84912],{"className":84911},[1480],[1482,84913,84914],{"xmlns":1484},[1487,84915,84916,84942],{},[1490,84917,84918,84920,84922,84924,84926,84928,84930,84932,84934,84936],{},[1493,84919,5289],{},[1493,84921,1998],{},[1506,84923,1508],{},[1680,84925,1796],{},[1506,84927,2162],{},[1680,84929,1752],{},[1493,84931,1520],{},[1506,84933,2162],{},[1680,84935,3687],{},[2315,84937,84938,84940],{},[1493,84939,1520],{},[1680,84941,1691],{},[1528,84943,84944],{"encoding":1530},"TC = 500 + 5Q + 0{,}5Q^2",[1035,84946,84948],{"className":84947},[1480],[1482,84949,84950],{"xmlns":1484},[1487,84951,84952,84974],{},[1490,84953,84954,84956,84958,84960,84962,84964,84966,84968],{},[1493,84955,5289],{},[1493,84957,1995],{},[1506,84959,1508],{},[1680,84961,8436],{},[1493,84963,1520],{},[1506,84965,1888],{},[1680,84967,1691],{},[2315,84969,84970,84972],{},[1493,84971,1520],{},[1680,84973,1691],{},[1528,84975,84976],{"encoding":1530},"TR = 20Q - 2Q^2",[1035,84978,84980],{"className":84979},[1480],[1482,84981,84982],{"xmlns":1484},[1487,84983,84984,85018],{},[1490,84985,84986,84988,84990,84992,84994,84996,84998,85000,85002,85004,85010,85012],{},[1493,84987,5289],{},[1493,84989,1998],{},[1506,84991,1508],{},[1680,84993,1691],{},[1506,84995,2162],{},[1680,84997,8436],{},[1493,84999,1520],{},[1506,85001,1888],{},[1680,85003,6138],{},[2315,85005,85006,85008],{},[1493,85007,1520],{},[1680,85009,1691],{},[1506,85011,2162],{},[2315,85013,85014,85016],{},[1493,85015,1520],{},[1680,85017,3201],{},[1528,85019,85020],{"encoding":1530},"TC = 2 + 20Q - 8Q^2 + Q^3",". (c) ",[1035,85023,85025],{"className":85024},[1480],[1482,85026,85027],{"xmlns":1484},[1487,85028,85029,85051],{},[1490,85030,85031,85033,85035,85037,85039,85041,85043,85045],{},[1493,85032,5289],{},[1493,85034,1995],{},[1506,85036,1508],{},[1680,85038,4007],{},[1493,85040,1520],{},[1506,85042,1888],{},[1680,85044,5051],{},[2315,85046,85047,85049],{},[1493,85048,1520],{},[1680,85050,1691],{},[1528,85052,85053],{"encoding":1530},"TR = 4Q - 0{,}25Q^2",[1035,85055,85057],{"className":85056},[1480],[1482,85058,85059],{"xmlns":1484},[1487,85060,85061,85109],{},[1490,85062,85063,85065,85067,85069,85071,85073,85075,85077,85079,85095,85097],{},[1493,85064,5289],{},[1493,85066,1998],{},[1506,85068,1508],{},[1680,85070,4007],{},[1506,85072,2162],{},[1680,85074,1691],{},[1493,85076,1520],{},[1506,85078,1888],{},[1869,85080,85081],{"scriptlevel":1871,"displaystyle":1552},[1510,85082,85083,85093],{},[1490,85084,85085,85087],{},[1680,85086,3201],{},[2315,85088,85089,85091],{},[1493,85090,1520],{},[1680,85092,1691],{},[1680,85094,1775],{},[1506,85096,2162],{},[1869,85098,85099],{"scriptlevel":1871,"displaystyle":1552},[1510,85100,85101,85107],{},[2315,85102,85103,85105],{},[1493,85104,1520],{},[1680,85106,3201],{},[1680,85108,8436],{},[1528,85110,85111],{"encoding":1530},"TC = 4 + 2Q - \\tfrac{3Q^2}{10} + \\tfrac{Q^3}{20}",[1030,85113,85114,85117,85118,85148,85149,85181,85182,37188,85212,85241],{},[1047,85115,85116],{},"3.24"," Firma řeší problém stanovení cen pro malé a velké odběratele za účelem maximalizace zisku. Poptávka pro maloodběratele je ",[1035,85119,85121],{"className":85120},[1480],[1482,85122,85123],{"xmlns":1484},[1487,85124,85125,85145],{},[1490,85126,85127,85133,85135,85137,85139],{},[1497,85128,85129,85131],{},[1493,85130,1501],{},[1680,85132,1682],{},[1506,85134,1508],{},[1680,85136,1796],{},[1506,85138,1888],{},[1497,85140,85141,85143],{},[1493,85142,1520],{},[1680,85144,1682],{},[1528,85146,85147],{"encoding":1530},"P_1 = 500 - Q_1",", pro velkoodběratele ",[1035,85150,85152],{"className":85151},[1480],[1482,85153,85154],{"xmlns":1484},[1487,85155,85156,85178],{},[1490,85157,85158,85164,85166,85168,85170,85172],{},[1497,85159,85160,85162],{},[1493,85161,1501],{},[1680,85163,1691],{},[1506,85165,1508],{},[1680,85167,5231],{},[1506,85169,1888],{},[1680,85171,77687],{},[1497,85173,85174,85176],{},[1493,85175,1520],{},[1680,85177,1691],{},[1528,85179,85180],{"encoding":1530},"P_2 = 300 - 1{,}5Q_2",". Celkové náklady firmy jsou ",[1035,85183,85185],{"className":85184},[1480],[1482,85186,85187],{"xmlns":1484},[1487,85188,85189,85209],{},[1490,85190,85191,85193,85195,85197,85199,85201,85203,85205,85207],{},[1493,85192,5289],{},[1493,85194,1998],{},[1506,85196,1508],{},[1680,85198,2292],{},[1988,85200,5016],{},[1680,85202,5608],{},[1506,85204,2162],{},[1680,85206,8436],{},[1493,85208,1520],{},[1528,85210,85211],{"encoding":1530},"TC = 50\\,000 + 20Q",[1035,85213,85215],{"className":85214},[1480],[1482,85216,85217],{"xmlns":1484},[1487,85218,85219,85239],{},[1490,85220,85221,85223,85225,85231,85233],{},[1493,85222,1520],{},[1506,85224,1508],{},[1497,85226,85227,85229],{},[1493,85228,1520],{},[1680,85230,1682],{},[1506,85232,2162],{},[1497,85234,85235,85237],{},[1493,85236,1520],{},[1680,85238,1691],{},[1528,85240,5335],{"encoding":1530},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk v obou případech.",[1030,85243,85244,85247,85248,85277,85278,85181,85310,37188,85340,85369],{},[1047,85245,85246],{},"3.25"," Firma řeší problém stanovení cen pro domácí a zahraniční trh za účelem maximalizace zisku. Poptávka pro domácí trh je ",[1035,85249,85251],{"className":85250},[1480],[1482,85252,85253],{"xmlns":1484},[1487,85254,85255,85275],{},[1490,85256,85257,85263,85265,85267,85269],{},[1497,85258,85259,85261],{},[1493,85260,1501],{},[1680,85262,1682],{},[1506,85264,1508],{},[1680,85266,5231],{},[1506,85268,1888],{},[1497,85270,85271,85273],{},[1493,85272,1520],{},[1680,85274,1682],{},[1528,85276,5242],{"encoding":1530},", pro zahraniční trh ",[1035,85279,85281],{"className":85280},[1480],[1482,85282,85283],{"xmlns":1484},[1487,85284,85285,85307],{},[1490,85286,85287,85293,85295,85297,85299,85301],{},[1497,85288,85289,85291],{},[1493,85290,1501],{},[1680,85292,1691],{},[1506,85294,1508],{},[1680,85296,5263],{},[1506,85298,1888],{},[1680,85300,3687],{},[1497,85302,85303,85305],{},[1493,85304,1520],{},[1680,85306,1691],{},[1528,85308,85309],{"encoding":1530},"P_2 = 200 - 0{,}5Q_2",[1035,85311,85313],{"className":85312},[1480],[1482,85314,85315],{"xmlns":1484},[1487,85316,85317,85337],{},[1490,85318,85319,85321,85323,85325,85327,85329,85331,85333,85335],{},[1493,85320,5289],{},[1493,85322,1998],{},[1506,85324,1508],{},[1680,85326,1752],{},[1988,85328,5016],{},[1680,85330,5608],{},[1506,85332,2162],{},[1680,85334,2916],{},[1493,85336,1520],{},[1528,85338,85339],{"encoding":1530},"TC = 5\\,000 + 100Q",[1035,85341,85343],{"className":85342},[1480],[1482,85344,85345],{"xmlns":1484},[1487,85346,85347,85367],{},[1490,85348,85349,85351,85353,85359,85361],{},[1493,85350,1520],{},[1506,85352,1508],{},[1497,85354,85355,85357],{},[1493,85356,1520],{},[1680,85358,1682],{},[1506,85360,2162],{},[1497,85362,85363,85365],{},[1493,85364,1520],{},[1680,85366,1691],{},[1528,85368,5335],{"encoding":1530},". Stanovte ceny, při kterých firma maximalizuje zisk: (a) s cenovou diskriminací, (b) bez cenové diskriminace. Porovnejte zisk firmy v obou případech.",[1304,85371,85373],{"id":85372},"konstrukce-nabídky-326328","Konstrukce nabídky (3.26–3.28)",[1030,85375,85376,85379,85380,85426,85427,85444],{},[1047,85377,85378],{},"3.26"," Jsou dány celkové variabilní náklady ",[1035,85381,85383],{"className":85382},[1480],[1482,85384,85385],{"xmlns":1484},[1487,85386,85387,85423],{},[1490,85388,85389,85391,85393,85395,85397,85400,85406,85408,85411,85417,85419,85421],{},[1493,85390,5289],{},[1493,85392,55105],{},[1493,85394,1998],{},[1506,85396,1508],{},[1680,85398,85399],{},"0,85",[2315,85401,85402,85404],{},[1493,85403,1520],{},[1680,85405,3201],{},[1506,85407,1888],{},[1680,85409,85410],{},"11,9",[2315,85412,85413,85415],{},[1493,85414,1520],{},[1680,85416,1691],{},[1506,85418,2162],{},[1680,85420,13342],{},[1493,85422,1520],{},[1528,85424,85425],{"encoding":1530},"TVC = 0{,}85Q^3 - 11{,}9Q^2 + 102Q",". Určete minimální cenu ",[1035,85428,85430],{"className":85429},[1480],[1482,85431,85432],{"xmlns":1484},[1487,85433,85434,85442],{},[1490,85435,85436],{},[2315,85437,85438,85440],{},[1493,85439,1501],{},[1506,85441,2287],{},[1528,85443,20114],{"encoding":1530}," nabídky a konstruujte nabídku. Graficky interpretujte.",[1030,85446,85447,83212,85450,85486],{},[1047,85448,85449],{},"3.27",[1035,85451,85453],{"className":85452},[1480],[1482,85454,85455],{"xmlns":1484},[1487,85456,85457,85483],{},[1490,85458,85459,85461,85463,85465,85467,85473,85475,85477,85479,85481],{},[1493,85460,1495],{},[1493,85462,1998],{},[1506,85464,1508],{},[1680,85466,18363],{},[2315,85468,85469,85471],{},[1493,85470,1520],{},[1680,85472,1691],{},[1506,85474,1888],{},[1680,85476,10052],{},[1493,85478,1520],{},[1506,85480,2162],{},[1680,85482,8140],{},[1528,85484,85485],{"encoding":1530},"MC = 4{,}2Q^2 - 48Q + 250",". Konstruujte nabídku.",[1030,85488,85489,82464,85492,85486],{},[1047,85490,85491],{},"3.28",[1035,85493,85495],{"className":85494},[1480],[1482,85496,85497],{"xmlns":1484},[1487,85498,85499,85535],{},[1490,85500,85501,85503,85505,85507,85509,85515,85517,85519,85525,85527,85529,85531,85533],{},[1493,85502,5289],{},[1493,85504,1998],{},[1506,85506,1508],{},[1680,85508,3687],{},[2315,85510,85511,85513],{},[1493,85512,1520],{},[1680,85514,3201],{},[1506,85516,1888],{},[1680,85518,16580],{},[2315,85520,85521,85523],{},[1493,85522,1520],{},[1680,85524,1691],{},[1506,85526,2162],{},[1680,85528,4965],{},[1493,85530,1520],{},[1506,85532,2162],{},[1680,85534,1796],{},[1528,85536,85537],{"encoding":1530},"TC = 0{,}5Q^3 - 7Q^2 + 60Q + 500",[1065,85539,31885],{"id":31884},[1203,85541,85542,85570,85615,85687,85752,85792,85884,85990,86030,86144,86237,86301,86333,86393,86399,86463,86512,86566,86674,86730],{},[1206,85543,85544,1656,85546,85569],{},[1047,85545,69927],{},[1035,85547,85549],{"className":85548},[1480],[1482,85550,85551],{"xmlns":1484},[1487,85552,85553,85567],{},[1490,85554,85555,85557,85559,85561,85563,85565],{},[1493,85556,5289],{},[1493,85558,1995],{},[1506,85560,1508],{},[1493,85562,1501],{},[1506,85564,1714],{},[1493,85566,1520],{},[1528,85568,79281],{"encoding":1530}," — křivka celkového příjmu (total revenue curve).",[1206,85571,85572,1656,85574,85614],{},[1047,85573,70409],{},[1035,85575,85577],{"className":85576},[1480],[1482,85578,85579],{"xmlns":1484},[1487,85580,85581,85611],{},[1490,85582,85583,85585,85587,85589,85601,85603,85605,85607,85609],{},[1493,85584,3633],{},[1493,85586,1995],{},[1506,85588,1508],{},[1869,85590,85591],{"scriptlevel":1871,"displaystyle":1552},[1510,85592,85593,85599],{},[1490,85594,85595,85597],{},[1493,85596,5289],{},[1493,85598,1995],{},[1493,85600,1520],{},[1506,85602,1508],{},[1493,85604,3712],{},[1506,85606,1553],{"stretchy":1552},[1493,85608,1520],{},[1506,85610,1564],{"stretchy":1552},[1528,85612,85613],{"encoding":1530},"AR = \\tfrac{TR}{Q} = D(Q)"," — shoduje se s poptávkovou funkcí.",[1206,85616,85617,1656,85619,85655,85656,85671,85672,2632],{},[1047,85618,70564],{},[1035,85620,85622],{"className":85621},[1480],[1482,85623,85624],{"xmlns":1484},[1487,85625,85626,85652],{},[1490,85627,85628,85630,85632,85634],{},[1493,85629,1495],{},[1493,85631,1995],{},[1506,85633,1508],{},[1869,85635,85636],{"scriptlevel":1871,"displaystyle":1552},[1510,85637,85638,85646],{},[1490,85639,85640,85642,85644],{},[1493,85641,3384],{"mathvariant":1516},[1493,85643,5289],{},[1493,85645,1995],{},[1490,85647,85648,85650],{},[1493,85649,3384],{"mathvariant":1516},[1493,85651,1520],{},[1528,85653,85654],{"encoding":1530},"MR = \\tfrac{\\mathrm{d}TR}{\\mathrm{d}Q}"," — rychlost změny ",[1035,85657,85659],{"className":85658},[1480],[1482,85660,85661],{"xmlns":1484},[1487,85662,85663,85669],{},[1490,85664,85665,85667],{},[1493,85666,5289],{},[1493,85668,1995],{},[1528,85670,16491],{"encoding":1530},"; pro lineární poptávku má sklon dvojnásobný vůči ",[1035,85673,85675],{"className":85674},[1480],[1482,85676,85677],{"xmlns":1484},[1487,85678,85679,85685],{},[1490,85680,85681,85683],{},[1493,85682,3633],{},[1493,85684,1995],{},[1528,85686,69623],{"encoding":1530},[1206,85688,85689,1656,85692,1732,85722,2632],{},[1047,85690,85691],{},"Diferenciál příjmu\u002Fnákladů",[1035,85693,85695],{"className":85694},[1480],[1482,85696,85697],{"xmlns":1484},[1487,85698,85699,85719],{},[1490,85700,85701,85703,85705,85707,85709,85711,85713,85715,85717],{},[1493,85702,2976],{"mathvariant":1516},[1493,85704,5289],{},[1493,85706,1995],{},[1506,85708,2343],{},[1493,85710,1495],{},[1493,85712,1995],{},[1988,85714,5016],{},[1493,85716,3384],{"mathvariant":1516},[1493,85718,1520],{},[1528,85720,85721],{"encoding":1530},"\\Delta TR \\approx MR \\, \\mathrm{d}Q",[1035,85723,85725],{"className":85724},[1480],[1482,85726,85727],{"xmlns":1484},[1487,85728,85729,85749],{},[1490,85730,85731,85733,85735,85737,85739,85741,85743,85745,85747],{},[1493,85732,2976],{"mathvariant":1516},[1493,85734,5289],{},[1493,85736,1998],{},[1506,85738,2343],{},[1493,85740,1495],{},[1493,85742,1998],{},[1988,85744,5016],{},[1493,85746,3384],{"mathvariant":1516},[1493,85748,1520],{},[1528,85750,85751],{"encoding":1530},"\\Delta TC \\approx MC \\, \\mathrm{d}Q",[1206,85753,85754,1656,85756,2632],{},[1047,85755,72375],{},[1035,85757,85759],{"className":85758},[1480],[1482,85760,85761],{"xmlns":1484},[1487,85762,85763,85789],{},[1490,85764,85765,85767,85769,85771,85773,85775,85777,85779,85781,85783,85785,85787],{},[1493,85766,5289],{},[1493,85768,1998],{},[1506,85770,1508],{},[1493,85772,10790],{},[1493,85774,1998],{},[1506,85776,2162],{},[1493,85778,5289],{},[1493,85780,55105],{},[1493,85782,1998],{},[1506,85784,1553],{"stretchy":1552},[1493,85786,1520],{},[1506,85788,1564],{"stretchy":1552},[1528,85790,85791],{"encoding":1530},"TC = FC + TVC(Q)",[1206,85793,85794,1656,85797,1732,85812,1656,85814,1732,85837,1656,85840,2632],{},[1047,85795,85796],{},"Fixní náklady",[1035,85798,85800],{"className":85799},[1480],[1482,85801,85802],{"xmlns":1484},[1487,85803,85804,85810],{},[1490,85805,85806,85808],{},[1493,85807,10790],{},[1493,85809,1998],{},[1528,85811,69669],{"encoding":1530},[1047,85813,72528],{},[1035,85815,85817],{"className":85816},[1480],[1482,85818,85819],{"xmlns":1484},[1487,85820,85821,85835],{},[1490,85822,85823,85825,85827,85829,85831,85833],{},[1493,85824,5289],{},[1493,85826,55105],{},[1493,85828,1998],{},[1506,85830,1553],{"stretchy":1552},[1493,85832,1520],{},[1506,85834,1564],{"stretchy":1552},[1528,85836,72525],{"encoding":1530},[1047,85838,85839],{},"variabilní náklady na jednotku",[1035,85841,85843],{"className":85842},[1480],[1482,85844,85845],{"xmlns":1484},[1487,85846,85847,85881],{},[1490,85848,85849,85851,85853,85855,85857,85859,85861],{},[1493,85850,55105],{},[1493,85852,1998],{},[1506,85854,1553],{"stretchy":1552},[1493,85856,1520],{},[1506,85858,1564],{"stretchy":1552},[1506,85860,1508],{},[1869,85862,85863],{"scriptlevel":1871,"displaystyle":1552},[1510,85864,85865,85879],{},[1490,85866,85867,85869,85871,85873,85875,85877],{},[1493,85868,5289],{},[1493,85870,55105],{},[1493,85872,1998],{},[1506,85874,1553],{"stretchy":1552},[1493,85876,1520],{},[1506,85878,1564],{"stretchy":1552},[1493,85880,1520],{},[1528,85882,85883],{"encoding":1530},"VC(Q) = \\tfrac{TVC(Q)}{Q}",[1206,85885,85886,1656,85888,1732,85918,1656,85921,1732,85953,1656,85956,2632],{},[1047,85887,72536],{},[1035,85889,85891],{"className":85890},[1480],[1482,85892,85893],{"xmlns":1484},[1487,85894,85895,85915],{},[1490,85896,85897,85899,85901,85903],{},[1493,85898,3633],{},[1493,85900,1998],{},[1506,85902,1508],{},[1869,85904,85905],{"scriptlevel":1871,"displaystyle":1552},[1510,85906,85907,85913],{},[1490,85908,85909,85911],{},[1493,85910,5289],{},[1493,85912,1998],{},[1493,85914,1520],{},[1528,85916,85917],{"encoding":1530},"AC = \\tfrac{TC}{Q}",[1047,85919,85920],{},"průměrné fixní",[1035,85922,85924],{"className":85923},[1480],[1482,85925,85926],{"xmlns":1484},[1487,85927,85928,85950],{},[1490,85929,85930,85932,85934,85936,85938],{},[1493,85931,3633],{},[1493,85933,10790],{},[1493,85935,1998],{},[1506,85937,1508],{},[1869,85939,85940],{"scriptlevel":1871,"displaystyle":1552},[1510,85941,85942,85948],{},[1490,85943,85944,85946],{},[1493,85945,10790],{},[1493,85947,1998],{},[1493,85949,1520],{},[1528,85951,85952],{"encoding":1530},"AFC = \\tfrac{FC}{Q}",[1047,85954,85955],{},"průměrné variabilní",[1035,85957,85959],{"className":85958},[1480],[1482,85960,85961],{"xmlns":1484},[1487,85962,85963,85987],{},[1490,85964,85965,85967,85969,85971,85973],{},[1493,85966,3633],{},[1493,85968,55105],{},[1493,85970,1998],{},[1506,85972,1508],{},[1869,85974,85975],{"scriptlevel":1871,"displaystyle":1552},[1510,85976,85977,85985],{},[1490,85978,85979,85981,85983],{},[1493,85980,5289],{},[1493,85982,55105],{},[1493,85984,1998],{},[1493,85986,1520],{},[1528,85988,85989],{"encoding":1530},"AVC = \\tfrac{TVC}{Q}",[1206,85991,85992,1656,85994,2632],{},[1047,85993,73512],{},[1035,85995,85997],{"className":85996},[1480],[1482,85998,85999],{"xmlns":1484},[1487,86000,86001,86027],{},[1490,86002,86003,86005,86007,86009],{},[1493,86004,1495],{},[1493,86006,1998],{},[1506,86008,1508],{},[1869,86010,86011],{"scriptlevel":1871,"displaystyle":1552},[1510,86012,86013,86021],{},[1490,86014,86015,86017,86019],{},[1493,86016,3384],{"mathvariant":1516},[1493,86018,5289],{},[1493,86020,1998],{},[1490,86022,86023,86025],{},[1493,86024,3384],{"mathvariant":1516},[1493,86026,1520],{},[1528,86028,86029],{"encoding":1530},"MC = \\tfrac{\\mathrm{d}TC}{\\mathrm{d}Q}",[1206,86031,86032,1656,86034,86082,86083,86096,86097,1732,86112,1732,86129,2632],{},[1047,86033,74413],{},[1035,86035,86037],{"className":86036},[1480],[1482,86038,86039],{"xmlns":1484},[1487,86040,86041,86079],{},[1490,86042,86043,86045,86047,86049,86051,86053,86055,86057,86059,86061,86063,86069,86071,86073],{},[1493,86044,5289],{},[1493,86046,1998],{},[1506,86048,1508],{},[1493,86050,10790],{},[1493,86052,1998],{},[1506,86054,2162],{},[1493,86056,1052],{},[1493,86058,1520],{},[1506,86060,2162],{},[1493,86062,2394],{},[2315,86064,86065,86067],{},[1493,86066,1520],{},[1680,86068,1691],{},[1506,86070,2162],{},[1493,86072,8730],{},[2315,86074,86075,86077],{},[1493,86076,1520],{},[1680,86078,3201],{},[1528,86080,86081],{"encoding":1530},"TC = FC + aQ + bQ^2 + cQ^3"," — „standardní\" tvar s ",[1035,86084,86086],{"className":86085},[1480],[1482,86087,86088],{"xmlns":1484},[1487,86089,86090,86094],{},[1490,86091,86092],{},[1493,86093,1668],{},[1528,86095,1668],{"encoding":1530},"-průběhem ",[1035,86098,86100],{"className":86099},[1480],[1482,86101,86102],{"xmlns":1484},[1487,86103,86104,86110],{},[1490,86105,86106,86108],{},[1493,86107,3633],{},[1493,86109,1998],{},[1528,86111,16523],{"encoding":1530},[1035,86113,86115],{"className":86114},[1480],[1482,86116,86117],{"xmlns":1484},[1487,86118,86119,86127],{},[1490,86120,86121,86123,86125],{},[1493,86122,3633],{},[1493,86124,55105],{},[1493,86126,1998],{},[1528,86128,69489],{"encoding":1530},[1035,86130,86132],{"className":86131},[1480],[1482,86133,86134],{"xmlns":1484},[1487,86135,86136,86142],{},[1490,86137,86138,86140],{},[1493,86139,1495],{},[1493,86141,1998],{},[1528,86143,69470],{"encoding":1530},[1206,86145,86146,86148,86149,26918,86164,86205,86206,75078,86221,86236],{},[1047,86147,75239],{},": v bodě minima ",[1035,86150,86152],{"className":86151},[1480],[1482,86153,86154],{"xmlns":1484},[1487,86155,86156,86162],{},[1490,86157,86158,86160],{},[1493,86159,3633],{},[1493,86161,1998],{},[1528,86163,16523],{"encoding":1530},[1035,86165,86167],{"className":86166},[1480],[1482,86168,86169],{"xmlns":1484},[1487,86170,86171,86203],{},[1490,86172,86173,86175,86177,86179,86185,86187,86189,86191,86193,86195,86201],{},[1493,86174,3633],{},[1493,86176,1998],{},[1506,86178,1553],{"stretchy":1552},[1497,86180,86181,86183],{},[1493,86182,1520],{},[1680,86184,1871],{},[1506,86186,1564],{"stretchy":1552},[1506,86188,1508],{},[1493,86190,1495],{},[1493,86192,1998],{},[1506,86194,1553],{"stretchy":1552},[1497,86196,86197,86199],{},[1493,86198,1520],{},[1680,86200,1871],{},[1506,86202,1564],{"stretchy":1552},[1528,86204,75877],{"encoding":1530},"; geometricky ",[1035,86207,86209],{"className":86208},[1480],[1482,86210,86211],{"xmlns":1484},[1487,86212,86213,86219],{},[1490,86214,86215,86217],{},[1493,86216,1495],{},[1493,86218,1998],{},[1528,86220,69470],{"encoding":1530},[1035,86222,86224],{"className":86223},[1480],[1482,86225,86226],{"xmlns":1484},[1487,86227,86228,86234],{},[1490,86229,86230,86232],{},[1493,86231,3633],{},[1493,86233,1998],{},[1528,86235,16523],{"encoding":1530}," v jejím minimu.",[1206,86238,86239,86148,86241,26918,86258,2632],{},[1047,86240,76597],{},[1035,86242,86244],{"className":86243},[1480],[1482,86245,86246],{"xmlns":1484},[1487,86247,86248,86256],{},[1490,86249,86250,86252,86254],{},[1493,86251,3633],{},[1493,86253,55105],{},[1493,86255,1998],{},[1528,86257,69489],{"encoding":1530},[1035,86259,86261],{"className":86260},[1480],[1482,86262,86263],{"xmlns":1484},[1487,86264,86265,86299],{},[1490,86266,86267,86269,86271,86273,86275,86281,86283,86285,86287,86289,86291,86297],{},[1493,86268,3633],{},[1493,86270,55105],{},[1493,86272,1998],{},[1506,86274,1553],{"stretchy":1552},[1497,86276,86277,86279],{},[1493,86278,1520],{},[1680,86280,1871],{},[1506,86282,1564],{"stretchy":1552},[1506,86284,1508],{},[1493,86286,1495],{},[1493,86288,1998],{},[1506,86290,1553],{"stretchy":1552},[1497,86292,86293,86295],{},[1493,86294,1520],{},[1680,86296,1871],{},[1506,86298,1564],{"stretchy":1552},[1528,86300,81391],{"encoding":1530},[1206,86302,86303,1656,86305,86332],{},[1047,86304,76781],{},[1035,86306,86308],{"className":86307},[1480],[1482,86309,86310],{"xmlns":1484},[1487,86311,86312,86330],{},[1490,86313,86314,86316,86318,86320,86322,86324,86326,86328],{},[1493,86315,1501],{},[1493,86317,1995],{},[1506,86319,1508],{},[1493,86321,5289],{},[1493,86323,1995],{},[1506,86325,1888],{},[1493,86327,5289],{},[1493,86329,1998],{},[1528,86331,9401],{"encoding":1530}," — rozdíl mezi celkovým příjmem a celkovými náklady.",[1206,86334,86335,7606,86337,86339,86340,86366,86367,86392],{},[1047,86336,77456],{},[1176,86338,76906],{},") — hodnoty ",[1035,86341,86343],{"className":86342},[1480],[1482,86344,86345],{"xmlns":1484},[1487,86346,86347,86363],{},[1490,86348,86349,86355,86357],{},[1497,86350,86351,86353],{},[1493,86352,1520],{},[1493,86354,3633],{},[1506,86356,1559],{"separator":1041},[1497,86358,86359,86361],{},[1493,86360,1520],{},[1493,86362,11353],{},[1528,86364,86365],{"encoding":1530},"Q_A, Q_B"," splňující ",[1035,86368,86370],{"className":86369},[1480],[1482,86371,86372],{"xmlns":1484},[1487,86373,86374,86390],{},[1490,86375,86376,86378,86380,86382,86384,86386,86388],{},[1493,86377,1501],{},[1493,86379,1995],{},[1506,86381,1553],{"stretchy":1552},[1493,86383,1520],{},[1506,86385,1564],{"stretchy":1552},[1506,86387,1508],{},[1680,86389,1871],{},[1528,86391,77189],{"encoding":1530},"; oddělují pásma ztráty a zisku.",[1206,86394,86395,86398],{},[1047,86396,86397],{},"Práh rentability"," — stav firmy v bodě zvratu.",[1206,86400,86401,86403,86404,26918,86421,86462],{},[1047,86402,77941],{}," — v bodě maxima zisku ",[1035,86405,86407],{"className":86406},[1480],[1482,86408,86409],{"xmlns":1484},[1487,86410,86411,86419],{},[1490,86412,86413],{},[1497,86414,86415,86417],{},[1493,86416,1520],{},[1680,86418,1871],{},[1528,86420,53236],{"encoding":1530},[1035,86422,86424],{"className":86423},[1480],[1482,86425,86426],{"xmlns":1484},[1487,86427,86428,86460],{},[1490,86429,86430,86432,86434,86436,86442,86444,86446,86448,86450,86452,86458],{},[1493,86431,1495],{},[1493,86433,1995],{},[1506,86435,1553],{"stretchy":1552},[1497,86437,86438,86440],{},[1493,86439,1520],{},[1680,86441,1871],{},[1506,86443,1564],{"stretchy":1552},[1506,86445,1508],{},[1493,86447,1495],{},[1493,86449,1998],{},[1506,86451,1553],{"stretchy":1552},[1497,86453,86454,86456],{},[1493,86455,1520],{},[1680,86457,1871],{},[1506,86459,1564],{"stretchy":1552},[1528,86461,78212],{"encoding":1530}," (3.13).",[1206,86464,86465,36023,86467,26918,86486,86511],{},[1047,86466,79241],{},[1035,86468,86470],{"className":86469},[1480],[1482,86471,86472],{"xmlns":1484},[1487,86473,86474,86483],{},[1490,86475,86476,86478,86480],{},[1493,86477,1501],{},[1506,86479,1508],{},[1988,86481,86482],{},"konst",[1528,86484,86485],{"encoding":1530},"P = \\text{konst}",[1035,86487,86489],{"className":86488},[1480],[1482,86490,86491],{"xmlns":1484},[1487,86492,86493,86509],{},[1490,86494,86495,86497,86499,86501,86503,86505,86507],{},[1493,86496,1501],{},[1506,86498,1508],{},[1493,86500,1495],{},[1493,86502,1998],{},[1506,86504,1553],{"stretchy":1552},[1493,86506,1520],{},[1506,86508,1564],{"stretchy":1552},[1528,86510,79935],{"encoding":1530}," (3.14).",[1206,86513,86514,86517,86518,86547,86548,86565],{},[1047,86515,86516],{},"Shutdown point"," — bod ",[1035,86519,86521],{"className":86520},[1480],[1482,86522,86523],{"xmlns":1484},[1487,86524,86525,86545],{},[1490,86526,86527,86529,86535,86537,86543],{},[1506,86528,1553],{"stretchy":1552},[2315,86530,86531,86533],{},[1493,86532,1520],{},[1506,86534,2287],{},[1506,86536,1559],{"separator":1041},[2315,86538,86539,86541],{},[1493,86540,1501],{},[1506,86542,2287],{},[1506,86544,1564],{"stretchy":1552},[1528,86546,80224],{"encoding":1530}," v minimu ",[1035,86549,86551],{"className":86550},[1480],[1482,86552,86553],{"xmlns":1484},[1487,86554,86555,86563],{},[1490,86556,86557,86559,86561],{},[1493,86558,3633],{},[1493,86560,55105],{},[1493,86562,1998],{},[1528,86564,69489],{"encoding":1530},"; pod ním se firmě nevyplatí produkovat.",[1206,86567,86568,1656,86571,22345,86606,80496,86627,86640,86641,86656,86657,2632],{},[1047,86569,86570],{},"Funkce nabídky firmy",[1035,86572,86574],{"className":86573},[1480],[1482,86575,86576],{"xmlns":1484},[1487,86577,86578,86604],{},[1490,86579,86580,86582,86584,86586,86588,86590,86592,86594,86596,86598,86600,86602],{},[1493,86581,1501],{},[1506,86583,1508],{},[1493,86585,2001],{},[1506,86587,1553],{"stretchy":1552},[1493,86589,1520],{},[1506,86591,1564],{"stretchy":1552},[1506,86593,1508],{},[1493,86595,1495],{},[1493,86597,1998],{},[1506,86599,1553],{"stretchy":1552},[1493,86601,1520],{},[1506,86603,1564],{"stretchy":1552},[1528,86605,81494],{"encoding":1530},[1035,86607,86609],{"className":86608},[1480],[1482,86610,86611],{"xmlns":1484},[1487,86612,86613,86625],{},[1490,86614,86615,86617,86619],{},[1493,86616,1520],{},[1506,86618,20200],{},[2315,86620,86621,86623],{},[1493,86622,1520],{},[1506,86624,2287],{},[1528,86626,80495],{"encoding":1530},[1035,86628,86630],{"className":86629},[1480],[1482,86631,86632],{"xmlns":1484},[1487,86633,86634,86638],{},[1490,86635,86636],{},[1680,86637,1871],{},[1528,86639,1871],{"encoding":1530}," (3.15); vychází z rostoucí části ",[1035,86642,86644],{"className":86643},[1480],[1482,86645,86646],{"xmlns":1484},[1487,86647,86648,86654],{},[1490,86649,86650,86652],{},[1493,86651,1495],{},[1493,86653,1998],{},[1528,86655,69470],{"encoding":1530}," nad minimem ",[1035,86658,86660],{"className":86659},[1480],[1482,86661,86662],{"xmlns":1484},[1487,86663,86664,86672],{},[1490,86665,86666,86668,86670],{},[1493,86667,3633],{},[1493,86669,55105],{},[1493,86671,1998],{},[1528,86673,69489],{"encoding":1530},[1206,86675,86676,22970,86678,86699,86700,2632],{},[1047,86677,64414],{},[1035,86679,86681],{"className":86680},[1480],[1482,86682,86683],{"xmlns":1484},[1487,86684,86685,86697],{},[1490,86686,86687,86689,86691],{},[1493,86688,1501],{},[1506,86690,1508],{},[2315,86692,86693,86695],{},[1493,86694,1501],{},[1506,86696,2287],{},[1528,86698,20068],{"encoding":1530}," konstantní ⇒ ",[1035,86701,86703],{"className":86702},[1480],[1482,86704,86705],{"xmlns":1484},[1487,86706,86707,86727],{},[1490,86708,86709,86711,86713,86715,86717,86719,86721],{},[1493,86710,3633],{},[1493,86712,1995],{},[1506,86714,1508],{},[1493,86716,1495],{},[1493,86718,1995],{},[1506,86720,1508],{},[2315,86722,86723,86725],{},[1493,86724,1501],{},[1506,86726,2287],{},[1528,86728,86729],{"encoding":1530},"AR = MR = P^*",[1206,86731,86732,86735],{},[1047,86733,86734],{},"Cenová diskriminace"," — stanovení odlišných cen pro různé segmenty trhu za účelem maximalizace zisku (úlohy 3.24–3.25).",[1065,86737,17159],{"id":17158},[1203,86739,86740,86760,86770],{},[1206,86741,86742,1656,86744,1732,86747,1732,86750,1732,86753,1732,86756],{},[1047,86743,65057],{},[1052,86745,17211],{"className":86746,"dataFsResolvedFilePath":3487,"href":3488},[1055],[1052,86748,17218],{"className":86749,"dataFsResolvedFilePath":3807,"href":3808},[1055],[1052,86751,3506],{"className":86752,"dataFsResolvedFilePath":16621,"href":16622},[1055],[1052,86754,17258],{"className":86755,"dataFsResolvedFilePath":17256,"href":17257},[1055],[1052,86757,86759],{"className":86758,"dataFsResolvedFilePath":1572,"href":1573},[1055],"Produkční funkce",[1206,86761,86762,1656,86764,1732,86767],{},[1047,86763,51799],{},[1052,86765,17190],{"className":86766,"dataFsResolvedFilePath":17188,"href":17189},[1055],[1052,86768,17196],{"className":86769,"dataFsResolvedFilePath":17194,"href":17195},[1055],[1206,86771,86772,1656,86774],{},[1047,86773,17176],{},[1052,86775,1058],{"className":86776,"dataFsResolvedFilePath":1056,"href":1057},[1055],{"title":17269,"searchDepth":141,"depth":141,"links":86778},[86779,86780,86787,86793,86797,86798,86802,86803,86804,86805,86811,86812],{"id":65287,"depth":141,"text":65288},{"id":69915,"depth":141,"text":69916,"children":86781},[86782,86783,86784,86785,86786],{"id":69926,"depth":96,"text":69927},{"id":70408,"depth":96,"text":70409},{"id":70563,"depth":96,"text":70564},{"id":71310,"depth":96,"text":71311},{"id":71964,"depth":96,"text":71965},{"id":72370,"depth":141,"text":72371,"children":86788},[86789,86790,86791,86792],{"id":72374,"depth":96,"text":72375},{"id":72535,"depth":96,"text":72536},{"id":73511,"depth":96,"text":73512},{"id":74412,"depth":96,"text":74413},{"id":75238,"depth":141,"text":75239,"children":86794},[86795,86796],{"id":32568,"depth":96,"text":32569},{"id":76596,"depth":96,"text":76597},{"id":76775,"depth":141,"text":76776},{"id":77940,"depth":141,"text":77941,"children":86799},[86800,86801],{"id":77954,"depth":96,"text":32569},{"id":79240,"depth":96,"text":79241},{"id":79872,"depth":141,"text":79873},{"id":81142,"depth":141,"text":81143},{"id":64216,"depth":141,"text":64217},{"id":81602,"depth":141,"text":81603,"children":86806},[86807,86808,86809,86810],{"id":81606,"depth":96,"text":81607},{"id":82457,"depth":96,"text":82458},{"id":84002,"depth":96,"text":84003},{"id":85372,"depth":96,"text":85373},{"id":31884,"depth":141,"text":31885},{"id":17158,"depth":141,"text":17159},{},"\u002Ftopics\u002Fprijem-naklady-zisk",{"title":69296,"description":17269},[26098,19272],"topics\u002Fprijem-naklady-zisk",[9,818,736,1008,384,688,734],"-YHZ3Iwmt82i8TkFT3lSyDuNV-lCxFmOIjEUcbUgJlc",{"id":86821,"title":1574,"body":86822,"course":9,"courses":17424,"created":26093,"description":17269,"extension":17426,"meta":98505,"navigation":17428,"path":98506,"seo":98507,"sources":98508,"stem":98509,"tags":98510,"type":19275,"updated":26102,"__hash__":98511},"topics\u002Ftopics\u002Fprodukce.md",{"type":1016,"value":86823,"toc":98462},[86824,86827,87185,87189,87192,87259,87311,87321,87325,87359,87400,87424,87447,87476,87543,87650,87698,87755,87830,87875,87879,87887,87895,87898,88163,88214,88294,88364,88387,88415,88460,88482,88486,88493,88543,88569,88723,88726,88762,88925,89033,89037,89074,89148,89217,89336,89457,89462,89503,89576,89669,89673,89709,89797,89910,90014,90099,90103,90151,90196,90202,90206,90209,90260,90310,90317,90383,90516,90561,90565,90586,90965,91065,91082,91135,91139,91221,91305,91475,91478,91521,91588,91662,91666,91671,91740,91748,91757,91835,91901,91906,92001,92044,92049,92097,92102,92150,92268,92354,92392,92495,92554,92695,92699,92742,92815,92839,92893,92900,92902,92946,92991,93002,93007,93043,93066,93075,93176,93243,93321,93328,93419,93481,93517,93574,93633,93821,93825,93829,93908,93913,94037,94123,94129,94239,94276,94367,94465,94468,94472,94538,94575,94697,94701,94729,94781,94855,94960,94984,95043,95047,95065,95207,95355,95357,95392,95396,95398,95488,95618,95744,95836,95911,95915,96031,96135,96325,96361,96455,96461,96574,96877,96883,97001,97100,97176,97178,98340,98342],[1019,86825,1574],{"id":86826},"produkce-produkční-funkce-cobb-douglas-mrts",[1023,86828,86830,86836],{"className":86829,"dataCallout":1028},[1026,1027],[1030,86831,86833,1042],{"className":86832},[1033],[1035,86834],{"className":86835,"ariaHidden":1041},[1038,1039,1040],[1030,86837,86838,86840,86841,51991,86854,86867,86868,32533,86881,7606,86883,86907,86908,1656,86910,1586,86944,1656,86947,86975,86976,26918,86995,87025,87026,7606,87029,87056,87057,87060,87061,87091,87092,87122,87123,1656,87126,87165,87166,87184],{},[1047,86839,86759],{}," popisuje vztah mezi vstupy (práce ",[1035,86842,86844],{"className":86843},[1480],[1482,86845,86846],{"xmlns":1484},[1487,86847,86848,86852],{},[1490,86849,86850],{},[1493,86851,1556],{},[1528,86853,1556],{"encoding":1530},[1035,86855,86857],{"className":86856},[1480],[1482,86858,86859],{"xmlns":1484},[1487,86860,86861,86865],{},[1490,86862,86863],{},[1493,86864,1504],{},[1528,86866,1504],{"encoding":1530},") a výstupem ",[1035,86869,86871],{"className":86870},[1480],[1482,86872,86873],{"xmlns":1484},[1487,86874,86875,86879],{},[1490,86876,86877],{},[1493,86878,1520],{},[1528,86880,1520],{"encoding":1530},[1047,86882,52058],{},[1035,86884,86886],{"className":86885},[1480],[1482,86887,86888],{"xmlns":1484},[1487,86889,86890,86904],{},[1490,86891,86892,86894,86896,86898,86900,86902],{},[1493,86893,1520],{},[1506,86895,1508],{},[1493,86897,1520],{},[1506,86899,1553],{"stretchy":1552},[1493,86901,1556],{},[1506,86903,1564],{"stretchy":1552},[1528,86905,86906],{"encoding":1530},"Q = Q(L)",") studujeme ",[1176,86909,26551],{},[1035,86911,86913],{"className":86912},[1480],[1482,86914,86915],{"xmlns":1484},[1487,86916,86917,86941],{},[1490,86918,86919,86921,86927,86929,86935,86937,86939],{},[1493,86920,1495],{},[1497,86922,86923,86925],{},[1493,86924,1501],{},[1493,86926,1556],{},[1506,86928,1508],{},[2315,86930,86931,86933],{},[1493,86932,1520],{},[1506,86934,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,86936,1553],{"stretchy":1552},[1493,86938,1556],{},[1506,86940,1564],{"stretchy":1552},[1528,86942,86943],{"encoding":1530},"MP_L = Q'(L)",[1176,86945,86946],{},"průměrný produkt",[1035,86948,86950],{"className":86949},[1480],[1482,86951,86952],{"xmlns":1484},[1487,86953,86954,86972],{},[1490,86955,86956,86958,86964,86966,86968,86970],{},[1493,86957,3633],{},[1497,86959,86960,86962],{},[1493,86961,1501],{},[1493,86963,1556],{},[1506,86965,1508],{},[1493,86967,1520],{},[1493,86969,1709],{"mathvariant":1516},[1493,86971,1556],{},[1528,86973,86974],{"encoding":1530},"AP_L = Q\u002FL","; v maximu ",[1035,86977,86979],{"className":86978},[1480],[1482,86980,86981],{"xmlns":1484},[1487,86982,86983,86993],{},[1490,86984,86985,86987],{},[1493,86986,3633],{},[1497,86988,86989,86991],{},[1493,86990,1501],{},[1493,86992,1556],{},[1528,86994,6827],{"encoding":1530},[1035,86996,86998],{"className":86997},[1480],[1482,86999,87000],{"xmlns":1484},[1487,87001,87002,87022],{},[1490,87003,87004,87006,87012,87014,87016],{},[1493,87005,1495],{},[1497,87007,87008,87010],{},[1493,87009,1501],{},[1493,87011,1556],{},[1506,87013,1508],{},[1493,87015,3633],{},[1497,87017,87018,87020],{},[1493,87019,1501],{},[1493,87021,1556],{},[1528,87023,87024],{"encoding":1530},"MP_L = AP_L",". Ve ",[1047,87027,87028],{},"dvoufaktorovém modelu",[1035,87030,87032],{"className":87031},[1480],[1482,87033,87034],{"xmlns":1484},[1487,87035,87036,87054],{},[1490,87037,87038,87040,87042,87044,87046,87048,87050,87052],{},[1493,87039,1520],{},[1506,87041,1508],{},[1493,87043,1520],{},[1506,87045,1553],{"stretchy":1552},[1493,87047,1556],{},[1506,87049,1559],{"separator":1041},[1493,87051,1504],{},[1506,87053,1564],{"stretchy":1552},[1528,87055,1567],{"encoding":1530},") dominují ",[1047,87058,87059],{},"Cobb-Douglasovy"," funkce ",[1035,87062,87064],{"className":87063},[1480],[1482,87065,87066],{"xmlns":1484},[1487,87067,87068,87088],{},[1490,87069,87070,87072,87074,87076,87082],{},[1493,87071,1520],{},[1506,87073,1508],{},[1493,87075,3633],{},[2315,87077,87078,87080],{},[1493,87079,1556],{},[1493,87081,1052],{},[2315,87083,87084,87086],{},[1493,87085,1504],{},[1493,87087,2394],{},[1528,87089,87090],{"encoding":1530},"Q = AL^a K^b","; mezní produkty ",[1035,87093,87095],{"className":87094},[1480],[1482,87096,87097],{"xmlns":1484},[1487,87098,87099,87119],{},[1490,87100,87101,87103,87109,87111,87113],{},[1493,87102,1495],{},[1497,87104,87105,87107],{},[1493,87106,1501],{},[1493,87108,1556],{},[1506,87110,1559],{"separator":1041},[1493,87112,1495],{},[1497,87114,87115,87117],{},[1493,87116,1501],{},[1493,87118,1504],{},[1528,87120,87121],{"encoding":1530},"MP_L, MP_K"," jsou parciální derivace a jejich podíl dává ",[1047,87124,87125],{},"mezní míru technické substituce",[1035,87127,87129],{"className":87128},[1480],[1482,87130,87131],{"xmlns":1484},[1487,87132,87133,87163],{},[1490,87134,87135,87137,87139,87141,87143,87145,87147,87153,87155,87157],{},[1493,87136,1495],{},[1493,87138,1995],{},[1493,87140,5289],{},[1493,87142,2001],{},[1506,87144,1508],{},[1493,87146,1495],{},[1497,87148,87149,87151],{},[1493,87150,1501],{},[1493,87152,1556],{},[1493,87154,1709],{"mathvariant":1516},[1493,87156,1495],{},[1497,87158,87159,87161],{},[1493,87160,1501],{},[1493,87162,1504],{},[1528,87164,16194],{"encoding":1530}," — sklon izokvanty. Součet exponentů ",[1035,87167,87169],{"className":87168},[1480],[1482,87170,87171],{"xmlns":1484},[1487,87172,87173,87181],{},[1490,87174,87175,87177,87179],{},[1493,87176,1052],{},[1506,87178,2162],{},[1493,87180,2394],{},[1528,87182,87183],{"encoding":1530},"a+b"," určuje typ výnosů z rozsahu.",[1065,87186,87188],{"id":87187},"úvod-cílové-znalosti-kapitoly-5","Úvod — cílové znalosti kapitoly 5",[1030,87190,87191],{},"Po prostudování kapitoly 5 student umí:",[1203,87193,87194,87200,87210,87216,87222,87227,87233,87243,87248,87253],{},[1206,87195,87196,87197,1559],{},"popsat ",[1047,87198,87199],{},"jednofaktorový model produkce",[1206,87201,87202,87203,1586,87206,87209],{},"vypočítat ",[1047,87204,87205],{},"mezní",[1047,87207,87208],{},"průměrný produkt práce"," a ekonomicky je interpretovat,",[1206,87211,87212,87213,1559],{},"charakterizovat průběh ",[1047,87214,87215],{},"křivky produkce",[1206,87217,87218,87219,1559],{},"formulovat ",[1047,87220,87221],{},"princip maximalizace průměrného produktu práce",[1206,87223,87196,87224,1559],{},[1047,87225,87226],{},"dvoufaktorový model produkce",[1206,87228,87229,87230,1559],{},"uvést tvar ",[1047,87231,87232],{},"Cobb–Douglasových produkčních funkcí",[1206,87234,87235,87236,1732,87238,1732,87240,1559],{},"vyložit, co jsou ",[1047,87237,40186],{},[1047,87239,3482],{},[1047,87241,87242],{},"klesající výnosy z rozsahu",[1206,87244,87202,87245,87209],{},[1047,87246,87247],{},"mezní produkty práce a kapitálu",[1206,87249,87250,87251,1559],{},"najít ",[1047,87252,225],{},[1206,87254,87202,87255,87258],{},[1047,87256,87257],{},"mezní míru technické substituce (MRTS)"," a ekonomicky ji interpretovat.",[1030,87260,87261,87262,87265,87266,87269,87270,1656,87273,1732,87286,1656,87289,1586,87302,87305,87306,87308,87309,2632],{},"Každý proces produkce je určován ",[1047,87263,87264],{},"faktory"," (též ",[1047,87267,87268],{},"vstupy",") produkce. K hlavním patří ",[1047,87271,87272],{},"práce",[1035,87274,87276],{"className":87275},[1480],[1482,87277,87278],{"xmlns":1484},[1487,87279,87280,87284],{},[1490,87281,87282],{},[1493,87283,1556],{},[1528,87285,1556],{"encoding":1530},[1047,87287,87288],{},"kapitál",[1035,87290,87292],{"className":87291},[1480],[1482,87293,87294],{"xmlns":1484},[1487,87295,87296,87300],{},[1490,87297,87298],{},[1493,87299,1504],{},[1528,87301,1504],{"encoding":1530},[1047,87303,87304],{},"půda",". Při modelování se půda obvykle považuje za dlouhodobě konstantní, takže endogenními faktory zůstávají práce a kapitál. Je-li kapitál neměnný, hovoříme o ",[1047,87307,52058],{}," (produkce závisí jen na práci); v opačném případě o ",[1047,87310,87028],{},[1030,87312,87313,87314,1732,87317,87320],{},"Související matematický aparát: ",[1052,87315,3506],{"className":87316,"dataFsResolvedFilePath":16621,"href":16622},[1055],[1052,87318,9472],{"className":87319,"dataFsResolvedFilePath":9470,"href":9471},[1055]," (parciální derivace a totální diferenciál).",[1065,87322,87324],{"id":87323},"jednofaktorový-model-produkce","Jednofaktorový model produkce",[1030,87326,87327,87328,87341,87342,87355,87356],{},"Uvažujeme proces v krátkém období, kdy kapitál lze považovat za konstantní. Závislost produkce ",[1035,87329,87331],{"className":87330},[1480],[1482,87332,87333],{"xmlns":1484},[1487,87334,87335,87339],{},[1490,87336,87337],{},[1493,87338,1520],{},[1528,87340,1520],{"encoding":1530}," na práci ",[1035,87343,87345],{"className":87344},[1480],[1482,87346,87347],{"xmlns":1484},[1487,87348,87349,87353],{},[1490,87350,87351],{},[1493,87352,1556],{},[1528,87354,1556],{"encoding":1530}," vyjadřuje ",[1047,87357,87358],{},"produkční funkce",[1035,87360,87362],{"className":87361},[1480],[1482,87363,87364],{"xmlns":1484,"display":1485},[1487,87365,87366,87397],{},[19617,87367,87368],{"width":19619},[19621,87369,87370,87372,87390,87392],{},[19624,87371],{"width":19626},[19624,87373,87374],{},[1490,87375,87376,87378,87380,87382,87384,87386,87388],{},[1493,87377,1520],{},[1506,87379,1508],{},[1493,87381,1520],{},[1506,87383,1553],{"stretchy":1552},[1493,87385,1556],{},[1506,87387,1564],{"stretchy":1552},[1506,87389,1559],{"separator":1041},[19624,87391],{"width":19626},[19624,87393,87394],{},[1988,87395,87396],{},"(5.1)",[1528,87398,87399],{"encoding":1530},"Q = Q(L), \\tag{5.1}",[1030,87401,87402,87403,7606,87406,87409,87410,87423],{},"jejíž graf se nazývá ",[1047,87404,87405],{},"křivka produkce",[1176,87407,87408],{},"production curve","). Práce ",[1035,87411,87413],{"className":87412},[1480],[1482,87414,87415],{"xmlns":1484},[1487,87416,87417,87421],{},[1490,87418,87419],{},[1493,87420,1556],{},[1528,87422,1556],{"encoding":1530}," se měří počtem pracovníků, případně počtem pracovních hodin.",[1065,87425,87427,87428,1564],{"id":87426},"mezní-produkt-práce-mplmp_l","Mezní produkt práce (",[1035,87429,87431],{"className":87430},[1480],[1482,87432,87433],{"xmlns":1484},[1487,87434,87435,87445],{},[1490,87436,87437,87439],{},[1493,87438,1495],{},[1497,87440,87441,87443],{},[1493,87442,1501],{},[1493,87444,1556],{},[1528,87446,26571],{"encoding":1530},[1030,87448,87449,7606,87452,87455,87456,87475],{},[1047,87450,87451],{},"Mezní produkt práce",[1176,87453,87454],{},"marginal product of labour",") ",[1035,87457,87459],{"className":87458},[1480],[1482,87460,87461],{"xmlns":1484},[1487,87462,87463,87473],{},[1490,87464,87465,87467],{},[1493,87466,1495],{},[1497,87468,87469,87471],{},[1493,87470,1501],{},[1493,87472,1556],{},[1528,87474,26571],{"encoding":1530}," je derivace produkce podle práce:",[1035,87477,87479],{"className":87478},[1480],[1482,87480,87481],{"xmlns":1484,"display":1485},[1487,87482,87483,87540],{},[19617,87484,87485],{"width":19619},[19621,87486,87487,87489,87533,87535],{},[19624,87488],{"width":19626},[19624,87490,87491],{},[1490,87492,87493,87495,87501,87503,87517,87519,87525,87527,87529,87531],{},[1493,87494,1495],{},[1497,87496,87497,87499],{},[1493,87498,1501],{},[1493,87500,1556],{},[1506,87502,1508],{},[1510,87504,87505,87511],{},[1490,87506,87507,87509],{},[1493,87508,3384],{},[1493,87510,1520],{},[1490,87512,87513,87515],{},[1493,87514,3384],{},[1493,87516,1556],{},[1506,87518,1508],{},[2315,87520,87521,87523],{},[1493,87522,1520],{},[1506,87524,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,87526,1553],{"stretchy":1552},[1493,87528,1556],{},[1506,87530,1564],{"stretchy":1552},[1493,87532,2632],{"mathvariant":1516},[19624,87534],{"width":19626},[19624,87536,87537],{},[1988,87538,87539],{},"(5.2)",[1528,87541,87542],{"encoding":1530},"MP_L = \\frac{dQ}{dL} = Q'(L). \\tag{5.2}",[1030,87544,87545,87546,35675,87564,87592,87593,87610,87611,18139,87628,16623],{},"Pro pevnou hodnotu ",[1035,87547,87549],{"className":87548},[1480],[1482,87550,87551],{"xmlns":1484},[1487,87552,87553,87561],{},[1490,87554,87555],{},[2315,87556,87557,87559],{},[1493,87558,1556],{},[1506,87560,2287],{},[1528,87562,87563],{"encoding":1530},"L^*",[1035,87565,87567],{"className":87566},[1480],[1482,87568,87569],{"xmlns":1484},[1487,87570,87571,87589],{},[1490,87572,87573,87579,87581,87587],{},[2315,87574,87575,87577],{},[1493,87576,1520],{},[1506,87578,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,87580,1553],{"stretchy":1552},[2315,87582,87583,87585],{},[1493,87584,1556],{},[1506,87586,2287],{},[1506,87588,1564],{"stretchy":1552},[1528,87590,87591],{"encoding":1530},"Q'(L^*)"," rychlost změny produkce vzhledem k práci v bodě ",[1035,87594,87596],{"className":87595},[1480],[1482,87597,87598],{"xmlns":1484},[1487,87599,87600,87608],{},[1490,87601,87602],{},[2315,87603,87604,87606],{},[1493,87605,1556],{},[1506,87607,2287],{},[1528,87609,87563],{"encoding":1530},", resp. přibližnou změnu produkce odpovídající jednotkové změně práce (z ",[1035,87612,87614],{"className":87613},[1480],[1482,87615,87616],{"xmlns":1484},[1487,87617,87618,87626],{},[1490,87619,87620],{},[2315,87621,87622,87624],{},[1493,87623,1556],{},[1506,87625,2287],{},[1528,87627,87563],{"encoding":1530},[1035,87629,87631],{"className":87630},[1480],[1482,87632,87633],{"xmlns":1484},[1487,87634,87635,87647],{},[1490,87636,87637,87643,87645],{},[2315,87638,87639,87641],{},[1493,87640,1556],{},[1506,87642,2287],{},[1506,87644,2162],{},[1680,87646,1682],{},[1528,87648,87649],{"encoding":1530},"L^*+1",[1023,87651,87653,87659],{"className":87652,"dataCallout":582},[1026,1186],[1030,87654,87656,6749],{"className":87655},[1033],[1035,87657],{"className":87658,"ariaHidden":1041},[1038,1193,1040],[1030,87660,87661,87680,87681,87684,87685,2632],{},[1035,87662,87664],{"className":87663},[1480],[1482,87665,87666],{"xmlns":1484},[1487,87667,87668,87678],{},[1490,87669,87670,87672],{},[1493,87671,1495],{},[1497,87673,87674,87676],{},[1493,87675,1501],{},[1493,87677,1556],{},[1528,87679,26571],{"encoding":1530}," odpovídá na otázku „",[1047,87682,87683],{},"kolik produkce přibude, když přidám jednoho dalšího pracovníka"," (při neměnném kapitálu)?\". Je to sklon křivky produkce v bodě ",[1035,87686,87688],{"className":87687},[1480],[1482,87689,87690],{"xmlns":1484},[1487,87691,87692,87696],{},[1490,87693,87694],{},[1493,87695,1556],{},[1528,87697,1556],{"encoding":1530},[1030,87699,87700,87703,87704,87720,87721,18139,87734,87754],{},[1047,87701,87702],{},"Přibližná změna produkce"," pro změnu práce o ",[1035,87705,87707],{"className":87706},[1480],[1482,87708,87709],{"xmlns":1484},[1487,87710,87711,87717],{},[1490,87712,87713,87715],{},[1493,87714,3384],{},[1493,87716,1556],{},[1528,87718,87719],{"encoding":1530},"dL"," (z ",[1035,87722,87724],{"className":87723},[1480],[1482,87725,87726],{"xmlns":1484},[1487,87727,87728,87732],{},[1490,87729,87730],{},[1493,87731,1556],{},[1528,87733,1556],{"encoding":1530},[1035,87735,87737],{"className":87736},[1480],[1482,87738,87739],{"xmlns":1484},[1487,87740,87741,87751],{},[1490,87742,87743,87745,87747,87749],{},[1493,87744,1556],{},[1506,87746,2162],{},[1493,87748,3384],{},[1493,87750,1556],{},[1528,87752,87753],{"encoding":1530},"L+dL",") pomocí diferenciálu:",[1035,87756,87758],{"className":87757},[1480],[1482,87759,87760],{"xmlns":1484,"display":1485},[1487,87761,87762,87827],{},[19617,87763,87764],{"width":19619},[19621,87765,87766,87768,87820,87822],{},[19624,87767],{"width":19626},[19624,87769,87770],{},[1490,87771,87772,87774,87776,87778,87780,87782,87784,87790,87792,87794,87796,87798,87800,87802,87804,87806,87812,87814,87816,87818],{},[1493,87773,2976],{"mathvariant":1516},[1493,87775,1520],{},[1506,87777,2343],{},[1493,87779,3384],{},[1493,87781,1520],{},[1506,87783,1508],{},[2315,87785,87786,87788],{},[1493,87787,1520],{},[1506,87789,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,87791,1553],{"stretchy":1552},[1493,87793,1556],{},[1506,87795,1564],{"stretchy":1552},[1988,87797,5016],{},[1493,87799,3384],{},[1493,87801,1556],{},[1506,87803,1508],{},[1493,87805,1495],{},[1497,87807,87808,87810],{},[1493,87809,1501],{},[1493,87811,1556],{},[1988,87813,5016],{},[1493,87815,3384],{},[1493,87817,1556],{},[1493,87819,2632],{"mathvariant":1516},[19624,87821],{"width":19626},[19624,87823,87824],{},[1988,87825,87826],{},"(5.3)",[1528,87828,87829],{"encoding":1530},"\\Delta Q \\approx dQ = Q'(L)\\,dL = MP_L\\,dL. \\tag{5.3}",[1030,87831,87832,87833,2632],{},"Skutečná změna je ",[1035,87834,87836],{"className":87835},[1480],[1482,87837,87838],{"xmlns":1484},[1487,87839,87840,87872],{},[1490,87841,87842,87844,87846,87848,87850,87852,87854,87856,87858,87860,87862,87864,87866,87868,87870],{},[1493,87843,2976],{"mathvariant":1516},[1493,87845,1520],{},[1506,87847,1508],{},[1493,87849,1520],{},[1506,87851,1553],{"stretchy":1552},[1493,87853,1556],{},[1506,87855,2162],{},[1493,87857,3384],{},[1493,87859,1556],{},[1506,87861,1564],{"stretchy":1552},[1506,87863,1888],{},[1493,87865,1520],{},[1506,87867,1553],{"stretchy":1552},[1493,87869,1556],{},[1506,87871,1564],{"stretchy":1552},[1528,87873,87874],{"encoding":1530},"\\Delta Q = Q(L+dL) - Q(L)",[1304,87876,87878],{"id":87877},"zákon-klesajících-mezních-výnosů","Zákon klesajících mezních výnosů",[1030,87880,87881,7606,87884,18579],{},[1047,87882,87883],{},"Zákon klesajících výnosů",[1176,87885,87886],{},"law of diminishing marginal productivity",[19516,87888,87889],{},[1030,87890,87891,87892,87894],{},"Roste-li postupně některý ze vstupů (",[1176,87893,52054],{},"), budou přírůstky výstupu od jistého bodu klesat.",[1030,87896,87897],{},"Typická křivka produkce má dvě fáze:",[1030,87899,87900,87901,1656,87922,87941,87942,87992,87993,87995,87996,1656,88016,88035,88036,87992,88068,18367,88070,88089,88090,37188,88107,88141,88142,8994,88159,88162],{},"1° ",[1047,87902,87903,87904,1274],{},"Do bodu ",[1035,87905,87907],{"className":87906},[1480],[1482,87908,87909],{"xmlns":1484},[1487,87910,87911,87919],{},[1490,87912,87913],{},[1497,87914,87915,87917],{},[1493,87916,1556],{},[1680,87918,1871],{},[1528,87920,87921],{"encoding":1530},"L_0",[1035,87923,87925],{"className":87924},[1480],[1482,87926,87927],{"xmlns":1484},[1487,87928,87929,87939],{},[1490,87930,87931,87933],{},[1493,87932,1495],{},[1497,87934,87935,87937],{},[1493,87936,1501],{},[1493,87938,1556],{},[1528,87940,26571],{"encoding":1530}," roste, tj. ",[1035,87943,87945],{"className":87944},[1480],[1482,87946,87947],{"xmlns":1484},[1487,87948,87949,87989],{},[1490,87950,87951,87953,87955,87961,87967,87969,87979,87981,87983,87985,87987],{},[1506,87952,1553],{"stretchy":1552},[1493,87954,1495],{},[1497,87956,87957,87959],{},[1493,87958,1501],{},[1493,87960,1556],{},[2315,87962,87963,87965],{},[1506,87964,1564],{"stretchy":1552},[1506,87966,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,87968,1508],{},[2315,87970,87971,87973],{},[1493,87972,1520],{},[1490,87974,87975,87977],{},[1506,87976,6927],{"mathvariant":1516},[1506,87978,6927],{"mathvariant":1516},[1506,87980,1553],{"stretchy":1552},[1493,87982,1556],{},[1506,87984,1564],{"stretchy":1552},[1506,87986,2796],{},[1680,87988,1871],{},[1528,87990,87991],{"encoding":1530},"(MP_L)' = Q''(L) > 0"," — křivka produkce je ",[1047,87994,52775],{},".\n2° ",[1047,87997,87998,87999,1274],{},"Od bodu ",[1035,88000,88002],{"className":88001},[1480],[1482,88003,88004],{"xmlns":1484},[1487,88005,88006,88014],{},[1490,88007,88008],{},[1497,88009,88010,88012],{},[1493,88011,1556],{},[1680,88013,1871],{},[1528,88015,87921],{"encoding":1530},[1035,88017,88019],{"className":88018},[1480],[1482,88020,88021],{"xmlns":1484},[1487,88022,88023,88033],{},[1490,88024,88025,88027],{},[1493,88026,1495],{},[1497,88028,88029,88031],{},[1493,88030,1501],{},[1493,88032,1556],{},[1528,88034,26571],{"encoding":1530}," klesá, ",[1035,88037,88039],{"className":88038},[1480],[1482,88040,88041],{"xmlns":1484},[1487,88042,88043,88065],{},[1490,88044,88045,88055,88057,88059,88061,88063],{},[2315,88046,88047,88049],{},[1493,88048,1520],{},[1490,88050,88051,88053],{},[1506,88052,6927],{"mathvariant":1516},[1506,88054,6927],{"mathvariant":1516},[1506,88056,1553],{"stretchy":1552},[1493,88058,1556],{},[1506,88060,1564],{"stretchy":1552},[1506,88062,3961],{},[1680,88064,1871],{},[1528,88066,88067],{"encoding":1530},"Q''(L) \u003C 0",[1047,88069,53416],{},[1035,88071,88073],{"className":88072},[1480],[1482,88074,88075],{"xmlns":1484},[1487,88076,88077,88087],{},[1490,88078,88079,88081],{},[1493,88080,1495],{},[1497,88082,88083,88085],{},[1493,88084,1501],{},[1493,88086,1556],{},[1528,88088,26571],{"encoding":1530}," v kladných hodnotách klesá do bodu ",[1035,88091,88093],{"className":88092},[1480],[1482,88094,88095],{"xmlns":1484},[1487,88096,88097,88105],{},[1490,88098,88099],{},[1497,88100,88101,88103],{},[1493,88102,1556],{},[1680,88104,1682],{},[1528,88106,29689],{"encoding":1530},[1035,88108,88110],{"className":88109},[1480],[1482,88111,88112],{"xmlns":1484},[1487,88113,88114,88138],{},[1490,88115,88116,88118,88124,88126,88132,88134,88136],{},[1493,88117,1495],{},[1497,88119,88120,88122],{},[1493,88121,1501],{},[1493,88123,1556],{},[1506,88125,1553],{"stretchy":1552},[1497,88127,88128,88130],{},[1493,88129,1556],{},[1680,88131,1682],{},[1506,88133,1564],{"stretchy":1552},[1506,88135,1508],{},[1680,88137,1871],{},[1528,88139,88140],{"encoding":1530},"MP_L(L_1) = 0"," (maximum produkce), a dále pokračuje v záporných hodnotách. Bod ",[1035,88143,88145],{"className":88144},[1480],[1482,88146,88147],{"xmlns":1484},[1487,88148,88149,88157],{},[1490,88150,88151],{},[1497,88152,88153,88155],{},[1493,88154,1556],{},[1680,88156,1871],{},[1528,88158,87921],{"encoding":1530},[1047,88160,88161],{},"inflexním bodem"," produkční funkce.",[1030,88164,88165,88166,26918,88183,2632],{},"Matematicky: zákon klesajících výnosů znamená, že od určitého ",[1035,88167,88169],{"className":88168},[1480],[1482,88170,88171],{"xmlns":1484},[1487,88172,88173,88181],{},[1490,88174,88175],{},[1497,88176,88177,88179],{},[1493,88178,1556],{},[1680,88180,1871],{},[1528,88182,87921],{"encoding":1530},[1035,88184,88186],{"className":88185},[1480],[1482,88187,88188],{"xmlns":1484},[1487,88189,88190,88212],{},[1490,88191,88192,88202,88204,88206,88208,88210],{},[2315,88193,88194,88196],{},[1493,88195,1520],{},[1490,88197,88198,88200],{},[1506,88199,6927],{"mathvariant":1516},[1506,88201,6927],{"mathvariant":1516},[1506,88203,1553],{"stretchy":1552},[1493,88205,1556],{},[1506,88207,1564],{"stretchy":1552},[1506,88209,3961],{},[1680,88211,1871],{},[1528,88213,88067],{"encoding":1530},[1030,88215,88216,1656,88219,21432,88259,1732,88276,88293],{},[1047,88217,88218],{},"Typický polynom třetího stupně:",[1035,88220,88222],{"className":88221},[1480],[1482,88223,88224],{"xmlns":1484},[1487,88225,88226,88256],{},[1490,88227,88228,88230,88232,88234,88236,88238,88240,88246,88248,88250],{},[1493,88229,1520],{},[1506,88231,1553],{"stretchy":1552},[1493,88233,1556],{},[1506,88235,1564],{"stretchy":1552},[1506,88237,1508],{},[1493,88239,1052],{},[2315,88241,88242,88244],{},[1493,88243,1556],{},[1680,88245,3201],{},[1506,88247,2162],{},[1493,88249,2394],{},[2315,88251,88252,88254],{},[1493,88253,1556],{},[1680,88255,1691],{},[1528,88257,88258],{"encoding":1530},"Q(L) = aL^3 + bL^2",[1035,88260,88262],{"className":88261},[1480],[1482,88263,88264],{"xmlns":1484},[1487,88265,88266,88274],{},[1490,88267,88268,88270,88272],{},[1493,88269,1052],{},[1506,88271,3961],{},[1680,88273,1871],{},[1528,88275,57642],{"encoding":1530},[1035,88277,88279],{"className":88278},[1480],[1482,88280,88281],{"xmlns":1484},[1487,88282,88283,88291],{},[1490,88284,88285,88287,88289],{},[1493,88286,2394],{},[1506,88288,2796],{},[1680,88290,1871],{},[1528,88292,34950],{"encoding":1530},". Pak",[1035,88295,88297],{"className":88296},[1480],[1482,88298,88299],{"xmlns":1484,"display":1485},[1487,88300,88301,88361],{},[1490,88302,88303,88309,88311,88313,88321,88329,88331,88333,88339,88341,88343,88351,88359],{},[1497,88304,88305,88307],{},[1493,88306,1556],{},[1680,88308,1871],{},[1506,88310,1508],{},[1506,88312,1888],{},[1869,88314,88315],{"scriptlevel":1871,"displaystyle":1552},[1510,88316,88317,88319],{},[1680,88318,1682],{},[1680,88320,3201],{},[1869,88322,88323],{"scriptlevel":1871,"displaystyle":1552},[1510,88324,88325,88327],{},[1493,88326,2394],{},[1493,88328,1052],{},[1506,88330,1559],{"separator":1041},[1912,88332],{"width":1914},[1497,88334,88335,88337],{},[1493,88336,1556],{},[1680,88338,1682],{},[1506,88340,1508],{},[1506,88342,1888],{},[1869,88344,88345],{"scriptlevel":1871,"displaystyle":1552},[1510,88346,88347,88349],{},[1680,88348,1691],{},[1680,88350,3201],{},[1869,88352,88353],{"scriptlevel":1871,"displaystyle":1552},[1510,88354,88355,88357],{},[1493,88356,2394],{},[1493,88358,1052],{},[1493,88360,2632],{"mathvariant":1516},[1528,88362,88363],{"encoding":1530},"L_0 = -\\tfrac{1}{3}\\tfrac{b}{a}, \\qquad L_1 = -\\tfrac{2}{3}\\tfrac{b}{a}.",[1065,88365,88367,88368,1564],{"id":88366},"průměrný-produkt-práce-aplap_l","Průměrný produkt práce (",[1035,88369,88371],{"className":88370},[1480],[1482,88372,88373],{"xmlns":1484},[1487,88374,88375,88385],{},[1490,88376,88377,88379],{},[1493,88378,3633],{},[1497,88380,88381,88383],{},[1493,88382,1501],{},[1493,88384,1556],{},[1528,88386,6827],{"encoding":1530},[1030,88388,88389,7606,88392,87455,88395,88414],{},[1047,88390,88391],{},"Průměrný produkt práce",[1176,88393,88394],{},"average product of labour",[1035,88396,88398],{"className":88397},[1480],[1482,88399,88400],{"xmlns":1484},[1487,88401,88402,88412],{},[1490,88403,88404,88406],{},[1493,88405,3633],{},[1497,88407,88408,88410],{},[1493,88409,1501],{},[1493,88411,1556],{},[1528,88413,6827],{"encoding":1530}," je podíl produkce a práce:",[1035,88416,88418],{"className":88417},[1480],[1482,88419,88420],{"xmlns":1484,"display":1485},[1487,88421,88422,88457],{},[19617,88423,88424],{"width":19619},[19621,88425,88426,88428,88450,88452],{},[19624,88427],{"width":19626},[19624,88429,88430],{},[1490,88431,88432,88434,88440,88442,88448],{},[1493,88433,3633],{},[1497,88435,88436,88438],{},[1493,88437,1501],{},[1493,88439,1556],{},[1506,88441,1508],{},[1510,88443,88444,88446],{},[1493,88445,1520],{},[1493,88447,1556],{},[1493,88449,2632],{"mathvariant":1516},[19624,88451],{"width":19626},[19624,88453,88454],{},[1988,88455,88456],{},"(5.4)",[1528,88458,88459],{"encoding":1530},"AP_L = \\frac{Q}{L}. \\tag{5.4}",[1030,88461,88462,88463,2632],{},"Je to nejjednodušší míra produktivity práce. Cílem optimalizace je maximalizace ",[1035,88464,88466],{"className":88465},[1480],[1482,88467,88468],{"xmlns":1484},[1487,88469,88470,88480],{},[1490,88471,88472,88474],{},[1493,88473,3633],{},[1497,88475,88476,88478],{},[1493,88477,1501],{},[1493,88479,1556],{},[1528,88481,6827],{"encoding":1530},[1065,88483,88485],{"id":88484},"princip-maximalizace-průměrného-produktu-práce","Princip maximalizace průměrného produktu práce",[1030,88487,88488],{},[18014,88489],{"alt":88490,"className":88491,"src":88492},"imek-q-mpl-apl-tripanel",[1055,18018],"\u002Fwiki-assets\u002Fimek-q-mpl-apl-tripanel.jpeg",[19516,88494,88495],{},[1030,88496,88497,88500,88501,11713,88520,88537,88538],{},[1047,88498,88499],{},"Princip:"," Má-li ",[1035,88502,88504],{"className":88503},[1480],[1482,88505,88506],{"xmlns":1484},[1487,88507,88508,88518],{},[1490,88509,88510,88512],{},[1493,88511,3633],{},[1497,88513,88514,88516],{},[1493,88515,1501],{},[1493,88517,1556],{},[1528,88519,6827],{"encoding":1530},[1035,88521,88523],{"className":88522},[1480],[1482,88524,88525],{"xmlns":1484},[1487,88526,88527,88535],{},[1490,88528,88529],{},[1497,88530,88531,88533],{},[1493,88532,1556],{},[1680,88534,1871],{},[1528,88536,87921],{"encoding":1530}," maximum, pak platí\n",[1035,88539,88542],{"className":88540,"title":88541,"style":25826},[25824],"ParseError: KaTeX parse error: \\tag works only in display equations","MP_L(L_0) = AP_L(L_0). \\tag{5.5}",[1030,88544,88545,88546,88549,88550,1656,88554,2632],{},"Slovně: ",[1047,88547,88548],{},"v bodě maxima průměrného produktu práce se mezní produkt práce rovná průměrnému produktu práce."," Jde o analogii ",[1052,88551,88553],{"className":88552,"dataFsResolvedFilePath":1299,"href":1300},[1055],"principu minimalizace průměrných nákladů",[1035,88555,88557],{"className":88556},[1480],[1482,88558,88559],{"xmlns":1484},[1487,88560,88561,88567],{},[1490,88562,88563,88565],{},[1493,88564,3633],{},[1493,88566,1998],{},[1528,88568,16523],{"encoding":1530},[1023,88570,88572,88598],{"className":88571,"dataCallout":1443},[1026,1442],[1030,88573,88575,88578,88579],{"className":88574},[1033],[1035,88576],{"className":88577,"ariaHidden":1041},[1038,1450,1040],"Postup — jak najít max ",[1035,88580,88582],{"className":88581},[1480],[1482,88583,88584],{"xmlns":1484},[1487,88585,88586,88596],{},[1490,88587,88588,88590],{},[1493,88589,3633],{},[1497,88591,88592,88594],{},[1493,88593,1501],{},[1493,88595,1556],{},[1528,88597,6827],{"encoding":1530},[1276,88599,88600,88638,88720],{},[1206,88601,88602,88603,88637],{},"Napište ",[1035,88604,88606],{"className":88605},[1480],[1482,88607,88608],{"xmlns":1484},[1487,88609,88610,88634],{},[1490,88611,88612,88614,88620,88622,88624,88626,88628,88630,88632],{},[1493,88613,3633],{},[1497,88615,88616,88618],{},[1493,88617,1501],{},[1493,88619,1556],{},[1506,88621,1508],{},[1493,88623,1520],{},[1506,88625,1553],{"stretchy":1552},[1493,88627,1556],{},[1506,88629,1564],{"stretchy":1552},[1493,88631,1709],{"mathvariant":1516},[1493,88633,1556],{},[1528,88635,88636],{"encoding":1530},"AP_L = Q(L)\u002FL"," a zderivujte.",[1206,88639,88640,88641,88673,88674,88677,88678,2632],{},"Položte ",[1035,88642,88644],{"className":88643},[1480],[1482,88645,88646],{"xmlns":1484},[1487,88647,88648,88670],{},[1490,88649,88650,88652,88654,88660,88666,88668],{},[1506,88651,1553],{"stretchy":1552},[1493,88653,3633],{},[1497,88655,88656,88658],{},[1493,88657,1501],{},[1493,88659,1556],{},[2315,88661,88662,88664],{},[1506,88663,1564],{"stretchy":1552},[1506,88665,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,88667,1508],{},[1680,88669,1871],{},[1528,88671,88672],{"encoding":1530},"(AP_L)' = 0"," a vyřešte. ",[1176,88675,88676],{},"Zkratka:"," můžete rovnou řešit ",[1035,88679,88681],{"className":88680},[1480],[1482,88682,88683],{"xmlns":1484},[1487,88684,88685,88717],{},[1490,88686,88687,88689,88695,88697,88699,88701,88703,88705,88711,88713,88715],{},[1493,88688,1495],{},[1497,88690,88691,88693],{},[1493,88692,1501],{},[1493,88694,1556],{},[1506,88696,1553],{"stretchy":1552},[1493,88698,1556],{},[1506,88700,1564],{"stretchy":1552},[1506,88702,1508],{},[1493,88704,3633],{},[1497,88706,88707,88709],{},[1493,88708,1501],{},[1493,88710,1556],{},[1506,88712,1553],{"stretchy":1552},[1493,88714,1556],{},[1506,88716,1564],{"stretchy":1552},[1528,88718,88719],{"encoding":1530},"MP_L(L) = AP_L(L)",[1206,88721,88722],{},"Ověřte 2. derivací (či grafem), že jde o maximum.",[1304,88724,78068],{"id":88725},"odvození",[1030,88727,7762,88728,88761],{},[1035,88729,88731],{"className":88730},[1480],[1482,88732,88733],{"xmlns":1484},[1487,88734,88735,88759],{},[1490,88736,88737,88739,88745,88747,88749,88751,88753,88755,88757],{},[1493,88738,3633],{},[1497,88740,88741,88743],{},[1493,88742,1501],{},[1493,88744,1556],{},[1506,88746,1508],{},[1493,88748,1520],{},[1506,88750,1553],{"stretchy":1552},[1493,88752,1556],{},[1506,88754,1564],{"stretchy":1552},[1493,88756,1709],{"mathvariant":1516},[1493,88758,1556],{},[1528,88760,88636],{"encoding":1530}," a derivace podílu:",[1035,88763,88765],{"className":88764},[1480],[1482,88766,88767],{"xmlns":1484,"display":1485},[1487,88768,88769,88922],{},[1490,88770,88771,88773,88775,88781,88787,88789,88791,88793,88795,88835,88837,88843,88877,88879,88885,88888,88890,88896,88898,88900,88902,88904,88906,88912,88914,88916,88918,88920],{},[1506,88772,1553],{"stretchy":1552},[1493,88774,3633],{},[1497,88776,88777,88779],{},[1493,88778,1501],{},[1493,88780,1556],{},[2315,88782,88783,88785],{},[1506,88784,1564],{"stretchy":1552},[1506,88786,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,88788,1553],{"stretchy":1552},[1493,88790,1556],{},[1506,88792,1564],{"stretchy":1552},[1506,88794,1508],{},[1510,88796,88797,88829],{},[1490,88798,88799,88805,88807,88809,88811,88813,88815,88817,88819,88821,88823,88825,88827],{},[2315,88800,88801,88803],{},[1493,88802,1520],{},[1506,88804,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,88806,1553],{"stretchy":1552},[1493,88808,1556],{},[1506,88810,1564],{"stretchy":1552},[1506,88812,1714],{},[1493,88814,1556],{},[1506,88816,1888],{},[1493,88818,1520],{},[1506,88820,1553],{"stretchy":1552},[1493,88822,1556],{},[1506,88824,1564],{"stretchy":1552},[1506,88826,1714],{},[1680,88828,1682],{},[2315,88830,88831,88833],{},[1493,88832,1556],{},[1680,88834,1691],{},[1506,88836,1508],{},[1510,88838,88839,88841],{},[1680,88840,1682],{},[1493,88842,1556],{},[1490,88844,88845,88847,88853,88855,88857,88859,88861,88875],{},[1506,88846,1553],{"fence":1041},[2315,88848,88849,88851],{},[1493,88850,1520],{},[1506,88852,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,88854,1553],{"stretchy":1552},[1493,88856,1556],{},[1506,88858,1564],{"stretchy":1552},[1506,88860,1888],{},[1510,88862,88863,88873],{},[1490,88864,88865,88867,88869,88871],{},[1493,88866,1520],{},[1506,88868,1553],{"stretchy":1552},[1493,88870,1556],{},[1506,88872,1564],{"stretchy":1552},[1493,88874,1556],{},[1506,88876,1564],{"fence":1041},[1506,88878,1508],{},[1510,88880,88881,88883],{},[1680,88882,1682],{},[1493,88884,1556],{},[1506,88886,1553],{"fence":1041,"stretchy":1041,"minsize":88887,"maxsize":88887},"1.2em",[1493,88889,1495],{},[1497,88891,88892,88894],{},[1493,88893,1501],{},[1493,88895,1556],{},[1506,88897,1553],{"stretchy":1552},[1493,88899,1556],{},[1506,88901,1564],{"stretchy":1552},[1506,88903,1888],{},[1493,88905,3633],{},[1497,88907,88908,88910],{},[1493,88909,1501],{},[1493,88911,1556],{},[1506,88913,1553],{"stretchy":1552},[1493,88915,1556],{},[1506,88917,1564],{"stretchy":1552},[1506,88919,1564],{"fence":1041,"stretchy":1041,"minsize":88887,"maxsize":88887},[1493,88921,2632],{"mathvariant":1516},[1528,88923,88924],{"encoding":1530},"(AP_L)'(L) = \\frac{Q'(L)\\cdot L - Q(L)\\cdot 1}{L^2} = \\frac{1}{L}\\left(Q'(L) - \\frac{Q(L)}{L}\\right) = \\frac{1}{L}\\bigl(MP_L(L) - AP_L(L)\\bigr).",[1030,88926,2364,88927,8994,88949,89032],{},[1035,88928,88930],{"className":88929},[1480],[1482,88931,88932],{"xmlns":1484},[1487,88933,88934,88946],{},[1490,88935,88936,88942,88944],{},[1497,88937,88938,88940],{},[1493,88939,1556],{},[1680,88941,1871],{},[1506,88943,2796],{},[1680,88945,1871],{},[1528,88947,88948],{"encoding":1530},"L_0 > 0",[1035,88950,88952],{"className":88951},[1480],[1482,88953,88954],{"xmlns":1484},[1487,88955,88956,89029],{},[1490,88957,88958,88960,88962,88968,88974,88976,88982,88984,88986,88988,88991,88993,88999,89001,89007,89009,89011,89013,89019,89021,89027],{},[1506,88959,1553],{"stretchy":1552},[1493,88961,3633],{},[1497,88963,88964,88966],{},[1493,88965,1501],{},[1493,88967,1556],{},[2315,88969,88970,88972],{},[1506,88971,1564],{"stretchy":1552},[1506,88973,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,88975,1553],{"stretchy":1552},[1497,88977,88978,88980],{},[1493,88979,1556],{},[1680,88981,1871],{},[1506,88983,1564],{"stretchy":1552},[1506,88985,1508],{},[1680,88987,1871],{},[1506,88989,88990],{},"⇔",[1493,88992,1495],{},[1497,88994,88995,88997],{},[1493,88996,1501],{},[1493,88998,1556],{},[1506,89000,1553],{"stretchy":1552},[1497,89002,89003,89005],{},[1493,89004,1556],{},[1680,89006,1871],{},[1506,89008,1564],{"stretchy":1552},[1506,89010,1508],{},[1493,89012,3633],{},[1497,89014,89015,89017],{},[1493,89016,1501],{},[1493,89018,1556],{},[1506,89020,1553],{"stretchy":1552},[1497,89022,89023,89025],{},[1493,89024,1556],{},[1680,89026,1871],{},[1506,89028,1564],{"stretchy":1552},[1528,89030,89031],{"encoding":1530},"(AP_L)'(L_0) = 0 \\Leftrightarrow MP_L(L_0) = AP_L(L_0)",", čímž je (5.5) dokázáno.",[1304,89034,89036],{"id":89035},"příklad-51","Příklad 5.1",[1030,89038,89039,89040,2632],{},"Je dána produkce ",[1035,89041,89043],{"className":89042},[1480],[1482,89044,89045],{"xmlns":1484},[1487,89046,89047,89071],{},[1490,89048,89049,89051,89053,89055,89061,89063,89065],{},[1493,89050,1520],{},[1506,89052,1508],{},[1680,89054,7508],{},[2315,89056,89057,89059],{},[1493,89058,1556],{},[1680,89060,1691],{},[1506,89062,1888],{},[1680,89064,2929],{},[2315,89066,89067,89069],{},[1493,89068,1556],{},[1680,89070,3201],{},[1528,89072,89073],{"encoding":1530},"Q = 6L^2 - 0{,}2L^3",[1030,89075,89076,8686,89078,89128,89129,2632],{},[1047,89077,1334],{},[1035,89079,89081],{"className":89080},[1480],[1482,89082,89083],{"xmlns":1484},[1487,89084,89085,89125],{},[1490,89086,89087,89089,89091,89093,89095,89097,89099,89101,89103,89105,89107,89109,89111,89113,89115,89117,89119,89121,89123],{},[1493,89088,1556],{},[1506,89090,1508],{},[1680,89092,1691],{},[1506,89094,1559],{"separator":1041},[1680,89096,1752],{},[1506,89098,1559],{"separator":1041},[1680,89100,6138],{},[1506,89102,1559],{"separator":1041},[1680,89104,1775],{},[1506,89106,1559],{"separator":1041},[1680,89108,38539],{},[1506,89110,1559],{"separator":1041},[1680,89112,9319],{},[1506,89114,1559],{"separator":1041},[1680,89116,8436],{},[1506,89118,1559],{"separator":1041},[1680,89120,53274],{},[1506,89122,1559],{"separator":1041},[1680,89124,2309],{},[1528,89126,89127],{"encoding":1530},"L = 2, 5, 8, 10, 14, 18, 20, 21, 25"," určíme ",[1035,89130,89132],{"className":89131},[1480],[1482,89133,89134],{"xmlns":1484},[1487,89135,89136,89146],{},[1490,89137,89138,89140],{},[1493,89139,1495],{},[1497,89141,89142,89144],{},[1493,89143,1501],{},[1493,89145,1556],{},[1528,89147,26571],{"encoding":1530},[1030,89149,89150,89151,50071],{},"Podle (5.2): ",[1035,89152,89154],{"className":89153},[1480],[1482,89155,89156],{"xmlns":1484},[1487,89157,89158,89214],{},[1490,89159,89160,89162,89168,89170,89176,89178,89180,89182,89184,89186,89188,89190,89192,89198,89200,89202,89204,89206,89208,89210,89212],{},[1493,89161,1495],{},[1497,89163,89164,89166],{},[1493,89165,1501],{},[1493,89167,1556],{},[1506,89169,1508],{},[2315,89171,89172,89174],{},[1493,89173,1520],{},[1506,89175,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,89177,1553],{"stretchy":1552},[1493,89179,1556],{},[1506,89181,1564],{"stretchy":1552},[1506,89183,1508],{},[1680,89185,6797],{},[1493,89187,1556],{},[1506,89189,1888],{},[1680,89191,3332],{},[2315,89193,89194,89196],{},[1493,89195,1556],{},[1680,89197,1691],{},[1506,89199,1508],{},[1493,89201,1556],{},[1506,89203,1553],{"stretchy":1552},[1680,89205,6797],{},[1506,89207,1888],{},[1680,89209,3332],{},[1493,89211,1556],{},[1506,89213,1564],{"stretchy":1552},[1528,89215,89216],{"encoding":1530},"MP_L = Q'(L) = 12L - 0{,}6L^2 = L(12 - 0{,}6L)",[1073,89218,89219,89256],{},[1076,89220,89221],{},[1079,89222,89223,89238,89240,89242,89244,89246,89248,89250,89252,89254],{},[1082,89224,89225],{},[1035,89226,89228],{"className":89227},[1480],[1482,89229,89230],{"xmlns":1484},[1487,89231,89232,89236],{},[1490,89233,89234],{},[1493,89235,1556],{},[1528,89237,1556],{"encoding":1530},[1082,89239,1691],{},[1082,89241,1752],{},[1082,89243,6138],{},[1082,89245,1775],{},[1082,89247,38539],{},[1082,89249,9319],{},[1082,89251,8436],{},[1082,89253,53274],{},[1082,89255,2309],{},[1092,89257,89258],{},[1079,89259,89260,89281,89284,89287,89290,89292,89295,89297,89299,89318],{},[1097,89261,89262],{},[1035,89263,89265],{"className":89264},[1480],[1482,89266,89267],{"xmlns":1484},[1487,89268,89269,89279],{},[1490,89270,89271,89273],{},[1493,89272,1495],{},[1497,89274,89275,89277],{},[1493,89276,1501],{},[1493,89278,1556],{},[1528,89280,26571],{"encoding":1530},[1097,89282,89283],{},"21,6",[1097,89285,89286],{},"45",[1097,89288,89289],{},"57,6",[1097,89291,4965],{},[1097,89293,89294],{},"50,4",[1097,89296,89283],{},[1097,89298,1871],{},[1097,89300,89301],{},[1035,89302,89304],{"className":89303},[1480],[1482,89305,89306],{"xmlns":1484},[1487,89307,89308,89315],{},[1490,89309,89310,89312],{},[1506,89311,1888],{},[1680,89313,89314],{},"12,6",[1528,89316,89317],{"encoding":1530},"-12{,}6",[1097,89319,89320],{},[1035,89321,89323],{"className":89322},[1480],[1482,89324,89325],{"xmlns":1484},[1487,89326,89327,89333],{},[1490,89328,89329,89331],{},[1506,89330,1888],{},[1680,89332,59791],{},[1528,89334,89335],{"encoding":1530},"-75",[1030,89337,89338,89357,89358,89376,89377,89394,89395,89412,89413,89437,89438,89456],{},[1035,89339,89341],{"className":89340},[1480],[1482,89342,89343],{"xmlns":1484},[1487,89344,89345,89355],{},[1490,89346,89347,89349],{},[1493,89348,1495],{},[1497,89350,89351,89353],{},[1493,89352,1501],{},[1493,89354,1556],{},[1528,89356,26571],{"encoding":1530}," nabývá maxima pro ",[1035,89359,89361],{"className":89360},[1480],[1482,89362,89363],{"xmlns":1484},[1487,89364,89365,89373],{},[1490,89366,89367,89369,89371],{},[1493,89368,1556],{},[1506,89370,1508],{},[1680,89372,1775],{},[1528,89374,89375],{"encoding":1530},"L = 10"," (60 jednotek\u002Fprac.). Od ",[1035,89378,89380],{"className":89379},[1480],[1482,89381,89382],{"xmlns":1484},[1487,89383,89384,89392],{},[1490,89385,89386,89388,89390],{},[1493,89387,1556],{},[1506,89389,1508],{},[1680,89391,1775],{},[1528,89393,89375],{"encoding":1530}," přírůstky klesají, v ",[1035,89396,89398],{"className":89397},[1480],[1482,89399,89400],{"xmlns":1484},[1487,89401,89402,89410],{},[1490,89403,89404,89406,89408],{},[1493,89405,1556],{},[1506,89407,1508],{},[1680,89409,8436],{},[1528,89411,12190],{"encoding":1530}," produkce přestává růst (maximum ",[1035,89414,89416],{"className":89415},[1480],[1482,89417,89418],{"xmlns":1484},[1487,89419,89420,89434],{},[1490,89421,89422,89424,89426,89428,89430,89432],{},[1493,89423,1520],{},[1506,89425,1553],{"stretchy":1552},[1680,89427,8436],{},[1506,89429,1564],{"stretchy":1552},[1506,89431,1508],{},[1680,89433,7494],{},[1528,89435,89436],{"encoding":1530},"Q(20) = 800","), od ",[1035,89439,89441],{"className":89440},[1480],[1482,89442,89443],{"xmlns":1484},[1487,89444,89445,89453],{},[1490,89446,89447,89449,89451],{},[1493,89448,1556],{},[1506,89450,2796],{},[1680,89452,8436],{},[1528,89454,89455],{"encoding":1530},"L > 20"," produkce klesá (fyzické přeplnění pracoviště při neměnném kapitálu).",[1030,89458,89459,89461],{},[1047,89460,1353],{}," Přibližná změna produkce při růstu pracovníků z 6 na 9.",[1030,89463,89464,89465,1732,89483,1274],{},"Podle (5.3) s ",[1035,89466,89468],{"className":89467},[1480],[1482,89469,89470],{"xmlns":1484},[1487,89471,89472,89480],{},[1490,89473,89474,89476,89478],{},[1493,89475,1556],{},[1506,89477,1508],{},[1680,89479,7508],{},[1528,89481,89482],{"encoding":1530},"L = 6",[1035,89484,89486],{"className":89485},[1480],[1482,89487,89488],{"xmlns":1484},[1487,89489,89490,89500],{},[1490,89491,89492,89494,89496,89498],{},[1493,89493,3384],{},[1493,89495,1556],{},[1506,89497,1508],{},[1680,89499,3201],{},[1528,89501,89502],{"encoding":1530},"dL = 3",[1035,89504,89506],{"className":89505},[1480],[1482,89507,89508],{"xmlns":1484,"display":1485},[1487,89509,89510,89573],{},[1490,89511,89512,89514,89516,89518,89520,89526,89528,89530,89532,89534,89536,89538,89540,89542,89544,89546,89548,89550,89552,89554,89556,89558,89560,89562,89564,89566,89568,89570],{},[1493,89513,3384],{},[1493,89515,1520],{},[1506,89517,1508],{},[1493,89519,1495],{},[1497,89521,89522,89524],{},[1493,89523,1501],{},[1493,89525,1556],{},[1506,89527,1553],{"stretchy":1552},[1680,89529,7508],{},[1506,89531,1564],{"stretchy":1552},[1506,89533,1714],{},[1680,89535,3201],{},[1506,89537,1508],{},[1506,89539,1553],{"stretchy":1552},[1680,89541,6797],{},[1506,89543,1714],{},[1680,89545,7508],{},[1506,89547,1888],{},[1680,89549,3332],{},[1506,89551,1714],{},[1680,89553,14846],{},[1506,89555,1564],{"stretchy":1552},[1506,89557,1714],{},[1680,89559,3201],{},[1506,89561,1508],{},[1680,89563,89294],{},[1506,89565,1714],{},[1680,89567,3201],{},[1506,89569,1508],{},[1680,89571,89572],{},"151,2.",[1528,89574,89575],{"encoding":1530},"dQ = MP_L(6)\\cdot 3 = (12\\cdot 6 - 0{,}6\\cdot 36)\\cdot 3 = 50{,}4 \\cdot 3 = 151{,}2.",[1030,89577,89578,89579,71836,89604,89618,89619,2632],{},"Produkce vzroste z ",[1035,89580,89582],{"className":89581},[1480],[1482,89583,89584],{"xmlns":1484},[1487,89585,89586,89601],{},[1490,89587,89588,89590,89592,89594,89596,89598],{},[1493,89589,1520],{},[1506,89591,1553],{"stretchy":1552},[1680,89593,7508],{},[1506,89595,1564],{"stretchy":1552},[1506,89597,1508],{},[1680,89599,89600],{},"172,8",[1528,89602,89603],{"encoding":1530},"Q(6) = 172{,}8",[1035,89605,89607],{"className":89606},[1480],[1482,89608,89609],{"xmlns":1484},[1487,89610,89611,89616],{},[1490,89612,89613],{},[1680,89614,89615],{},"324",[1528,89617,89615],{"encoding":1530},". Skutečná hodnota: ",[1035,89620,89622],{"className":89621},[1480],[1482,89623,89624],{"xmlns":1484},[1487,89625,89626,89666],{},[1490,89627,89628,89630,89632,89634,89636,89638,89640,89642,89644,89646,89648,89650,89652,89654,89657,89659,89661,89663],{},[1493,89629,2976],{"mathvariant":1516},[1493,89631,1520],{},[1506,89633,1508],{},[1493,89635,1520],{},[1506,89637,1553],{"stretchy":1552},[1680,89639,14365],{},[1506,89641,1564],{"stretchy":1552},[1506,89643,1888],{},[1493,89645,1520],{},[1506,89647,1553],{"stretchy":1552},[1680,89649,7508],{},[1506,89651,1564],{"stretchy":1552},[1506,89653,1508],{},[1680,89655,89656],{},"340,2",[1506,89658,1888],{},[1680,89660,89600],{},[1506,89662,1508],{},[1680,89664,89665],{},"167,4",[1528,89667,89668],{"encoding":1530},"\\Delta Q = Q(9) - Q(6) = 340{,}2 - 172{,}8 = 167{,}4",[1304,89670,89672],{"id":89671},"příklad-52","Příklad 5.2",[1030,89674,89675,89676,2632],{},"Ověříme princip (5.5) pro ",[1035,89677,89679],{"className":89678},[1480],[1482,89680,89681],{"xmlns":1484},[1487,89682,89683,89707],{},[1490,89684,89685,89687,89689,89691,89697,89699,89701],{},[1493,89686,1520],{},[1506,89688,1508],{},[1680,89690,7508],{},[2315,89692,89693,89695],{},[1493,89694,1556],{},[1680,89696,1691],{},[1506,89698,1888],{},[1680,89700,2929],{},[2315,89702,89703,89705],{},[1493,89704,1556],{},[1680,89706,3201],{},[1528,89708,89073],{"encoding":1530},[1035,89710,89712],{"className":89711},[1480],[1482,89713,89714],{"xmlns":1484,"display":1485},[1487,89715,89716,89794],{},[1490,89717,89718,89720,89726,89728,89734,89736,89738,89740,89742,89744,89750,89752,89754,89756,89764,89766,89768,89770,89772,89774,89776,89778,89780,89782,89784,89790,89792],{},[1493,89719,3633],{},[1497,89721,89722,89724],{},[1493,89723,1501],{},[1493,89725,1556],{},[1506,89727,1508],{},[1510,89729,89730,89732],{},[1493,89731,1520],{},[1493,89733,1556],{},[1506,89735,1508],{},[1680,89737,7508],{},[1493,89739,1556],{},[1506,89741,1888],{},[1680,89743,2929],{},[2315,89745,89746,89748],{},[1493,89747,1556],{},[1680,89749,1691],{},[1506,89751,1559],{"separator":1041},[1912,89753],{"width":2108},[1493,89755,3633],{},[1697,89757,89758,89760,89762],{},[1493,89759,1501],{},[1493,89761,1556],{},[1506,89763,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,89765,1508],{},[1680,89767,7508],{},[1506,89769,1888],{},[1680,89771,3322],{},[1493,89773,1556],{},[1506,89775,1508],{},[1680,89777,1871],{},[1988,89779,1990],{},[1506,89781,2183],{},[1988,89783,1990],{},[1497,89785,89786,89788],{},[1493,89787,1556],{},[1680,89789,1871],{},[1506,89791,1508],{},[1680,89793,80694],{},[1528,89795,89796],{"encoding":1530},"AP_L = \\frac{Q}{L} = 6L - 0{,}2L^2, \\quad AP_L' = 6 - 0{,}4L = 0 \\;\\Rightarrow\\; L_0 = 15.",[1030,89798,89799,89834,89835,89853,89854,2632],{},[1035,89800,89802],{"className":89801},[1480],[1482,89803,89804],{"xmlns":1484},[1487,89805,89806,89832],{},[1490,89807,89808,89810,89822,89824,89826,89828,89830],{},[1493,89809,3633],{},[1697,89811,89812,89814,89816],{},[1493,89813,1501],{},[1493,89815,1556],{},[1490,89817,89818,89820],{},[1506,89819,6927],{"mathvariant":1516},[1506,89821,6927],{"mathvariant":1516},[1506,89823,1508],{},[1506,89825,1888],{},[1680,89827,3322],{},[1506,89829,3961],{},[1680,89831,1871],{},[1528,89833,6997],{"encoding":1530},", takže v ",[1035,89836,89838],{"className":89837},[1480],[1482,89839,89840],{"xmlns":1484},[1487,89841,89842,89850],{},[1490,89843,89844,89846,89848],{},[1493,89845,1556],{},[1506,89847,1508],{},[1680,89849,9787],{},[1528,89851,89852],{"encoding":1530},"L = 15"," je maximum, ",[1035,89855,89857],{"className":89856},[1480],[1482,89858,89859],{"xmlns":1484},[1487,89860,89861,89907],{},[1490,89862,89863,89865,89871,89873,89875,89877,89879,89881,89883,89885,89887,89889,89891,89894,89896,89899,89901,89903,89905],{},[1493,89864,3633],{},[1497,89866,89867,89869],{},[1493,89868,1501],{},[1493,89870,1556],{},[1506,89872,1553],{"stretchy":1552},[1680,89874,9787],{},[1506,89876,1564],{"stretchy":1552},[1506,89878,1508],{},[1680,89880,7508],{},[1506,89882,1714],{},[1680,89884,9787],{},[1506,89886,1888],{},[1680,89888,2929],{},[1506,89890,1714],{},[1680,89892,89893],{},"225",[1506,89895,1508],{},[1680,89897,89898],{},"90",[1506,89900,1888],{},[1680,89902,89286],{},[1506,89904,1508],{},[1680,89906,89286],{},[1528,89908,89909],{"encoding":1530},"AP_L(15) = 6\\cdot 15 - 0{,}2\\cdot 225 = 90 - 45 = 45",[1030,89911,89912,56428,89967,90013],{},[1035,89913,89915],{"className":89914},[1480],[1482,89916,89917],{"xmlns":1484},[1487,89918,89919,89964],{},[1490,89920,89921,89923,89929,89931,89933,89935,89937,89939,89941,89943,89945,89947,89949,89951,89953,89955,89957,89960,89962],{},[1493,89922,1495],{},[1497,89924,89925,89927],{},[1493,89926,1501],{},[1493,89928,1556],{},[1506,89930,1553],{"stretchy":1552},[1680,89932,9787],{},[1506,89934,1564],{"stretchy":1552},[1506,89936,1508],{},[1680,89938,6797],{},[1506,89940,1714],{},[1680,89942,9787],{},[1506,89944,1888],{},[1680,89946,3332],{},[1506,89948,1714],{},[1680,89950,89893],{},[1506,89952,1508],{},[1680,89954,7047],{},[1506,89956,1888],{},[1680,89958,89959],{},"135",[1506,89961,1508],{},[1680,89963,89286],{},[1528,89965,89966],{"encoding":1530},"MP_L(15) = 12\\cdot 15 - 0{,}6\\cdot 225 = 180 - 135 = 45",[1035,89968,89970],{"className":89969},[1480],[1482,89971,89972],{"xmlns":1484},[1487,89973,89974,90010],{},[1490,89975,89976,89978,89984,89986,89988,89990,89992,89994,90000,90002,90004,90006,90008],{},[1493,89977,1495],{},[1497,89979,89980,89982],{},[1493,89981,1501],{},[1493,89983,1556],{},[1506,89985,1553],{"stretchy":1552},[1680,89987,9787],{},[1506,89989,1564],{"stretchy":1552},[1506,89991,1508],{},[1493,89993,3633],{},[1497,89995,89996,89998],{},[1493,89997,1501],{},[1493,89999,1556],{},[1506,90001,1553],{"stretchy":1552},[1680,90003,9787],{},[1506,90005,1564],{"stretchy":1552},[1506,90007,1508],{},[1680,90009,89286],{},[1528,90011,90012],{"encoding":1530},"MP_L(15) = AP_L(15) = 45",", jak požaduje (5.5).",[1030,90015,90016,90019,90020,33723,90049,2632],{},[1047,90017,90018],{},"Zkratka bez hledání extrému:"," stačí řešit ",[1035,90021,90023],{"className":90022},[1480],[1482,90024,90025],{"xmlns":1484},[1487,90026,90027,90047],{},[1490,90028,90029,90031,90037,90039,90041],{},[1493,90030,1495],{},[1497,90032,90033,90035],{},[1493,90034,1501],{},[1493,90036,1556],{},[1506,90038,1508],{},[1493,90040,3633],{},[1497,90042,90043,90045],{},[1493,90044,1501],{},[1493,90046,1556],{},[1528,90048,87024],{"encoding":1530},[1035,90050,90052],{"className":90051},[1480],[1482,90053,90054],{"xmlns":1484},[1487,90055,90056,90096],{},[1490,90057,90058,90060,90062,90064,90066,90072,90074,90076,90078,90080,90082,90088,90090,90092,90094],{},[1680,90059,6797],{},[1493,90061,1556],{},[1506,90063,1888],{},[1680,90065,3332],{},[2315,90067,90068,90070],{},[1493,90069,1556],{},[1680,90071,1691],{},[1506,90073,1508],{},[1680,90075,7508],{},[1493,90077,1556],{},[1506,90079,1888],{},[1680,90081,2929],{},[2315,90083,90084,90086],{},[1493,90085,1556],{},[1680,90087,1691],{},[1506,90089,2183],{},[1493,90091,1556],{},[1506,90093,1508],{},[1680,90095,9787],{},[1528,90097,90098],{"encoding":1530},"12L - 0{,}6L^2 = 6L - 0{,}2L^2 \\Rightarrow L = 15",[1065,90100,90102],{"id":90101},"dvoufaktorový-model-produkce","Dvoufaktorový model produkce",[1030,90104,90105,90106,18139,90119,1656,90122,22060,90135,1656,90138,1274],{},"V dvoufaktorovém modelu závisí produkce ",[1035,90107,90109],{"className":90108},[1480],[1482,90110,90111],{"xmlns":1484},[1487,90112,90113,90117],{},[1490,90114,90115],{},[1493,90116,1520],{},[1528,90118,1520],{"encoding":1530},[1047,90120,90121],{},"práci",[1035,90123,90125],{"className":90124},[1480],[1482,90126,90127],{"xmlns":1484},[1487,90128,90129,90133],{},[1490,90130,90131],{},[1493,90132,1556],{},[1528,90134,1556],{"encoding":1530},[1047,90136,90137],{},"kapitálu",[1035,90139,90141],{"className":90140},[1480],[1482,90142,90143],{"xmlns":1484},[1487,90144,90145,90149],{},[1490,90146,90147],{},[1493,90148,1504],{},[1528,90150,1504],{"encoding":1530},[1035,90152,90154],{"className":90153},[1480],[1482,90155,90156],{"xmlns":1484,"display":1485},[1487,90157,90158,90193],{},[19617,90159,90160],{"width":19619},[19621,90161,90162,90164,90186,90188],{},[19624,90163],{"width":19626},[19624,90165,90166],{},[1490,90167,90168,90170,90172,90174,90176,90178,90180,90182,90184],{},[1493,90169,1520],{},[1506,90171,1508],{},[1493,90173,1520],{},[1506,90175,1553],{"stretchy":1552},[1493,90177,1556],{},[1506,90179,1559],{"separator":1041},[1493,90181,1504],{},[1506,90183,1564],{"stretchy":1552},[1493,90185,2632],{"mathvariant":1516},[19624,90187],{"width":19626},[19624,90189,90190],{},[1988,90191,90192],{},"(5.6)",[1528,90194,90195],{"encoding":1530},"Q = Q(L, K). \\tag{5.6}",[1030,90197,90198,90199,90201],{},"Půda je nadále standardní exogenní proměnnou. Vztah (5.6) se nazývá ",[1047,90200,87358],{}," (v širším smyslu oproti jednofaktorovému modelu).",[1065,90203,90205],{"id":90204},"cobb-douglasova-produkční-funkce","Cobb-Douglasova produkční funkce",[1030,90207,90208],{},"Široce používané produkční funkce mají tvar",[1035,90210,90212],{"className":90211},[1480],[1482,90213,90214],{"xmlns":1484,"display":1485},[1487,90215,90216,90257],{},[19617,90217,90218],{"width":19619},[19621,90219,90220,90222,90250,90252],{},[19624,90221],{"width":19626},[19624,90223,90224],{},[1490,90225,90226,90228,90230,90232,90234,90240,90242,90248],{},[1493,90227,1520],{},[1506,90229,1508],{},[1493,90231,3633],{},[1988,90233,5016],{},[2315,90235,90236,90238],{},[1493,90237,1556],{},[1493,90239,1052],{},[1988,90241,5016],{},[2315,90243,90244,90246],{},[1493,90245,1504],{},[1493,90247,2394],{},[1506,90249,1559],{"separator":1041},[19624,90251],{"width":19626},[19624,90253,90254],{},[1988,90255,90256],{},"(5.7)",[1528,90258,90259],{"encoding":1530},"Q = A\\,L^a\\,K^b, \\tag{5.7}",[1030,90261,20022,90262,90284,90285,90287,90288,2632],{},[1035,90263,90265],{"className":90264},[1480],[1482,90266,90267],{"xmlns":1484},[1487,90268,90269,90281],{},[1490,90270,90271,90273,90275,90277,90279],{},[1493,90272,3633],{},[1506,90274,1559],{"separator":1041},[1493,90276,1052],{},[1506,90278,1559],{"separator":1041},[1493,90280,2394],{},[1528,90282,90283],{"encoding":1530},"A, a, b"," jsou kladné konstanty. Nazývají se ",[1047,90286,87059],{}," (poprvé publikovány v roce 1939). V ekonomických analýzách zpravidla ",[1035,90289,90291],{"className":90290},[1480],[1482,90292,90293],{"xmlns":1484},[1487,90294,90295,90307],{},[1490,90296,90297,90299,90301,90303,90305],{},[1493,90298,1052],{},[1506,90300,1559],{"separator":1041},[1493,90302,2394],{},[1506,90304,3961],{},[1680,90306,1682],{},[1528,90308,90309],{"encoding":1530},"a, b \u003C 1",[1030,90311,90312],{},[18014,90313],{"alt":90314,"className":90315,"src":90316},"imek-vynosy-z-rozsahu-3typy",[1055,18018],"\u002Fwiki-assets\u002Fimek-vynosy-z-rozsahu-3typy.jpeg",[1030,90318,90319,90320,90323,90324,18139,90337,90353,90354,18139,90367,1274],{},"Reflektují ekonomickou zákonitost, že ",[1047,90321,90322],{},"proporcionální změny vstupů mají odezvu v proporcionální změně výstupu",". Změní-li se práce z ",[1035,90325,90327],{"className":90326},[1480],[1482,90328,90329],{"xmlns":1484},[1487,90330,90331,90335],{},[1490,90332,90333],{},[1493,90334,1556],{},[1528,90336,1556],{"encoding":1530},[1035,90338,90340],{"className":90339},[1480],[1482,90341,90342],{"xmlns":1484},[1487,90343,90344,90350],{},[1490,90345,90346,90348],{},[1493,90347,7740],{},[1493,90349,1556],{},[1528,90351,90352],{"encoding":1530},"rL"," a kapitál z ",[1035,90355,90357],{"className":90356},[1480],[1482,90358,90359],{"xmlns":1484},[1487,90360,90361,90365],{},[1490,90362,90363],{},[1493,90364,1504],{},[1528,90366,1504],{"encoding":1530},[1035,90368,90370],{"className":90369},[1480],[1482,90371,90372],{"xmlns":1484},[1487,90373,90374,90380],{},[1490,90375,90376,90378],{},[1493,90377,7740],{},[1493,90379,1504],{},[1528,90381,90382],{"encoding":1530},"rK",[1035,90384,90386],{"className":90385},[1480],[1482,90387,90388],{"xmlns":1484,"display":1485},[1487,90389,90390,90513],{},[19617,90391,90392],{"width":19619},[19621,90393,90394,90396,90506,90508],{},[19624,90395],{"width":19626},[19624,90397,90398],{},[1490,90399,90400,90402,90404,90406,90408,90410,90412,90414,90416,90418,90420,90422,90424,90426,90432,90434,90436,90438,90444,90446,90448,90450,90462,90464,90470,90476,90478,90490,90492,90494,90496,90498,90500,90502,90504],{},[1493,90401,1520],{},[1506,90403,1553],{"stretchy":1552},[1493,90405,7740],{},[1493,90407,1556],{},[1506,90409,1559],{"separator":1041},[1493,90411,7740],{},[1493,90413,1504],{},[1506,90415,1564],{"stretchy":1552},[1506,90417,1508],{},[1493,90419,3633],{},[1506,90421,1553],{"stretchy":1552},[1493,90423,7740],{},[1493,90425,1556],{},[2315,90427,90428,90430],{},[1506,90429,1564],{"stretchy":1552},[1493,90431,1052],{},[1506,90433,1553],{"stretchy":1552},[1493,90435,7740],{},[1493,90437,1504],{},[2315,90439,90440,90442],{},[1506,90441,1564],{"stretchy":1552},[1493,90443,2394],{},[1506,90445,1508],{},[1493,90447,3633],{},[1988,90449,5016],{},[2315,90451,90452,90454],{},[1493,90453,7740],{},[1490,90455,90456,90458,90460],{},[1493,90457,1052],{},[1506,90459,2162],{},[1493,90461,2394],{},[1988,90463,5016],{},[2315,90465,90466,90468],{},[1493,90467,1556],{},[1493,90469,1052],{},[2315,90471,90472,90474],{},[1493,90473,1504],{},[1493,90475,2394],{},[1506,90477,1508],{},[2315,90479,90480,90482],{},[1493,90481,7740],{},[1490,90483,90484,90486,90488],{},[1493,90485,1052],{},[1506,90487,2162],{},[1493,90489,2394],{},[1988,90491,5016],{},[1493,90493,1520],{},[1506,90495,1553],{"stretchy":1552},[1493,90497,1556],{},[1506,90499,1559],{"separator":1041},[1493,90501,1504],{},[1506,90503,1564],{"stretchy":1552},[1493,90505,2632],{"mathvariant":1516},[19624,90507],{"width":19626},[19624,90509,90510],{},[1988,90511,90512],{},"(5.8)",[1528,90514,90515],{"encoding":1530},"Q(rL, rK) = A(rL)^a(rK)^b = A\\,r^{a+b}\\,L^a K^b = r^{a+b}\\,Q(L, K). \\tag{5.8}",[1030,90517,90518,90519],{},"Volně: ",[1047,90520,90521,90522,90535,90536,90560],{},"změní-li se vstupy ",[1035,90523,90525],{"className":90524},[1480],[1482,90526,90527],{"xmlns":1484},[1487,90528,90529,90533],{},[1490,90530,90531],{},[1493,90532,7740],{},[1528,90534,7740],{"encoding":1530},"-krát, změní se výstup ",[1035,90537,90539],{"className":90538},[1480],[1482,90540,90541],{"xmlns":1484},[1487,90542,90543,90557],{},[1490,90544,90545],{},[2315,90546,90547,90549],{},[1493,90548,7740],{},[1490,90550,90551,90553,90555],{},[1493,90552,1052],{},[1506,90554,2162],{},[1493,90556,2394],{},[1528,90558,90559],{"encoding":1530},"r^{a+b}","-krát.",[1304,90562,90564],{"id":90563},"výnosy-z-rozsahu","Výnosy z rozsahu",[1030,90566,90567,90568,90585],{},"Součet exponentů ",[1035,90569,90571],{"className":90570},[1480],[1482,90572,90573],{"xmlns":1484},[1487,90574,90575,90583],{},[1490,90576,90577,90579,90581],{},[1493,90578,1052],{},[1506,90580,2162],{},[1493,90582,2394],{},[1528,90584,87183],{"encoding":1530}," určuje typ výnosů z rozsahu:",[1073,90587,90588,90617],{},[1076,90589,90590],{},[1079,90591,90592,90595,90598,90615],{},[1082,90593,90594],{},"Typ",[1082,90596,90597],{},"Podmínka",[1082,90599,90600,90601,90614],{},"Chování produkce při ",[1035,90602,90604],{"className":90603},[1480],[1482,90605,90606],{"xmlns":1484},[1487,90607,90608,90612],{},[1490,90609,90610],{},[1493,90611,7740],{},[1528,90613,7740],{"encoding":1530},"-násobném zvýšení vstupů",[1082,90616,3910],{},[1092,90618,90619,90730,90845],{},[1079,90620,90621,90629,90653,90686],{},[1097,90622,87900,90623,7606,90626,1564],{},[1047,90624,90625],{},"Konstantní",[1176,90627,90628],{},"constant returns",[1097,90630,90631],{},[1035,90632,90634],{"className":90633},[1480],[1482,90635,90636],{"xmlns":1484},[1487,90637,90638,90650],{},[1490,90639,90640,90642,90644,90646,90648],{},[1493,90641,1052],{},[1506,90643,2162],{},[1493,90645,2394],{},[1506,90647,1508],{},[1680,90649,1682],{},[1528,90651,90652],{"encoding":1530},"a+b = 1",[1097,90654,90655,90668,90669,1656,90672,90685],{},[1035,90656,90658],{"className":90657},[1480],[1482,90659,90660],{"xmlns":1484},[1487,90661,90662,90666],{},[1490,90663,90664],{},[1493,90665,1520],{},[1528,90667,1520],{"encoding":1530}," vzroste ",[1047,90670,90671],{},"přesně",[1035,90673,90675],{"className":90674},[1480],[1482,90676,90677],{"xmlns":1484},[1487,90678,90679,90683],{},[1490,90680,90681],{},[1493,90682,7740],{},[1528,90684,7740],{"encoding":1530},"-krát",[1097,90687,90688],{},[1035,90689,90691],{"className":90690},[1480],[1482,90692,90693],{"xmlns":1484},[1487,90694,90695,90727],{},[1490,90696,90697,90699,90701,90703,90715],{},[1493,90698,1520],{},[1506,90700,1508],{},[1680,90702,1691],{},[2315,90704,90705,90707],{},[1493,90706,1556],{},[1490,90708,90709,90711,90713],{},[1680,90710,1682],{},[1493,90712,1709],{"mathvariant":1516},[1680,90714,4007],{},[2315,90716,90717,90719],{},[1493,90718,1504],{},[1490,90720,90721,90723,90725],{},[1680,90722,3201],{},[1493,90724,1709],{"mathvariant":1516},[1680,90726,4007],{},[1528,90728,90729],{"encoding":1530},"Q = 2L^{1\u002F4}K^{3\u002F4}",[1079,90731,90732,90741,90765,90795],{},[1097,90733,90734,90735,7606,90738,1564],{},"2° ",[1047,90736,90737],{},"Rostoucí",[1176,90739,90740],{},"increasing returns",[1097,90742,90743],{},[1035,90744,90746],{"className":90745},[1480],[1482,90747,90748],{"xmlns":1484},[1487,90749,90750,90762],{},[1490,90751,90752,90754,90756,90758,90760],{},[1493,90753,1052],{},[1506,90755,2162],{},[1493,90757,2394],{},[1506,90759,2796],{},[1680,90761,1682],{},[1528,90763,90764],{"encoding":1530},"a+b > 1",[1097,90766,90767,90668,90780,65568,90782,90685],{},[1035,90768,90770],{"className":90769},[1480],[1482,90771,90772],{"xmlns":1484},[1487,90773,90774,90778],{},[1490,90775,90776],{},[1493,90777,1520],{},[1528,90779,1520],{"encoding":1530},[1047,90781,40840],{},[1035,90783,90785],{"className":90784},[1480],[1482,90786,90787],{"xmlns":1484},[1487,90788,90789,90793],{},[1490,90790,90791],{},[1493,90792,7740],{},[1528,90794,7740],{"encoding":1530},[1097,90796,90797,7606,90823,1564],{},[1035,90798,90800],{"className":90799},[1480],[1482,90801,90802],{"xmlns":1484},[1487,90803,90804,90820],{},[1490,90805,90806,90808,90810,90812,90814],{},[1493,90807,1520],{},[1506,90809,1508],{},[1680,90811,16580],{},[1493,90813,1556],{},[2315,90815,90816,90818],{},[1493,90817,1504],{},[1680,90819,1691],{},[1528,90821,90822],{"encoding":1530},"Q = 7LK^2",[1035,90824,90826],{"className":90825},[1480],[1482,90827,90828],{"xmlns":1484},[1487,90829,90830,90842],{},[1490,90831,90832,90834,90836,90838,90840],{},[1493,90833,1052],{},[1506,90835,2162],{},[1493,90837,2394],{},[1506,90839,1508],{},[1680,90841,3201],{},[1528,90843,90844],{"encoding":1530},"a+b = 3",[1079,90846,90847,90856,90880,90911],{},[1097,90848,90849,90850,7606,90853,1564],{},"3° ",[1047,90851,90852],{},"Klesající",[1176,90854,90855],{},"decreasing returns",[1097,90857,90858],{},[1035,90859,90861],{"className":90860},[1480],[1482,90862,90863],{"xmlns":1484},[1487,90864,90865,90877],{},[1490,90866,90867,90869,90871,90873,90875],{},[1493,90868,1052],{},[1506,90870,2162],{},[1493,90872,2394],{},[1506,90874,3961],{},[1680,90876,1682],{},[1528,90878,90879],{"encoding":1530},"a+b \u003C 1",[1097,90881,90882,90668,90895,65568,90898,90685],{},[1035,90883,90885],{"className":90884},[1480],[1482,90886,90887],{"xmlns":1484},[1487,90888,90889,90893],{},[1490,90890,90891],{},[1493,90892,1520],{},[1528,90894,1520],{"encoding":1530},[1047,90896,90897],{},"méně",[1035,90899,90901],{"className":90900},[1480],[1482,90902,90903],{"xmlns":1484},[1487,90904,90905,90909],{},[1490,90906,90907],{},[1493,90908,7740],{},[1528,90910,7740],{"encoding":1530},[1097,90912,90913,7606,90943,1564],{},[1035,90914,90916],{"className":90915},[1480],[1482,90917,90918],{"xmlns":1484},[1487,90919,90920,90940],{},[1490,90921,90922,90924,90926,90928,90934],{},[1493,90923,1520],{},[1506,90925,1508],{},[1680,90927,1775],{},[2315,90929,90930,90932],{},[1493,90931,1556],{},[1680,90933,80622],{},[2315,90935,90936,90938],{},[1493,90937,1504],{},[1680,90939,3687],{},[1528,90941,90942],{"encoding":1530},"Q = 10L^{0{,}3}K^{0{,}5}",[1035,90944,90946],{"className":90945},[1480],[1482,90947,90948],{"xmlns":1484},[1487,90949,90950,90962],{},[1490,90951,90952,90954,90956,90958,90960],{},[1493,90953,1052],{},[1506,90955,2162],{},[1493,90957,2394],{},[1506,90959,1508],{},[1680,90961,2939],{},[1528,90963,90964],{"encoding":1530},"a+b = 0{,}8",[1023,90966,90968,90974],{"className":90967,"dataCallout":1155},[1026,1154],[1030,90969,90971,52427],{"className":90970},[1033],[1035,90972],{"className":90973,"ariaHidden":1041},[1038,1162,1040],[1030,90975,90976,90977,90994,90995,90998,90999,1656,91002,91038,91039,91061,91062,2632],{},"Součet ",[1035,90978,90980],{"className":90979},[1480],[1482,90981,90982],{"xmlns":1484},[1487,90983,90984,90992],{},[1490,90985,90986,90988,90990],{},[1493,90987,1052],{},[1506,90989,2162],{},[1493,90991,2394],{},[1528,90993,87183],{"encoding":1530}," neudává velikost produkce, ale ",[1047,90996,90997],{},"elasticitu vůči škálování vstupů",". Speciálně ",[1047,91000,91001],{},"ryzí Cobb-Douglas",[1035,91003,91005],{"className":91004},[1480],[1482,91006,91007],{"xmlns":1484},[1487,91008,91009,91035],{},[1490,91010,91011,91013,91015,91017,91023],{},[1493,91012,1520],{},[1506,91014,1508],{},[1493,91016,3633],{},[2315,91018,91019,91021],{},[1493,91020,1556],{},[1493,91022,1052],{},[2315,91024,91025,91027],{},[1493,91026,1504],{},[1490,91028,91029,91031,91033],{},[1680,91030,1682],{},[1506,91032,1888],{},[1493,91034,1052],{},[1528,91036,91037],{"encoding":1530},"Q = AL^a K^{1-a}"," má ",[1035,91040,91042],{"className":91041},[1480],[1482,91043,91044],{"xmlns":1484},[1487,91045,91046,91058],{},[1490,91047,91048,91050,91052,91054,91056],{},[1493,91049,2394],{},[1506,91051,1508],{},[1680,91053,1682],{},[1506,91055,1888],{},[1493,91057,1052],{},[1528,91059,91060],{"encoding":1530},"b = 1-a",", tedy vždy ",[1047,91063,91064],{},"konstantní výnosy z rozsahu",[1304,91066,91068,91069],{"id":91067},"parametr-efektivity-aa","Parametr efektivity ",[1035,91070,91072],{"className":91071},[1480],[1482,91073,91074],{"xmlns":1484},[1487,91075,91076,91080],{},[1490,91077,91078],{},[1493,91079,3633],{},[1528,91081,3633],{"encoding":1530},[1030,91083,91084,91085,91098,91099,91112,91113,91130,91131,91134],{},"Konstanta ",[1035,91086,91088],{"className":91087},[1480],[1482,91089,91090],{"xmlns":1484},[1487,91091,91092,91096],{},[1490,91093,91094],{},[1493,91095,3633],{},[1528,91097,3633],{"encoding":1530}," v (5.7) proporcionálně ovlivňuje úroveň produkce ",[1035,91100,91102],{"className":91101},[1480],[1482,91103,91104],{"xmlns":1484},[1487,91105,91106,91110],{},[1490,91107,91108],{},[1493,91109,1520],{},[1528,91111,1520],{"encoding":1530}," při pevně zadaných ",[1035,91114,91116],{"className":91115},[1480],[1482,91117,91118],{"xmlns":1484},[1487,91119,91120,91128],{},[1490,91121,91122,91124,91126],{},[1493,91123,1556],{},[1506,91125,1559],{"separator":1041},[1493,91127,1504],{},[1528,91129,6501],{"encoding":1530},", a lze ji proto chápat jako ",[1047,91132,91133],{},"parametr efektivity"," — indikátor stavu technologie.",[1304,91136,91138],{"id":91137},"příklad-53","Příklad 5.3",[1030,91140,91141,91142,91038,91184,91186,91187,2632],{},"Produkční funkce ",[1035,91143,91145],{"className":91144},[1480],[1482,91146,91147],{"xmlns":1484},[1487,91148,91149,91181],{},[1490,91150,91151,91153,91155,91157,91169],{},[1493,91152,1520],{},[1506,91154,1508],{},[1680,91156,1691],{},[2315,91158,91159,91161],{},[1493,91160,1556],{},[1490,91162,91163,91165,91167],{},[1680,91164,1682],{},[1493,91166,1709],{"mathvariant":1516},[1680,91168,4007],{},[2315,91170,91171,91173],{},[1493,91172,1504],{},[1490,91174,91175,91177,91179],{},[1680,91176,3201],{},[1493,91178,1709],{"mathvariant":1516},[1680,91180,4007],{},[1528,91182,91183],{"encoding":1530},"Q = 2L^{1\u002F4} K^{3\u002F4}",[1047,91185,40186],{}," výnosy z rozsahu, neboť ",[1035,91188,91190],{"className":91189},[1480],[1482,91191,91192],{"xmlns":1484},[1487,91193,91194,91218],{},[1490,91195,91196,91204,91206,91214,91216],{},[1869,91197,91198],{"scriptlevel":1871,"displaystyle":1552},[1510,91199,91200,91202],{},[1680,91201,1682],{},[1680,91203,4007],{},[1506,91205,2162],{},[1869,91207,91208],{"scriptlevel":1871,"displaystyle":1552},[1510,91209,91210,91212],{},[1680,91211,3201],{},[1680,91213,4007],{},[1506,91215,1508],{},[1680,91217,1682],{},[1528,91219,91220],{"encoding":1530},"\\tfrac{1}{4} + \\tfrac{3}{4} = 1",[1030,91222,91223,91224,22060,91237,91250,91251,1656,91264,91304],{},"Změní-li se ",[1035,91225,91227],{"className":91226},[1480],[1482,91228,91229],{"xmlns":1484},[1487,91230,91231,91235],{},[1490,91232,91233],{},[1493,91234,1556],{},[1528,91236,1556],{"encoding":1530},[1035,91238,91240],{"className":91239},[1480],[1482,91241,91242],{"xmlns":1484},[1487,91243,91244,91248],{},[1490,91245,91246],{},[1493,91247,1504],{},[1528,91249,1504],{"encoding":1530}," čtyřnásobně, změní se ",[1035,91252,91254],{"className":91253},[1480],[1482,91255,91256],{"xmlns":1484},[1487,91257,91258,91262],{},[1490,91259,91260],{},[1493,91261,1520],{},[1528,91263,1520],{"encoding":1530},[1035,91265,91267],{"className":91266},[1480],[1482,91268,91269],{"xmlns":1484},[1487,91270,91271,91301],{},[1490,91272,91273,91293,91295],{},[2315,91274,91275,91277],{},[1680,91276,4007],{},[1490,91278,91279,91281,91283,91285,91287,91289,91291],{},[1680,91280,1682],{},[1493,91282,1709],{"mathvariant":1516},[1680,91284,4007],{},[1506,91286,2162],{},[1680,91288,3201],{},[1493,91290,1709],{"mathvariant":1516},[1680,91292,4007],{},[1506,91294,1508],{},[2315,91296,91297,91299],{},[1680,91298,4007],{},[1680,91300,1682],{},[1528,91302,91303],{"encoding":1530},"4^{1\u002F4 + 3\u002F4} = 4^1","-krát:",[1035,91306,91308],{"className":91307},[1480],[1482,91309,91310],{"xmlns":1484,"display":1485},[1487,91311,91312,91472],{},[1490,91313,91314,91316,91318,91320,91322,91324,91326,91328,91330,91332,91334,91336,91338,91340,91352,91354,91356,91358,91370,91372,91374,91376,91396,91408,91420,91422,91424,91426,91428,91440,91452,91454,91456,91458,91460,91462,91464,91466,91468,91470],{},[1493,91315,1520],{},[1506,91317,1553],{"stretchy":1552},[1680,91319,4007],{},[1493,91321,1556],{},[1506,91323,1559],{"separator":1041},[1680,91325,4007],{},[1493,91327,1504],{},[1506,91329,1564],{"stretchy":1552},[1506,91331,1508],{},[1680,91333,1691],{},[1506,91335,1553],{"stretchy":1552},[1680,91337,4007],{},[1493,91339,1556],{},[2315,91341,91342,91344],{},[1506,91343,1564],{"stretchy":1552},[1490,91345,91346,91348,91350],{},[1680,91347,1682],{},[1493,91349,1709],{"mathvariant":1516},[1680,91351,4007],{},[1506,91353,1553],{"stretchy":1552},[1680,91355,4007],{},[1493,91357,1504],{},[2315,91359,91360,91362],{},[1506,91361,1564],{"stretchy":1552},[1490,91363,91364,91366,91368],{},[1680,91365,3201],{},[1493,91367,1709],{"mathvariant":1516},[1680,91369,4007],{},[1506,91371,1508],{},[1680,91373,1691],{},[1506,91375,1714],{},[2315,91377,91378,91380],{},[1680,91379,4007],{},[1490,91381,91382,91384,91386,91388,91390,91392,91394],{},[1680,91383,1682],{},[1493,91385,1709],{"mathvariant":1516},[1680,91387,4007],{},[1506,91389,2162],{},[1680,91391,3201],{},[1493,91393,1709],{"mathvariant":1516},[1680,91395,4007],{},[2315,91397,91398,91400],{},[1493,91399,1556],{},[1490,91401,91402,91404,91406],{},[1680,91403,1682],{},[1493,91405,1709],{"mathvariant":1516},[1680,91407,4007],{},[2315,91409,91410,91412],{},[1493,91411,1504],{},[1490,91413,91414,91416,91418],{},[1680,91415,3201],{},[1493,91417,1709],{"mathvariant":1516},[1680,91419,4007],{},[1506,91421,1508],{},[1680,91423,4007],{},[1506,91425,1714],{},[1680,91427,1691],{},[2315,91429,91430,91432],{},[1493,91431,1556],{},[1490,91433,91434,91436,91438],{},[1680,91435,1682],{},[1493,91437,1709],{"mathvariant":1516},[1680,91439,4007],{},[2315,91441,91442,91444],{},[1493,91443,1504],{},[1490,91445,91446,91448,91450],{},[1680,91447,3201],{},[1493,91449,1709],{"mathvariant":1516},[1680,91451,4007],{},[1506,91453,1508],{},[1680,91455,4007],{},[1988,91457,5016],{},[1493,91459,1520],{},[1506,91461,1553],{"stretchy":1552},[1493,91463,1556],{},[1506,91465,1559],{"separator":1041},[1493,91467,1504],{},[1506,91469,1564],{"stretchy":1552},[1493,91471,2632],{"mathvariant":1516},[1528,91473,91474],{"encoding":1530},"Q(4L, 4K) = 2(4L)^{1\u002F4}(4K)^{3\u002F4} = 2\\cdot 4^{1\u002F4+3\u002F4} L^{1\u002F4} K^{3\u002F4} = 4\\cdot 2L^{1\u002F4}K^{3\u002F4} = 4\\,Q(L,K).",[1304,91476,91477],{"id":52277},"Homogenita",[1030,91479,91480,91481,8994,91504,91520],{},"Funkce ",[1035,91482,91484],{"className":91483},[1480],[1482,91485,91486],{"xmlns":1484},[1487,91487,91488,91502],{},[1490,91489,91490,91492,91494,91496,91498,91500],{},[1493,91491,1520],{},[1506,91493,1553],{"stretchy":1552},[1493,91495,1556],{},[1506,91497,1559],{"separator":1041},[1493,91499,1504],{},[1506,91501,1564],{"stretchy":1552},[1528,91503,26524],{"encoding":1530},[1047,91505,91506,91507],{},"homogenní stupně ",[1035,91508,91510],{"className":91509},[1480],[1482,91511,91512],{"xmlns":1484},[1487,91513,91514,91518],{},[1490,91515,91516],{},[1493,91517,7781],{},[1528,91519,7781],{"encoding":1530},", jestliže",[1035,91522,91524],{"className":91523},[1480],[1482,91525,91526],{"xmlns":1484,"display":1485},[1487,91527,91528,91585],{},[19617,91529,91530],{"width":19619},[19621,91531,91532,91534,91578,91580],{},[19624,91533],{"width":19626},[19624,91535,91536],{},[1490,91537,91538,91540,91542,91544,91546,91548,91550,91552,91554,91556,91562,91564,91566,91568,91570,91572,91574,91576],{},[1493,91539,1520],{},[1506,91541,1553],{"stretchy":1552},[1493,91543,7740],{},[1493,91545,1556],{},[1506,91547,1559],{"separator":1041},[1493,91549,7740],{},[1493,91551,1504],{},[1506,91553,1564],{"stretchy":1552},[1506,91555,1508],{},[2315,91557,91558,91560],{},[1493,91559,7740],{},[1493,91561,7781],{},[1988,91563,5016],{},[1493,91565,1520],{},[1506,91567,1553],{"stretchy":1552},[1493,91569,1556],{},[1506,91571,1559],{"separator":1041},[1493,91573,1504],{},[1506,91575,1564],{"stretchy":1552},[1506,91577,1559],{"separator":1041},[19624,91579],{"width":19626},[19624,91581,91582],{},[1988,91583,91584],{},"(5.10)",[1528,91586,91587],{"encoding":1530},"Q(rL, rK) = r^n\\,Q(L, K), \\tag{5.10}",[1030,91589,20022,91590,91608,91609,91627,91628,58116,91641,91644,91645,2632],{},[1035,91591,91593],{"className":91592},[1480],[1482,91594,91595],{"xmlns":1484},[1487,91596,91597,91605],{},[1490,91598,91599,91601,91603],{},[1493,91600,7781],{},[1506,91602,20200],{},[1680,91604,1871],{},[1528,91606,91607],{"encoding":1530},"n \\geq 0"," je celé číslo a ",[1035,91610,91612],{"className":91611},[1480],[1482,91613,91614],{"xmlns":1484},[1487,91615,91616,91624],{},[1490,91617,91618,91620,91622],{},[1493,91619,7740],{},[1506,91621,2796],{},[1680,91623,1871],{},[1528,91625,91626],{"encoding":1530},"r > 0",". Homogenní funkce stupně ",[1035,91629,91631],{"className":91630},[1480],[1482,91632,91633],{"xmlns":1484},[1487,91634,91635,91639],{},[1490,91636,91637],{},[1680,91638,1682],{},[1528,91640,1682],{"encoding":1530},[1047,91642,91643],{},"lineárně homogenní",". Cobb-Douglasovy funkce jsou homogenní stupně ",[1035,91646,91648],{"className":91647},[1480],[1482,91649,91650],{"xmlns":1484},[1487,91651,91652,91660],{},[1490,91653,91654,91656,91658],{},[1493,91655,1052],{},[1506,91657,2162],{},[1493,91659,2394],{},[1528,91661,87183],{"encoding":1530},[1065,91663,91665],{"id":91664},"ryzí-cobb-douglas-a-ces","Ryzí Cobb-Douglas a CES",[1030,91667,91668],{},[1047,91669,91670],{},"Ryzí Cobb-Douglasovy funkce:",[1035,91672,91674],{"className":91673},[1480],[1482,91675,91676],{"xmlns":1484,"display":1485},[1487,91677,91678,91737],{},[19617,91679,91680],{"width":19619},[19621,91681,91682,91684,91730,91732],{},[19624,91683],{"width":19626},[19624,91685,91686],{},[1490,91687,91688,91690,91692,91694,91696,91702,91704,91716,91718,91720,91722,91724,91726,91728],{},[1493,91689,1520],{},[1506,91691,1508],{},[1493,91693,3633],{},[1988,91695,5016],{},[2315,91697,91698,91700],{},[1493,91699,1556],{},[1493,91701,1052],{},[1988,91703,5016],{},[2315,91705,91706,91708],{},[1493,91707,1504],{},[1490,91709,91710,91712,91714],{},[1680,91711,1682],{},[1506,91713,1888],{},[1493,91715,1052],{},[1506,91717,1559],{"separator":1041},[1912,91719],{"width":2108},[1680,91721,1871],{},[1506,91723,3961],{},[1493,91725,1052],{},[1506,91727,3961],{},[1680,91729,29734],{},[19624,91731],{"width":19626},[19624,91733,91734],{},[1988,91735,91736],{},"(5.9)",[1528,91738,91739],{"encoding":1530},"Q = A\\,L^a\\,K^{1-a}, \\quad 0 \u003C a \u003C 1. \\tag{5.9}",[1030,91741,91742,91743,91745,91746,2632],{},"Mají vždy ",[1047,91744,91064],{}," a jsou ",[1047,91747,91643],{},[1030,91749,91750,7606,91753,91756],{},[1047,91751,91752],{},"CES produkční funkce",[1176,91754,91755],{},"Constant Elasticity of Substitution",", 1961):",[1035,91758,91760],{"className":91759},[1480],[1482,91761,91762],{"xmlns":1484,"display":1485},[1487,91763,91764,91832],{},[1490,91765,91766,91768,91770,91772,91830],{},[1493,91767,1520],{},[1506,91769,1508],{},[1493,91771,3633],{},[2315,91773,91774,91818],{},[1490,91775,91776,91778,91780,91782,91784,91786,91788,91790,91800,91802,91804,91806,91816],{},[1506,91777,14314],{"fence":1041},[1506,91779,1553],{"stretchy":1552},[1680,91781,1682],{},[1506,91783,1888],{},[1493,91785,1052],{},[1506,91787,1564],{"stretchy":1552},[1988,91789,5016],{},[2315,91791,91792,91794],{},[1493,91793,1556],{},[1490,91795,91796,91798],{},[1506,91797,1888],{},[1493,91799,2394],{},[1506,91801,2162],{},[1493,91803,1052],{},[1988,91805,5016],{},[2315,91807,91808,91810],{},[1493,91809,1504],{},[1490,91811,91812,91814],{},[1506,91813,1888],{},[1493,91815,2394],{},[1506,91817,14323],{"fence":1041},[1490,91819,91820,91822],{},[1506,91821,1888],{},[1869,91823,91824],{"scriptlevel":1871,"displaystyle":1552},[1510,91825,91826,91828],{},[1680,91827,1682],{},[1493,91829,2394],{},[1506,91831,1559],{"separator":1041},[1528,91833,91834],{"encoding":1530},"Q = A\\left[(1-a)\\,L^{-b} + a\\,K^{-b}\\right]^{-\\tfrac{1}{b}},",[1030,91836,20022,91837,1732,91855,1732,91876,91900],{},[1035,91838,91840],{"className":91839},[1480],[1482,91841,91842],{"xmlns":1484},[1487,91843,91844,91852],{},[1490,91845,91846,91848,91850],{},[1493,91847,3633],{},[1506,91849,2796],{},[1680,91851,1871],{},[1528,91853,91854],{"encoding":1530},"A > 0",[1035,91856,91858],{"className":91857},[1480],[1482,91859,91860],{"xmlns":1484},[1487,91861,91862,91874],{},[1490,91863,91864,91866,91868,91870,91872],{},[1680,91865,1871],{},[1506,91867,3961],{},[1493,91869,1052],{},[1506,91871,3961],{},[1680,91873,1682],{},[1528,91875,34972],{"encoding":1530},[1035,91877,91879],{"className":91878},[1480],[1482,91880,91881],{"xmlns":1484},[1487,91882,91883,91897],{},[1490,91884,91885,91887,91889,91891,91893,91895],{},[1506,91886,1888],{},[1680,91888,1682],{},[1506,91890,3961],{},[1493,91892,2394],{},[1506,91894,18796],{"mathvariant":1516},[1680,91896,1871],{},[1528,91898,91899],{"encoding":1530},"-1 \u003C b \\neq 0",". Cobb-Douglasovy funkce jsou jejich zvláštním případem.",[1030,91902,91903],{},[1047,91904,91905],{},"Další typy:",[1203,91907,91908,91950],{},[1206,91909,91910,1656,91913,91949],{},[1047,91911,91912],{},"Lineární:",[1035,91914,91916],{"className":91915},[1480],[1482,91917,91918],{"xmlns":1484},[1487,91919,91920,91946],{},[1490,91921,91922,91924,91926,91928,91930,91932,91934,91936,91938,91940,91942,91944],{},[1493,91923,1520],{},[1506,91925,1553],{"stretchy":1552},[1493,91927,1556],{},[1506,91929,1559],{"separator":1041},[1493,91931,1504],{},[1506,91933,1564],{"stretchy":1552},[1506,91935,1508],{},[1493,91937,1052],{},[1493,91939,1556],{},[1506,91941,2162],{},[1493,91943,2394],{},[1493,91945,1504],{},[1528,91947,91948],{"encoding":1530},"Q(L, K) = aL + bK"," — dokonalé substituty.",[1206,91951,91952,1656,91955,92000],{},[1047,91953,91954],{},"Leontiefova:",[1035,91956,91958],{"className":91957},[1480],[1482,91959,91960],{"xmlns":1484},[1487,91961,91962,91997],{},[1490,91963,91964,91966,91968,91970,91972,91974,91976,91978,91981,91983,91985,91987,91989,91991,91993,91995],{},[1493,91965,1520],{},[1506,91967,1553],{"stretchy":1552},[1493,91969,1556],{},[1506,91971,1559],{"separator":1041},[1493,91973,1504],{},[1506,91975,1564],{"stretchy":1552},[1506,91977,1508],{},[1493,91979,91980],{},"min",[1506,91982,7574],{},[1506,91984,1553],{"stretchy":1552},[1493,91986,1052],{},[1493,91988,1556],{},[1506,91990,1559],{"separator":1041},[1493,91992,2394],{},[1493,91994,1504],{},[1506,91996,1564],{"stretchy":1552},[1528,91998,91999],{"encoding":1530},"Q(L, K) = \\min(aL, bK)"," — dokonalé komplementy (fixní proporce).",[1065,92002,92004,92005,1732,92024,92043],{"id":92003},"mezní-produkty-mplmp_l-mpkmp_k-a-totální-diferenciál","Mezní produkty ",[1035,92006,92008],{"className":92007},[1480],[1482,92009,92010],{"xmlns":1484},[1487,92011,92012,92022],{},[1490,92013,92014,92016],{},[1493,92015,1495],{},[1497,92017,92018,92020],{},[1493,92019,1501],{},[1493,92021,1556],{},[1528,92023,26571],{"encoding":1530},[1035,92025,92027],{"className":92026},[1480],[1482,92028,92029],{"xmlns":1484},[1487,92030,92031,92041],{},[1490,92032,92033,92035],{},[1493,92034,1495],{},[1497,92036,92037,92039],{},[1493,92038,1501],{},[1493,92040,1504],{},[1528,92042,26616],{"encoding":1530}," a totální diferenciál",[1030,92045,92046],{},[1047,92047,92048],{},"Mezní produkt práce:",[1035,92050,92052],{"className":92051},[1480],[1482,92053,92054],{"xmlns":1484,"display":1485},[1487,92055,92056,92094],{},[1490,92057,92058,92060,92066,92068,92076,92078,92092],{},[1493,92059,1495],{},[1497,92061,92062,92064],{},[1493,92063,1501],{},[1493,92065,1556],{},[1506,92067,1508],{},[1697,92069,92070,92072,92074],{},[1493,92071,1520],{},[1493,92073,1556],{},[1506,92075,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,92077,1508],{},[1510,92079,92080,92086],{},[1490,92081,92082,92084],{},[1493,92083,1517],{"mathvariant":1516},[1493,92085,1520],{},[1490,92087,92088,92090],{},[1493,92089,1517],{"mathvariant":1516},[1493,92091,1556],{},[1493,92093,2632],{"mathvariant":1516},[1528,92095,92096],{"encoding":1530},"MP_L = Q'_L = \\frac{\\partial Q}{\\partial L}.",[1030,92098,92099],{},[1047,92100,92101],{},"Mezní produkt kapitálu:",[1035,92103,92105],{"className":92104},[1480],[1482,92106,92107],{"xmlns":1484,"display":1485},[1487,92108,92109,92147],{},[1490,92110,92111,92113,92119,92121,92129,92131,92145],{},[1493,92112,1495],{},[1497,92114,92115,92117],{},[1493,92116,1501],{},[1493,92118,1504],{},[1506,92120,1508],{},[1697,92122,92123,92125,92127],{},[1493,92124,1520],{},[1493,92126,1504],{},[1506,92128,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,92130,1508],{},[1510,92132,92133,92139],{},[1490,92134,92135,92137],{},[1493,92136,1517],{"mathvariant":1516},[1493,92138,1520],{},[1490,92140,92141,92143],{},[1493,92142,1517],{"mathvariant":1516},[1493,92144,1504],{},[1493,92146,2632],{"mathvariant":1516},[1528,92148,92149],{"encoding":1530},"MP_K = Q'_K = \\frac{\\partial Q}{\\partial K}.",[1030,92151,92152,92182,92183,92204,92205,92223,92224,92237,92238,2632],{},[1035,92153,92155],{"className":92154},[1480],[1482,92156,92157],{"xmlns":1484},[1487,92158,92159,92179],{},[1490,92160,92161,92163,92169,92171,92173,92175,92177],{},[1493,92162,1495],{},[1497,92164,92165,92167],{},[1493,92166,1501],{},[1493,92168,1556],{},[1506,92170,1553],{"stretchy":1552},[1493,92172,1052],{},[1506,92174,1559],{"separator":1041},[1493,92176,2394],{},[1506,92178,1564],{"stretchy":1552},[1528,92180,92181],{"encoding":1530},"MP_L(a, b)"," udává rychlost změny produkce vzhledem k práci v bodě ",[1035,92184,92186],{"className":92185},[1480],[1482,92187,92188],{"xmlns":1484},[1487,92189,92190,92202],{},[1490,92191,92192,92194,92196,92198,92200],{},[1506,92193,14314],{"stretchy":1552},[1493,92195,1052],{},[1506,92197,1559],{"separator":1041},[1493,92199,2394],{},[1506,92201,14323],{"stretchy":1552},[1528,92203,27339],{"encoding":1530}," (na hladině ",[1035,92206,92208],{"className":92207},[1480],[1482,92209,92210],{"xmlns":1484},[1487,92211,92212,92220],{},[1490,92213,92214,92216,92218],{},[1493,92215,1504],{},[1506,92217,1508],{},[1493,92219,2394],{},[1528,92221,92222],{"encoding":1530},"K = b","), resp. přibližnou změnu produkce při jednotkové změně ",[1035,92225,92227],{"className":92226},[1480],[1482,92228,92229],{"xmlns":1484},[1487,92230,92231,92235],{},[1490,92232,92233],{},[1493,92234,1556],{},[1528,92236,1556],{"encoding":1530},". Analogicky ",[1035,92239,92241],{"className":92240},[1480],[1482,92242,92243],{"xmlns":1484},[1487,92244,92245,92265],{},[1490,92246,92247,92249,92255,92257,92259,92261,92263],{},[1493,92248,1495],{},[1497,92250,92251,92253],{},[1493,92252,1501],{},[1493,92254,1504],{},[1506,92256,1553],{"stretchy":1552},[1493,92258,1052],{},[1506,92260,1559],{"separator":1041},[1493,92262,2394],{},[1506,92264,1564],{"stretchy":1552},[1528,92266,92267],{"encoding":1530},"MP_K(a, b)",[1023,92269,92271,92277],{"className":92270,"dataCallout":582},[1026,1186],[1030,92272,92274,6749],{"className":92273},[1033],[1035,92275],{"className":92276,"ariaHidden":1041},[1038,1193,1040],[1203,92278,92279,92317],{},[1206,92280,92281,11074,92300],{},[1035,92282,92284],{"className":92283},[1480],[1482,92285,92286],{"xmlns":1484},[1487,92287,92288,92298],{},[1490,92289,92290,92292],{},[1493,92291,1495],{},[1497,92293,92294,92296],{},[1493,92295,1501],{},[1493,92297,1556],{},[1528,92299,26571],{"encoding":1530},[1176,92301,92302,92303,92316],{},"„o kolik vzroste ",[1035,92304,92306],{"className":92305},[1480],[1482,92307,92308],{"xmlns":1484},[1487,92309,92310,92314],{},[1490,92311,92312],{},[1493,92313,1520],{},[1528,92315,1520],{"encoding":1530},", když přidám jednu jednotku práce (a kapitál držím pevně)?\"",[1206,92318,92319,11074,92338],{},[1035,92320,92322],{"className":92321},[1480],[1482,92323,92324],{"xmlns":1484},[1487,92325,92326,92336],{},[1490,92327,92328,92330],{},[1493,92329,1495],{},[1497,92331,92332,92334],{},[1493,92333,1501],{},[1493,92335,1504],{},[1528,92337,26616],{"encoding":1530},[1176,92339,92302,92340,92353],{},[1035,92341,92343],{"className":92342},[1480],[1482,92344,92345],{"xmlns":1484},[1487,92346,92347,92351],{},[1490,92348,92349],{},[1493,92350,1520],{},[1528,92352,1520],{"encoding":1530},", když přidám jednu jednotku kapitálu (a práci držím pevně)?\"",[1030,92355,92356,92359,92360,92375,92376,1274],{},[1047,92357,92358],{},"Totální diferenciál"," — přibližná změna produkce při změně práce o ",[1035,92361,92363],{"className":92362},[1480],[1482,92364,92365],{"xmlns":1484},[1487,92366,92367,92373],{},[1490,92368,92369,92371],{},[1493,92370,3384],{},[1493,92372,1556],{},[1528,92374,87719],{"encoding":1530}," a kapitálu o ",[1035,92377,92379],{"className":92378},[1480],[1482,92380,92381],{"xmlns":1484},[1487,92382,92383,92389],{},[1490,92384,92385,92387],{},[1493,92386,3384],{},[1493,92388,1504],{},[1528,92390,92391],{"encoding":1530},"dK",[1035,92393,92395],{"className":92394},[1480],[1482,92396,92397],{"xmlns":1484,"display":1485},[1487,92398,92399,92492],{},[19617,92400,92401],{"width":19619},[19621,92402,92403,92405,92485,92487],{},[19624,92404],{"width":19626},[19624,92406,92407],{},[1490,92408,92409,92411,92413,92415,92417,92419,92421,92429,92431,92433,92435,92437,92445,92447,92449,92451,92453,92455,92461,92463,92465,92467,92469,92471,92477,92479,92481,92483],{},[1493,92410,2976],{"mathvariant":1516},[1493,92412,1520],{},[1506,92414,2343],{},[1493,92416,3384],{},[1493,92418,1520],{},[1506,92420,1508],{},[1697,92422,92423,92425,92427],{},[1493,92424,1520],{},[1493,92426,1556],{},[1506,92428,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1988,92430,5016],{},[1493,92432,3384],{},[1493,92434,1556],{},[1506,92436,2162],{},[1697,92438,92439,92441,92443],{},[1493,92440,1520],{},[1493,92442,1504],{},[1506,92444,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1988,92446,5016],{},[1493,92448,3384],{},[1493,92450,1504],{},[1506,92452,1508],{},[1493,92454,1495],{},[1497,92456,92457,92459],{},[1493,92458,1501],{},[1493,92460,1556],{},[1988,92462,5016],{},[1493,92464,3384],{},[1493,92466,1556],{},[1506,92468,2162],{},[1493,92470,1495],{},[1497,92472,92473,92475],{},[1493,92474,1501],{},[1493,92476,1504],{},[1988,92478,5016],{},[1493,92480,3384],{},[1493,92482,1504],{},[1493,92484,2632],{"mathvariant":1516},[19624,92486],{"width":19626},[19624,92488,92489],{},[1988,92490,92491],{},"(5.11)",[1528,92493,92494],{"encoding":1530},"\\Delta Q \\approx dQ = Q'_L\\,dL + Q'_K\\,dK = MP_L\\,dL + MP_K\\,dK. \\tag{5.11}",[1030,92496,92497,92498,2632],{},"Skutečná změna: ",[1035,92499,92501],{"className":92500},[1480],[1482,92502,92503],{"xmlns":1484},[1487,92504,92505,92551],{},[1490,92506,92507,92509,92511,92513,92515,92517,92519,92521,92523,92525,92527,92529,92531,92533,92535,92537,92539,92541,92543,92545,92547,92549],{},[1493,92508,2976],{"mathvariant":1516},[1493,92510,1520],{},[1506,92512,1508],{},[1493,92514,1520],{},[1506,92516,1553],{"stretchy":1552},[1493,92518,1556],{},[1506,92520,2162],{},[1493,92522,3384],{},[1493,92524,1556],{},[1506,92526,1559],{"separator":1041},[1493,92528,1504],{},[1506,92530,2162],{},[1493,92532,3384],{},[1493,92534,1504],{},[1506,92536,1564],{"stretchy":1552},[1506,92538,1888],{},[1493,92540,1520],{},[1506,92542,1553],{"stretchy":1552},[1493,92544,1556],{},[1506,92546,1559],{"separator":1041},[1493,92548,1504],{},[1506,92550,1564],{"stretchy":1552},[1528,92552,92553],{"encoding":1530},"\\Delta Q = Q(L+dL, K+dK) - Q(L, K)",[1030,92555,92556,92558,92559,92577,92578,92591,92592,92611,92612,92644,92645,92677,92678,2632],{},[1047,92557,87883],{}," platí ve 2F modelu pro oba vstupy: pro pevné ",[1035,92560,92562],{"className":92561},[1480],[1482,92563,92564],{"xmlns":1484},[1487,92565,92566,92574],{},[1490,92567,92568],{},[1497,92569,92570,92572],{},[1493,92571,1504],{},[1680,92573,1871],{},[1528,92575,92576],{"encoding":1530},"K_0"," se od jistého ",[1035,92579,92581],{"className":92580},[1480],[1482,92582,92583],{"xmlns":1484},[1487,92584,92585,92589],{},[1490,92586,92587],{},[1493,92588,1556],{},[1528,92590,1556],{"encoding":1530}," stane ",[1035,92593,92595],{"className":92594},[1480],[1482,92596,92597],{"xmlns":1484},[1487,92598,92599,92609],{},[1490,92600,92601,92603],{},[1493,92602,1495],{},[1497,92604,92605,92607],{},[1493,92606,1501],{},[1493,92608,1556],{},[1528,92610,26571],{"encoding":1530}," klesající (",[1035,92613,92615],{"className":92614},[1480],[1482,92616,92617],{"xmlns":1484},[1487,92618,92619,92641],{},[1490,92620,92621,92637,92639],{},[1697,92622,92623,92625,92631],{},[1493,92624,1520],{},[1490,92626,92627,92629],{},[1493,92628,1556],{},[1493,92630,1556],{},[1490,92632,92633,92635],{},[1506,92634,6927],{"mathvariant":1516},[1506,92636,6927],{"mathvariant":1516},[1506,92638,3961],{},[1680,92640,1871],{},[1528,92642,92643],{"encoding":1530},"Q''_{LL} \u003C 0","); analogicky ",[1035,92646,92648],{"className":92647},[1480],[1482,92649,92650],{"xmlns":1484},[1487,92651,92652,92674],{},[1490,92653,92654,92670,92672],{},[1697,92655,92656,92658,92664],{},[1493,92657,1520],{},[1490,92659,92660,92662],{},[1493,92661,1504],{},[1493,92663,1504],{},[1490,92665,92666,92668],{},[1506,92667,6927],{"mathvariant":1516},[1506,92669,6927],{"mathvariant":1516},[1506,92671,3961],{},[1680,92673,1871],{},[1528,92675,92676],{"encoding":1530},"Q''_{KK} \u003C 0"," pro pevné ",[1035,92679,92681],{"className":92680},[1480],[1482,92682,92683],{"xmlns":1484},[1487,92684,92685,92693],{},[1490,92686,92687],{},[1497,92688,92689,92691],{},[1493,92690,1556],{},[1680,92692,1871],{},[1528,92694,87921],{"encoding":1530},[1065,92696,92698],{"id":92697},"eulerova-věta-pro-homogenní-funkce","Eulerova věta pro homogenní funkce",[1030,92700,92701,92704,92705,92728,92729,45271],{},[1047,92702,92703],{},"Eulerova věta"," (úloha 5.10): pro homogenní funkci ",[1035,92706,92708],{"className":92707},[1480],[1482,92709,92710],{"xmlns":1484},[1487,92711,92712,92726],{},[1490,92713,92714,92716,92718,92720,92722,92724],{},[1493,92715,1520],{},[1506,92717,1553],{"stretchy":1552},[1493,92719,1556],{},[1506,92721,1559],{"separator":1041},[1493,92723,1504],{},[1506,92725,1564],{"stretchy":1552},[1528,92727,26524],{"encoding":1530}," stupně ",[1035,92730,92732],{"className":92731},[1480],[1482,92733,92734],{"xmlns":1484},[1487,92735,92736,92740],{},[1490,92737,92738],{},[1493,92739,7781],{},[1528,92741,7781],{"encoding":1530},[1035,92743,92745],{"className":92744},[1480],[1482,92746,92747],{"xmlns":1484,"display":1485},[1487,92748,92749,92812],{},[19617,92750,92751],{"width":19619},[19621,92752,92753,92755,92805,92807],{},[19624,92754],{"width":19626},[19624,92756,92757],{},[1490,92758,92759,92761,92763,92771,92773,92775,92777,92785,92787,92789,92791,92793,92795,92797,92799,92801,92803],{},[1493,92760,1556],{},[1988,92762,5016],{},[1697,92764,92765,92767,92769],{},[1493,92766,1520],{},[1493,92768,1556],{},[1506,92770,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,92772,2162],{},[1493,92774,1504],{},[1988,92776,5016],{},[1697,92778,92779,92781,92783],{},[1493,92780,1520],{},[1493,92782,1504],{},[1506,92784,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,92786,1508],{},[1493,92788,7781],{},[1988,92790,5016],{},[1493,92792,1520],{},[1506,92794,1553],{"stretchy":1552},[1493,92796,1556],{},[1506,92798,1559],{"separator":1041},[1493,92800,1504],{},[1506,92802,1564],{"stretchy":1552},[1493,92804,2632],{"mathvariant":1516},[19624,92806],{"width":19626},[19624,92808,92809],{},[1988,92810,92811],{},"(5.12)",[1528,92813,92814],{"encoding":1530},"L\\,Q'_L + K\\,Q'_K = n\\,Q(L, K). \\tag{5.12}",[1030,92816,92817,92838],{},[1047,92818,92819,92820],{},"Speciální případ ",[1035,92821,92823],{"className":92822},[1480],[1482,92824,92825],{"xmlns":1484},[1487,92826,92827,92835],{},[1490,92828,92829,92831,92833],{},[1493,92830,7781],{},[1506,92832,1508],{},[1680,92834,1682],{},[1528,92836,92837],{"encoding":1530},"n = 1"," (konstantní výnosy z rozsahu):",[1035,92840,92842],{"className":92841},[1480],[1482,92843,92844],{"xmlns":1484,"display":1485},[1487,92845,92846,92890],{},[1490,92847,92848,92850,92852,92854,92860,92862,92864,92866,92868,92874,92876,92878,92880,92882,92884,92886,92888],{},[1493,92849,1556],{},[1506,92851,1714],{},[1493,92853,1495],{},[1497,92855,92856,92858],{},[1493,92857,1501],{},[1493,92859,1556],{},[1506,92861,2162],{},[1493,92863,1504],{},[1506,92865,1714],{},[1493,92867,1495],{},[1497,92869,92870,92872],{},[1493,92871,1501],{},[1493,92873,1504],{},[1506,92875,1508],{},[1493,92877,1520],{},[1506,92879,1553],{"stretchy":1552},[1493,92881,1556],{},[1506,92883,1559],{"separator":1041},[1493,92885,1504],{},[1506,92887,1564],{"stretchy":1552},[1493,92889,2632],{"mathvariant":1516},[1528,92891,92892],{"encoding":1530},"L\\cdot MP_L + K\\cdot MP_K = Q(L, K).",[1030,92894,92895,92896,92899],{},"Slovně — ",[1047,92897,92898],{},"v případě konstantních výnosů z rozsahu se součet součinů počtu jednotek vstupů (práce a kapitálu) a jejich mezních produktů rovná výstupu"," (důchodové pravidlo: celkový produkt je přesně rozdělen mezi vstupy podle jejich mezních produktů).",[1065,92901,26311],{"id":225},[1030,92903,92904,7606,92906,92909,92910,92932,92933,1274],{},[1047,92905,26311],{},[1176,92907,92908],{},"isoquants",") jsou křivky stejné produkce — množina dvojic ",[1035,92911,92913],{"className":92912},[1480],[1482,92914,92915],{"xmlns":1484},[1487,92916,92917,92929],{},[1490,92918,92919,92921,92923,92925,92927],{},[1506,92920,14314],{"stretchy":1552},[1493,92922,1556],{},[1506,92924,1559],{"separator":1041},[1493,92926,1504],{},[1506,92928,14323],{"stretchy":1552},[1528,92930,92931],{"encoding":1530},"[L, K]",", pro něž produkční funkce nabývá pevně zvolené hodnoty ",[1035,92934,92936],{"className":92935},[1480],[1482,92937,92938],{"xmlns":1484},[1487,92939,92940,92944],{},[1490,92941,92942],{},[1493,92943,7792],{},[1528,92945,7792],{"encoding":1530},[1035,92947,92949],{"className":92948},[1480],[1482,92950,92951],{"xmlns":1484,"display":1485},[1487,92952,92953,92988],{},[19617,92954,92955],{"width":19619},[19621,92956,92957,92959,92981,92983],{},[19624,92958],{"width":19626},[19624,92960,92961],{},[1490,92962,92963,92965,92967,92969,92971,92973,92975,92977,92979],{},[1493,92964,1520],{},[1506,92966,1553],{"stretchy":1552},[1493,92968,1556],{},[1506,92970,1559],{"separator":1041},[1493,92972,1504],{},[1506,92974,1564],{"stretchy":1552},[1506,92976,1508],{},[1493,92978,7792],{},[1493,92980,2632],{"mathvariant":1516},[19624,92982],{"width":19626},[19624,92984,92985],{},[1988,92986,92987],{},"(5.13)",[1528,92989,92990],{"encoding":1530},"Q(L, K) = q. \\tag{5.13}",[1030,92992,92993,92994,92997,92998,16623],{},"Jsou to ",[1047,92995,92996],{},"indiferenční křivky"," produkční funkce (analogie s indiferenčními křivkami u ",[1052,92999,93001],{"className":93000,"dataFsResolvedFilePath":6613,"href":6614},[1055],"užitečnosti",[1030,93003,93004],{},[1047,93005,93006],{},"Vlastnosti izokvant Cobb-Douglasových funkcí:",[1203,93008,93009,93014,93019,93024],{},[1206,93010,93011,93013],{},[1047,93012,29004],{}," — pokles kapitálu vyžaduje kompenzující růst práce k udržení produkce;",[1206,93015,93016,93018],{},[1047,93017,52775],{}," (úloha 5.14);",[1206,93020,93021,6065],{},[1047,93022,93023],{},"neprotínají se",[1206,93025,93026,93027,3397,93040,2632],{},"s rostoucím ",[1035,93028,93030],{"className":93029},[1480],[1482,93031,93032],{"xmlns":1484},[1487,93033,93034,93038],{},[1490,93035,93036],{},[1493,93037,7792],{},[1528,93039,7792],{"encoding":1530},[1047,93041,93042],{},"vzdalují od počátku",[1065,93044,93046,93047,1564],{"id":93045},"mezní-míra-technické-substituce-mrtsmrts","Mezní míra technické substituce (",[1035,93048,93050],{"className":93049},[1480],[1482,93051,93052],{"xmlns":1484},[1487,93053,93054,93064],{},[1490,93055,93056,93058,93060,93062],{},[1493,93057,1495],{},[1493,93059,1995],{},[1493,93061,5289],{},[1493,93063,2001],{},[1528,93065,16555],{"encoding":1530},[1030,93067,93068,7606,93071,93074],{},[1047,93069,93070],{},"Mezní míra technické substituce",[1176,93072,93073],{},"marginal rate of technical substitution",") je podíl mezních produktů:",[1035,93076,93078],{"className":93077},[1480],[1482,93079,93080],{"xmlns":1484,"display":1485},[1487,93081,93082,93173],{},[19617,93083,93084],{"width":19619},[19621,93085,93086,93088,93166,93168],{},[19624,93087],{"width":19626},[19624,93089,93090],{},[1490,93091,93092,93094,93096,93098,93100,93102,93104,93106,93108,93110,93112,93114,93116,93118,93120,93122,93144,93146,93164],{},[1493,93093,1495],{},[1493,93095,1995],{},[1493,93097,5289],{},[1493,93099,2001],{},[1506,93101,1508],{},[1493,93103,1495],{},[1493,93105,1995],{},[1493,93107,5289],{},[1493,93109,2001],{},[1506,93111,1553],{"stretchy":1552},[1493,93113,1556],{},[1506,93115,1559],{"separator":1041},[1493,93117,1504],{},[1506,93119,1564],{"stretchy":1552},[1506,93121,1508],{},[1510,93123,93124,93134],{},[1490,93125,93126,93128],{},[1493,93127,1495],{},[1497,93129,93130,93132],{},[1493,93131,1501],{},[1493,93133,1556],{},[1490,93135,93136,93138],{},[1493,93137,1495],{},[1497,93139,93140,93142],{},[1493,93141,1501],{},[1493,93143,1504],{},[1506,93145,1508],{},[1510,93147,93148,93156],{},[1697,93149,93150,93152,93154],{},[1493,93151,1520],{},[1493,93153,1556],{},[1506,93155,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1697,93157,93158,93160,93162],{},[1493,93159,1520],{},[1493,93161,1504],{},[1506,93163,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1493,93165,2632],{"mathvariant":1516},[19624,93167],{"width":19626},[19624,93169,93170],{},[1988,93171,93172],{},"(5.14)",[1528,93174,93175],{"encoding":1530},"MRTS = MRTS(L, K) = \\frac{MP_L}{MP_K} = \\frac{Q'_L}{Q'_K}. \\tag{5.14}",[1030,93177,93178,1656,93180,93210,93211,93242],{},[1047,93179,12171],{},[1035,93181,93183],{"className":93182},[1480],[1482,93184,93185],{"xmlns":1484},[1487,93186,93187,93207],{},[1490,93188,93189,93191,93193,93195,93197,93199,93201,93203,93205],{},[1493,93190,1495],{},[1493,93192,1995],{},[1493,93194,5289],{},[1493,93196,2001],{},[1506,93198,1553],{"stretchy":1552},[1493,93200,1556],{},[1506,93202,1559],{"separator":1041},[1493,93204,1504],{},[1506,93206,1564],{"stretchy":1552},[1528,93208,93209],{"encoding":1530},"MRTS(L, K)"," udává, ",[1047,93212,93213,93214,93227,93228,93241],{},"o kolik se musí přibližně změnit kapitál ",[1035,93215,93217],{"className":93216},[1480],[1482,93218,93219],{"xmlns":1484},[1487,93220,93221,93225],{},[1490,93222,93223],{},[1493,93224,1504],{},[1528,93226,1504],{"encoding":1530},", jestliže se práce ",[1035,93229,93231],{"className":93230},[1480],[1482,93232,93233],{"xmlns":1484},[1487,93234,93235,93239],{},[1490,93236,93237],{},[1493,93238,1556],{},[1528,93240,1556],{"encoding":1530}," změní o jednotku, aby byla zachována produkce"," (pohyb po izokvantě).",[1023,93244,93246,93252],{"className":93245,"dataCallout":582},[1026,1186],[1030,93247,93249,6749],{"className":93248},[1033],[1035,93250],{"className":93251,"ariaHidden":1041},[1038,1193,1040],[1030,93253,93254,93273,93274,93311,93312,93315,93316,93320],{},[1035,93255,93257],{"className":93256},[1480],[1482,93258,93259],{"xmlns":1484},[1487,93260,93261,93271],{},[1490,93262,93263,93265,93267,93269],{},[1493,93264,1495],{},[1493,93266,1995],{},[1493,93268,5289],{},[1493,93270,2001],{},[1528,93272,16555],{"encoding":1530}," říká: ",[1176,93275,93276,93277,93296,93297,93310],{},"„jednu jednotku práce musím nahradit přibližně ",[1035,93278,93280],{"className":93279},[1480],[1482,93281,93282],{"xmlns":1484},[1487,93283,93284,93294],{},[1490,93285,93286,93288,93290,93292],{},[1493,93287,1495],{},[1493,93289,1995],{},[1493,93291,5289],{},[1493,93293,2001],{},[1528,93295,16555],{"encoding":1530}," jednotkami kapitálu, aby produkce ",[1035,93298,93300],{"className":93299},[1480],[1482,93301,93302],{"xmlns":1484},[1487,93303,93304,93308],{},[1490,93305,93306],{},[1493,93307,1520],{},[1528,93309,1520],{"encoding":1530}," zůstala stejná.\""," Je to ",[1047,93313,93314],{},"směnný kurz mezi vstupy"," při zachování produkce — přesná analogie ",[1052,93317,93319],{"className":93318,"dataFsResolvedFilePath":6613,"href":6614},[1055],"MRCS z teorie užitečnosti",", kde nahrazujeme spotřební statky při zachování užitku.",[1030,93322,93323],{},[18014,93324],{"alt":93325,"className":93326,"src":93327},"imek-izokvanty-mrts",[1055,18018],"\u002Fwiki-assets\u002Fimek-izokvanty-mrts.jpeg",[1030,93329,93330,93333,93334,8994,93364,93386,93387,18579],{},[1047,93331,93332],{},"Geometrická interpretace:"," sklon tečny k izokvantě v bodě ",[1035,93335,93337],{"className":93336},[1480],[1482,93338,93339],{"xmlns":1484},[1487,93340,93341,93361],{},[1490,93342,93343,93345,93351,93353,93359],{},[1506,93344,14314],{"stretchy":1552},[1497,93346,93347,93349],{},[1493,93348,1556],{},[1680,93350,1871],{},[1506,93352,1559],{"separator":1041},[1497,93354,93355,93357],{},[1493,93356,1504],{},[1680,93358,1871],{},[1506,93360,14323],{"stretchy":1552},[1528,93362,93363],{"encoding":1530},"[L_0, K_0]",[1035,93365,93367],{"className":93366},[1480],[1482,93368,93369],{"xmlns":1484},[1487,93370,93371,93383],{},[1490,93372,93373,93375,93377,93379,93381],{},[1506,93374,1888],{},[1493,93376,1495],{},[1493,93378,1995],{},[1493,93380,5289],{},[1493,93382,2001],{},[1528,93384,93385],{"encoding":1530},"-MRTS",". Z derivace implicitní funkce (při ",[1035,93388,93390],{"className":93389},[1480],[1482,93391,93392],{"xmlns":1484},[1487,93393,93394,93416],{},[1490,93395,93396,93398,93400,93402,93404,93406,93408,93410],{},[1493,93397,1520],{},[1506,93399,1553],{"stretchy":1552},[1493,93401,1556],{},[1506,93403,1559],{"separator":1041},[1493,93405,1504],{},[1506,93407,1564],{"stretchy":1552},[1506,93409,1508],{},[1497,93411,93412,93414],{},[1493,93413,7792],{},[1680,93415,1871],{},[1528,93417,93418],{"encoding":1530},"Q(L,K) = q_0",[1035,93420,93422],{"className":93421},[1480],[1482,93423,93424],{"xmlns":1484,"display":1485},[1487,93425,93426,93478],{},[1490,93427,93428,93442,93444,93446,93464,93466,93468,93470,93472,93474,93476],{},[1510,93429,93430,93436],{},[1490,93431,93432,93434],{},[1493,93433,3384],{},[1493,93435,1504],{},[1490,93437,93438,93440],{},[1493,93439,3384],{},[1493,93441,1556],{},[1506,93443,1508],{},[1506,93445,1888],{},[1510,93447,93448,93456],{},[1697,93449,93450,93452,93454],{},[1493,93451,1520],{},[1493,93453,1556],{},[1506,93455,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1697,93457,93458,93460,93462],{},[1493,93459,1520],{},[1493,93461,1504],{},[1506,93463,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,93465,1508],{},[1506,93467,1888],{},[1493,93469,1495],{},[1493,93471,1995],{},[1493,93473,5289],{},[1493,93475,2001],{},[1493,93477,2632],{"mathvariant":1516},[1528,93479,93480],{"encoding":1530},"\\frac{dK}{dL} = -\\frac{Q'_L}{Q'_K} = -MRTS.",[1030,93482,93483,93484,93499,93500,93516],{},"Změní-li se práce o ",[1035,93485,93487],{"className":93486},[1480],[1482,93488,93489],{"xmlns":1484},[1487,93490,93491,93497],{},[1490,93492,93493,93495],{},[1493,93494,3384],{},[1493,93496,1556],{},[1528,93498,87719],{"encoding":1530},", lze pro odhad změny kapitálu ",[1035,93501,93503],{"className":93502},[1480],[1482,93504,93505],{"xmlns":1484},[1487,93506,93507,93513],{},[1490,93508,93509,93511],{},[1493,93510,2976],{"mathvariant":1516},[1493,93512,1504],{},[1528,93514,93515],{"encoding":1530},"\\Delta K"," k udržení produkce použít diferenciál:",[1035,93518,93520],{"className":93519},[1480],[1482,93521,93522],{"xmlns":1484,"display":1485},[1487,93523,93524,93571],{},[19617,93525,93526],{"width":19619},[19621,93527,93528,93530,93564,93566],{},[19624,93529],{"width":19626},[19624,93531,93532],{},[1490,93533,93534,93536,93538,93540,93542,93544,93546,93548,93550,93552,93554,93556,93558,93560,93562],{},[1493,93535,2976],{"mathvariant":1516},[1493,93537,1504],{},[1506,93539,2343],{},[1493,93541,3384],{},[1493,93543,1504],{},[1506,93545,1508],{},[1506,93547,1888],{},[1493,93549,1495],{},[1493,93551,1995],{},[1493,93553,5289],{},[1493,93555,2001],{},[1988,93557,5016],{},[1493,93559,3384],{},[1493,93561,1556],{},[1506,93563,1559],{"separator":1041},[19624,93565],{"width":19626},[19624,93567,93568],{},[1988,93569,93570],{},"(5.15)",[1528,93572,93573],{"encoding":1530},"\\Delta K \\approx dK = -MRTS\\,dL, \\tag{5.15}",[1035,93575,93577],{"className":93576},[1480],[1482,93578,93579],{"xmlns":1484,"display":1485},[1487,93580,93581,93630],{},[19617,93582,93583],{"width":19619},[19621,93584,93585,93587,93623,93625],{},[19624,93586],{"width":19626},[19624,93588,93589],{},[1490,93590,93591,93593,93595,93597,93615,93617,93619,93621],{},[1493,93592,3384],{},[1493,93594,1556],{},[1506,93596,1508],{},[1510,93598,93599,93605],{},[1490,93600,93601,93603],{},[1506,93602,1888],{},[1680,93604,1682],{},[1490,93606,93607,93609,93611,93613],{},[1493,93608,1495],{},[1493,93610,1995],{},[1493,93612,5289],{},[1493,93614,2001],{},[1988,93616,5016],{},[1493,93618,3384],{},[1493,93620,1504],{},[1493,93622,2632],{"mathvariant":1516},[19624,93624],{"width":19626},[19624,93626,93627],{},[1988,93628,93629],{},"(5.16)",[1528,93631,93632],{"encoding":1530},"dL = \\frac{-1}{MRTS}\\,dK. \\tag{5.16}",[1023,93634,93636,93662],{"className":93635,"dataCallout":1443},[1026,1442],[1030,93637,93639,93642,93643],{"className":93638},[1033],[1035,93640],{"className":93641,"ariaHidden":1041},[1038,1450,1040],"Postup — jak spočítat ",[1035,93644,93646],{"className":93645},[1480],[1482,93647,93648],{"xmlns":1484},[1487,93649,93650,93660],{},[1490,93651,93652,93654,93656,93658],{},[1493,93653,1495],{},[1493,93655,1995],{},[1493,93657,5289],{},[1493,93659,2001],{},[1528,93661,16555],{"encoding":1530},[1276,93663,93664,93705,93748,93780],{},[1206,93665,93666,93667,1586,93686,2632],{},"Vypočtěte parciální derivace ",[1035,93668,93670],{"className":93669},[1480],[1482,93671,93672],{"xmlns":1484},[1487,93673,93674,93684],{},[1490,93675,93676],{},[1697,93677,93678,93680,93682],{},[1493,93679,1520],{},[1493,93681,1556],{},[1506,93683,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,93685,26548],{"encoding":1530},[1035,93687,93689],{"className":93688},[1480],[1482,93690,93691],{"xmlns":1484},[1487,93692,93693,93703],{},[1490,93694,93695],{},[1697,93696,93697,93699,93701],{},[1493,93698,1520],{},[1493,93700,1504],{},[1506,93702,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,93704,26593],{"encoding":1530},[1206,93706,78411,93707,93747],{},[1035,93708,93710],{"className":93709},[1480],[1482,93711,93712],{"xmlns":1484},[1487,93713,93714,93744],{},[1490,93715,93716,93718,93720,93722,93724,93726,93734,93736],{},[1493,93717,1495],{},[1493,93719,1995],{},[1493,93721,5289],{},[1493,93723,2001],{},[1506,93725,1508],{},[1697,93727,93728,93730,93732],{},[1493,93729,1520],{},[1493,93731,1556],{},[1506,93733,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1493,93735,1709],{"mathvariant":1516},[1697,93737,93738,93740,93742],{},[1493,93739,1520],{},[1493,93741,1504],{},[1506,93743,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,93745,93746],{"encoding":1530},"MRTS = Q'_L \u002F Q'_K"," (zlomek zjednodušte).",[1206,93749,93750,93751,2632],{},"Případně dosaďte konkrétní ",[1035,93752,93754],{"className":93753},[1480],[1482,93755,93756],{"xmlns":1484},[1487,93757,93758,93778],{},[1490,93759,93760,93762,93768,93770,93776],{},[1506,93761,14314],{"stretchy":1552},[1497,93763,93764,93766],{},[1493,93765,1556],{},[1680,93767,1871],{},[1506,93769,1559],{"separator":1041},[1497,93771,93772,93774],{},[1493,93773,1504],{},[1680,93775,1871],{},[1506,93777,14323],{"stretchy":1552},[1528,93779,93363],{"encoding":1530},[1206,93781,93782,93783,93817,93818,93820],{},"Pro odhad substituce použijte ",[1035,93784,93786],{"className":93785},[1480],[1482,93787,93788],{"xmlns":1484},[1487,93789,93790,93814],{},[1490,93791,93792,93794,93796,93798,93800,93802,93804,93806,93808,93810,93812],{},[1493,93793,2976],{"mathvariant":1516},[1493,93795,1504],{},[1506,93797,2343],{},[1506,93799,1888],{},[1493,93801,1495],{},[1493,93803,1995],{},[1493,93805,5289],{},[1493,93807,2001],{},[1506,93809,1714],{},[1493,93811,2976],{"mathvariant":1516},[1493,93813,1556],{},[1528,93815,93816],{"encoding":1530},"\\Delta K \\approx -MRTS \\cdot \\Delta L"," (znaménko ",[1047,93819,66848],{}," — substituce, ne doplnění).",[1065,93822,93824],{"id":93823},"příklady-dvoufaktorový-model","Příklady (dvoufaktorový model)",[1304,93826,93828],{"id":93827},"příklad-54","Příklad 5.4",[1030,93830,89039,93831,1732,93873,1732,93890,2632],{},[1035,93832,93834],{"className":93833},[1480],[1482,93835,93836],{"xmlns":1484},[1487,93837,93838,93870],{},[1490,93839,93840,93842,93844,93846,93858],{},[1493,93841,1520],{},[1506,93843,1508],{},[1680,93845,9787],{},[2315,93847,93848,93850],{},[1493,93849,1556],{},[1490,93851,93852,93854,93856],{},[1680,93853,1682],{},[1493,93855,1709],{"mathvariant":1516},[1680,93857,1691],{},[2315,93859,93860,93862],{},[1493,93861,1504],{},[1490,93863,93864,93866,93868],{},[1680,93865,1682],{},[1493,93867,1709],{"mathvariant":1516},[1680,93869,3201],{},[1528,93871,93872],{"encoding":1530},"Q = 15 L^{1\u002F2} K^{1\u002F3}",[1035,93874,93876],{"className":93875},[1480],[1482,93877,93878],{"xmlns":1484},[1487,93879,93880,93888],{},[1490,93881,93882,93884,93886],{},[1493,93883,1556],{},[1506,93885,1508],{},[1680,93887,8436],{},[1528,93889,12190],{"encoding":1530},[1035,93891,93893],{"className":93892},[1480],[1482,93894,93895],{"xmlns":1484},[1487,93896,93897,93905],{},[1490,93898,93899,93901,93903],{},[1493,93900,1504],{},[1506,93902,1508],{},[1680,93904,2916],{},[1528,93906,93907],{"encoding":1530},"K = 100",[1030,93909,93910],{},[1047,93911,93912],{},"(a) Rychlost změny produkce vzhledem k práci.",[1035,93914,93916],{"className":93915},[1480],[1482,93917,93918],{"xmlns":1484,"display":1485},[1487,93919,93920,94034],{},[1490,93921,93922,93924,93930,93932,93940,93942,93950,93964,93976,93978,93980,93982,93988,93990,93992,93994,93996,93998,94000,94008,94010,94020,94022,94029,94031],{},[1493,93923,1495],{},[1497,93925,93926,93928],{},[1493,93927,1501],{},[1493,93929,1556],{},[1506,93931,1508],{},[1697,93933,93934,93936,93938],{},[1493,93935,1520],{},[1493,93937,1556],{},[1506,93939,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,93941,1508],{},[1869,93943,93944],{"scriptlevel":1871,"displaystyle":1552},[1510,93945,93946,93948],{},[1680,93947,9787],{},[1680,93949,1691],{},[2315,93951,93952,93954],{},[1493,93953,1556],{},[1490,93955,93956,93958,93960,93962],{},[1506,93957,1888],{},[1680,93959,1682],{},[1493,93961,1709],{"mathvariant":1516},[1680,93963,1691],{},[2315,93965,93966,93968],{},[1493,93967,1504],{},[1490,93969,93970,93972,93974],{},[1680,93971,1682],{},[1493,93973,1709],{"mathvariant":1516},[1680,93975,3201],{},[1506,93977,1559],{"separator":1041},[1912,93979],{"width":2108},[1493,93981,1495],{},[1497,93983,93984,93986],{},[1493,93985,1501],{},[1493,93987,1556],{},[1506,93989,1553],{"stretchy":1552},[1680,93991,8436],{},[1506,93993,1559],{"separator":1041},[1680,93995,2916],{},[1506,93997,1564],{"stretchy":1552},[1506,93999,1508],{},[1869,94001,94002],{"scriptlevel":1871,"displaystyle":1552},[1510,94003,94004,94006],{},[1680,94005,9787],{},[1680,94007,1691],{},[1506,94009,1714],{},[1869,94011,94012],{"scriptlevel":1871,"displaystyle":1552},[1510,94013,94014,94016],{},[1680,94015,1682],{},[2324,94017,94018],{},[1680,94019,8436],{},[1506,94021,1714],{},[94023,94024,94025,94027],"mroot",{},[1680,94026,2916],{},[1680,94028,3201],{},[1506,94030,2343],{},[1680,94032,94033],{},"7,153.",[1528,94035,94036],{"encoding":1530},"MP_L = Q'_L = \\tfrac{15}{2} L^{-1\u002F2} K^{1\u002F3}, \\quad MP_L(20, 100) = \\tfrac{15}{2}\\cdot \\tfrac{1}{\\sqrt{20}}\\cdot \\sqrt[3]{100} \\approx 7{,}153.",[1030,94038,94039,94040,94062,94063,26759,94080,94101,94102,2632],{},"Přibližná změna při ",[1035,94041,94043],{"className":94042},[1480],[1482,94044,94045],{"xmlns":1484},[1487,94046,94047,94059],{},[1490,94048,94049,94051,94053,94055,94057],{},[1493,94050,1556],{},[1506,94052,1274],{},[1680,94054,8436],{},[1506,94056,6380],{},[1680,94058,53274],{},[1528,94060,94061],{"encoding":1530},"L: 20 \\to 21"," (při ",[1035,94064,94066],{"className":94065},[1480],[1482,94067,94068],{"xmlns":1484},[1487,94069,94070,94078],{},[1490,94071,94072,94074,94076],{},[1493,94073,1504],{},[1506,94075,1508],{},[1680,94077,2916],{},[1528,94079,93907],{"encoding":1530},[1035,94081,94083],{"className":94082},[1480],[1482,94084,94085],{"xmlns":1484},[1487,94086,94087,94098],{},[1490,94088,94089,94091,94093,94095],{},[1493,94090,2976],{"mathvariant":1516},[1493,94092,1520],{},[1506,94094,2343],{},[1680,94096,94097],{},"7,153",[1528,94099,94100],{"encoding":1530},"\\Delta Q \\approx 7{,}153",". Skutečně ",[1035,94103,94105],{"className":94104},[1480],[1482,94106,94107],{"xmlns":1484},[1487,94108,94109,94120],{},[1490,94110,94111,94113,94115,94117],{},[1493,94112,2976],{"mathvariant":1516},[1493,94114,1520],{},[1506,94116,2343],{},[1680,94118,94119],{},"26,888",[1528,94121,94122],{"encoding":1530},"\\Delta Q \\approx 26{,}888",[1030,94124,94125,94128],{},[1047,94126,94127],{},"(b) Pokles kapitálu o 1"," (z 100 na 99).",[1035,94130,94132],{"className":94131},[1480],[1482,94133,94134],{"xmlns":1484,"display":1485},[1487,94135,94136,94236],{},[1490,94137,94138,94140,94146,94148,94156,94158,94160,94172,94186,94188,94190,94192,94198,94200,94202,94204,94206,94208,94210,94212,94216,94218,94231,94233],{},[1493,94139,1495],{},[1497,94141,94142,94144],{},[1493,94143,1501],{},[1493,94145,1504],{},[1506,94147,1508],{},[1697,94149,94150,94152,94154],{},[1493,94151,1520],{},[1493,94153,1504],{},[1506,94155,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,94157,1508],{},[1680,94159,1752],{},[2315,94161,94162,94164],{},[1493,94163,1556],{},[1490,94165,94166,94168,94170],{},[1680,94167,1682],{},[1493,94169,1709],{"mathvariant":1516},[1680,94171,1691],{},[2315,94173,94174,94176],{},[1493,94175,1504],{},[1490,94177,94178,94180,94182,94184],{},[1506,94179,1888],{},[1680,94181,1691],{},[1493,94183,1709],{"mathvariant":1516},[1680,94185,3201],{},[1506,94187,1559],{"separator":1041},[1912,94189],{"width":2108},[1493,94191,1495],{},[1497,94193,94194,94196],{},[1493,94195,1501],{},[1493,94197,1504],{},[1506,94199,1553],{"stretchy":1552},[1680,94201,8436],{},[1506,94203,1559],{"separator":1041},[1680,94205,2916],{},[1506,94207,1564],{"stretchy":1552},[1506,94209,1508],{},[1680,94211,1752],{},[2324,94213,94214],{},[1680,94215,8436],{},[1506,94217,1714],{},[1869,94219,94220],{"scriptlevel":1871,"displaystyle":1552},[1510,94221,94222,94224],{},[1680,94223,1682],{},[94023,94225,94226,94229],{},[1680,94227,94228],{},"10000",[1680,94230,3201],{},[1506,94232,2343],{},[1680,94234,94235],{},"4,525.",[1528,94237,94238],{"encoding":1530},"MP_K = Q'_K = 5 L^{1\u002F2} K^{-2\u002F3}, \\quad MP_K(20, 100) = 5\\sqrt{20}\\cdot \\tfrac{1}{\\sqrt[3]{10000}} \\approx 4{,}525.",[1030,94240,94241,94242,18139,94259,16623],{},"Produkce poklesne přibližně o 4,525 (z ",[1035,94243,94245],{"className":94244},[1480],[1482,94246,94247],{"xmlns":1484},[1487,94248,94249,94256],{},[1490,94250,94251,94253],{},[1506,94252,2343],{},[1680,94254,94255],{},"905,126",[1528,94257,94258],{"encoding":1530},"\\approx 905{,}126",[1035,94260,94262],{"className":94261},[1480],[1482,94263,94264],{"xmlns":1484},[1487,94265,94266,94273],{},[1490,94267,94268,94270],{},[1506,94269,2343],{},[1680,94271,94272],{},"900,601",[1528,94274,94275],{"encoding":1530},"\\approx 900{,}601",[1030,94277,94278,18559,94325,1732,94347,16623],{},[1047,94279,94280,94281,1586,94303],{},"(c) Změna ",[1035,94282,94284],{"className":94283},[1480],[1482,94285,94286],{"xmlns":1484},[1487,94287,94288,94300],{},[1490,94289,94290,94292,94294,94296,94298],{},[1493,94291,1556],{},[1506,94293,1274],{},[1680,94295,8436],{},[1506,94297,6380],{},[1680,94299,9787],{},[1528,94301,94302],{"encoding":1530},"L: 20 \\to 15",[1035,94304,94306],{"className":94305},[1480],[1482,94307,94308],{"xmlns":1484},[1487,94309,94310,94322],{},[1490,94311,94312,94314,94316,94318,94320],{},[1493,94313,1504],{},[1506,94315,1274],{},[1680,94317,2916],{},[1506,94319,6380],{},[1680,94321,5551],{},[1528,94323,94324],{"encoding":1530},"K: 100 \\to 150",[1035,94326,94328],{"className":94327},[1480],[1482,94329,94330],{"xmlns":1484},[1487,94331,94332,94344],{},[1490,94333,94334,94336,94338,94340,94342],{},[1493,94335,3384],{},[1493,94337,1556],{},[1506,94339,1508],{},[1506,94341,1888],{},[1680,94343,1752],{},[1528,94345,94346],{"encoding":1530},"dL = -5",[1035,94348,94350],{"className":94349},[1480],[1482,94351,94352],{"xmlns":1484},[1487,94353,94354,94364],{},[1490,94355,94356,94358,94360,94362],{},[1493,94357,3384],{},[1493,94359,1504],{},[1506,94361,1508],{},[1680,94363,2292],{},[1528,94365,94366],{"encoding":1530},"dK = 50",[1035,94368,94370],{"className":94369},[1480],[1482,94371,94372],{"xmlns":1484,"display":1485},[1487,94373,94374,94462],{},[1490,94375,94376,94378,94380,94382,94384,94390,94392,94394,94396,94398,94400,94402,94404,94406,94408,94410,94412,94414,94420,94422,94424,94426,94428,94430,94432,94434,94436,94438,94440,94442,94444,94446,94448,94450,94453,94455,94457,94459],{},[1493,94377,3384],{},[1493,94379,1520],{},[1506,94381,1508],{},[1493,94383,1495],{},[1497,94385,94386,94388],{},[1493,94387,1501],{},[1493,94389,1556],{},[1506,94391,1553],{"stretchy":1552},[1680,94393,8436],{},[1506,94395,1559],{"separator":1041},[1680,94397,2916],{},[1506,94399,1564],{"stretchy":1552},[1506,94401,1714],{},[1506,94403,1553],{"stretchy":1552},[1506,94405,1888],{},[1680,94407,1752],{},[1506,94409,1564],{"stretchy":1552},[1506,94411,2162],{},[1493,94413,1495],{},[1497,94415,94416,94418],{},[1493,94417,1501],{},[1493,94419,1504],{},[1506,94421,1553],{"stretchy":1552},[1680,94423,8436],{},[1506,94425,1559],{"separator":1041},[1680,94427,2916],{},[1506,94429,1564],{"stretchy":1552},[1506,94431,1714],{},[1680,94433,2292],{},[1506,94435,1508],{},[1680,94437,94097],{},[1506,94439,1714],{},[1506,94441,1553],{"stretchy":1552},[1506,94443,1888],{},[1680,94445,1752],{},[1506,94447,1564],{"stretchy":1552},[1506,94449,2162],{},[1680,94451,94452],{},"4,525",[1506,94454,1714],{},[1680,94456,2292],{},[1506,94458,2343],{},[1680,94460,94461],{},"190,485.",[1528,94463,94464],{"encoding":1530},"dQ = MP_L(20,100)\\cdot(-5) + MP_K(20,100)\\cdot 50 = 7{,}153\\cdot(-5) + 4{,}525\\cdot 50 \\approx 190{,}485.",[1030,94466,94467],{},"Produkce vzroste přibližně z 905,126 na 995,611.",[1304,94469,94471],{"id":94470},"příklad-55","Příklad 5.5",[1030,94473,94474,94475,94511,94512,2632],{},"Pro produkci ",[1035,94476,94478],{"className":94477},[1480],[1482,94479,94480],{"xmlns":1484},[1487,94481,94482,94508],{},[1490,94483,94484,94486,94488,94490,94492,94494,94496,94498,94504],{},[1493,94485,1520],{},[1506,94487,1553],{"stretchy":1552},[1493,94489,1556],{},[1506,94491,1559],{"separator":1041},[1493,94493,1504],{},[1506,94495,1564],{"stretchy":1552},[1506,94497,1508],{},[94023,94499,94500,94502],{},[1493,94501,1556],{},[1680,94503,3201],{},[2324,94505,94506],{},[1493,94507,1504],{},[1528,94509,94510],{"encoding":1530},"Q(L, K) = \\sqrt[3]{L}\\sqrt{K}"," mají izokvanty rovnici ",[1035,94513,94515],{"className":94514},[1480],[1482,94516,94517],{"xmlns":1484},[1487,94518,94519,94535],{},[1490,94520,94521,94527,94531,94533],{},[94023,94522,94523,94525],{},[1493,94524,1556],{},[1680,94526,3201],{},[2324,94528,94529],{},[1493,94530,1504],{},[1506,94532,1508],{},[1493,94534,7792],{},[1528,94536,94537],{"encoding":1530},"\\sqrt[3]{L}\\sqrt{K} = q",[1030,94539,94540,94541,2632],{},"Umocněním na druhou: ",[1035,94542,94544],{"className":94543},[1480],[1482,94545,94546],{"xmlns":1484},[1487,94547,94548,94572],{},[1490,94549,94550,94552,94554,94560,94562],{},[1493,94551,1504],{},[1506,94553,1508],{},[2315,94555,94556,94558],{},[1493,94557,7792],{},[1680,94559,1691],{},[1493,94561,1709],{"mathvariant":1516},[94023,94563,94564,94570],{},[2315,94565,94566,94568],{},[1493,94567,1556],{},[1680,94569,1691],{},[1680,94571,3201],{},[1528,94573,94574],{"encoding":1530},"K = q^2 \u002F \\sqrt[3]{L^2}",[1203,94576,94577,94617,94657],{},[1206,94578,94579],{},[1035,94580,94582],{"className":94581},[1480],[1482,94583,94584],{"xmlns":1484},[1487,94585,94586,94614],{},[1490,94587,94588,94590,94592,94594,94596,94598,94600,94602,94604],{},[1493,94589,7792],{},[1506,94591,1508],{},[1680,94593,1682],{},[1506,94595,2183],{},[1493,94597,1504],{},[1506,94599,1508],{},[1680,94601,1682],{},[1493,94603,1709],{"mathvariant":1516},[94023,94605,94606,94612],{},[2315,94607,94608,94610],{},[1493,94609,1556],{},[1680,94611,1691],{},[1680,94613,3201],{},[1528,94615,94616],{"encoding":1530},"q = 1 \\Rightarrow K = 1\u002F\\sqrt[3]{L^2}",[1206,94618,94619],{},[1035,94620,94622],{"className":94621},[1480],[1482,94623,94624],{"xmlns":1484},[1487,94625,94626,94654],{},[1490,94627,94628,94630,94632,94634,94636,94638,94640,94642,94644],{},[1493,94629,7792],{},[1506,94631,1508],{},[1680,94633,1691],{},[1506,94635,2183],{},[1493,94637,1504],{},[1506,94639,1508],{},[1680,94641,4007],{},[1493,94643,1709],{"mathvariant":1516},[94023,94645,94646,94652],{},[2315,94647,94648,94650],{},[1493,94649,1556],{},[1680,94651,1691],{},[1680,94653,3201],{},[1528,94655,94656],{"encoding":1530},"q = 2 \\Rightarrow K = 4\u002F\\sqrt[3]{L^2}",[1206,94658,94659],{},[1035,94660,94662],{"className":94661},[1480],[1482,94663,94664],{"xmlns":1484},[1487,94665,94666,94694],{},[1490,94667,94668,94670,94672,94674,94676,94678,94680,94682,94684],{},[1493,94669,7792],{},[1506,94671,1508],{},[1680,94673,3201],{},[1506,94675,2183],{},[1493,94677,1504],{},[1506,94679,1508],{},[1680,94681,14365],{},[1493,94683,1709],{"mathvariant":1516},[94023,94685,94686,94692],{},[2315,94687,94688,94690],{},[1493,94689,1556],{},[1680,94691,1691],{},[1680,94693,3201],{},[1528,94695,94696],{"encoding":1530},"q = 3 \\Rightarrow K = 9\u002F\\sqrt[3]{L^2}",[1304,94698,94700],{"id":94699},"příklad-56","Příklad 5.6",[1030,94702,89039,94703,2632],{},[1035,94704,94706],{"className":94705},[1480],[1482,94707,94708],{"xmlns":1484},[1487,94709,94710,94726],{},[1490,94711,94712,94714,94716,94718,94720,94722],{},[1493,94713,1520],{},[1506,94715,1508],{},[1680,94717,1691],{},[1493,94719,1556],{},[1506,94721,2162],{},[2324,94723,94724],{},[1493,94725,1504],{},[1528,94727,94728],{"encoding":1530},"Q = 2L + \\sqrt{K}",[1035,94730,94732],{"className":94731},[1480],[1482,94733,94734],{"xmlns":1484,"display":1485},[1487,94735,94736,94778],{},[1490,94737,94738,94740,94746,94748,94750,94752,94754,94756,94762,94764,94776],{},[1493,94739,1495],{},[1497,94741,94742,94744],{},[1493,94743,1501],{},[1493,94745,1556],{},[1506,94747,1508],{},[1680,94749,1691],{},[1506,94751,1559],{"separator":1041},[1912,94753],{"width":1914},[1493,94755,1495],{},[1497,94757,94758,94760],{},[1493,94759,1501],{},[1493,94761,1504],{},[1506,94763,1508],{},[1510,94765,94766,94768],{},[1680,94767,1682],{},[1490,94769,94770,94772],{},[1680,94771,1691],{},[2324,94773,94774],{},[1493,94775,1504],{},[1493,94777,2632],{"mathvariant":1516},[1528,94779,94780],{"encoding":1530},"MP_L = 2, \\qquad MP_K = \\frac{1}{2\\sqrt{K}}.",[1035,94782,94784],{"className":94783},[1480],[1482,94785,94786],{"xmlns":1484,"display":1485},[1487,94787,94788,94852],{},[1490,94789,94790,94792,94794,94796,94798,94800,94822,94824,94842,94844,94846,94850],{},[1493,94791,1495],{},[1493,94793,1995],{},[1493,94795,5289],{},[1493,94797,2001],{},[1506,94799,1508],{},[1510,94801,94802,94812],{},[1490,94803,94804,94806],{},[1493,94805,1495],{},[1497,94807,94808,94810],{},[1493,94809,1501],{},[1493,94811,1556],{},[1490,94813,94814,94816],{},[1493,94815,1495],{},[1497,94817,94818,94820],{},[1493,94819,1501],{},[1493,94821,1504],{},[1506,94823,1508],{},[1510,94825,94826,94828],{},[1680,94827,1691],{},[1869,94829,94830],{"scriptlevel":1871,"displaystyle":1552},[1510,94831,94832,94834],{},[1680,94833,1682],{},[1490,94835,94836,94838],{},[1680,94837,1691],{},[2324,94839,94840],{},[1493,94841,1504],{},[1506,94843,1508],{},[1680,94845,4007],{},[2324,94847,94848],{},[1493,94849,1504],{},[1493,94851,2632],{"mathvariant":1516},[1528,94853,94854],{"encoding":1530},"MRTS = \\frac{MP_L}{MP_K} = \\frac{2}{\\tfrac{1}{2\\sqrt{K}}} = 4\\sqrt{K}.",[1030,94856,94857,94858,94901,94902,94941,94942,2632],{},"Například ",[1035,94859,94861],{"className":94860},[1480],[1482,94862,94863],{"xmlns":1484},[1487,94864,94865,94898],{},[1490,94866,94867,94869,94871,94873,94875,94877,94879,94881,94883,94885,94887,94889,94893,94895],{},[1493,94868,1495],{},[1493,94870,1995],{},[1493,94872,5289],{},[1493,94874,2001],{},[1506,94876,1553],{"stretchy":1552},[1680,94878,4007],{},[1506,94880,1559],{"separator":1041},[1680,94882,16580],{},[1506,94884,1564],{"stretchy":1552},[1506,94886,1508],{},[1680,94888,4007],{},[2324,94890,94891],{},[1680,94892,16580],{},[1506,94894,2343],{},[1680,94896,94897],{},"10,58",[1528,94899,94900],{"encoding":1530},"MRTS(4, 7) = 4\\sqrt{7} \\approx 10{,}58",". Klesne-li práce z 4 na 3, je k udržení produkce ",[1035,94903,94905],{"className":94904},[1480],[1482,94906,94907],{"xmlns":1484},[1487,94908,94909,94938],{},[1490,94910,94911,94913,94915,94917,94919,94921,94923,94925,94927,94929,94933,94935],{},[1493,94912,1520],{},[1506,94914,1553],{"stretchy":1552},[1680,94916,4007],{},[1506,94918,1559],{"separator":1041},[1680,94920,16580],{},[1506,94922,1564],{"stretchy":1552},[1506,94924,1508],{},[1680,94926,6138],{},[1506,94928,2162],{},[2324,94930,94931],{},[1680,94932,16580],{},[1506,94934,2343],{},[1680,94936,94937],{},"10,646",[1528,94939,94940],{"encoding":1530},"Q(4,7) = 8 + \\sqrt{7} \\approx 10{,}646"," třeba zvýšit kapitál přibližně o ",[1035,94943,94945],{"className":94944},[1480],[1482,94946,94947],{"xmlns":1484},[1487,94948,94949,94957],{},[1490,94950,94951,94953],{},[1680,94952,4007],{},[2324,94954,94955],{},[1680,94956,16580],{},[1528,94958,94959],{"encoding":1530},"4\\sqrt{7}",[1030,94961,94962,94963,94983],{},"Pokud se práce naopak zvýší ze 4 na 6 (",[1035,94964,94966],{"className":94965},[1480],[1482,94967,94968],{"xmlns":1484},[1487,94969,94970,94980],{},[1490,94971,94972,94974,94976,94978],{},[1493,94973,3384],{},[1493,94975,1556],{},[1506,94977,1508],{},[1680,94979,1691],{},[1528,94981,94982],{"encoding":1530},"dL = 2","), k udržení produkce stačí snížit kapitál o",[1035,94985,94987],{"className":94986},[1480],[1482,94988,94989],{"xmlns":1484,"display":1485},[1487,94990,94991,95040],{},[1490,94992,94993,94995,94997,94999,95001,95003,95005,95007,95009,95011,95013,95015,95017,95019,95021,95023,95025,95027,95029,95033,95035,95037],{},[1493,94994,3384],{},[1493,94996,1504],{},[1506,94998,1508],{},[1506,95000,1888],{},[1493,95002,1495],{},[1493,95004,1995],{},[1493,95006,5289],{},[1493,95008,2001],{},[1506,95010,1553],{"stretchy":1552},[1680,95012,4007],{},[1506,95014,1559],{"separator":1041},[1680,95016,16580],{},[1506,95018,1564],{"stretchy":1552},[1506,95020,1714],{},[1680,95022,1691],{},[1506,95024,1508],{},[1506,95026,1888],{},[1680,95028,6138],{},[2324,95030,95031],{},[1680,95032,16580],{},[1506,95034,2343],{},[1506,95036,1888],{},[1680,95038,95039],{},"21,17.",[1528,95041,95042],{"encoding":1530},"dK = -MRTS(4,7)\\cdot 2 = -8\\sqrt{7} \\approx -21{,}17.",[1065,95044,95046],{"id":95045},"shrnutí-kapitoly-5","Shrnutí kapitoly 5",[1030,95048,95049,95050,1732,95052,1586,95054,95056,95057,95060,95061,95064],{},"Hlavními faktory produkce jsou ",[1047,95051,87272],{},[1047,95053,87288],{},[1047,95055,87304],{},"; půda je standardní exogenní proměnná. Přicházejí proto v úvahu ",[1047,95058,95059],{},"jednofaktorový"," (pouze práce) a ",[1047,95062,95063],{},"dvoufaktorový"," (práce + kapitál) model.",[1030,95066,55970,95067,95070,95071,95073,95074,95076,95077,11074,95080,95099,95100,95117,95118,95135,95136,95158,95159,3397,95178,2632],{},[1047,95068,95069],{},"1F modelu"," se definuje ",[1047,95072,26551],{}," (derivace produkce podle práce) a ",[1047,95075,87208],{}," (podíl produkce a práce). Produkční funkce má typický tvar díky ",[1047,95078,95079],{},"zákonu klesajících výnosů",[1035,95081,95083],{"className":95082},[1480],[1482,95084,95085],{"xmlns":1484},[1487,95086,95087,95097],{},[1490,95088,95089,95091],{},[1493,95090,1495],{},[1497,95092,95093,95095],{},[1493,95094,1501],{},[1493,95096,1556],{},[1528,95098,26571],{"encoding":1530}," nejprve roste, od inflexního bodu ",[1035,95101,95103],{"className":95102},[1480],[1482,95104,95105],{"xmlns":1484},[1487,95106,95107,95115],{},[1490,95108,95109],{},[1497,95110,95111,95113],{},[1493,95112,1556],{},[1680,95114,1871],{},[1528,95116,87921],{"encoding":1530}," klesá a v bodě ",[1035,95119,95121],{"className":95120},[1480],[1482,95122,95123],{"xmlns":1484},[1487,95124,95125,95133],{},[1490,95126,95127],{},[1497,95128,95129,95131],{},[1493,95130,1556],{},[1680,95132,1682],{},[1528,95134,29689],{"encoding":1530}," dosahuje nuly (maximum produkce). Platí ",[1047,95137,95138,95139],{},"princip maximalizace ",[1035,95140,95142],{"className":95141},[1480],[1482,95143,95144],{"xmlns":1484},[1487,95145,95146,95156],{},[1490,95147,95148,95150],{},[1493,95149,3633],{},[1497,95151,95152,95154],{},[1493,95153,1501],{},[1493,95155,1556],{},[1528,95157,6827],{"encoding":1530},": v bodě maxima ",[1035,95160,95162],{"className":95161},[1480],[1482,95163,95164],{"xmlns":1484},[1487,95165,95166,95176],{},[1490,95167,95168,95170],{},[1493,95169,3633],{},[1497,95171,95172,95174],{},[1493,95173,1501],{},[1493,95175,1556],{},[1528,95177,6827],{"encoding":1530},[1035,95179,95181],{"className":95180},[1480],[1482,95182,95183],{"xmlns":1484},[1487,95184,95185,95205],{},[1490,95186,95187,95189,95195,95197,95199],{},[1493,95188,1495],{},[1497,95190,95191,95193],{},[1493,95192,1501],{},[1493,95194,1556],{},[1506,95196,1508],{},[1493,95198,3633],{},[1497,95200,95201,95203],{},[1493,95202,1501],{},[1493,95204,1556],{},[1528,95206,87024],{"encoding":1530},[1030,95208,95209,95210,95213,95214,1656,95217,95246,95247,95264,95265,95268,95269,95298,95299,95301,95302,8994,95332,95354],{},"Ve ",[1047,95211,95212],{},"2F modelu"," se obvykle používají ",[1047,95215,95216],{},"Cobb-Douglasovy funkce",[1035,95218,95220],{"className":95219},[1480],[1482,95221,95222],{"xmlns":1484},[1487,95223,95224,95244],{},[1490,95225,95226,95228,95230,95232,95238],{},[1493,95227,1520],{},[1506,95229,1508],{},[1493,95231,3633],{},[2315,95233,95234,95236],{},[1493,95235,1556],{},[1493,95237,1052],{},[2315,95239,95240,95242],{},[1493,95241,1504],{},[1493,95243,2394],{},[1528,95245,87090],{"encoding":1530},", které reflektují proporcionalitu změn vstupů a výstupu. Podle ",[1035,95248,95250],{"className":95249},[1480],[1482,95251,95252],{"xmlns":1484},[1487,95253,95254,95262],{},[1490,95255,95256,95258,95260],{},[1493,95257,1052],{},[1506,95259,2162],{},[1493,95261,2394],{},[1528,95263,87183],{"encoding":1530}," rozlišujeme ",[1047,95266,95267],{},"konstantní, rostoucí, klesající výnosy z rozsahu",". Mezní produkty ",[1035,95270,95272],{"className":95271},[1480],[1482,95273,95274],{"xmlns":1484},[1487,95275,95276,95296],{},[1490,95277,95278,95280,95286,95288,95290],{},[1493,95279,1495],{},[1497,95281,95282,95284],{},[1493,95283,1501],{},[1493,95285,1556],{},[1506,95287,1559],{"separator":1041},[1493,95289,1495],{},[1497,95291,95292,95294],{},[1493,95293,1501],{},[1493,95295,1504],{},[1528,95297,87121],{"encoding":1530}," jsou parciální derivace, totální diferenciál dává přibližnou změnu produkce. ",[1047,95300,26311],{}," jsou indiferenční křivky produkční funkce. Podíl ",[1035,95303,95305],{"className":95304},[1480],[1482,95306,95307],{"xmlns":1484},[1487,95308,95309,95329],{},[1490,95310,95311,95313,95319,95321,95323],{},[1493,95312,1495],{},[1497,95314,95315,95317],{},[1493,95316,1501],{},[1493,95318,1556],{},[1493,95320,1709],{"mathvariant":1516},[1493,95322,1495],{},[1497,95324,95325,95327],{},[1493,95326,1501],{},[1493,95328,1504],{},[1528,95330,95331],{"encoding":1530},"MP_L\u002FMP_K",[1047,95333,95334,95335,1564],{},"mezní míra technické substituce (",[1035,95336,95338],{"className":95337},[1480],[1482,95339,95340],{"xmlns":1484},[1487,95341,95342,95352],{},[1490,95343,95344,95346,95348,95350],{},[1493,95345,1495],{},[1493,95347,1995],{},[1493,95349,5289],{},[1493,95351,2001],{},[1528,95353,16555],{"encoding":1530}," — udává, o kolik se musí změnit kapitál při jednotkové změně práce pro zachování produkce.",[1065,95356,64217],{"id":64216},[1276,95358,95359,95362,95365,95368,95371,95374,95377,95380,95383,95386,95389],{},[1206,95360,95361],{},"Jaké jsou faktory produkce?",[1206,95363,95364],{},"Jak se dospěje k jednofaktorovému a dvoufaktorovému modelu produkce?",[1206,95366,95367],{},"Jak je zadána produkční funkce u jednofaktorového modelu?",[1206,95369,95370],{},"Co udává mezní produkt práce?",[1206,95372,95373],{},"Co musí respektovat průběh křivky produkce?",[1206,95375,95376],{},"Jak lze matematicky vyjádřit zákon klesajících výnosů?",[1206,95378,95379],{},"Jaký základní ekonomický požadavek respektují Cobb-Douglasovy funkce?",[1206,95381,95382],{},"Jak se vypočtou mezní produkty práce a kapitálu?",[1206,95384,95385],{},"Jak se stanoví přibližná změna produkce v závislosti na změnách práce a kapitálu?",[1206,95387,95388],{},"Co vyjadřují izokvanty? Jaké jsou jejich typické vlastnosti?",[1206,95390,95391],{},"Jak se vypočte mezní míra technické substituce a co vyjadřuje?",[1065,95393,95395],{"id":95394},"úlohy-51517","Úlohy 5.1–5.17",[1304,95397,55217],{"id":55216},[1030,95399,95400,95403,95404,95426,95427,1732,95447,1732,95467,95487],{},[1047,95401,95402],{},"5.1"," Je dána produkce ",[1035,95405,95407],{"className":95406},[1480],[1482,95408,95409],{"xmlns":1484},[1487,95410,95411,95423],{},[1490,95412,95413,95415,95417,95419],{},[1493,95414,1520],{},[1506,95416,1508],{},[1680,95418,1775],{},[2324,95420,95421],{},[1493,95422,1556],{},[1528,95424,95425],{"encoding":1530},"Q = 10\\sqrt{L}",". (a) Vypočtěte ",[1035,95428,95430],{"className":95429},[1480],[1482,95431,95432],{"xmlns":1484},[1487,95433,95434,95444],{},[1490,95435,95436,95438,95440,95442],{},[1493,95437,1520],{},[1506,95439,1553],{"stretchy":1552},[1680,95441,1682],{},[1506,95443,1564],{"stretchy":1552},[1528,95445,95446],{"encoding":1530},"Q(1)",[1035,95448,95450],{"className":95449},[1480],[1482,95451,95452],{"xmlns":1484},[1487,95453,95454,95464],{},[1490,95455,95456,95458,95460,95462],{},[1493,95457,1520],{},[1506,95459,1553],{"stretchy":1552},[1680,95461,4007],{},[1506,95463,1564],{"stretchy":1552},[1528,95465,95466],{"encoding":1530},"Q(4)",[1035,95468,95470],{"className":95469},[1480],[1482,95471,95472],{"xmlns":1484},[1487,95473,95474,95484],{},[1490,95475,95476,95478,95480,95482],{},[1493,95477,1520],{},[1506,95479,1553],{"stretchy":1552},[1680,95481,14365],{},[1506,95483,1564],{"stretchy":1552},[1528,95485,95486],{"encoding":1530},"Q(9)",". (b) Rozhodněte, kdy produkce roste, resp. klesá. (c) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (d) Načrtněte křivku produkce.",[1030,95489,95490,95403,95493,95529,95530,95543,95544,95563,95564,95590,95591,18139,95604,95617],{},[1047,95491,95492],{},"5.2",[1035,95494,95496],{"className":95495},[1480],[1482,95497,95498],{"xmlns":1484},[1487,95499,95500,95526],{},[1490,95501,95502,95504,95506,95508,95510,95516,95518,95520],{},[1493,95503,1520],{},[1506,95505,1508],{},[1506,95507,1888],{},[1680,95509,13237],{},[2315,95511,95512,95514],{},[1493,95513,1556],{},[1680,95515,3201],{},[1506,95517,2162],{},[1680,95519,14365],{},[2315,95521,95522,95524],{},[1493,95523,1556],{},[1680,95525,1691],{},[1528,95527,95528],{"encoding":1530},"Q = -0{,}1 L^{3} + 9 L^{2}",". (a) Rozhodněte, kdy produkce roste, resp. klesá. (b) Rozhodněte, kdy je křivka produkce konvexní, resp. konkávní. (c) Určete ",[1035,95531,95533],{"className":95532},[1480],[1482,95534,95535],{"xmlns":1484},[1487,95536,95537,95541],{},[1490,95538,95539],{},[1493,95540,1556],{},[1528,95542,1556],{"encoding":1530}," (počet pracovníků), které maximalizuje produkci a stanovte příslušné maximum produkce. (d) Načrtněte křivku produkce. (e) Najděte mezní produkt práce ",[1035,95545,95547],{"className":95546},[1480],[1482,95548,95549],{"xmlns":1484},[1487,95550,95551,95561],{},[1490,95552,95553,95555],{},[1493,95554,1495],{},[1497,95556,95557,95559],{},[1493,95558,1501],{},[1493,95560,1556],{},[1528,95562,26571],{"encoding":1530},". (f) Vypočtěte ",[1035,95565,95567],{"className":95566},[1480],[1482,95568,95569],{"xmlns":1484},[1487,95570,95571,95587],{},[1490,95572,95573,95575,95581,95583,95585],{},[1493,95574,1495],{},[1497,95576,95577,95579],{},[1493,95578,1501],{},[1493,95580,1556],{},[1506,95582,1553],{"stretchy":1552},[1680,95584,1775],{},[1506,95586,1564],{"stretchy":1552},[1528,95588,95589],{"encoding":1530},"MP_L(10)"," a ekonomicky interpretujte. (g) Určete přibližnou změnu produkce v důsledku zvýšení počtu pracovníků z ",[1035,95592,95594],{"className":95593},[1480],[1482,95595,95596],{"xmlns":1484},[1487,95597,95598,95602],{},[1490,95599,95600],{},[1680,95601,1775],{},[1528,95603,1775],{"encoding":1530},[1035,95605,95607],{"className":95606},[1480],[1482,95608,95609],{"xmlns":1484},[1487,95610,95611,95615],{},[1490,95612,95613],{},[1680,95614,56835],{},[1528,95616,56835],{"encoding":1530}," a porovnejte se skutečnou změnou produkce.",[1030,95619,95620,95623,95624,95646,95647,95675,95676,95707,95708,2632],{},[1047,95621,95622],{},"5.3"," Pro zadanou produkci ověřte platnost zákona klesajících výnosů a charakterizujte vlastnosti mezního produktu práce:\n(a) ",[1035,95625,95627],{"className":95626},[1480],[1482,95628,95629],{"xmlns":1484},[1487,95630,95631,95643],{},[1490,95632,95633,95635,95637,95639],{},[1493,95634,1520],{},[1506,95636,1508],{},[1680,95638,1796],{},[2324,95640,95641],{},[1493,95642,1556],{},[1528,95644,95645],{"encoding":1530},"Q = 500\\sqrt{L}",".\n(b) ",[1035,95648,95650],{"className":95649},[1480],[1482,95651,95652],{"xmlns":1484},[1487,95653,95654,95672],{},[1490,95655,95656,95658,95660,95662,95666,95668,95670],{},[1493,95657,1520],{},[1506,95659,1508],{},[1680,95661,5231],{},[2324,95663,95664],{},[1493,95665,1556],{},[1506,95667,1888],{},[1680,95669,4007],{},[1493,95671,1556],{},[1528,95673,95674],{"encoding":1530},"Q = 300\\sqrt{L} - 4L",".\n(c) ",[1035,95677,95679],{"className":95678},[1480],[1482,95680,95681],{"xmlns":1484},[1487,95682,95683,95704],{},[1490,95684,95685,95687,95689,95691,95693,95695,95698],{},[1493,95686,1520],{},[1506,95688,1508],{},[1680,95690,2292],{},[1493,95692,1556],{},[1506,95694,1888],{},[1680,95696,95697],{},"0,01",[2315,95699,95700,95702],{},[1493,95701,1556],{},[1680,95703,1691],{},[1528,95705,95706],{"encoding":1530},"Q = 50L - 0{,}01 L^{2}",".\n(d) ",[1035,95709,95711],{"className":95710},[1480],[1482,95712,95713],{"xmlns":1484},[1487,95714,95715,95741],{},[1490,95716,95717,95719,95721,95723,95725,95731,95733,95735],{},[1493,95718,1520],{},[1506,95720,1508],{},[1506,95722,1888],{},[1680,95724,80622],{},[2315,95726,95727,95729],{},[1493,95728,1556],{},[1680,95730,3201],{},[1506,95732,2162],{},[1680,95734,14365],{},[2315,95736,95737,95739],{},[1493,95738,1556],{},[1680,95740,1691],{},[1528,95742,95743],{"encoding":1530},"Q = -0{,}3 L^{3} + 9 L^{2}",[1030,95745,95746,95749,95750,11713,95769,84565,95786,2632],{},[1047,95747,95748],{},"5.4"," Dokažte, že má-li průměrný produkt práce ",[1035,95751,95753],{"className":95752},[1480],[1482,95754,95755],{"xmlns":1484},[1487,95756,95757,95767],{},[1490,95758,95759,95761],{},[1493,95760,3633],{},[1497,95762,95763,95765],{},[1493,95764,1501],{},[1493,95766,1556],{},[1528,95768,6827],{"encoding":1530},[1035,95770,95772],{"className":95771},[1480],[1482,95773,95774],{"xmlns":1484},[1487,95775,95776,95784],{},[1490,95777,95778],{},[1497,95779,95780,95782],{},[1493,95781,1556],{},[1680,95783,1871],{},[1528,95785,87921],{"encoding":1530},[1035,95787,95789],{"className":95788},[1480],[1482,95790,95791],{"xmlns":1484},[1487,95792,95793,95833],{},[1490,95794,95795,95797,95803,95805,95811,95813,95815,95817,95823,95825,95831],{},[1493,95796,3633],{},[1497,95798,95799,95801],{},[1493,95800,1501],{},[1493,95802,1556],{},[1506,95804,1553],{"stretchy":1552},[1497,95806,95807,95809],{},[1493,95808,1556],{},[1680,95810,1871],{},[1506,95812,1564],{"stretchy":1552},[1506,95814,1508],{},[1493,95816,1495],{},[1497,95818,95819,95821],{},[1493,95820,1501],{},[1493,95822,1556],{},[1506,95824,1553],{"stretchy":1552},[1497,95826,95827,95829],{},[1493,95828,1556],{},[1680,95830,1871],{},[1506,95832,1564],{"stretchy":1552},[1528,95834,95835],{"encoding":1530},"AP_L(L_0) = MP_L(L_0)",[1030,95837,95838,95403,95841,37188,95877,95890,95891,95910],{},[1047,95839,95840],{},"5.5",[1035,95842,95844],{"className":95843},[1480],[1482,95845,95846],{"xmlns":1484},[1487,95847,95848,95874],{},[1490,95849,95850,95852,95854,95856,95858,95864,95866,95868],{},[1493,95851,1520],{},[1506,95853,1508],{},[1506,95855,1888],{},[1680,95857,2929],{},[2315,95859,95860,95862],{},[1493,95861,1556],{},[1680,95863,3201],{},[1506,95865,2162],{},[1680,95867,6797],{},[2315,95869,95870,95872],{},[1493,95871,1556],{},[1680,95873,1691],{},[1528,95875,95876],{"encoding":1530},"Q = -0{,}2 L^{3} + 12 L^{2}",[1035,95878,95880],{"className":95879},[1480],[1482,95881,95882],{"xmlns":1484},[1487,95883,95884,95888],{},[1490,95885,95886],{},[1493,95887,1556],{},[1528,95889,1556],{"encoding":1530}," je počet pracovníků. (a) Určete počet pracovníků, při kterém je dosaženo nejvyšší produktivity práce (= maximálního průměrného produktu práce ",[1035,95892,95894],{"className":95893},[1480],[1482,95895,95896],{"xmlns":1484},[1487,95897,95898,95908],{},[1490,95899,95900,95902],{},[1493,95901,3633],{},[1497,95903,95904,95906],{},[1493,95905,1501],{},[1493,95907,1556],{},[1528,95909,6827],{"encoding":1530},") a stanovte, kolik jednotek produkce připadá na jednoho pracovníka. (b) Určete počet pracovníků s využitím principu maximalizace průměrného produktu práce. (c) Ověřte platnost principu maximalizujícího produkci a stanovte příslušné maximum produkce. (d) Porovnejte počet pracovníků v případech (a), (c). (e) Graficky interpretujte získané výsledky.",[1304,95912,95914],{"id":95913},"dvoufaktorový-model","Dvoufaktorový model",[1030,95916,95917,95920,95921,95646,95947,95675,95989,2632],{},[1047,95918,95919],{},"5.6"," Pro zadanou produkci rozhodněte, jaké výnosy z rozsahu představují:\n(a) ",[1035,95922,95924],{"className":95923},[1480],[1482,95925,95926],{"xmlns":1484},[1487,95927,95928,95944],{},[1490,95929,95930,95932,95934,95936,95938],{},[1493,95931,1520],{},[1506,95933,1508],{},[1680,95935,16580],{},[1493,95937,1556],{},[2315,95939,95940,95942],{},[1493,95941,1504],{},[1680,95943,1691],{},[1528,95945,95946],{"encoding":1530},"Q = 7 L K^{2}",[1035,95948,95950],{"className":95949},[1480],[1482,95951,95952],{"xmlns":1484},[1487,95953,95954,95986],{},[1490,95955,95956,95958,95960,95962,95974],{},[1493,95957,1520],{},[1506,95959,1508],{},[1680,95961,2292],{},[2315,95963,95964,95966],{},[1493,95965,1556],{},[1490,95967,95968,95970,95972],{},[1680,95969,1691],{},[1493,95971,1709],{"mathvariant":1516},[1680,95973,3201],{},[2315,95975,95976,95978],{},[1493,95977,1504],{},[1490,95979,95980,95982,95984],{},[1680,95981,1682],{},[1493,95983,1709],{"mathvariant":1516},[1680,95985,3201],{},[1528,95987,95988],{"encoding":1530},"Q = 50 L^{2\u002F3} K^{1\u002F3}",[1035,95990,95992],{"className":95991},[1480],[1482,95993,95994],{"xmlns":1484},[1487,95995,95996,96028],{},[1490,95997,95998,96000,96002,96004,96016],{},[1493,95999,1520],{},[1506,96001,1508],{},[1680,96003,9319],{},[2315,96005,96006,96008],{},[1493,96007,1556],{},[1490,96009,96010,96012,96014],{},[1680,96011,3201],{},[1493,96013,1709],{"mathvariant":1516},[1680,96015,1752],{},[2315,96017,96018,96020],{},[1493,96019,1504],{},[1490,96021,96022,96024,96026],{},[1680,96023,1691],{},[1493,96025,1709],{"mathvariant":1516},[1680,96027,1752],{},[1528,96029,96030],{"encoding":1530},"Q = 18 L^{3\u002F5} K^{2\u002F5}",[1030,96032,96033,95403,96036,96078,96079,1732,96097,96116,96117,96134],{},[1047,96034,96035],{},"5.7",[1035,96037,96039],{"className":96038},[1480],[1482,96040,96041],{"xmlns":1484},[1487,96042,96043,96075],{},[1490,96044,96045,96047,96049,96051,96063],{},[1493,96046,1520],{},[1506,96048,1508],{},[1680,96050,1775],{},[2315,96052,96053,96055],{},[1493,96054,1556],{},[1490,96056,96057,96059,96061],{},[1680,96058,1682],{},[1493,96060,1709],{"mathvariant":1516},[1680,96062,1691],{},[2315,96064,96065,96067],{},[1493,96066,1504],{},[1490,96068,96069,96071,96073],{},[1680,96070,1682],{},[1493,96072,1709],{"mathvariant":1516},[1680,96074,1691],{},[1528,96076,96077],{"encoding":1530},"Q = 10 L^{1\u002F2} K^{1\u002F2}",". (a) Vypočtěte produkci pro ",[1035,96080,96082],{"className":96081},[1480],[1482,96083,96084],{"xmlns":1484},[1487,96085,96086,96094],{},[1490,96087,96088,96090,96092],{},[1493,96089,1556],{},[1506,96091,1508],{},[1680,96093,5765],{},[1528,96095,96096],{"encoding":1530},"L = 400",[1035,96098,96100],{"className":96099},[1480],[1482,96101,96102],{"xmlns":1484},[1487,96103,96104,96113],{},[1490,96105,96106,96108,96110],{},[1493,96107,1504],{},[1506,96109,1508],{},[1680,96111,96112],{},"17576",[1528,96114,96115],{"encoding":1530},"K = 17576",". (b) Rozhodněte o tom, jaké výnosy z rozsahu představuje a vyložte, jak se změní produkce, jestliže se vstupy ",[1035,96118,96120],{"className":96119},[1480],[1482,96121,96122],{"xmlns":1484},[1487,96123,96124,96132],{},[1490,96125,96126,96128,96130],{},[1493,96127,1556],{},[1506,96129,1559],{"separator":1041},[1493,96131,1504],{},[1528,96133,6501],{"encoding":1530}," zdvojnásobí.",[1030,96136,96137,96140,96141,96078,96172,1732,96190,81956,96208,96238,96239,96269,96270,18139,96283,96297,96298,18139,96311,96324],{},[1047,96138,96139],{},"5.8"," V jedné empirické studii (40. léta 20. století) ze sektoru manufaktur odhadli Cobb a Douglas produkci ze zjištěných údajů ve tvaru ",[1035,96142,96144],{"className":96143},[1480],[1482,96145,96146],{"xmlns":1484},[1487,96147,96148,96169],{},[1490,96149,96150,96152,96154,96157,96163],{},[1493,96151,1520],{},[1506,96153,1508],{},[1680,96155,96156],{},"1,01",[2315,96158,96159,96161],{},[1493,96160,1556],{},[1680,96162,39315],{},[2315,96164,96165,96167],{},[1493,96166,1504],{},[1680,96168,5051],{},[1528,96170,96171],{"encoding":1530},"Q = 1{,}01 L^{0{,}75} K^{0{,}25}",[1035,96173,96175],{"className":96174},[1480],[1482,96176,96177],{"xmlns":1484},[1487,96178,96179,96187],{},[1490,96180,96181,96183,96185],{},[1493,96182,1556],{},[1506,96184,1508],{},[1680,96186,8140],{},[1528,96188,96189],{"encoding":1530},"L = 250",[1035,96191,96193],{"className":96192},[1480],[1482,96194,96195],{"xmlns":1484},[1487,96196,96197,96205],{},[1490,96198,96199,96201,96203],{},[1493,96200,1504],{},[1506,96202,1508],{},[1680,96204,1401],{},[1528,96206,96207],{"encoding":1530},"K = 1000",[1035,96209,96211],{"className":96210},[1480],[1482,96212,96213],{"xmlns":1484},[1487,96214,96215,96235],{},[1490,96216,96217,96219,96225,96227,96229,96231,96233],{},[1493,96218,1495],{},[1497,96220,96221,96223],{},[1493,96222,1501],{},[1493,96224,1556],{},[1506,96226,1553],{"stretchy":1552},[1680,96228,8140],{},[1506,96230,1559],{"separator":1041},[1680,96232,1401],{},[1506,96234,1564],{"stretchy":1552},[1528,96236,96237],{"encoding":1530},"MP_L(250, 1000)"," a výsledek ekonomicky interpretujte. (c) Vypočtěte ",[1035,96240,96242],{"className":96241},[1480],[1482,96243,96244],{"xmlns":1484},[1487,96245,96246,96266],{},[1490,96247,96248,96250,96256,96258,96260,96262,96264],{},[1493,96249,1495],{},[1497,96251,96252,96254],{},[1493,96253,1501],{},[1493,96255,1504],{},[1506,96257,1553],{"stretchy":1552},[1680,96259,8140],{},[1506,96261,1559],{"separator":1041},[1680,96263,1401],{},[1506,96265,1564],{"stretchy":1552},[1528,96267,96268],{"encoding":1530},"MP_K(250, 1000)"," a výsledek ekonomicky interpretujte. (d) Odhadněte změnu produkce v důsledku zvýšení ",[1035,96271,96273],{"className":96272},[1480],[1482,96274,96275],{"xmlns":1484},[1487,96276,96277,96281],{},[1490,96278,96279],{},[1493,96280,1556],{},[1528,96282,1556],{"encoding":1530},[1035,96284,96286],{"className":96285},[1480],[1482,96287,96288],{"xmlns":1484},[1487,96289,96290,96295],{},[1490,96291,96292],{},[1680,96293,96294],{},"260",[1528,96296,96294],{"encoding":1530}," a současném poklesu ",[1035,96299,96301],{"className":96300},[1480],[1482,96302,96303],{"xmlns":1484},[1487,96304,96305,96309],{},[1490,96306,96307],{},[1493,96308,1504],{},[1528,96310,1504],{"encoding":1530},[1035,96312,96314],{"className":96313},[1480],[1482,96315,96316],{"xmlns":1484},[1487,96317,96318,96322],{},[1490,96319,96320],{},[1680,96321,7032],{},[1528,96323,7032],{"encoding":1530}," vzhledem k hladině dle (a) a porovnejte se skutečnou změnou produkce.",[1030,96326,96327,96330,96331,2632],{},[1047,96328,96329],{},"5.9"," Ověřte platnost zákona klesajících výnosů pro produkci ",[1035,96332,96334],{"className":96333},[1480],[1482,96335,96336],{"xmlns":1484},[1487,96337,96338,96358],{},[1490,96339,96340,96342,96344,96346,96352],{},[1493,96341,1520],{},[1506,96343,1508],{},[1680,96345,1775],{},[2315,96347,96348,96350],{},[1493,96349,1556],{},[1680,96351,80622],{},[2315,96353,96354,96356],{},[1493,96355,1504],{},[1680,96357,3687],{},[1528,96359,96360],{"encoding":1530},"Q = 10 L^{0{,}3} K^{0{,}5}",[1030,96362,96363,96366,96367,92728,96390,26918,96403,7606,96453,16623],{},[1047,96364,96365],{},"5.10"," Dokažte, že pro homogenní funkci ",[1035,96368,96370],{"className":96369},[1480],[1482,96371,96372],{"xmlns":1484},[1487,96373,96374,96388],{},[1490,96375,96376,96378,96380,96382,96384,96386],{},[1493,96377,1520],{},[1506,96379,1553],{"stretchy":1552},[1493,96381,1556],{},[1506,96383,1559],{"separator":1041},[1493,96385,1504],{},[1506,96387,1564],{"stretchy":1552},[1528,96389,26524],{"encoding":1530},[1035,96391,96393],{"className":96392},[1480],[1482,96394,96395],{"xmlns":1484},[1487,96396,96397,96401],{},[1490,96398,96399],{},[1493,96400,7781],{},[1528,96402,7781],{"encoding":1530},[1035,96404,96406],{"className":96405},[1480],[1482,96407,96408],{"xmlns":1484},[1487,96409,96410,96450],{},[1490,96411,96412,96414,96422,96424,96426,96434,96436,96438,96440,96442,96444,96446,96448],{},[1493,96413,1556],{},[1697,96415,96416,96418,96420],{},[1493,96417,1520],{},[1493,96419,1556],{},[1506,96421,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,96423,2162],{},[1493,96425,1504],{},[1697,96427,96428,96430,96432],{},[1493,96429,1520],{},[1493,96431,1504],{},[1506,96433,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,96435,1508],{},[1493,96437,7781],{},[1493,96439,1520],{},[1506,96441,1553],{"stretchy":1552},[1493,96443,1556],{},[1506,96445,1559],{"separator":1041},[1493,96447,1504],{},[1506,96449,1564],{"stretchy":1552},[1528,96451,96452],{"encoding":1530},"L Q'_L + K Q'_K = n Q(L, K)",[1176,96454,92703],{},[1030,96456,96457,96460],{},[1047,96458,96459],{},"5.11"," Ověřte platnost Eulerovy věty (úloha 5.10) pro Cobb-Douglasovu produkční funkci.",[1030,96462,96463,95403,96466,96506,96507,1732,96529,1732,96551,96573],{},[1047,96464,96465],{},"5.12",[1035,96467,96469],{"className":96468},[1480],[1482,96470,96471],{"xmlns":1484},[1487,96472,96473,96503],{},[1490,96474,96475,96477,96479,96491],{},[1493,96476,1520],{},[1506,96478,1508],{},[2315,96480,96481,96483],{},[1493,96482,1556],{},[1490,96484,96485,96487,96489],{},[1680,96486,1682],{},[1493,96488,1709],{"mathvariant":1516},[1680,96490,3201],{},[2315,96492,96493,96495],{},[1493,96494,1504],{},[1490,96496,96497,96499,96501],{},[1680,96498,1682],{},[1493,96500,1709],{"mathvariant":1516},[1680,96502,4007],{},[1528,96504,96505],{"encoding":1530},"Q = L^{1\u002F3} K^{1\u002F4}",". (a) Najděte rovnici izokvant. (b) Najděte rovnici izokvant pro produkci ",[1035,96508,96510],{"className":96509},[1480],[1482,96511,96512],{"xmlns":1484},[1487,96513,96514,96526],{},[1490,96515,96516,96522,96524],{},[1497,96517,96518,96520],{},[1493,96519,7792],{},[1680,96521,1871],{},[1506,96523,1508],{},[1680,96525,1682],{},[1528,96527,96528],{"encoding":1530},"q_0 = 1",[1035,96530,96532],{"className":96531},[1480],[1482,96533,96534],{"xmlns":1484},[1487,96535,96536,96548],{},[1490,96537,96538,96544,96546],{},[1497,96539,96540,96542],{},[1493,96541,7792],{},[1680,96543,1682],{},[1506,96545,1508],{},[1680,96547,1691],{},[1528,96549,96550],{"encoding":1530},"q_1 = 2",[1035,96552,96554],{"className":96553},[1480],[1482,96555,96556],{"xmlns":1484},[1487,96557,96558,96570],{},[1490,96559,96560,96566,96568],{},[1497,96561,96562,96564],{},[1493,96563,7792],{},[1680,96565,1691],{},[1506,96567,1508],{},[1680,96569,3201],{},[1528,96571,96572],{"encoding":1530},"q_2 = 3",". (c) Načrtněte izokvanty.",[1030,96575,96576,95403,96579,96619,96620,1732,96648,1732,96676,1732,96704,1732,96733,1732,96762,1732,96791,1732,96820,1732,96849,2632],{},[1047,96577,96578],{},"5.13",[1035,96580,96582],{"className":96581},[1480],[1482,96583,96584],{"xmlns":1484},[1487,96585,96586,96616],{},[1490,96587,96588,96590,96592,96604],{},[1493,96589,1520],{},[1506,96591,1508],{},[2315,96593,96594,96596],{},[1493,96595,1556],{},[1490,96597,96598,96600,96602],{},[1680,96599,1682],{},[1493,96601,1709],{"mathvariant":1516},[1680,96603,3201],{},[2315,96605,96606,96608],{},[1493,96607,1504],{},[1490,96609,96610,96612,96614],{},[1680,96611,1682],{},[1493,96613,1709],{"mathvariant":1516},[1680,96615,1691],{},[1528,96617,96618],{"encoding":1530},"Q = L^{1\u002F3} K^{1\u002F2}",". Rozhodněte, které ze zadaných bodů leží na téže izokvantě a v kladném případě stanovte, jaká produkce je na příslušné izokvantě dosažena (užijte kalkulátoru): ",[1035,96621,96623],{"className":96622},[1480],[1482,96624,96625],{"xmlns":1484},[1487,96626,96627,96645],{},[1490,96628,96629,96635,96637,96639,96641,96643],{},[1497,96630,96631,96633],{},[1493,96632,3633],{},[1680,96634,1682],{},[1506,96636,14314],{"stretchy":1552},[1680,96638,1682],{},[1506,96640,6065],{"separator":1041},[1680,96642,1682],{},[1506,96644,14323],{"stretchy":1552},[1528,96646,96647],{"encoding":1530},"A_1[1; 1]",[1035,96649,96651],{"className":96650},[1480],[1482,96652,96653],{"xmlns":1484},[1487,96654,96655,96673],{},[1490,96656,96657,96663,96665,96667,96669,96671],{},[1497,96658,96659,96661],{},[1493,96660,3633],{},[1680,96662,1691],{},[1506,96664,14314],{"stretchy":1552},[1680,96666,1682],{},[1506,96668,6065],{"separator":1041},[1680,96670,6138],{},[1506,96672,14323],{"stretchy":1552},[1528,96674,96675],{"encoding":1530},"A_2[1; 8]",[1035,96677,96679],{"className":96678},[1480],[1482,96680,96681],{"xmlns":1484},[1487,96682,96683,96701],{},[1490,96684,96685,96691,96693,96695,96697,96699],{},[1497,96686,96687,96689],{},[1493,96688,3633],{},[1680,96690,3201],{},[1506,96692,14314],{"stretchy":1552},[1680,96694,1682],{},[1506,96696,6065],{"separator":1041},[1680,96698,15165],{},[1506,96700,14323],{"stretchy":1552},[1528,96702,96703],{"encoding":1530},"A_3[1; 27]",[1035,96705,96707],{"className":96706},[1480],[1482,96708,96709],{"xmlns":1484},[1487,96710,96711,96730],{},[1490,96712,96713,96719,96721,96723,96725,96728],{},[1497,96714,96715,96717],{},[1493,96716,3633],{},[1680,96718,4007],{},[1506,96720,14314],{"stretchy":1552},[1680,96722,1691],{},[1506,96724,6065],{"separator":1041},[1680,96726,96727],{},"0,353",[1506,96729,14323],{"stretchy":1552},[1528,96731,96732],{"encoding":1530},"A_4[2; 0{,}353]",[1035,96734,96736],{"className":96735},[1480],[1482,96737,96738],{"xmlns":1484},[1487,96739,96740,96759],{},[1490,96741,96742,96748,96750,96752,96754,96757],{},[1497,96743,96744,96746],{},[1493,96745,3633],{},[1680,96747,1752],{},[1506,96749,14314],{"stretchy":1552},[1680,96751,1691],{},[1506,96753,6065],{"separator":1041},[1680,96755,96756],{},"2,828",[1506,96758,14323],{"stretchy":1552},[1528,96760,96761],{"encoding":1530},"A_5[2; 2{,}828]",[1035,96763,96765],{"className":96764},[1480],[1482,96766,96767],{"xmlns":1484},[1487,96768,96769,96788],{},[1490,96770,96771,96777,96779,96781,96783,96786],{},[1497,96772,96773,96775],{},[1493,96774,3633],{},[1680,96776,7508],{},[1506,96778,14314],{"stretchy":1552},[1680,96780,1691],{},[1506,96782,6065],{"separator":1041},[1680,96784,96785],{},"9,545",[1506,96787,14323],{"stretchy":1552},[1528,96789,96790],{"encoding":1530},"A_6[2; 9{,}545]",[1035,96792,96794],{"className":96793},[1480],[1482,96795,96796],{"xmlns":1484},[1487,96797,96798,96817],{},[1490,96799,96800,96806,96808,96810,96812,96815],{},[1497,96801,96802,96804],{},[1493,96803,3633],{},[1680,96805,16580],{},[1506,96807,14314],{"stretchy":1552},[1680,96809,77687],{},[1506,96811,6065],{"separator":1041},[1680,96813,96814],{},"0,544",[1506,96816,14323],{"stretchy":1552},[1528,96818,96819],{"encoding":1530},"A_7[1{,}5; 0{,}544]",[1035,96821,96823],{"className":96822},[1480],[1482,96824,96825],{"xmlns":1484},[1487,96826,96827,96846],{},[1490,96828,96829,96835,96837,96839,96841,96844],{},[1497,96830,96831,96833],{},[1493,96832,3633],{},[1680,96834,6138],{},[1506,96836,14314],{"stretchy":1552},[1680,96838,77687],{},[1506,96840,6065],{"separator":1041},[1680,96842,96843],{},"14,696",[1506,96845,14323],{"stretchy":1552},[1528,96847,96848],{"encoding":1530},"A_8[1{,}5; 14{,}696]",[1035,96850,96852],{"className":96851},[1480],[1482,96853,96854],{"xmlns":1484},[1487,96855,96856,96874],{},[1490,96857,96858,96864,96866,96868,96870,96872],{},[1497,96859,96860,96862],{},[1493,96861,3633],{},[1680,96863,14365],{},[1506,96865,14314],{"stretchy":1552},[1680,96867,1691],{},[1506,96869,6065],{"separator":1041},[1680,96871,1752],{},[1506,96873,14323],{"stretchy":1552},[1528,96875,96876],{"encoding":1530},"A_9[2; 5]",[1030,96878,96879,96882],{},[1047,96880,96881],{},"5.14"," Dokažte, že izokvanty Cobb-Douglasovy produkční funkce jsou klesající a konvexní.",[1030,96884,96885,96888,96889,96919,96920,96933,96934,96947,96948,81689,96967,96986,96987,2632],{},[1047,96886,96887],{},"5.15"," Produkce firmy je dána vztahem ",[1035,96890,96892],{"className":96891},[1480],[1482,96893,96894],{"xmlns":1484},[1487,96895,96896,96916],{},[1490,96897,96898,96900,96902,96904,96910],{},[1493,96899,1520],{},[1506,96901,1508],{},[1680,96903,1691],{},[2315,96905,96906,96908],{},[1493,96907,1556],{},[1680,96909,3687],{},[2315,96911,96912,96914],{},[1493,96913,1504],{},[1680,96915,5051],{},[1528,96917,96918],{"encoding":1530},"Q = 2 L^{0{,}5} K^{0{,}25}",". (a) Vypočtěte produkci, mezní produkt práce a mezní produkt kapitálu, zaměstnává-li firma ",[1035,96921,96923],{"className":96922},[1480],[1482,96924,96925],{"xmlns":1484},[1487,96926,96927,96931],{},[1490,96928,96929],{},[1680,96930,2916],{},[1528,96932,2916],{"encoding":1530}," pracovníků a disponuje-li ",[1035,96935,96937],{"className":96936},[1480],[1482,96938,96939],{"xmlns":1484},[1487,96940,96941,96945],{},[1490,96942,96943],{},[1680,96944,14703],{},[1528,96946,14703],{"encoding":1530}," jednotkami kapitálu. (b) Určete mezní míru technické substituce ",[1035,96949,96951],{"className":96950},[1480],[1482,96952,96953],{"xmlns":1484},[1487,96954,96955,96965],{},[1490,96956,96957,96959,96961,96963],{},[1493,96958,1495],{},[1493,96960,1995],{},[1493,96962,5289],{},[1493,96964,2001],{},[1528,96966,16555],{"encoding":1530},[1035,96968,96970],{"className":96969},[1480],[1482,96971,96972],{"xmlns":1484},[1487,96973,96974,96984],{},[1490,96975,96976,96978,96980,96982],{},[1493,96977,1495],{},[1493,96979,1995],{},[1493,96981,5289],{},[1493,96983,2001],{},[1528,96985,16555],{"encoding":1530}," na hladině dle (a) a výsledek ekonomicky interpretujte. (d) Odhadněte změnu kapitálu potřebné k udržení produkce na hladině dle (a), jestliže počet pracovníků poklesne na ",[1035,96988,96990],{"className":96989},[1480],[1482,96991,96992],{"xmlns":1484},[1487,96993,96994,96999],{},[1490,96995,96996],{},[1680,96997,96998],{},"95",[1528,97000,96998],{"encoding":1530},[1030,97002,97003,95403,97006,83361,97038,97057,97058,97071,97072,97085,97086,97099],{},[1047,97004,97005],{},"5.16",[1035,97007,97009],{"className":97008},[1480],[1482,97010,97011],{"xmlns":1484},[1487,97012,97013,97035],{},[1490,97014,97015,97017,97019,97025,97027,97029],{},[1493,97016,1520],{},[1506,97018,1508],{},[2315,97020,97021,97023],{},[1493,97022,1504],{},[1680,97024,1691],{},[1506,97026,2162],{},[1680,97028,1691],{},[2315,97030,97031,97033],{},[1493,97032,1556],{},[1680,97034,1691],{},[1528,97036,97037],{"encoding":1530},"Q = K^{2} + 2 L^{2}",[1035,97039,97041],{"className":97040},[1480],[1482,97042,97043],{"xmlns":1484},[1487,97044,97045,97055],{},[1490,97046,97047,97049,97051,97053],{},[1493,97048,1495],{},[1493,97050,1995],{},[1493,97052,5289],{},[1493,97054,2001],{},[1528,97056,16555],{"encoding":1530},". (b) Odhadněte změnu práce potřebné k udržení produkce, která je realizována ",[1035,97059,97061],{"className":97060},[1480],[1482,97062,97063],{"xmlns":1484},[1487,97064,97065,97069],{},[1490,97066,97067],{},[1680,97068,2292],{},[1528,97070,2292],{"encoding":1530}," pracovníky a ",[1035,97073,97075],{"className":97074},[1480],[1482,97076,97077],{"xmlns":1484},[1487,97078,97079,97083],{},[1490,97080,97081],{},[1680,97082,89898],{},[1528,97084,89898],{"encoding":1530}," jednotkami kapitálu, jestliže se kapitál sníží na ",[1035,97087,97089],{"className":97088},[1480],[1482,97090,97091],{"xmlns":1484},[1487,97092,97093,97097],{},[1490,97094,97095],{},[1680,97096,11232],{},[1528,97098,11232],{"encoding":1530}," jednotek.",[1030,97101,97102,97105,97106,26918,97136,2632],{},[1047,97103,97104],{},"5.17"," Odvoďte, že pro Cobb-Douglasovu produkční funkci ",[1035,97107,97109],{"className":97108},[1480],[1482,97110,97111],{"xmlns":1484},[1487,97112,97113,97133],{},[1490,97114,97115,97117,97119,97121,97127],{},[1493,97116,1520],{},[1506,97118,1508],{},[1493,97120,3633],{},[2315,97122,97123,97125],{},[1493,97124,1556],{},[1493,97126,1052],{},[2315,97128,97129,97131],{},[1493,97130,1504],{},[1493,97132,2394],{},[1528,97134,97135],{"encoding":1530},"Q = A L^{a} K^{b}",[1035,97137,97139],{"className":97138},[1480],[1482,97140,97141],{"xmlns":1484},[1487,97142,97143,97173],{},[1490,97144,97145,97147,97149,97151,97153,97155,97163,97165],{},[1493,97146,1495],{},[1493,97148,1995],{},[1493,97150,5289],{},[1493,97152,2001],{},[1506,97154,1508],{},[1869,97156,97157],{"scriptlevel":1871,"displaystyle":1552},[1510,97158,97159,97161],{},[1493,97160,1052],{},[1493,97162,2394],{},[1506,97164,1714],{},[1869,97166,97167],{"scriptlevel":1871,"displaystyle":1552},[1510,97168,97169,97171],{},[1493,97170,1504],{},[1493,97172,1556],{},[1528,97174,97175],{"encoding":1530},"MRTS = \\tfrac{a}{b}\\cdot \\tfrac{K}{L}",[1065,97177,31885],{"id":31884},[1203,97179,97180,97213,97240,97249,97299,97330,97383,97406,97461,97534,97612,97655,97687,97720,97761,97833,97894,97960,97977,98050,98116,98168,98224,98258,98301],{},[1206,97181,97182,97185,97186,51991,97199,97212],{},[1047,97183,97184],{},"Faktory (vstupy) produkce:"," práce ",[1035,97187,97189],{"className":97188},[1480],[1482,97190,97191],{"xmlns":1484},[1487,97192,97193,97197],{},[1490,97194,97195],{},[1493,97196,1556],{},[1528,97198,1556],{"encoding":1530},[1035,97200,97202],{"className":97201},[1480],[1482,97203,97204],{"xmlns":1484},[1487,97205,97206,97210],{},[1490,97207,97208],{},[1493,97209,1504],{},[1528,97211,1504],{"encoding":1530},", půda.",[1206,97214,97215,22970,97217,2632],{},[1047,97216,55217],{},[1035,97218,97220],{"className":97219},[1480],[1482,97221,97222],{"xmlns":1484},[1487,97223,97224,97238],{},[1490,97225,97226,97228,97230,97232,97234,97236],{},[1493,97227,1520],{},[1506,97229,1508],{},[1493,97231,1520],{},[1506,97233,1553],{"stretchy":1552},[1493,97235,1556],{},[1506,97237,1564],{"stretchy":1552},[1528,97239,86906],{"encoding":1530},[1206,97241,97242,7606,97244,28611,97247,2632],{},[1047,97243,86759],{},[1176,97245,97246],{},"production function",[1047,97248,87405],{},[1206,97250,97251,1656,97253,2632],{},[1047,97252,87451],{},[1035,97254,97256],{"className":97255},[1480],[1482,97257,97258],{"xmlns":1484},[1487,97259,97260,97296],{},[1490,97261,97262,97264,97270,97272,97274,97276,97278,97280,97282,97284,97290,97292,97294],{},[1493,97263,1495],{},[1497,97265,97266,97268],{},[1493,97267,1501],{},[1493,97269,1556],{},[1506,97271,1508],{},[1493,97273,3384],{},[1493,97275,1520],{},[1493,97277,1709],{"mathvariant":1516},[1493,97279,3384],{},[1493,97281,1556],{},[1506,97283,1508],{},[2315,97285,97286,97288],{},[1493,97287,1520],{},[1506,97289,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,97291,1553],{"stretchy":1552},[1493,97293,1556],{},[1506,97295,1564],{"stretchy":1552},[1528,97297,97298],{"encoding":1530},"MP_L = dQ\u002FdL = Q'(L)",[1206,97300,97301,1656,97303,2632],{},[1047,97302,88391],{},[1035,97304,97306],{"className":97305},[1480],[1482,97307,97308],{"xmlns":1484},[1487,97309,97310,97328],{},[1490,97311,97312,97314,97320,97322,97324,97326],{},[1493,97313,3633],{},[1497,97315,97316,97318],{},[1493,97317,1501],{},[1493,97319,1556],{},[1506,97321,1508],{},[1493,97323,1520],{},[1493,97325,1709],{"mathvariant":1516},[1493,97327,1556],{},[1528,97329,86974],{"encoding":1530},[1206,97331,97332,97334,97335,26918,97352,2632],{},[1047,97333,87878],{}," — od určitého ",[1035,97336,97338],{"className":97337},[1480],[1482,97339,97340],{"xmlns":1484},[1487,97341,97342,97350],{},[1490,97343,97344],{},[1497,97345,97346,97348],{},[1493,97347,1556],{},[1680,97349,1871],{},[1528,97351,87921],{"encoding":1530},[1035,97353,97355],{"className":97354},[1480],[1482,97356,97357],{"xmlns":1484},[1487,97358,97359,97381],{},[1490,97360,97361,97371,97373,97375,97377,97379],{},[2315,97362,97363,97365],{},[1493,97364,1520],{},[1490,97366,97367,97369],{},[1506,97368,6927],{"mathvariant":1516},[1506,97370,6927],{"mathvariant":1516},[1506,97372,1553],{"stretchy":1552},[1493,97374,1556],{},[1506,97376,1564],{"stretchy":1552},[1506,97378,3961],{},[1680,97380,1871],{},[1528,97382,88067],{"encoding":1530},[1206,97384,97385,1656,97388,97405],{},[1047,97386,97387],{},"Inflexní bod",[1035,97389,97391],{"className":97390},[1480],[1482,97392,97393],{"xmlns":1484},[1487,97394,97395,97403],{},[1490,97396,97397],{},[1497,97398,97399,97401],{},[1493,97400,1556],{},[1680,97402,1871],{},[1528,97404,87921],{"encoding":1530}," — přechod z konvexity do konkavity.",[1206,97407,97408,1656,97411,22970,97428,2632],{},[1047,97409,97410],{},"Bod maxima produkce",[1035,97412,97414],{"className":97413},[1480],[1482,97415,97416],{"xmlns":1484},[1487,97417,97418,97426],{},[1490,97419,97420],{},[1497,97421,97422,97424],{},[1493,97423,1556],{},[1680,97425,1682],{},[1528,97427,29689],{"encoding":1530},[1035,97429,97431],{"className":97430},[1480],[1482,97432,97433],{"xmlns":1484},[1487,97434,97435,97459],{},[1490,97436,97437,97439,97445,97447,97453,97455,97457],{},[1493,97438,1495],{},[1497,97440,97441,97443],{},[1493,97442,1501],{},[1493,97444,1556],{},[1506,97446,1553],{"stretchy":1552},[1497,97448,97449,97451],{},[1493,97450,1556],{},[1680,97452,1682],{},[1506,97454,1564],{"stretchy":1552},[1506,97456,1508],{},[1680,97458,1871],{},[1528,97460,88140],{"encoding":1530},[1206,97462,97463,97485,97486,26918,97505,2632],{},[1047,97464,97465,97466],{},"Princip maximalizace ",[1035,97467,97469],{"className":97468},[1480],[1482,97470,97471],{"xmlns":1484},[1487,97472,97473,97483],{},[1490,97474,97475,97477],{},[1493,97476,3633],{},[1497,97478,97479,97481],{},[1493,97480,1501],{},[1493,97482,1556],{},[1528,97484,6827],{"encoding":1530}," — v bodě maxima ",[1035,97487,97489],{"className":97488},[1480],[1482,97490,97491],{"xmlns":1484},[1487,97492,97493,97503],{},[1490,97494,97495,97497],{},[1493,97496,3633],{},[1497,97498,97499,97501],{},[1493,97500,1501],{},[1493,97502,1556],{},[1528,97504,6827],{"encoding":1530},[1035,97506,97508],{"className":97507},[1480],[1482,97509,97510],{"xmlns":1484},[1487,97511,97512,97532],{},[1490,97513,97514,97516,97522,97524,97526],{},[1493,97515,1495],{},[1497,97517,97518,97520],{},[1493,97519,1501],{},[1493,97521,1556],{},[1506,97523,1508],{},[1493,97525,3633],{},[1497,97527,97528,97530],{},[1493,97529,1501],{},[1493,97531,1556],{},[1528,97533,87024],{"encoding":1530},[1206,97535,97536,1656,97539,1732,97578,1732,97595,2632],{},[1047,97537,97538],{},"Polynomiální produkční funkce",[1035,97540,97542],{"className":97541},[1480],[1482,97543,97544],{"xmlns":1484},[1487,97545,97546,97576],{},[1490,97547,97548,97550,97552,97554,97556,97558,97560,97566,97568,97570],{},[1493,97549,1520],{},[1506,97551,1553],{"stretchy":1552},[1493,97553,1556],{},[1506,97555,1564],{"stretchy":1552},[1506,97557,1508],{},[1493,97559,1052],{},[2315,97561,97562,97564],{},[1493,97563,1556],{},[1680,97565,3201],{},[1506,97567,2162],{},[1493,97569,2394],{},[2315,97571,97572,97574],{},[1493,97573,1556],{},[1680,97575,1691],{},[1528,97577,88258],{"encoding":1530},[1035,97579,97581],{"className":97580},[1480],[1482,97582,97583],{"xmlns":1484},[1487,97584,97585,97593],{},[1490,97586,97587,97589,97591],{},[1493,97588,1052],{},[1506,97590,3961],{},[1680,97592,1871],{},[1528,97594,57642],{"encoding":1530},[1035,97596,97598],{"className":97597},[1480],[1482,97599,97600],{"xmlns":1484},[1487,97601,97602,97610],{},[1490,97603,97604,97606,97608],{},[1493,97605,2394],{},[1506,97607,2796],{},[1680,97609,1871],{},[1528,97611,34950],{"encoding":1530},[1206,97613,97614,1656,97617,2632],{},[1047,97615,97616],{},"Diferenciál produkce",[1035,97618,97620],{"className":97619},[1480],[1482,97621,97622],{"xmlns":1484},[1487,97623,97624,97652],{},[1490,97625,97626,97628,97630,97632,97634,97636,97638,97640,97646,97648,97650],{},[1493,97627,2976],{"mathvariant":1516},[1493,97629,1520],{},[1506,97631,2343],{},[1493,97633,3384],{},[1493,97635,1520],{},[1506,97637,1508],{},[1493,97639,1495],{},[1497,97641,97642,97644],{},[1493,97643,1501],{},[1493,97645,1556],{},[1988,97647,5016],{},[1493,97649,3384],{},[1493,97651,1556],{},[1528,97653,97654],{"encoding":1530},"\\Delta Q \\approx dQ = MP_L\\,dL",[1206,97656,97657,22970,97659,2632],{},[1047,97658,95914],{},[1035,97660,97662],{"className":97661},[1480],[1482,97663,97664],{"xmlns":1484},[1487,97665,97666,97684],{},[1490,97667,97668,97670,97672,97674,97676,97678,97680,97682],{},[1493,97669,1520],{},[1506,97671,1508],{},[1493,97673,1520],{},[1506,97675,1553],{"stretchy":1552},[1493,97677,1556],{},[1506,97679,1559],{"separator":1041},[1493,97681,1504],{},[1506,97683,1564],{"stretchy":1552},[1528,97685,97686],{"encoding":1530},"Q = Q(L, K)",[1206,97688,97689,22970,97691,2632],{},[1047,97690,90205],{},[1035,97692,97694],{"className":97693},[1480],[1482,97695,97696],{"xmlns":1484},[1487,97697,97698,97718],{},[1490,97699,97700,97702,97704,97706,97712],{},[1493,97701,1520],{},[1506,97703,1508],{},[1493,97705,3633],{},[2315,97707,97708,97710],{},[1493,97709,1556],{},[1493,97711,1052],{},[2315,97713,97714,97716],{},[1493,97715,1504],{},[1493,97717,2394],{},[1528,97719,87090],{"encoding":1530},[1206,97721,97722,22970,97725,97760],{},[1047,97723,97724],{},"Ryzí Cobb-Douglas",[1035,97726,97728],{"className":97727},[1480],[1482,97729,97730],{"xmlns":1484},[1487,97731,97732,97758],{},[1490,97733,97734,97736,97738,97740,97746],{},[1493,97735,1520],{},[1506,97737,1508],{},[1493,97739,3633],{},[2315,97741,97742,97744],{},[1493,97743,1556],{},[1493,97745,1052],{},[2315,97747,97748,97750],{},[1493,97749,1504],{},[1490,97751,97752,97754,97756],{},[1680,97753,1682],{},[1506,97755,1888],{},[1493,97757,1052],{},[1528,97759,91037],{"encoding":1530}," (konstantní výnosy).",[1206,97762,97763,22970,97765,2632],{},[1047,97764,91752],{},[1035,97766,97768],{"className":97767},[1480],[1482,97769,97770],{"xmlns":1484},[1487,97771,97772,97830],{},[1490,97773,97774,97776,97778,97780,97782,97784,97786,97788,97790,97792,97802,97804,97806,97816],{},[1493,97775,1520],{},[1506,97777,1508],{},[1493,97779,3633],{},[1506,97781,14314],{"stretchy":1552},[1506,97783,1553],{"stretchy":1552},[1680,97785,1682],{},[1506,97787,1888],{},[1493,97789,1052],{},[1506,97791,1564],{"stretchy":1552},[2315,97793,97794,97796],{},[1493,97795,1556],{},[1490,97797,97798,97800],{},[1506,97799,1888],{},[1493,97801,2394],{},[1506,97803,2162],{},[1493,97805,1052],{},[2315,97807,97808,97810],{},[1493,97809,1504],{},[1490,97811,97812,97814],{},[1506,97813,1888],{},[1493,97815,2394],{},[2315,97817,97818,97820],{},[1506,97819,14323],{"stretchy":1552},[1490,97821,97822,97824,97826,97828],{},[1506,97823,1888],{},[1680,97825,1682],{},[1493,97827,1709],{"mathvariant":1516},[1493,97829,2394],{},[1528,97831,97832],{"encoding":1530},"Q = A[(1-a)L^{-b} + aK^{-b}]^{-1\u002Fb}",[1206,97834,97835,7606,97838,28611,97860,7606,97863,97893],{},[1047,97836,97837],{},"Lineární",[1035,97839,97841],{"className":97840},[1480],[1482,97842,97843],{"xmlns":1484},[1487,97844,97845,97857],{},[1490,97846,97847,97849,97851,97853,97855],{},[1493,97848,1052],{},[1493,97850,1556],{},[1506,97852,2162],{},[1493,97854,2394],{},[1493,97856,1504],{},[1528,97858,97859],{"encoding":1530},"aL + bK",[1047,97861,97862],{},"Leontiefova",[1035,97864,97866],{"className":97865},[1480],[1482,97867,97868],{"xmlns":1484},[1487,97869,97870,97890],{},[1490,97871,97872,97874,97876,97878,97880,97882,97884,97886,97888],{},[1493,97873,91980],{},[1506,97875,7574],{},[1506,97877,1553],{"stretchy":1552},[1493,97879,1052],{},[1493,97881,1556],{},[1506,97883,1559],{"separator":1041},[1493,97885,2394],{},[1493,97887,1504],{},[1506,97889,1564],{"stretchy":1552},[1528,97891,97892],{"encoding":1530},"\\min(aL, bK)",") produkční funkce.",[1206,97895,97896,22970,97912,2632],{},[1047,97897,97898,97899],{},"Homogenita stupně ",[1035,97900,97902],{"className":97901},[1480],[1482,97903,97904],{"xmlns":1484},[1487,97905,97906,97910],{},[1490,97907,97908],{},[1493,97909,7781],{},[1528,97911,7781],{"encoding":1530},[1035,97913,97915],{"className":97914},[1480],[1482,97916,97917],{"xmlns":1484},[1487,97918,97919,97957],{},[1490,97920,97921,97923,97925,97927,97929,97931,97933,97935,97937,97939,97945,97947,97949,97951,97953,97955],{},[1493,97922,1520],{},[1506,97924,1553],{"stretchy":1552},[1493,97926,7740],{},[1493,97928,1556],{},[1506,97930,1559],{"separator":1041},[1493,97932,7740],{},[1493,97934,1504],{},[1506,97936,1564],{"stretchy":1552},[1506,97938,1508],{},[2315,97940,97941,97943],{},[1493,97942,7740],{},[1493,97944,7781],{},[1493,97946,1520],{},[1506,97948,1553],{"stretchy":1552},[1493,97950,1556],{},[1506,97952,1559],{"separator":1041},[1493,97954,1504],{},[1506,97956,1564],{"stretchy":1552},[1528,97958,97959],{"encoding":1530},"Q(rL, rK) = r^n Q(L, K)",[1206,97961,97962,91134],{},[1047,97963,91068,97964],{},[1035,97965,97967],{"className":97966},[1480],[1482,97968,97969],{"xmlns":1484},[1487,97970,97971,97975],{},[1490,97972,97973],{},[1493,97974,3633],{},[1528,97976,3633],{"encoding":1530},[1206,97978,97979,97981,97982,98004,98005,98027,98028,16623],{},[1047,97980,90564],{}," — konstantní (",[1035,97983,97985],{"className":97984},[1480],[1482,97986,97987],{"xmlns":1484},[1487,97988,97989,98001],{},[1490,97990,97991,97993,97995,97997,97999],{},[1493,97992,1052],{},[1506,97994,2162],{},[1493,97996,2394],{},[1506,97998,1508],{},[1680,98000,1682],{},[1528,98002,98003],{"encoding":1530},"a+b=1","), rostoucí (",[1035,98006,98008],{"className":98007},[1480],[1482,98009,98010],{"xmlns":1484},[1487,98011,98012,98024],{},[1490,98013,98014,98016,98018,98020,98022],{},[1493,98015,1052],{},[1506,98017,2162],{},[1493,98019,2394],{},[1506,98021,2796],{},[1680,98023,1682],{},[1528,98025,98026],{"encoding":1530},"a+b>1","), klesající (",[1035,98029,98031],{"className":98030},[1480],[1482,98032,98033],{"xmlns":1484},[1487,98034,98035,98047],{},[1490,98036,98037,98039,98041,98043,98045],{},[1493,98038,1052],{},[1506,98040,2162],{},[1493,98042,2394],{},[1506,98044,3961],{},[1680,98046,1682],{},[1528,98048,98049],{"encoding":1530},"a+b\u003C1",[1206,98051,98052,1656,98054,1732,98084,1656,98086,2632],{},[1047,98053,87451],{},[1035,98055,98057],{"className":98056},[1480],[1482,98058,98059],{"xmlns":1484},[1487,98060,98061,98081],{},[1490,98062,98063,98065,98071,98073],{},[1493,98064,1495],{},[1497,98066,98067,98069],{},[1493,98068,1501],{},[1493,98070,1556],{},[1506,98072,1508],{},[1697,98074,98075,98077,98079],{},[1493,98076,1520],{},[1493,98078,1556],{},[1506,98080,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,98082,98083],{"encoding":1530},"MP_L = Q'_L",[1047,98085,90137],{},[1035,98087,98089],{"className":98088},[1480],[1482,98090,98091],{"xmlns":1484},[1487,98092,98093,98113],{},[1490,98094,98095,98097,98103,98105],{},[1493,98096,1495],{},[1497,98098,98099,98101],{},[1493,98100,1501],{},[1493,98102,1504],{},[1506,98104,1508],{},[1697,98106,98107,98109,98111],{},[1493,98108,1520],{},[1493,98110,1504],{},[1506,98112,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,98114,98115],{"encoding":1530},"MP_K = Q'_K",[1206,98117,98118,1656,98120,2632],{},[1047,98119,92358],{},[1035,98121,98123],{"className":98122},[1480],[1482,98124,98125],{"xmlns":1484},[1487,98126,98127,98165],{},[1490,98128,98129,98131,98133,98135,98137,98143,98145,98147,98149,98151,98153,98159,98161,98163],{},[1493,98130,3384],{},[1493,98132,1520],{},[1506,98134,1508],{},[1493,98136,1495],{},[1497,98138,98139,98141],{},[1493,98140,1501],{},[1493,98142,1556],{},[1988,98144,5016],{},[1493,98146,3384],{},[1493,98148,1556],{},[1506,98150,2162],{},[1493,98152,1495],{},[1497,98154,98155,98157],{},[1493,98156,1501],{},[1493,98158,1504],{},[1988,98160,5016],{},[1493,98162,3384],{},[1493,98164,1504],{},[1528,98166,98167],{"encoding":1530},"dQ = MP_L\\,dL + MP_K\\,dK",[1206,98169,98170,22970,98172,2632],{},[1047,98171,92703],{},[1035,98173,98175],{"className":98174},[1480],[1482,98176,98177],{"xmlns":1484},[1487,98178,98179,98221],{},[1490,98180,98181,98183,98191,98193,98195,98203,98205,98207,98209,98211,98213,98215,98217,98219],{},[1493,98182,1556],{},[1697,98184,98185,98187,98189],{},[1493,98186,1520],{},[1493,98188,1556],{},[1506,98190,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,98192,2162],{},[1493,98194,1504],{},[1697,98196,98197,98199,98201],{},[1493,98198,1520],{},[1493,98200,1504],{},[1506,98202,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,98204,1508],{},[1493,98206,7781],{},[1988,98208,5016],{},[1493,98210,1520],{},[1506,98212,1553],{"stretchy":1552},[1493,98214,1556],{},[1506,98216,1559],{"separator":1041},[1493,98218,1504],{},[1506,98220,1564],{"stretchy":1552},[1528,98222,98223],{"encoding":1530},"L Q'_L + K Q'_K = n\\,Q(L,K)",[1206,98225,98226,98229,98230,2632],{},[1047,98227,98228],{},"Izokvanta"," — křivka ",[1035,98231,98233],{"className":98232},[1480],[1482,98234,98235],{"xmlns":1484},[1487,98236,98237,98255],{},[1490,98238,98239,98241,98243,98245,98247,98249,98251,98253],{},[1493,98240,1520],{},[1506,98242,1553],{"stretchy":1552},[1493,98244,1556],{},[1506,98246,1559],{"separator":1041},[1493,98248,1504],{},[1506,98250,1564],{"stretchy":1552},[1506,98252,1508],{},[1493,98254,7792],{},[1528,98256,98257],{"encoding":1530},"Q(L, K) = q",[1206,98259,98260,1656,98262,2632],{},[1047,98261,93070],{},[1035,98263,98265],{"className":98264},[1480],[1482,98266,98267],{"xmlns":1484},[1487,98268,98269,98299],{},[1490,98270,98271,98273,98275,98277,98279,98281,98283,98289,98291,98293],{},[1493,98272,1495],{},[1493,98274,1995],{},[1493,98276,5289],{},[1493,98278,2001],{},[1506,98280,1508],{},[1493,98282,1495],{},[1497,98284,98285,98287],{},[1493,98286,1501],{},[1493,98288,1556],{},[1493,98290,1709],{"mathvariant":1516},[1493,98292,1495],{},[1497,98294,98295,98297],{},[1493,98296,1501],{},[1493,98298,1504],{},[1528,98300,16194],{"encoding":1530},[1206,98302,98303,1656,98306,2632],{},[1047,98304,98305],{},"Substituční vztah",[1035,98307,98309],{"className":98308},[1480],[1482,98310,98311],{"xmlns":1484},[1487,98312,98313,98337],{},[1490,98314,98315,98317,98319,98321,98323,98325,98327,98329,98331,98333,98335],{},[1493,98316,2976],{"mathvariant":1516},[1493,98318,1504],{},[1506,98320,2343],{},[1506,98322,1888],{},[1493,98324,1495],{},[1493,98326,1995],{},[1493,98328,5289],{},[1493,98330,2001],{},[1988,98332,5016],{},[1493,98334,3384],{},[1493,98336,1556],{},[1528,98338,98339],{"encoding":1530},"\\Delta K \\approx -MRTS\\,dL",[1065,98341,17159],{"id":17158},[1203,98343,98344,98441,98448,98455],{},[1206,98345,98346,1656,98348,98351,98352,1732,98355,98358,98359,98362,98363,98382,98383,34788,98402,98405,98406,98425,98426,16623],{},[1047,98347,65057],{},[1052,98349,9472],{"className":98350,"dataFsResolvedFilePath":9470,"href":9471},[1055]," (parciální derivace, totální diferenciál), ",[1052,98353,3506],{"className":98354,"dataFsResolvedFilePath":16621,"href":16622},[1055],[1052,98356,17267],{"className":98357,"dataFsResolvedFilePath":17265,"href":17266},[1055]," (optimalizace produkce s rozpočtovým omezením), ",[1052,98360,6615],{"className":98361,"dataFsResolvedFilePath":6613,"href":6614},[1055]," (paralela: izokvanty ↔ indiferenční křivky, ",[1035,98364,98366],{"className":98365},[1480],[1482,98367,98368],{"xmlns":1484},[1487,98369,98370,98380],{},[1490,98371,98372,98374,98376,98378],{},[1493,98373,1495],{},[1493,98375,1995],{},[1493,98377,5289],{},[1493,98379,2001],{},[1528,98381,16555],{"encoding":1530}," ↔ ",[1035,98384,98386],{"className":98385},[1480],[1482,98387,98388],{"xmlns":1484},[1487,98389,98390,98400],{},[1490,98391,98392,98394,98396,98398],{},[1493,98393,1495],{},[1493,98395,1995],{},[1493,98397,1998],{},[1493,98399,2001],{},[1528,98401,13960],{"encoding":1530},[1052,98403,1301],{"className":98404,"dataFsResolvedFilePath":1299,"href":1300},[1055]," (analogie principu max ",[1035,98407,98409],{"className":98408},[1480],[1482,98410,98411],{"xmlns":1484},[1487,98412,98413,98423],{},[1490,98414,98415,98417],{},[1493,98416,3633],{},[1497,98418,98419,98421],{},[1493,98420,1501],{},[1493,98422,1556],{},[1528,98424,6827],{"encoding":1530}," ↔ min ",[1035,98427,98429],{"className":98428},[1480],[1482,98430,98431],{"xmlns":1484},[1487,98432,98433,98439],{},[1490,98434,98435,98437],{},[1493,98436,3633],{},[1493,98438,1998],{},[1528,98440,16523],{"encoding":1530},[1206,98442,98443,1656,98445,2632],{},[1047,98444,19217],{},[1052,98446,17218],{"className":98447,"dataFsResolvedFilePath":3807,"href":3808},[1055],[1206,98449,98450,1656,98452,2632],{},[1047,98451,32375],{},[1052,98453,17196],{"className":98454,"dataFsResolvedFilePath":17194,"href":17195},[1055],[1206,98456,98457,1656,98459,2632],{},[1047,98458,17176],{},[1052,98460,1058],{"className":98461,"dataFsResolvedFilePath":1056,"href":1057},[1055],{"title":17269,"searchDepth":141,"depth":141,"links":98463},[98464,98465,98466,98470,98472,98477,98478,98485,98486,98488,98489,98490,98492,98497,98498,98499,98503,98504],{"id":87187,"depth":141,"text":87188},{"id":87323,"depth":141,"text":87324},{"id":87426,"depth":141,"text":98467,"children":98468},"Mezní produkt práce (MPLMP_L)",[98469],{"id":87877,"depth":96,"text":87878},{"id":88366,"depth":141,"text":98471},"Průměrný produkt práce (APLAP_L)",{"id":88484,"depth":141,"text":88485,"children":98473},[98474,98475,98476],{"id":88725,"depth":96,"text":78068},{"id":89035,"depth":96,"text":89036},{"id":89671,"depth":96,"text":89672},{"id":90101,"depth":141,"text":90102},{"id":90204,"depth":141,"text":90205,"children":98479},[98480,98481,98483,98484],{"id":90563,"depth":96,"text":90564},{"id":91067,"depth":96,"text":98482},"Parametr efektivity AA",{"id":91137,"depth":96,"text":91138},{"id":52277,"depth":96,"text":91477},{"id":91664,"depth":141,"text":91665},{"id":92003,"depth":141,"text":98487},"Mezní produkty MPLMP_L, MPKMP_K a totální diferenciál",{"id":92697,"depth":141,"text":92698},{"id":225,"depth":141,"text":26311},{"id":93045,"depth":141,"text":98491},"Mezní míra technické substituce (MRTSMRTS)",{"id":93823,"depth":141,"text":93824,"children":98493},[98494,98495,98496],{"id":93827,"depth":96,"text":93828},{"id":94470,"depth":96,"text":94471},{"id":94699,"depth":96,"text":94700},{"id":95045,"depth":141,"text":95046},{"id":64216,"depth":141,"text":64217},{"id":95394,"depth":141,"text":95395,"children":98500},[98501,98502],{"id":55216,"depth":96,"text":55217},{"id":95913,"depth":96,"text":95914},{"id":31884,"depth":141,"text":31885},{"id":17158,"depth":141,"text":17159},{},"\u002Ftopics\u002Fprodukce",{"title":1574,"description":17269},[26098,26099],"topics\u002Fprodukce",[9,287,836,722,98,225,257,516],"Ffig8em78PwzbJ1wmJJMQidhh62tT2h69HrOQ0h5O0c",{"id":98513,"title":98514,"body":98515,"course":9,"courses":17424,"created":26093,"description":17269,"extension":17426,"meta":106957,"navigation":17428,"path":106958,"seo":106959,"sources":106960,"stem":106961,"tags":106962,"type":19275,"updated":26102,"__hash__":106963},"topics\u002Ftopics\u002Fuzitecnost.md","Užitečnost, Cobb-Douglasova funkce užitečnosti a optimalizace spotřebitele",{"type":1016,"value":98516,"toc":106931},[98517,98520,98522,98718,98727,98731,98734,98786,98790,98802,98806,98809,98826,98954,98960,99104,99113,99117,99152,99188,99236,99293,99353,99395,99976,99980,100063,100172,100265,100528,100531,100584,100695,100777,100781,100792,101025,101080,101086,101126,101189,101200,101354,101402,101407,101521,101559,101685,101731,101758,101835,101910,101990,102120,102181,102269,102273,102276,102345,102428,102435,102495,102808,102812,102818,102871,102887,102938,103077,103397,103401,103408,103572,103576,103598,103695,103815,103934,103957,104020,104077,104333,104341,104345,104352,104605,104655,104711,104714,104883,104887,104985,104987,105019,105023,105156,105398,105582,105750,106057,106190,106377,106395,106397,106832,106834],[1019,98518,98514],{"id":98519},"užitečnost-cobb-douglasova-funkce-užitečnosti-a-optimalizace-spotřebitele",[1065,98521,1042],{"id":28491},[1030,98523,98524,1656,98526,98557,98558,98561,98562,98592,98593,98611,98612,98651,98652,98655,98656,98669,98670,43819,98673,98686,98687,98700,98701,98714,98715,2632],{},[1047,98525,6615],{},[1035,98527,98529],{"className":98528},[1480],[1482,98530,98531],{"xmlns":1484},[1487,98532,98533,98555],{},[1490,98534,98535,98537,98539,98545,98547,98553],{},[1493,98536,1668],{},[1506,98538,1553],{"stretchy":1552},[1497,98540,98541,98543],{},[1493,98542,1520],{},[1680,98544,1682],{},[1506,98546,1559],{"separator":1041},[1497,98548,98549,98551],{},[1493,98550,1520],{},[1680,98552,1691],{},[1506,98554,1564],{"stretchy":1552},[1528,98556,32500],{"encoding":1530}," je číselné vyjádření uspokojení spotřebitele ze svazku zboží — v ordinalistickém přístupu slouží jen k ",[1047,98559,98560],{},"uspořádání"," svazků (nikoli k měření v jednotkách). Klíčové nástroje jsou mezní užitečnosti ",[1035,98563,98565],{"className":98564},[1480],[1482,98566,98567],{"xmlns":1484},[1487,98568,98569,98589],{},[1490,98570,98571,98573,98579,98581],{},[1493,98572,1495],{},[1497,98574,98575,98577],{},[1493,98576,1668],{},[1493,98578,6277],{},[1506,98580,1508],{},[1697,98582,98583,98585,98587],{},[1493,98584,1668],{},[1493,98586,6277],{},[1506,98588,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,98590,98591],{"encoding":1530},"MU_i = U'_i",", indiferenční křivky ",[1035,98594,98596],{"className":98595},[1480],[1482,98597,98598],{"xmlns":1484},[1487,98599,98600,98608],{},[1490,98601,98602,98604,98606],{},[1493,98603,1668],{},[1506,98605,1508],{},[1493,98607,8730],{},[1528,98609,98610],{"encoding":1530},"U = c"," a mezní míra komoditní substituce ",[1035,98613,98615],{"className":98614},[1480],[1482,98616,98617],{"xmlns":1484},[1487,98618,98619,98649],{},[1490,98620,98621,98623,98625,98627,98629,98631,98633,98639,98641,98643],{},[1493,98622,1495],{},[1493,98624,1995],{},[1493,98626,1998],{},[1493,98628,2001],{},[1506,98630,1508],{},[1493,98632,1495],{},[1497,98634,98635,98637],{},[1493,98636,1668],{},[1680,98638,1682],{},[1493,98640,1709],{"mathvariant":1516},[1493,98642,1495],{},[1497,98644,98645,98647],{},[1493,98646,1668],{},[1680,98648,1691],{},[1528,98650,9084],{"encoding":1530},". Tato stránka pokrývá ",[1047,98653,98654],{},"teorii užitečnosti"," — funkce ",[1035,98657,98659],{"className":98658},[1480],[1482,98660,98661],{"xmlns":1484},[1487,98662,98663,98667],{},[1490,98664,98665],{},[1493,98666,1668],{},[1528,98668,1668],{"encoding":1530},", její vlastnosti, Cobb-Douglasův tvar, indiferenční křivky a MRCS. ",[1047,98671,98672],{},"Optimalizaci spotřebitele",[1035,98674,98676],{"className":98675},[1480],[1482,98677,98678],{"xmlns":1484},[1487,98679,98680,98684],{},[1490,98681,98682],{},[1493,98683,1668],{},[1528,98685,1668],{"encoding":1530}," při rozpočtu, min ",[1035,98688,98690],{"className":98689},[1480],[1482,98691,98692],{"xmlns":1484},[1487,98693,98694,98698],{},[1490,98695,98696],{},[1493,98697,2711],{},[1528,98699,2711],{"encoding":1530}," při dané ",[1035,98702,98704],{"className":98703},[1480],[1482,98705,98706],{"xmlns":1484},[1487,98707,98708,98712],{},[1490,98709,98710],{},[1493,98711,1668],{},[1528,98713,1668],{"encoding":1530},", Lagrange, funkce poptávky) viz ",[1052,98716,1843],{"className":98717,"dataFsResolvedFilePath":1841,"href":1842},[1055],[1030,98719,98720,98721,98723,98724,2632],{},"Kapitola 6 knihy ",[1176,98722,1058],{}," — model rozhodování spotřebitele. Zde: funkce užitečnosti, indiferenční křivky, mezní míra komoditní substituce. Navazující optimalizace je v ",[1052,98725,774],{"className":98726,"dataFsResolvedFilePath":1841,"href":1842},[1055],[1065,98728,98730],{"id":98729},"úvod-cílové-znalosti-kapitoly-6","Úvod — cílové znalosti kapitoly 6",[1030,98732,98733],{},"Po prostudování této kapitoly byste měli umět:",[1203,98735,98736,98741,98750,98755,98758,98764,98770,98773,98779],{},[1206,98737,98738,98739,1559],{},"vyložit, co se rozumí termínem ",[1047,98740,6505],{},[1206,98742,98743,98744,1586,98747,1559],{},"definovat pojmy ",[1047,98745,98746],{},"svazek zboží",[1047,98748,98749],{},"funkce užitečnosti",[1206,98751,87202,98752,87209],{},[1047,98753,98754],{},"mezní užitečnosti",[1206,98756,98757],{},"vyjmenovat základní vlastnosti funkcí užitečnosti,",[1206,98759,87229,98760,98763],{},[1047,98761,98762],{},"Cobb-Douglasových"," funkcí užitečnosti,",[1206,98765,87250,98766,98769],{},[1047,98767,98768],{},"křivky užitečnosti"," (indiferenční křivky),",[1206,98771,98772],{},"vyjmenovat jejich základní vlastnosti,",[1206,98774,87202,98775,98778],{},[1047,98776,98777],{},"mezní míru komoditní substituce"," a ekonomicky ji interpretovat,",[1206,98780,98781,98782,98785],{},"řešit ",[1047,98783,98784],{},"optimalizační úlohy"," s ohledem na užitečnost.",[1065,98787,98789],{"id":98788},"_61-pojetí-užitečnosti","6.1 Pojetí užitečnosti",[1030,98791,98792,98793,98797,98798,98801],{},"Spotřebitel typicky přijímá tři typy rozhodnutí: (i) kolik kterého zboží či služby nakoupit, (ii) kolik času věnovat práci vs. odpočinku, (iii) zda spotřebovat více než důchod (půjčky) nebo méně (spoření). Teorie se soustředí na typ (i), který bezprostředně určuje ",[1052,98794,98796],{"className":98795,"dataFsResolvedFilePath":3487,"href":3488},[1055],"poptávku",". Centrálním pojmem je ",[1047,98799,98800],{},"užitečnost (utility)"," — vše, co vede spotřebitele k nákupu zboží (uspokojení, potěšení, splnění přání, pohodlí).",[1304,98803,98805],{"id":98804},"kardinalistický-vs-ordinalistický-přístup","Kardinalistický vs. ordinalistický přístup",[1030,98807,98808],{},"Historicky se vyvíjela dvě pojetí „měření\" užitečnosti:",[1203,98810,98811,98817],{},[1206,98812,98813,98816],{},[1047,98814,98815],{},"Kardinalistický přístup"," (19. století — Gossen, Jevons, Walras): užitečnost měřena kvantitativně (např. peněžními jednotkami). Tento přístup se ukázal být nevýhodný.",[1206,98818,98819,98822,98823,98825],{},[1047,98820,98821],{},"Ordinalistický přístup"," (v současnosti preferovaný): postačuje ",[1047,98824,98560],{}," svazků zboží podle preferencí; kvantitativní číselné hodnocení užitečnosti se nepožaduje.",[1023,98827,98829,98839],{"className":98828,"dataCallout":1155},[1026,1154],[1030,98830,98832,98835,98836],{"className":98831},[1033],[1035,98833],{"className":98834,"ariaHidden":1041},[1038,1162,1040],"Pozor — ordinalisté užitečnost ",[1047,98837,98838],{},"neměří",[1030,98840,98841,98842,1656,98855,98858,98859,1586,98872,98891,98892,1732,98918,98945,98946,98949,98950,98953],{},"V ordinalistickém přístupu hodnoty funkce ",[1035,98843,98845],{"className":98844},[1480],[1482,98846,98847],{"xmlns":1484},[1487,98848,98849,98853],{},[1490,98850,98851],{},[1493,98852,1668],{},[1528,98854,1668],{"encoding":1530},[1047,98856,98857],{},"nemají samostatný ekonomický význam"," — slouží pouze k uspořádání svazků. Dvě funkce ",[1035,98860,98862],{"className":98861},[1480],[1482,98863,98864],{"xmlns":1484},[1487,98865,98866,98870],{},[1490,98867,98868],{},[1493,98869,1668],{},[1528,98871,1668],{"encoding":1530},[1035,98873,98875],{"className":98874},[1480],[1482,98876,98877],{"xmlns":1484},[1487,98878,98879,98888],{},[1490,98880,98881],{},[2178,98882,98883,98885],{"accent":1041},[1493,98884,1668],{},[1506,98886,98887],{},"~",[1528,98889,98890],{"encoding":1530},"\\tilde U"," reprezentují tytéž preference, jsou-li navzájem monotónní transformací (např. ",[1035,98893,98895],{"className":98894},[1480],[1482,98896,98897],{"xmlns":1484},[1487,98898,98899,98915],{},[1490,98900,98901,98907,98909],{},[2178,98902,98903,98905],{"accent":1041},[1493,98904,1668],{},[1506,98906,98887],{},[1506,98908,1508],{},[2315,98910,98911,98913],{},[1493,98912,1668],{},[1680,98914,1691],{},[1528,98916,98917],{"encoding":1530},"\\tilde U = U^2",[1035,98919,98921],{"className":98920},[1480],[1482,98922,98923],{"xmlns":1484},[1487,98924,98925,98942],{},[1490,98926,98927,98933,98935,98938,98940],{},[2178,98928,98929,98931],{"accent":1041},[1493,98930,1668],{},[1506,98932,98887],{},[1506,98934,1508],{},[1493,98936,98937],{},"ln",[1506,98939,7574],{},[1493,98941,1668],{},[1528,98943,98944],{"encoding":1530},"\\tilde U = \\ln U","). Výroky typu „užitečnost je 250 jednotek\" proto samy o sobě nic neříkají — smysl mají jen ",[1047,98947,98948],{},"porovnání"," mezi svazky a ",[1047,98951,98952],{},"poměry"," mezních veličin.",[1030,98955,98956,98957,1274],{},"Ordinalistický přístup vychází z ",[1047,98958,98959],{},"pěti hlavních předpokladů",[1276,98961,98962,98968,98974,99092,99098],{},[1206,98963,98964,98967],{},[1047,98965,98966],{},"Racionalita."," Spotřebitel jedná racionálně — snaží se maximalizovat své uspokojení (užitečnost) s ohledem na daný důchod a tržní ceny; disponuje všemi potřebnými informacemi.",[1206,98969,98970,98973],{},[1047,98971,98972],{},"Ordinalita."," Spotřebitel dokáže uspořádat skupiny zboží podle míry uspokojení — rozhodne, který svazek je lepší, nebo zda jsou oba stejně dobré. Není však nutné, aby míru uspokojení vyjadřoval číselně.",[1206,98975,98976,98979,98980,75045,98993,99006,99007,75045,99020,18367,99033,99036,99037,1586,99056,75878,99074,2632],{},[1047,98977,98978],{},"Konzistence a tranzitivita."," Preferuje-li v jisté době svazek ",[1035,98981,98983],{"className":98982},[1480],[1482,98984,98985],{"xmlns":1484},[1487,98986,98987,98991],{},[1490,98988,98989],{},[1493,98990,3633],{},[1528,98992,3633],{"encoding":1530},[1035,98994,98996],{"className":98995},[1480],[1482,98997,98998],{"xmlns":1484},[1487,98999,99000,99004],{},[1490,99001,99002],{},[1493,99003,11353],{},[1528,99005,11353],{"encoding":1530},", nebude jindy preferovat ",[1035,99008,99010],{"className":99009},[1480],[1482,99011,99012],{"xmlns":1484},[1487,99013,99014,99018],{},[1490,99015,99016],{},[1493,99017,11353],{},[1528,99019,11353],{"encoding":1530},[1035,99021,99023],{"className":99022},[1480],[1482,99024,99025],{"xmlns":1484},[1487,99026,99027,99031],{},[1490,99028,99029],{},[1493,99030,3633],{},[1528,99032,3633],{"encoding":1530},[1047,99034,99035],{},"Tranzitivita",": pokud ",[1035,99038,99040],{"className":99039},[1480],[1482,99041,99042],{"xmlns":1484},[1487,99043,99044,99053],{},[1490,99045,99046,99048,99051],{},[1493,99047,3633],{},[1506,99049,99050],{},"≻",[1493,99052,11353],{},[1528,99054,99055],{"encoding":1530},"A \\succ B",[1035,99057,99059],{"className":99058},[1480],[1482,99060,99061],{"xmlns":1484},[1487,99062,99063,99071],{},[1490,99064,99065,99067,99069],{},[1493,99066,11353],{},[1506,99068,99050],{},[1493,99070,1998],{},[1528,99072,99073],{"encoding":1530},"B \\succ C",[1035,99075,99077],{"className":99076},[1480],[1482,99078,99079],{"xmlns":1484},[1487,99080,99081,99089],{},[1490,99082,99083,99085,99087],{},[1493,99084,3633],{},[1506,99086,99050],{},[1493,99088,1998],{},[1528,99090,99091],{"encoding":1530},"A \\succ C",[1206,99093,99094,99097],{},[1047,99095,99096],{},"Rostoucí užitečnost."," Uspokojení roste s množstvím zboží.",[1206,99099,99100,99103],{},[1047,99101,99102],{},"Klesající mezní užitečnost."," „Přírůstky\" uspokojení klesají s růstem množství zboží.",[1030,99105,99106,99107,99109,99110,2632],{},"K naplnění předpokladů je ordinalistický přístup založen na pojmech ",[1176,99108,812],{}," a na příbuzné ",[1176,99111,99112],{},"funkci užitečnosti",[1065,99114,99116],{"id":99115},"_62-model-užitečnosti-svazek-zboží-a-funkce-užitečnosti","6.2 Model užitečnosti — svazek zboží a funkce užitečnosti",[1030,99118,99119,99120,99133,99134,99137,99138,99151],{},"Uvažujme ",[1035,99121,99123],{"className":99122},[1480],[1482,99124,99125],{"xmlns":1484},[1487,99126,99127,99131],{},[1490,99128,99129],{},[1493,99130,7781],{},[1528,99132,7781],{"encoding":1530}," různých zboží. ",[1047,99135,99136],{},"Svazek zboží (bundle of goods)"," je uspořádaná ",[1035,99139,99141],{"className":99140},[1480],[1482,99142,99143],{"xmlns":1484},[1487,99144,99145,99149],{},[1490,99146,99147],{},[1493,99148,7781],{},[1528,99150,7781],{"encoding":1530},"-tice",[1035,99153,99155],{"className":99154},[1480],[1482,99156,99157],{"xmlns":1484,"display":1485},[1487,99158,99159,99185],{},[1490,99160,99161,99163,99169,99171,99173,99175,99181,99183],{},[1506,99162,1553],{"stretchy":1552},[1497,99164,99165,99167],{},[1493,99166,1520],{},[1680,99168,1682],{},[1506,99170,1559],{"separator":1041},[1506,99172,26181],{},[1506,99174,1559],{"separator":1041},[1497,99176,99177,99179],{},[1493,99178,1520],{},[1493,99180,7781],{},[1506,99182,1564],{"stretchy":1552},[1506,99184,1559],{"separator":1041},[1528,99186,99187],{"encoding":1530}," (Q_1, \\dots, Q_n), ",[1030,99189,20022,99190,99207,99208,99221,99222,99225,99226,99229,99230,99233,99234,1274],{},[1035,99191,99193],{"className":99192},[1480],[1482,99194,99195],{"xmlns":1484},[1487,99196,99197,99205],{},[1490,99198,99199],{},[1497,99200,99201,99203],{},[1493,99202,1520],{},[1493,99204,6277],{},[1528,99206,61873],{"encoding":1530}," značí množství ",[1035,99209,99211],{"className":99210},[1480],[1482,99212,99213],{"xmlns":1484},[1487,99214,99215,99219],{},[1490,99216,99217],{},[1493,99218,6277],{},[1528,99220,6277],{"encoding":1530},"-tého zboží. Spotřebitel je schopen svazky ",[1047,99223,99224],{},"uspořádat"," s rostoucí užitečností, případně je prohlásit za ",[1047,99227,99228],{},"indiferentní"," (tj. stejně užitečné). Tím je definována ",[1047,99231,99232],{},"relace preference",". Preferenci vyjadřujeme číselně: svazku preferovanému přiřadíme větší číslo, indiferentním svazkům stejné číslo. Dostáváme ",[1047,99235,99112],{},[1035,99237,99239],{"className":99238},[1480],[1482,99240,99241],{"xmlns":1484,"display":1485},[1487,99242,99243,99290],{},[19617,99244,99245],{"width":19619},[19621,99246,99247,99249,99283,99285],{},[19624,99248],{"width":19626},[19624,99250,99251],{},[1490,99252,99253,99255,99257,99259,99261,99267,99269,99271,99273,99279,99281],{},[1493,99254,1668],{},[1506,99256,1508],{},[1493,99258,1668],{},[1506,99260,1553],{"stretchy":1552},[1497,99262,99263,99265],{},[1493,99264,1520],{},[1680,99266,1682],{},[1506,99268,1559],{"separator":1041},[1506,99270,26181],{},[1506,99272,1559],{"separator":1041},[1497,99274,99275,99277],{},[1493,99276,1520],{},[1493,99278,7781],{},[1506,99280,1564],{"stretchy":1552},[1506,99282,1559],{"separator":1041},[19624,99284],{"width":19626},[19624,99286,99287],{},[1988,99288,99289],{},"(6.1)",[1528,99291,99292],{"encoding":1530},"U = U(Q_1, \\dots, Q_n), \\tag{6.1}",[1030,99294,20022,99295,99325,99326,99348,99349,99352],{},[1035,99296,99298],{"className":99297},[1480],[1482,99299,99300],{"xmlns":1484},[1487,99301,99302,99322],{},[1490,99303,99304,99310,99312,99314,99316],{},[1497,99305,99306,99308],{},[1493,99307,1520],{},[1680,99309,1682],{},[1506,99311,1559],{"separator":1041},[1506,99313,26181],{},[1506,99315,1559],{"separator":1041},[1497,99317,99318,99320],{},[1493,99319,1520],{},[1493,99321,7781],{},[1528,99323,99324],{"encoding":1530},"Q_1, \\dots, Q_n"," jsou množství jednotlivých zboží. Funkce užitečnosti (utility function) „umisťuje\" svazky na určitá místa v posloupnosti preference — sama žádnou konkrétní hodnotu uspokojení neměří. Dvě funkce ",[1035,99327,99329],{"className":99328},[1480],[1482,99330,99331],{"xmlns":1484},[1487,99332,99333,99345],{},[1490,99334,99335,99337,99339],{},[1493,99336,1668],{},[1506,99338,1559],{"separator":1041},[2178,99340,99341,99343],{"accent":1041},[1493,99342,1668],{},[1506,99344,98887],{},[1528,99346,99347],{"encoding":1530},"U, \\tilde U"," reprezentují stejné preference, pokud mezi nimi existuje ",[1047,99350,99351],{},"monotónní transformace"," zachovávající pořadí.",[1030,99354,99355,99356,22970,99359,2632],{},"Dále se omezíme na funkce pro ",[1047,99357,99358],{},"dvě zboží",[1035,99360,99362],{"className":99361},[1480],[1482,99363,99364],{"xmlns":1484},[1487,99365,99366,99392],{},[1490,99367,99368,99370,99372,99374,99376,99382,99384,99390],{},[1493,99369,1668],{},[1506,99371,1508],{},[1493,99373,1668],{},[1506,99375,1553],{"stretchy":1552},[1497,99377,99378,99380],{},[1493,99379,1520],{},[1680,99381,1682],{},[1506,99383,1559],{"separator":1041},[1497,99385,99386,99388],{},[1493,99387,1520],{},[1680,99389,1691],{},[1506,99391,1564],{"stretchy":1552},[1528,99393,99394],{"encoding":1530},"U = U(Q_1, Q_2)",[1023,99396,99398,99405,99477],{"className":99397,"dataCallout":66935},[1026,66934],[1030,99399,99401,99404],{"className":99400},[1033],[1035,99402],{"className":99403,"ariaHidden":1041},[1038,66942,1040],"Příklad 6.1 — uspořádání a indiference",[1030,99406,2364,99407,1274],{},[1035,99408,99410],{"className":99409},[1480],[1482,99411,99412],{"xmlns":1484},[1487,99413,99414,99474],{},[1490,99415,99416,99418,99420,99422,99424,99430,99432,99438,99440,99446,99448,99450,99452],{},[1493,99417,1668],{},[1506,99419,1508],{},[1493,99421,1668],{},[1506,99423,1553],{"stretchy":1552},[1497,99425,99426,99428],{},[1493,99427,1520],{},[1680,99429,1682],{},[1506,99431,1559],{"separator":1041},[1497,99433,99434,99436],{},[1493,99435,1520],{},[1680,99437,1691],{},[1506,99439,1559],{"separator":1041},[1497,99441,99442,99444],{},[1493,99443,1520],{},[1680,99445,3201],{},[1506,99447,1564],{"stretchy":1552},[1506,99449,1508],{},[1680,99451,1691],{},[2324,99453,99454],{},[1490,99455,99456,99462,99468],{},[1497,99457,99458,99460],{},[1493,99459,1520],{},[1680,99461,1682],{},[1497,99463,99464,99466],{},[1493,99465,1520],{},[1680,99467,1691],{},[1497,99469,99470,99472],{},[1493,99471,1520],{},[1680,99473,3201],{},[1528,99475,99476],{"encoding":1530},"U = U(Q_1, Q_2, Q_3) = 2\\sqrt{Q_1 Q_2 Q_3}",[1203,99478,99479,99672],{},[1206,99480,99481,99482,99508,99509,29411,99535,1586,99594,21352,99654,6065],{},"svazek ",[1035,99483,99485],{"className":99484},[1480],[1482,99486,99487],{"xmlns":1484},[1487,99488,99489,99505],{},[1490,99490,99491,99493,99495,99497,99499,99501,99503],{},[1506,99492,1553],{"stretchy":1552},[1680,99494,9961],{},[1506,99496,1559],{"separator":1041},[1680,99498,4007],{},[1506,99500,1559],{"separator":1041},[1680,99502,7466],{},[1506,99504,1564],{"stretchy":1552},[1528,99506,99507],{"encoding":1530},"(16, 4, 64)"," je preferován před ",[1035,99510,99512],{"className":99511},[1480],[1482,99513,99514],{"xmlns":1484},[1487,99515,99516,99532],{},[1490,99517,99518,99520,99522,99524,99526,99528,99530],{},[1506,99519,1553],{"stretchy":1552},[1680,99521,14365],{},[1506,99523,1559],{"separator":1041},[1680,99525,14365],{},[1506,99527,1559],{"separator":1041},[1680,99529,15165],{},[1506,99531,1564],{"stretchy":1552},[1528,99533,99534],{"encoding":1530},"(9, 9, 27)",[1035,99536,99538],{"className":99537},[1480],[1482,99539,99540],{"xmlns":1484},[1487,99541,99542,99591],{},[1490,99543,99544,99546,99548,99550,99552,99554,99556,99558,99560,99562,99564,99578,99580,99582,99587,99589],{},[1493,99545,1668],{},[1506,99547,1553],{"stretchy":1552},[1680,99549,9961],{},[1506,99551,1559],{"separator":1041},[1680,99553,4007],{},[1506,99555,1559],{"separator":1041},[1680,99557,7466],{},[1506,99559,1564],{"stretchy":1552},[1506,99561,1508],{},[1680,99563,1691],{},[2324,99565,99566],{},[1490,99567,99568,99570,99572,99574,99576],{},[1680,99569,9961],{},[1506,99571,1714],{},[1680,99573,4007],{},[1506,99575,1714],{},[1680,99577,7466],{},[1506,99579,1508],{},[1680,99581,1691],{},[2324,99583,99584],{},[1680,99585,99586],{},"4096",[1506,99588,1508],{},[1680,99590,21380],{},[1528,99592,99593],{"encoding":1530},"U(16,4,64) = 2\\sqrt{16 \\cdot 4 \\cdot 64} = 2\\sqrt{4096} = 128",[1035,99595,99597],{"className":99596},[1480],[1482,99598,99599],{"xmlns":1484},[1487,99600,99601,99651],{},[1490,99602,99603,99605,99607,99609,99611,99613,99615,99617,99619,99621,99623,99637,99639,99641,99646,99648],{},[1493,99604,1668],{},[1506,99606,1553],{"stretchy":1552},[1680,99608,14365],{},[1506,99610,1559],{"separator":1041},[1680,99612,14365],{},[1506,99614,1559],{"separator":1041},[1680,99616,15165],{},[1506,99618,1564],{"stretchy":1552},[1506,99620,1508],{},[1680,99622,1691],{},[2324,99624,99625],{},[1490,99626,99627,99629,99631,99633,99635],{},[1680,99628,14365],{},[1506,99630,1714],{},[1680,99632,14365],{},[1506,99634,1714],{},[1680,99636,15165],{},[1506,99638,1508],{},[1680,99640,1691],{},[2324,99642,99643],{},[1680,99644,99645],{},"2187",[1506,99647,21771],{},[1680,99649,99650],{},"93,53",[1528,99652,99653],{"encoding":1530},"U(9,9,27) = 2\\sqrt{9 \\cdot 9 \\cdot 27} = 2\\sqrt{2187} \\doteq 93{,}53",[1035,99655,99657],{"className":99656},[1480],[1482,99658,99659],{"xmlns":1484},[1487,99660,99661,99669],{},[1490,99662,99663,99665,99667],{},[1680,99664,21380],{},[1506,99666,2796],{},[1680,99668,99650],{},[1528,99670,99671],{"encoding":1530},"128 > 93{,}53",[1206,99673,99674,99675,1586,99701,99727,99728,1586,99768,99809,99810,99856,99857,1586,99883,18288,99909,1586,99927,99945,99946,2632],{},"svazky ",[1035,99676,99678],{"className":99677},[1480],[1482,99679,99680],{"xmlns":1484},[1487,99681,99682,99698],{},[1490,99683,99684,99686,99688,99690,99692,99694,99696],{},[1506,99685,1553],{"stretchy":1552},[1680,99687,4007],{},[1506,99689,1559],{"separator":1041},[1680,99691,6138],{},[1506,99693,1559],{"separator":1041},[1680,99695,1691],{},[1506,99697,1564],{"stretchy":1552},[1528,99699,99700],{"encoding":1530},"(4, 8, 2)",[1035,99702,99704],{"className":99703},[1480],[1482,99705,99706],{"xmlns":1484},[1487,99707,99708,99724],{},[1490,99709,99710,99712,99714,99716,99718,99720,99722],{},[1506,99711,1553],{"stretchy":1552},[1680,99713,7466],{},[1506,99715,1559],{"separator":1041},[1680,99717,1682],{},[1506,99719,1559],{"separator":1041},[1680,99721,4007],{},[1506,99723,1564],{"stretchy":1552},[1528,99725,99726],{"encoding":1530},"(64, 1, 4)"," jsou indiferentní, protože ",[1035,99729,99731],{"className":99730},[1480],[1482,99732,99733],{"xmlns":1484},[1487,99734,99735,99765],{},[1490,99736,99737,99739,99741,99743,99745,99747,99749,99751,99753,99755,99757,99761,99763],{},[1493,99738,1668],{},[1506,99740,1553],{"stretchy":1552},[1680,99742,4007],{},[1506,99744,1559],{"separator":1041},[1680,99746,6138],{},[1506,99748,1559],{"separator":1041},[1680,99750,1691],{},[1506,99752,1564],{"stretchy":1552},[1506,99754,1508],{},[1680,99756,1691],{},[2324,99758,99759],{},[1680,99760,7466],{},[1506,99762,1508],{},[1680,99764,9961],{},[1528,99766,99767],{"encoding":1530},"U(4,8,2) = 2\\sqrt{64} = 16",[1035,99769,99771],{"className":99770},[1480],[1482,99772,99773],{"xmlns":1484},[1487,99774,99775,99806],{},[1490,99776,99777,99779,99781,99783,99785,99787,99789,99791,99793,99795,99797,99802,99804],{},[1493,99778,1668],{},[1506,99780,1553],{"stretchy":1552},[1680,99782,7466],{},[1506,99784,1559],{"separator":1041},[1680,99786,1682],{},[1506,99788,1559],{"separator":1041},[1680,99790,4007],{},[1506,99792,1564],{"stretchy":1552},[1506,99794,1508],{},[1680,99796,1691],{},[2324,99798,99799],{},[1680,99800,99801],{},"256",[1506,99803,1508],{},[1680,99805,84726],{},[1528,99807,99808],{"encoding":1530},"U(64,1,4) = 2\\sqrt{256} = 32"," — jsou stejně užitečné mezi sebou, pokud ",[1035,99811,99813],{"className":99812},[1480],[1482,99814,99815],{"xmlns":1484},[1487,99816,99817,99853],{},[1490,99818,99819,99821,99823,99825,99827,99829,99831,99833,99835,99837,99839,99841,99843,99845,99847,99849,99851],{},[1493,99820,1668],{},[1506,99822,1553],{"stretchy":1552},[1680,99824,4007],{},[1506,99826,1559],{"separator":1041},[1680,99828,6138],{},[1506,99830,1559],{"separator":1041},[1680,99832,1691],{},[1506,99834,1564],{"stretchy":1552},[1506,99836,1508],{},[1493,99838,1668],{},[1506,99840,1553],{"stretchy":1552},[1680,99842,7466],{},[1506,99844,1559],{"separator":1041},[1680,99846,1682],{},[1506,99848,1559],{"separator":1041},[1680,99850,4007],{},[1506,99852,1564],{"stretchy":1552},[1528,99854,99855],{"encoding":1530},"U(4,8,2) = U(64,1,4)","; ověření: ",[1035,99858,99860],{"className":99859},[1480],[1482,99861,99862],{"xmlns":1484},[1487,99863,99864,99880],{},[1490,99865,99866,99868,99870,99872,99874,99876,99878],{},[1680,99867,4007],{},[1506,99869,1714],{},[1680,99871,6138],{},[1506,99873,1714],{},[1680,99875,1691],{},[1506,99877,1508],{},[1680,99879,7466],{},[1528,99881,99882],{"encoding":1530},"4 \\cdot 8 \\cdot 2 = 64",[1035,99884,99886],{"className":99885},[1480],[1482,99887,99888],{"xmlns":1484},[1487,99889,99890,99906],{},[1490,99891,99892,99894,99896,99898,99900,99902,99904],{},[1680,99893,7466],{},[1506,99895,1714],{},[1680,99897,1682],{},[1506,99899,1714],{},[1680,99901,4007],{},[1506,99903,1508],{},[1680,99905,99801],{},[1528,99907,99908],{"encoding":1530},"64 \\cdot 1 \\cdot 4 = 256",[1035,99910,99912],{"className":99911},[1480],[1482,99913,99914],{"xmlns":1484},[1487,99915,99916,99924],{},[1490,99917,99918,99920,99922],{},[1493,99919,1668],{},[1506,99921,1508],{},[1680,99923,9961],{},[1528,99925,99926],{"encoding":1530},"U = 16",[1035,99928,99930],{"className":99929},[1480],[1482,99931,99932],{"xmlns":1484},[1487,99933,99934,99942],{},[1490,99935,99936,99938,99940],{},[1493,99937,1668],{},[1506,99939,1508],{},[1680,99941,84726],{},[1528,99943,99944],{"encoding":1530},"U = 32"," — nejsou indiferentní. Správně indiferentní jsou svazky s týmž součinem ",[1035,99947,99949],{"className":99948},[1480],[1482,99950,99951],{"xmlns":1484},[1487,99952,99953,99973],{},[1490,99954,99955,99961,99967],{},[1497,99956,99957,99959],{},[1493,99958,1520],{},[1680,99960,1682],{},[1497,99962,99963,99965],{},[1493,99964,1520],{},[1680,99966,1691],{},[1497,99968,99969,99971],{},[1493,99970,1520],{},[1680,99972,3201],{},[1528,99974,99975],{"encoding":1530},"Q_1 Q_2 Q_3",[1065,99977,99979],{"id":99978},"mezní-užitečnost-mu","Mezní užitečnost (MU)",[1030,99981,99982,99983,8994,100018,1656,100021,56364,100038,7606,100055,100058,100059,100062],{},"Pro funkci užitečnosti ",[1035,99984,99986],{"className":99985},[1480],[1482,99987,99988],{"xmlns":1484},[1487,99989,99990,100016],{},[1490,99991,99992,99994,99996,99998,100000,100006,100008,100014],{},[1493,99993,1668],{},[1506,99995,1508],{},[1493,99997,1668],{},[1506,99999,1553],{"stretchy":1552},[1497,100001,100002,100004],{},[1493,100003,1520],{},[1680,100005,1682],{},[1506,100007,1559],{"separator":1041},[1497,100009,100010,100012],{},[1493,100011,1520],{},[1680,100013,1691],{},[1506,100015,1564],{"stretchy":1552},[1528,100017,99394],{"encoding":1530},[1047,100019,100020],{},"mezní užitečnost",[1035,100022,100024],{"className":100023},[1480],[1482,100025,100026],{"xmlns":1484},[1487,100027,100028,100036],{},[1490,100029,100030],{},[1497,100031,100032,100034],{},[1493,100033,1520],{},[1680,100035,1682],{},[1528,100037,6702],{"encoding":1530},[1035,100039,100041],{"className":100040},[1480],[1482,100042,100043],{"xmlns":1484},[1487,100044,100045,100053],{},[1490,100046,100047],{},[1497,100048,100049,100051],{},[1493,100050,1520],{},[1680,100052,1691],{},[1528,100054,6683],{"encoding":1530},[1047,100056,100057],{},"marginal utility",") parciální ",[1052,100060,102],{"className":100061,"dataFsResolvedFilePath":16621,"href":16622},[1055]," užitečnosti podle příslušné proměnné:",[1035,100064,100066],{"className":100065},[1480],[1482,100067,100068],{"xmlns":1484,"display":1485},[1487,100069,100070,100169],{},[19617,100071,100072],{"width":19619},[19621,100073,100074,100076,100162,100164],{},[19624,100075],{"width":19626},[19624,100077,100078],{},[1490,100079,100080,100082,100088,100090,100098,100100,100118,100120,100122,100124,100130,100132,100140,100142,100160],{},[1493,100081,1495],{},[1497,100083,100084,100086],{},[1493,100085,1668],{},[1680,100087,1682],{},[1506,100089,1508],{},[1697,100091,100092,100094,100096],{},[1493,100093,1668],{},[1680,100095,1682],{},[1506,100097,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,100099,1508],{},[1510,100101,100102,100108],{},[1490,100103,100104,100106],{},[1493,100105,1517],{"mathvariant":1516},[1493,100107,1668],{},[1490,100109,100110,100112],{},[1493,100111,1517],{"mathvariant":1516},[1497,100113,100114,100116],{},[1493,100115,1520],{},[1680,100117,1682],{},[1506,100119,1559],{"separator":1041},[1912,100121],{"width":2108},[1493,100123,1495],{},[1497,100125,100126,100128],{},[1493,100127,1668],{},[1680,100129,1691],{},[1506,100131,1508],{},[1697,100133,100134,100136,100138],{},[1493,100135,1668],{},[1680,100137,1691],{},[1506,100139,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,100141,1508],{},[1510,100143,100144,100150],{},[1490,100145,100146,100148],{},[1493,100147,1517],{"mathvariant":1516},[1493,100149,1668],{},[1490,100151,100152,100154],{},[1493,100153,1517],{"mathvariant":1516},[1497,100155,100156,100158],{},[1493,100157,1520],{},[1680,100159,1691],{},[1493,100161,2632],{"mathvariant":1516},[19624,100163],{"width":19626},[19624,100165,100166],{},[1988,100167,100168],{},"(6.2)",[1528,100170,100171],{"encoding":1530},"MU_1 = U'_1 = \\frac{\\partial U}{\\partial Q_1}, \\quad MU_2 = U'_2 = \\frac{\\partial U}{\\partial Q_2}. \\tag{6.2}",[1030,100173,100174,100175,100209,100210,100240,100241,1656,100244,2632],{},"Pro pevné ",[1035,100176,100178],{"className":100177},[1480],[1482,100179,100180],{"xmlns":1484},[1487,100181,100182,100206],{},[1490,100183,100184,100190,100192,100194,100196,100202,100204],{},[1497,100185,100186,100188],{},[1493,100187,1520],{},[1680,100189,1682],{},[1506,100191,1508],{},[1493,100193,1052],{},[1506,100195,1559],{"separator":1041},[1497,100197,100198,100200],{},[1493,100199,1520],{},[1680,100201,1691],{},[1506,100203,1508],{},[1493,100205,2394],{},[1528,100207,100208],{"encoding":1530},"Q_1 = a, Q_2 = b"," se hodnota ",[1035,100211,100213],{"className":100212},[1480],[1482,100214,100215],{"xmlns":1484},[1487,100216,100217,100237],{},[1490,100218,100219,100221,100227,100229,100231,100233,100235],{},[1493,100220,1495],{},[1497,100222,100223,100225],{},[1493,100224,1668],{},[1680,100226,1682],{},[1506,100228,1553],{"stretchy":1552},[1493,100230,1052],{},[1506,100232,1559],{"separator":1041},[1493,100234,2394],{},[1506,100236,1564],{"stretchy":1552},[1528,100238,100239],{"encoding":1530},"MU_1(a, b)"," nazývá mezní užitečnost ",[1047,100242,100243],{},"v bodě (na hladině)",[1035,100245,100247],{"className":100246},[1480],[1482,100248,100249],{"xmlns":1484},[1487,100250,100251,100263],{},[1490,100252,100253,100255,100257,100259,100261],{},[1506,100254,14314],{"stretchy":1552},[1493,100256,1052],{},[1506,100258,1559],{"separator":1041},[1493,100260,2394],{},[1506,100262,14323],{"stretchy":1552},[1528,100264,27339],{"encoding":1530},[1023,100266,100268,100305],{"className":100267,"dataCallout":582},[1026,1186],[1030,100269,100271,100274,100275],{"className":100270},[1033],[1035,100272],{"className":100273,"ariaHidden":1041},[1038,1193,1040],"Intuice — co říká ",[1035,100276,100278],{"className":100277},[1480],[1482,100279,100280],{"xmlns":1484},[1487,100281,100282,100302],{},[1490,100283,100284,100286,100292,100294,100296,100298,100300],{},[1493,100285,1495],{},[1497,100287,100288,100290],{},[1493,100289,1668],{},[1680,100291,1682],{},[1506,100293,1553],{"stretchy":1552},[1493,100295,1052],{},[1506,100297,1559],{"separator":1041},[1493,100299,2394],{},[1506,100301,1564],{"stretchy":1552},[1528,100303,100304],{"encoding":1530},"MU_1(a,b)",[1030,100306,100307,100336,100337,18065,100350,11713,100367,100388,100389,18125,100406,18139,100419,100436,100437,100459,100460,100489,100490,22345,100510,100527],{},[1035,100308,100310],{"className":100309},[1480],[1482,100311,100312],{"xmlns":1484},[1487,100313,100314,100334],{},[1490,100315,100316,100318,100324,100326,100328,100330,100332],{},[1493,100317,1495],{},[1497,100319,100320,100322],{},[1493,100321,1668],{},[1680,100323,1682],{},[1506,100325,1553],{"stretchy":1552},[1493,100327,1052],{},[1506,100329,1559],{"separator":1041},[1493,100331,2394],{},[1506,100333,1564],{"stretchy":1552},[1528,100335,100239],{"encoding":1530}," je rychlost změny ",[1035,100338,100340],{"className":100339},[1480],[1482,100341,100342],{"xmlns":1484},[1487,100343,100344,100348],{},[1490,100345,100346],{},[1493,100347,1668],{},[1528,100349,1668],{"encoding":1530},[1035,100351,100353],{"className":100352},[1480],[1482,100354,100355],{"xmlns":1484},[1487,100356,100357,100365],{},[1490,100358,100359],{},[1497,100360,100361,100363],{},[1493,100362,1520],{},[1680,100364,1682],{},[1528,100366,6702],{"encoding":1530},[1035,100368,100370],{"className":100369},[1480],[1482,100371,100372],{"xmlns":1484},[1487,100373,100374,100386],{},[1490,100375,100376,100378,100380,100382,100384],{},[1506,100377,14314],{"stretchy":1552},[1493,100379,1052],{},[1506,100381,1559],{"separator":1041},[1493,100383,2394],{},[1506,100385,14323],{"stretchy":1552},[1528,100387,27339],{"encoding":1530},". Přibližně: změní-li se ",[1035,100390,100392],{"className":100391},[1480],[1482,100393,100394],{"xmlns":1484},[1487,100395,100396,100404],{},[1490,100397,100398],{},[1497,100399,100400,100402],{},[1493,100401,1520],{},[1680,100403,1682],{},[1528,100405,6702],{"encoding":1530},[1035,100407,100409],{"className":100408},[1480],[1482,100410,100411],{"xmlns":1484},[1487,100412,100413,100417],{},[1490,100414,100415],{},[1493,100416,1052],{},[1528,100418,1052],{"encoding":1530},[1035,100420,100422],{"className":100421},[1480],[1482,100423,100424],{"xmlns":1484},[1487,100425,100426,100434],{},[1490,100427,100428,100430,100432],{},[1493,100429,1052],{},[1506,100431,2162],{},[1680,100433,1682],{},[1528,100435,18157],{"encoding":1530}," při pevném ",[1035,100438,100440],{"className":100439},[1480],[1482,100441,100442],{"xmlns":1484},[1487,100443,100444,100456],{},[1490,100445,100446,100452,100454],{},[1497,100447,100448,100450],{},[1493,100449,1520],{},[1680,100451,1691],{},[1506,100453,1508],{},[1493,100455,2394],{},[1528,100457,100458],{"encoding":1530},"Q_2 = b",", změní se užitečnost zhruba o ",[1035,100461,100463],{"className":100462},[1480],[1482,100464,100465],{"xmlns":1484},[1487,100466,100467,100487],{},[1490,100468,100469,100471,100477,100479,100481,100483,100485],{},[1493,100470,1495],{},[1497,100472,100473,100475],{},[1493,100474,1668],{},[1680,100476,1682],{},[1506,100478,1553],{"stretchy":1552},[1493,100480,1052],{},[1506,100482,1559],{"separator":1041},[1493,100484,2394],{},[1506,100486,1564],{"stretchy":1552},[1528,100488,100239],{"encoding":1530},". Stejně tak ",[1035,100491,100493],{"className":100492},[1480],[1482,100494,100495],{"xmlns":1484},[1487,100496,100497,100507],{},[1490,100498,100499,100501],{},[1493,100500,1495],{},[1497,100502,100503,100505],{},[1493,100504,1668],{},[1680,100506,1691],{},[1528,100508,100509],{"encoding":1530},"MU_2",[1035,100511,100513],{"className":100512},[1480],[1482,100514,100515],{"xmlns":1484},[1487,100516,100517,100525],{},[1490,100518,100519],{},[1497,100520,100521,100523],{},[1493,100522,1520],{},[1680,100524,1691],{},[1528,100526,6683],{"encoding":1530},". Mezní užitečnost tedy odpovídá „užitku z další jednotky\" a podle předpokladu 5 s množstvím klesá.",[1304,100529,92358],{"id":100530},"totální-diferenciál",[1030,100532,100533,100534,62675,100550,100580,100581,1274],{},"Přibližnou změnu užitečnosti ",[1035,100535,100537],{"className":100536},[1480],[1482,100538,100539],{"xmlns":1484},[1487,100540,100541,100547],{},[1490,100542,100543,100545],{},[1493,100544,2976],{"mathvariant":1516},[1493,100546,1668],{},[1528,100548,100549],{"encoding":1530},"\\Delta U",[1035,100551,100553],{"className":100552},[1480],[1482,100554,100555],{"xmlns":1484},[1487,100556,100557,100577],{},[1490,100558,100559,100561,100567,100569,100571],{},[1493,100560,3384],{"mathvariant":1516},[1497,100562,100563,100565],{},[1493,100564,1520],{},[1680,100566,1682],{},[1506,100568,1559],{"separator":1041},[1493,100570,3384],{"mathvariant":1516},[1497,100572,100573,100575],{},[1493,100574,1520],{},[1680,100576,1691],{},[1528,100578,100579],{"encoding":1530},"\\mathrm{d} Q_1, \\mathrm{d} Q_2"," stanovíme pomocí ",[1047,100582,100583],{},"totálního diferenciálu",[1035,100585,100587],{"className":100586},[1480],[1482,100588,100589],{"xmlns":1484,"display":1485},[1487,100590,100591,100692],{},[19617,100592,100593],{"width":19619},[19621,100594,100595,100597,100685,100687],{},[19624,100596],{"width":19626},[19624,100598,100599],{},[1490,100600,100601,100603,100605,100607,100609,100611,100613,100621,100623,100629,100631,100639,100641,100647,100649,100651,100657,100659,100665,100667,100669,100675,100677,100683],{},[1493,100602,2976],{"mathvariant":1516},[1493,100604,1668],{},[1506,100606,2343],{},[1493,100608,3384],{"mathvariant":1516},[1493,100610,1668],{},[1506,100612,1508],{},[1697,100614,100615,100617,100619],{},[1493,100616,1668],{},[1680,100618,1682],{},[1506,100620,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1493,100622,3384],{"mathvariant":1516},[1497,100624,100625,100627],{},[1493,100626,1520],{},[1680,100628,1682],{},[1506,100630,2162],{},[1697,100632,100633,100635,100637],{},[1493,100634,1668],{},[1680,100636,1691],{},[1506,100638,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1493,100640,3384],{"mathvariant":1516},[1497,100642,100643,100645],{},[1493,100644,1520],{},[1680,100646,1691],{},[1506,100648,1508],{},[1493,100650,1495],{},[1497,100652,100653,100655],{},[1493,100654,1668],{},[1680,100656,1682],{},[1493,100658,3384],{"mathvariant":1516},[1497,100660,100661,100663],{},[1493,100662,1520],{},[1680,100664,1682],{},[1506,100666,2162],{},[1493,100668,1495],{},[1497,100670,100671,100673],{},[1493,100672,1668],{},[1680,100674,1691],{},[1493,100676,3384],{"mathvariant":1516},[1497,100678,100679,100681],{},[1493,100680,1520],{},[1680,100682,1691],{},[1493,100684,2632],{"mathvariant":1516},[19624,100686],{"width":19626},[19624,100688,100689],{},[1988,100690,100691],{},"(6.3)",[1528,100693,100694],{"encoding":1530},"\\Delta U \\approx \\mathrm{d} U = U'_1 \\mathrm{d} Q_1 + U'_2 \\mathrm{d} Q_2 = MU_1 \\mathrm{d} Q_1 + MU_2 \\mathrm{d} Q_2. \\tag{6.3}",[1030,100696,87832,100697,2632],{},[1035,100698,100700],{"className":100699},[1480],[1482,100701,100702],{"xmlns":1484},[1487,100703,100704,100774],{},[1490,100705,100706,100708,100710,100712,100714,100716,100722,100724,100726,100732,100734,100740,100742,100744,100750,100752,100754,100756,100758,100764,100766,100772],{},[1493,100707,2976],{"mathvariant":1516},[1493,100709,1668],{},[1506,100711,1508],{},[1493,100713,1668],{},[1506,100715,1553],{"stretchy":1552},[1497,100717,100718,100720],{},[1493,100719,1520],{},[1680,100721,1682],{},[1506,100723,2162],{},[1493,100725,3384],{"mathvariant":1516},[1497,100727,100728,100730],{},[1493,100729,1520],{},[1680,100731,1682],{},[1506,100733,1559],{"separator":1041},[1497,100735,100736,100738],{},[1493,100737,1520],{},[1680,100739,1691],{},[1506,100741,2162],{},[1493,100743,3384],{"mathvariant":1516},[1497,100745,100746,100748],{},[1493,100747,1520],{},[1680,100749,1691],{},[1506,100751,1564],{"stretchy":1552},[1506,100753,1888],{},[1493,100755,1668],{},[1506,100757,1553],{"stretchy":1552},[1497,100759,100760,100762],{},[1493,100761,1520],{},[1680,100763,1682],{},[1506,100765,1559],{"separator":1041},[1497,100767,100768,100770],{},[1493,100769,1520],{},[1680,100771,1691],{},[1506,100773,1564],{"stretchy":1552},[1528,100775,100776],{"encoding":1530},"\\Delta U = U(Q_1 + \\mathrm{d} Q_1, Q_2 + \\mathrm{d} Q_2) - U(Q_1, Q_2)",[1065,100778,100780],{"id":100779},"vlastnosti-funkce-užitečnosti","Vlastnosti funkce užitečnosti",[1030,100782,100783,100784,100787,100788,100791],{},"Funkce užitečnosti musí vyjadřovat dva ekonomicky zásadní předpoklady — ",[1047,100785,100786],{},"rostoucí užitečnost"," (předpoklad 4) a ",[1047,100789,100790],{},"klesající mezní užitečnost"," (předpoklad 5).",[1030,100793,100794,100797,100798,56364,100824,100850,100851,1732,100883,100915,100916,1586,100970,101024],{},[1047,100795,100796],{},"Předpoklad 4"," (rostoucí užitečnost) znamená, že při pevně zadaných ",[1035,100799,100801],{"className":100800},[1480],[1482,100802,100803],{"xmlns":1484},[1487,100804,100805,100821],{},[1490,100806,100807,100813,100815],{},[1497,100808,100809,100811],{},[1493,100810,1520],{},[1680,100812,1691],{},[1506,100814,1508],{},[1497,100816,100817,100819],{},[1493,100818,1052],{},[1680,100820,1871],{},[1528,100822,100823],{"encoding":1530},"Q_2 = a_0",[1035,100825,100827],{"className":100826},[1480],[1482,100828,100829],{"xmlns":1484},[1487,100830,100831,100847],{},[1490,100832,100833,100839,100841],{},[1497,100834,100835,100837],{},[1493,100836,1520],{},[1680,100838,1682],{},[1506,100840,1508],{},[1497,100842,100843,100845],{},[1493,100844,2394],{},[1680,100846,1871],{},[1528,100848,100849],{"encoding":1530},"Q_1 = b_0"," jsou funkce jedné proměnné ",[1035,100852,100854],{"className":100853},[1480],[1482,100855,100856],{"xmlns":1484},[1487,100857,100858,100880],{},[1490,100859,100860,100862,100864,100870,100872,100878],{},[1493,100861,1668],{},[1506,100863,1553],{"stretchy":1552},[1497,100865,100866,100868],{},[1493,100867,1520],{},[1680,100869,1682],{},[1506,100871,1559],{"separator":1041},[1497,100873,100874,100876],{},[1493,100875,1052],{},[1680,100877,1871],{},[1506,100879,1564],{"stretchy":1552},[1528,100881,100882],{"encoding":1530},"U(Q_1, a_0)",[1035,100884,100886],{"className":100885},[1480],[1482,100887,100888],{"xmlns":1484},[1487,100889,100890,100912],{},[1490,100891,100892,100894,100896,100902,100904,100910],{},[1493,100893,1668],{},[1506,100895,1553],{"stretchy":1552},[1497,100897,100898,100900],{},[1493,100899,2394],{},[1680,100901,1871],{},[1506,100903,1559],{"separator":1041},[1497,100905,100906,100908],{},[1493,100907,1520],{},[1680,100909,1691],{},[1506,100911,1564],{"stretchy":1552},[1528,100913,100914],{"encoding":1530},"U(b_0, Q_2)"," rostoucí. To platí, jestliže ",[1035,100917,100919],{"className":100918},[1480],[1482,100920,100921],{"xmlns":1484},[1487,100922,100923,100967],{},[1490,100924,100925,100963,100965],{},[1869,100926,100927],{"scriptlevel":1871,"displaystyle":1041},[1510,100928,100929,100953],{},[1490,100930,100931,100933,100935,100937,100943,100945,100951],{},[1493,100932,3384],{"mathvariant":1516},[1493,100934,1668],{},[1506,100936,1553],{"stretchy":1552},[1497,100938,100939,100941],{},[1493,100940,1520],{},[1680,100942,1682],{},[1506,100944,1559],{"separator":1041},[1497,100946,100947,100949],{},[1493,100948,1052],{},[1680,100950,1871],{},[1506,100952,1564],{"stretchy":1552},[1490,100954,100955,100957],{},[1493,100956,3384],{"mathvariant":1516},[1497,100958,100959,100961],{},[1493,100960,1520],{},[1680,100962,1682],{},[1506,100964,2796],{},[1680,100966,1871],{},[1528,100968,100969],{"encoding":1530},"\\dfrac{\\mathrm{d} U(Q_1, a_0)}{\\mathrm{d} Q_1} > 0",[1035,100971,100973],{"className":100972},[1480],[1482,100974,100975],{"xmlns":1484},[1487,100976,100977,101021],{},[1490,100978,100979,101017,101019],{},[1869,100980,100981],{"scriptlevel":1871,"displaystyle":1041},[1510,100982,100983,101007],{},[1490,100984,100985,100987,100989,100991,100997,100999,101005],{},[1493,100986,3384],{"mathvariant":1516},[1493,100988,1668],{},[1506,100990,1553],{"stretchy":1552},[1497,100992,100993,100995],{},[1493,100994,2394],{},[1680,100996,1871],{},[1506,100998,1559],{"separator":1041},[1497,101000,101001,101003],{},[1493,101002,1520],{},[1680,101004,1691],{},[1506,101006,1564],{"stretchy":1552},[1490,101008,101009,101011],{},[1493,101010,3384],{"mathvariant":1516},[1497,101012,101013,101015],{},[1493,101014,1520],{},[1680,101016,1691],{},[1506,101018,2796],{},[1680,101020,1871],{},[1528,101022,101023],{"encoding":1530},"\\dfrac{\\mathrm{d} U(b_0, Q_2)}{\\mathrm{d} Q_2} > 0",", tj.",[1035,101026,101028],{"className":101027},[1480],[1482,101029,101030],{"xmlns":1484,"display":1485},[1487,101031,101032,101077],{},[19617,101033,101034],{"width":19619},[19621,101035,101036,101038,101070,101072],{},[19624,101037],{"width":19626},[19624,101039,101040],{},[1490,101041,101042,101050,101052,101054,101056,101058,101066,101068],{},[1697,101043,101044,101046,101048],{},[1493,101045,1668],{},[1680,101047,1682],{},[1506,101049,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,101051,2796],{},[1680,101053,1871],{},[1506,101055,1559],{"separator":1041},[1912,101057],{"width":2108},[1697,101059,101060,101062,101064],{},[1493,101061,1668],{},[1680,101063,1691],{},[1506,101065,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,101067,2796],{},[1680,101069,28945],{},[19624,101071],{"width":19626},[19624,101073,101074],{},[1988,101075,101076],{},"(6.4)",[1528,101078,101079],{"encoding":1530},"U'_1 > 0, \\quad U'_2 > 0. \\tag{6.4}",[1030,101081,101082,101083,101085],{},"Tedy mezní užitečnosti obou zboží jsou ",[1047,101084,66919],{}," — užitečnost roste s množstvím každého zboží.",[1030,101087,101088,101091,101092,101122,101123,1274],{},[1047,101089,101090],{},"Předpoklad 5"," (klesající mezní užitečnost) požaduje, aby ",[1035,101093,101095],{"className":101094},[1480],[1482,101096,101097],{"xmlns":1484},[1487,101098,101099,101119],{},[1490,101100,101101,101109,101111],{},[1697,101102,101103,101105,101107],{},[1493,101104,1668],{},[1680,101106,1682],{},[1506,101108,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,101110,1559],{"separator":1041},[1697,101112,101113,101115,101117],{},[1493,101114,1668],{},[1680,101116,1691],{},[1506,101118,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,101120,101121],{"encoding":1530},"U'_1, U'_2"," byly klesající funkce. To znamená, že jejich parciální derivace podle příslušné proměnné jsou ",[1047,101124,101125],{},"záporné",[1035,101127,101129],{"className":101128},[1480],[1482,101130,101131],{"xmlns":1484,"display":1485},[1487,101132,101133,101186],{},[19617,101134,101135],{"width":19619},[19621,101136,101137,101139,101179,101181],{},[19624,101138],{"width":19626},[19624,101140,101141],{},[1490,101142,101143,101155,101157,101159,101161,101163,101175,101177],{},[1697,101144,101145,101147,101149],{},[1493,101146,1668],{},[1680,101148,8542],{},[1490,101150,101151,101153],{},[1506,101152,6927],{"mathvariant":1516},[1506,101154,6927],{"mathvariant":1516},[1506,101156,3961],{},[1680,101158,1871],{},[1506,101160,1559],{"separator":1041},[1912,101162],{"width":2108},[1697,101164,101165,101167,101169],{},[1493,101166,1668],{},[1680,101168,9923],{},[1490,101170,101171,101173],{},[1506,101172,6927],{"mathvariant":1516},[1506,101174,6927],{"mathvariant":1516},[1506,101176,3961],{},[1680,101178,28945],{},[19624,101180],{"width":19626},[19624,101182,101183],{},[1988,101184,101185],{},"(6.5)",[1528,101187,101188],{"encoding":1530},"U''_{11} \u003C 0, \\quad U''_{22} \u003C 0. \\tag{6.5}",[1030,101190,101191,101192,101195,101196,2632],{},"Podmínka (6.5) je známa jako ",[1047,101193,101194],{},"zákon klesající mezní užitečnosti (law of diminishing marginal utility)"," — mezní užitečnost každého zboží klesá s růstem jeho množství. Jde o analogii zákona klesajících výnosů z ",[1052,101197,101199],{"className":101198,"dataFsResolvedFilePath":1572,"href":1573},[1055],"produkční teorie",[1030,101201,101202,101203,1586,101235,101267,101268,1586,101294,101320,101321,101349,101350,1586,101352,2632],{},"Podmínky (6.4), (6.5) určují tvary křivek ",[1035,101204,101206],{"className":101205},[1480],[1482,101207,101208],{"xmlns":1484},[1487,101209,101210,101232],{},[1490,101211,101212,101214,101216,101222,101224,101230],{},[1493,101213,1668],{},[1506,101215,1553],{"stretchy":1552},[1497,101217,101218,101220],{},[1493,101219,1520],{},[1680,101221,1682],{},[1506,101223,1559],{"separator":1041},[1497,101225,101226,101228],{},[1493,101227,2394],{},[1680,101229,1871],{},[1506,101231,1564],{"stretchy":1552},[1528,101233,101234],{"encoding":1530},"U(Q_1, b_0)",[1035,101236,101238],{"className":101237},[1480],[1482,101239,101240],{"xmlns":1484},[1487,101241,101242,101264],{},[1490,101243,101244,101246,101248,101254,101256,101262],{},[1493,101245,1668],{},[1506,101247,1553],{"stretchy":1552},[1497,101249,101250,101252],{},[1493,101251,1052],{},[1680,101253,1871],{},[1506,101255,1559],{"separator":1041},[1497,101257,101258,101260],{},[1493,101259,1520],{},[1680,101261,1691],{},[1506,101263,1564],{"stretchy":1552},[1528,101265,101266],{"encoding":1530},"U(a_0, Q_2)"," v souřadnicových rovinách ",[1035,101269,101271],{"className":101270},[1480],[1482,101272,101273],{"xmlns":1484},[1487,101274,101275,101291],{},[1490,101276,101277,101279,101281,101283,101289],{},[1506,101278,1553],{"stretchy":1552},[1493,101280,1668],{},[1506,101282,1559],{"separator":1041},[1497,101284,101285,101287],{},[1493,101286,1520],{},[1680,101288,1682],{},[1506,101290,1564],{"stretchy":1552},[1528,101292,101293],{"encoding":1530},"(U, Q_1)",[1035,101295,101297],{"className":101296},[1480],[1482,101298,101299],{"xmlns":1484},[1487,101300,101301,101317],{},[1490,101302,101303,101305,101307,101309,101315],{},[1506,101304,1553],{"stretchy":1552},[1493,101306,1668],{},[1506,101308,1559],{"separator":1041},[1497,101310,101311,101313],{},[1493,101312,1520],{},[1680,101314,1691],{},[1506,101316,1564],{"stretchy":1552},[1528,101318,101319],{"encoding":1530},"(U, Q_2)",". Tyto křivky procházejí počátkem (neboť obvykle ",[1035,101322,101324],{"className":101323},[1480],[1482,101325,101326],{"xmlns":1484},[1487,101327,101328,101346],{},[1490,101329,101330,101332,101334,101336,101338,101340,101342,101344],{},[1493,101331,1668],{},[1506,101333,1553],{"stretchy":1552},[1680,101335,1871],{},[1506,101337,1559],{"separator":1041},[1680,101339,1871],{},[1506,101341,1564],{"stretchy":1552},[1506,101343,1508],{},[1680,101345,1871],{},[1528,101347,101348],{"encoding":1530},"U(0, 0) = 0","), jsou ",[1047,101351,3482],{},[1047,101353,53416],{},[1304,101355,101357,101358],{"id":101356},"příklad-62-ověření-vlastností-a-dopočet-pro-uq112q213u-q_112-q_213","Příklad 6.2 — ověření vlastností a dopočet pro ",[1035,101359,101361],{"className":101360},[1480],[1482,101362,101363],{"xmlns":1484},[1487,101364,101365,101399],{},[1490,101366,101367,101369,101371,101385],{},[1493,101368,1668],{},[1506,101370,1508],{},[1697,101372,101373,101375,101377],{},[1493,101374,1520],{},[1680,101376,1682],{},[1490,101378,101379,101381,101383],{},[1680,101380,1682],{},[1493,101382,1709],{"mathvariant":1516},[1680,101384,1691],{},[1697,101386,101387,101389,101391],{},[1493,101388,1520],{},[1680,101390,1691],{},[1490,101392,101393,101395,101397],{},[1680,101394,1682],{},[1493,101396,1709],{"mathvariant":1516},[1680,101398,3201],{},[1528,101400,101401],{"encoding":1530},"U = Q_1^{1\u002F2} Q_2^{1\u002F3}",[1030,101403,101404],{},[1047,101405,101406],{},"Ověření (6.4) a (6.5).",[1035,101408,101410],{"className":101409},[1480],[1482,101411,101412],{"xmlns":1484,"display":1485},[1487,101413,101414,101518],{},[1490,101415,101416,101424,101426,101434,101450,101464,101466,101468,101476,101478,101486,101500,101516],{},[1697,101417,101418,101420,101422],{},[1493,101419,1668],{},[1680,101421,1682],{},[1506,101423,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,101425,1508],{},[1869,101427,101428],{"scriptlevel":1871,"displaystyle":1552},[1510,101429,101430,101432],{},[1680,101431,1682],{},[1680,101433,1691],{},[1697,101435,101436,101438,101440],{},[1493,101437,1520],{},[1680,101439,1682],{},[1490,101441,101442,101444,101446,101448],{},[1506,101443,1888],{},[1680,101445,1682],{},[1493,101447,1709],{"mathvariant":1516},[1680,101449,1691],{},[1697,101451,101452,101454,101456],{},[1493,101453,1520],{},[1680,101455,1691],{},[1490,101457,101458,101460,101462],{},[1680,101459,1682],{},[1493,101461,1709],{"mathvariant":1516},[1680,101463,3201],{},[1506,101465,1559],{"separator":1041},[1912,101467],{"width":2108},[1697,101469,101470,101472,101474],{},[1493,101471,1668],{},[1680,101473,1691],{},[1506,101475,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,101477,1508],{},[1869,101479,101480],{"scriptlevel":1871,"displaystyle":1552},[1510,101481,101482,101484],{},[1680,101483,1682],{},[1680,101485,3201],{},[1697,101487,101488,101490,101492],{},[1493,101489,1520],{},[1680,101491,1682],{},[1490,101493,101494,101496,101498],{},[1680,101495,1682],{},[1493,101497,1709],{"mathvariant":1516},[1680,101499,1691],{},[1697,101501,101502,101504,101506],{},[1493,101503,1520],{},[1680,101505,1691],{},[1490,101507,101508,101510,101512,101514],{},[1506,101509,1888],{},[1680,101511,1691],{},[1493,101513,1709],{"mathvariant":1516},[1680,101515,3201],{},[1506,101517,1559],{"separator":1041},[1528,101519,101520],{"encoding":1530},"U'_1 = \\tfrac{1}{2} Q_1^{-1\u002F2} Q_2^{1\u002F3}, \\quad U'_2 = \\tfrac{1}{3} Q_1^{1\u002F2} Q_2^{-2\u002F3},",[1030,101522,101523,101524,101558],{},"zřejmě ",[1035,101525,101527],{"className":101526},[1480],[1482,101528,101529],{"xmlns":1484},[1487,101530,101531,101555],{},[1490,101532,101533,101541,101543,101551,101553],{},[1697,101534,101535,101537,101539],{},[1493,101536,1668],{},[1680,101538,1682],{},[1506,101540,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,101542,1559],{"separator":1041},[1697,101544,101545,101547,101549],{},[1493,101546,1668],{},[1680,101548,1691],{},[1506,101550,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,101552,2796],{},[1680,101554,1871],{},[1528,101556,101557],{"encoding":1530},"U'_1, U'_2 > 0"," a platí (6.4). Dále:",[1035,101560,101562],{"className":101561},[1480],[1482,101563,101564],{"xmlns":1484,"display":1485},[1487,101565,101566,101682],{},[1490,101567,101568,101580,101582,101584,101592,101608,101622,101624,101626,101638,101640,101642,101650,101664,101680],{},[1697,101569,101570,101572,101574],{},[1493,101571,1668],{},[1680,101573,8542],{},[1490,101575,101576,101578],{},[1506,101577,6927],{"mathvariant":1516},[1506,101579,6927],{"mathvariant":1516},[1506,101581,1508],{},[1506,101583,1888],{},[1869,101585,101586],{"scriptlevel":1871,"displaystyle":1552},[1510,101587,101588,101590],{},[1680,101589,1682],{},[1680,101591,4007],{},[1697,101593,101594,101596,101598],{},[1493,101595,1520],{},[1680,101597,1682],{},[1490,101599,101600,101602,101604,101606],{},[1506,101601,1888],{},[1680,101603,3201],{},[1493,101605,1709],{"mathvariant":1516},[1680,101607,1691],{},[1697,101609,101610,101612,101614],{},[1493,101611,1520],{},[1680,101613,1691],{},[1490,101615,101616,101618,101620],{},[1680,101617,1682],{},[1493,101619,1709],{"mathvariant":1516},[1680,101621,3201],{},[1506,101623,1559],{"separator":1041},[1912,101625],{"width":2108},[1697,101627,101628,101630,101632],{},[1493,101629,1668],{},[1680,101631,9923],{},[1490,101633,101634,101636],{},[1506,101635,6927],{"mathvariant":1516},[1506,101637,6927],{"mathvariant":1516},[1506,101639,1508],{},[1506,101641,1888],{},[1869,101643,101644],{"scriptlevel":1871,"displaystyle":1552},[1510,101645,101646,101648],{},[1680,101647,1691],{},[1680,101649,14365],{},[1697,101651,101652,101654,101656],{},[1493,101653,1520],{},[1680,101655,1682],{},[1490,101657,101658,101660,101662],{},[1680,101659,1682],{},[1493,101661,1709],{"mathvariant":1516},[1680,101663,1691],{},[1697,101665,101666,101668,101670],{},[1493,101667,1520],{},[1680,101669,1691],{},[1490,101671,101672,101674,101676,101678],{},[1506,101673,1888],{},[1680,101675,1752],{},[1493,101677,1709],{"mathvariant":1516},[1680,101679,3201],{},[1506,101681,1559],{"separator":1041},[1528,101683,101684],{"encoding":1530},"U''_{11} = -\\tfrac{1}{4} Q_1^{-3\u002F2} Q_2^{1\u002F3}, \\quad U''_{22} = -\\tfrac{2}{9} Q_1^{1\u002F2} Q_2^{-5\u002F3},",[1030,101686,101687,101688,101730],{},"opět ",[1035,101689,101691],{"className":101690},[1480],[1482,101692,101693],{"xmlns":1484},[1487,101694,101695,101727],{},[1490,101696,101697,101709,101711,101723,101725],{},[1697,101698,101699,101701,101703],{},[1493,101700,1668],{},[1680,101702,8542],{},[1490,101704,101705,101707],{},[1506,101706,6927],{"mathvariant":1516},[1506,101708,6927],{"mathvariant":1516},[1506,101710,1559],{"separator":1041},[1697,101712,101713,101715,101717],{},[1493,101714,1668],{},[1680,101716,9923],{},[1490,101718,101719,101721],{},[1506,101720,6927],{"mathvariant":1516},[1506,101722,6927],{"mathvariant":1516},[1506,101724,3961],{},[1680,101726,1871],{},[1528,101728,101729],{"encoding":1530},"U''_{11}, U''_{22} \u003C 0",", platí (6.5).",[1030,101732,101733],{},[1047,101734,101735,101736,2632],{},"(a) Mezní užitečnosti v bodě ",[1035,101737,101739],{"className":101738},[1480],[1482,101740,101741],{"xmlns":1484},[1487,101742,101743,101755],{},[1490,101744,101745,101747,101749,101751,101753],{},[1506,101746,14314],{"stretchy":1552},[1680,101748,2916],{},[1506,101750,1559],{"separator":1041},[1680,101752,5263],{},[1506,101754,14323],{"stretchy":1552},[1528,101756,101757],{"encoding":1530},"[100, 200]",[1035,101759,101761],{"className":101760},[1480],[1482,101762,101763],{"xmlns":1484,"display":1485},[1487,101764,101765,101832],{},[1490,101766,101767,101769,101775,101777,101779,101781,101783,101785,101787,101795,101797,101811,101813,101825,101827,101830],{},[1493,101768,1495],{},[1497,101770,101771,101773],{},[1493,101772,1668],{},[1680,101774,1682],{},[1506,101776,1553],{"stretchy":1552},[1680,101778,2916],{},[1506,101780,1559],{"separator":1041},[1680,101782,5263],{},[1506,101784,1564],{"stretchy":1552},[1506,101786,1508],{},[1869,101788,101789],{"scriptlevel":1871,"displaystyle":1552},[1510,101790,101791,101793],{},[1680,101792,1682],{},[1680,101794,1691],{},[1506,101796,1714],{},[2315,101798,101799,101801],{},[1680,101800,2916],{},[1490,101802,101803,101805,101807,101809],{},[1506,101804,1888],{},[1680,101806,1682],{},[1493,101808,1709],{"mathvariant":1516},[1680,101810,1691],{},[1506,101812,1714],{},[2315,101814,101815,101817],{},[1680,101816,5263],{},[1490,101818,101819,101821,101823],{},[1680,101820,1682],{},[1493,101822,1709],{"mathvariant":1516},[1680,101824,3201],{},[1506,101826,21771],{},[1680,101828,101829],{},"0,4204",[1506,101831,1559],{"separator":1041},[1528,101833,101834],{"encoding":1530},"MU_1(100, 200) = \\tfrac{1}{2} \\cdot 100^{-1\u002F2} \\cdot 200^{1\u002F3} \\doteq 0{,}4204,",[1035,101836,101838],{"className":101837},[1480],[1482,101839,101840],{"xmlns":1484,"display":1485},[1487,101841,101842,101907],{},[1490,101843,101844,101846,101852,101854,101856,101858,101860,101862,101864,101872,101874,101886,101888,101902,101904],{},[1493,101845,1495],{},[1497,101847,101848,101850],{},[1493,101849,1668],{},[1680,101851,1691],{},[1506,101853,1553],{"stretchy":1552},[1680,101855,2916],{},[1506,101857,1559],{"separator":1041},[1680,101859,5263],{},[1506,101861,1564],{"stretchy":1552},[1506,101863,1508],{},[1869,101865,101866],{"scriptlevel":1871,"displaystyle":1552},[1510,101867,101868,101870],{},[1680,101869,1682],{},[1680,101871,3201],{},[1506,101873,1714],{},[2315,101875,101876,101878],{},[1680,101877,2916],{},[1490,101879,101880,101882,101884],{},[1680,101881,1682],{},[1493,101883,1709],{"mathvariant":1516},[1680,101885,1691],{},[1506,101887,1714],{},[2315,101889,101890,101892],{},[1680,101891,5263],{},[1490,101893,101894,101896,101898,101900],{},[1506,101895,1888],{},[1680,101897,1691],{},[1493,101899,1709],{"mathvariant":1516},[1680,101901,3201],{},[1506,101903,21771],{},[1680,101905,101906],{},"0,63067.",[1528,101908,101909],{"encoding":1530},"MU_2(100, 200) = \\tfrac{1}{3} \\cdot 100^{1\u002F2} \\cdot 200^{-2\u002F3} \\doteq 0{,}63067.",[1030,101911,101912,1656,101914,101949,101950,101971,101972,101989],{},[1176,101913,12171],{},[1035,101915,101917],{"className":101916},[1480],[1482,101918,101919],{"xmlns":1484},[1487,101920,101921,101946],{},[1490,101922,101923,101925,101931,101933,101935,101937,101939,101941,101943],{},[1493,101924,1495],{},[1497,101926,101927,101929],{},[1493,101928,1668],{},[1680,101930,1691],{},[1506,101932,1553],{"stretchy":1552},[1680,101934,2916],{},[1506,101936,1559],{"separator":1041},[1680,101938,5263],{},[1506,101940,1564],{"stretchy":1552},[1506,101942,21771],{},[1680,101944,101945],{},"0,63067",[1528,101947,101948],{"encoding":1530},"MU_2(100, 200) \\doteq 0{,}63067"," znamená, že na hladině ",[1035,101951,101953],{"className":101952},[1480],[1482,101954,101955],{"xmlns":1484},[1487,101956,101957,101969],{},[1490,101958,101959,101961,101963,101965,101967],{},[1506,101960,14314],{"stretchy":1552},[1680,101962,2916],{},[1506,101964,1559],{"separator":1041},[1680,101966,5263],{},[1506,101968,14323],{"stretchy":1552},[1528,101970,101757],{"encoding":1530}," roste užitečnost při jednotkové změně ",[1035,101973,101975],{"className":101974},[1480],[1482,101976,101977],{"xmlns":1484},[1487,101978,101979,101987],{},[1490,101980,101981],{},[1497,101982,101983,101985],{},[1493,101984,1520],{},[1680,101986,1691],{},[1528,101988,6683],{"encoding":1530}," přibližně o 0,63067.",[1030,101991,101992,102011,102012,54060,102033,102050,102051,102077,102078,102095,102096,18579],{},[1047,101993,101994,101995,102010],{},"(b) Odhad změny ",[1035,101996,101998],{"className":101997},[1480],[1482,101999,102000],{"xmlns":1484},[1487,102001,102002,102008],{},[1490,102003,102004,102006],{},[1493,102005,2976],{"mathvariant":1516},[1493,102007,1668],{},[1528,102009,100549],{"encoding":1530}," pomocí totálního diferenciálu (6.3)."," Klesne-li vzhledem k hladině ",[1035,102013,102015],{"className":102014},[1480],[1482,102016,102017],{"xmlns":1484},[1487,102018,102019,102031],{},[1490,102020,102021,102023,102025,102027,102029],{},[1506,102022,14314],{"stretchy":1552},[1680,102024,2916],{},[1506,102026,1559],{"separator":1041},[1680,102028,5263],{},[1506,102030,14323],{"stretchy":1552},[1528,102032,101757],{"encoding":1530},[1035,102034,102036],{"className":102035},[1480],[1482,102037,102038],{"xmlns":1484},[1487,102039,102040,102048],{},[1490,102041,102042],{},[1497,102043,102044,102046],{},[1493,102045,1520],{},[1680,102047,1682],{},[1528,102049,6702],{"encoding":1530}," na 98 (tj. ",[1035,102052,102054],{"className":102053},[1480],[1482,102055,102056],{"xmlns":1484},[1487,102057,102058,102074],{},[1490,102059,102060,102062,102068,102070,102072],{},[1493,102061,3384],{"mathvariant":1516},[1497,102063,102064,102066],{},[1493,102065,1520],{},[1680,102067,1682],{},[1506,102069,1508],{},[1506,102071,1888],{},[1680,102073,1691],{},[1528,102075,102076],{"encoding":1530},"\\mathrm{d} Q_1 = -2",") a vzroste-li ",[1035,102079,102081],{"className":102080},[1480],[1482,102082,102083],{"xmlns":1484},[1487,102084,102085,102093],{},[1490,102086,102087],{},[1497,102088,102089,102091],{},[1493,102090,1520],{},[1680,102092,1691],{},[1528,102094,6683],{"encoding":1530}," o 3 (tj. ",[1035,102097,102099],{"className":102098},[1480],[1482,102100,102101],{"xmlns":1484},[1487,102102,102103,102117],{},[1490,102104,102105,102107,102113,102115],{},[1493,102106,3384],{"mathvariant":1516},[1497,102108,102109,102111],{},[1493,102110,1520],{},[1680,102112,1691],{},[1506,102114,1508],{},[1680,102116,3201],{},[1528,102118,102119],{"encoding":1530},"\\mathrm{d} Q_2 = 3",[1035,102121,102123],{"className":102122},[1480],[1482,102124,102125],{"xmlns":1484,"display":1485},[1487,102126,102127,102178],{},[1490,102128,102129,102131,102133,102135,102137,102139,102141,102143,102145,102147,102149,102151,102153,102155,102157,102159,102161,102163,102165,102168,102170,102173,102175],{},[1493,102130,2976],{"mathvariant":1516},[1493,102132,1668],{},[1506,102134,2343],{},[1493,102136,3384],{"mathvariant":1516},[1493,102138,1668],{},[1506,102140,1508],{},[1680,102142,101829],{},[1506,102144,1714],{},[1506,102146,1553],{"stretchy":1552},[1506,102148,1888],{},[1680,102150,1691],{},[1506,102152,1564],{"stretchy":1552},[1506,102154,2162],{},[1680,102156,101945],{},[1506,102158,1714],{},[1680,102160,3201],{},[1506,102162,1508],{},[1506,102164,1888],{},[1680,102166,102167],{},"0,8408",[1506,102169,2162],{},[1680,102171,102172],{},"1,89201",[1506,102174,21771],{},[1680,102176,102177],{},"1,05.",[1528,102179,102180],{"encoding":1530},"\\Delta U \\approx \\mathrm{d} U = 0{,}4204 \\cdot (-2) + 0{,}63067 \\cdot 3 = -0{,}8408 + 1{,}89201 \\doteq 1{,}05.",[1030,102182,102183,102184,102187,102188,102239,102240,2632],{},"Užitečnost se tedy zvýší přibližně o ",[1047,102185,102186],{},"1,05",". Skutečná změna je ",[1035,102189,102191],{"className":102190},[1480],[1482,102192,102193],{"xmlns":1484},[1487,102194,102195,102236],{},[1490,102196,102197,102199,102201,102203,102205,102207,102210,102212,102215,102217,102219,102221,102223,102225,102227,102229,102231,102233],{},[1493,102198,2976],{"mathvariant":1516},[1493,102200,1668],{},[1506,102202,1508],{},[1493,102204,1668],{},[1506,102206,1553],{"stretchy":1552},[1680,102208,102209],{},"98",[1506,102211,1559],{"separator":1041},[1680,102213,102214],{},"203",[1506,102216,1564],{"stretchy":1552},[1506,102218,1888],{},[1493,102220,1668],{},[1506,102222,1553],{"stretchy":1552},[1680,102224,2916],{},[1506,102226,1559],{"separator":1041},[1680,102228,5263],{},[1506,102230,1564],{"stretchy":1552},[1506,102232,21771],{},[1680,102234,102235],{},"1,031",[1528,102237,102238],{"encoding":1530},"\\Delta U = U(98, 203) - U(100, 200) \\doteq 1{,}031"," — relativní chyba odhadu je zhruba 2 %. Aproximace totálním diferenciálem je uspokojivá pro malé ",[1035,102241,102243],{"className":102242},[1480],[1482,102244,102245],{"xmlns":1484},[1487,102246,102247,102267],{},[1490,102248,102249,102251,102257,102259,102261],{},[1493,102250,3384],{"mathvariant":1516},[1497,102252,102253,102255],{},[1493,102254,1520],{},[1680,102256,1682],{},[1506,102258,1559],{"separator":1041},[1493,102260,3384],{"mathvariant":1516},[1497,102262,102263,102265],{},[1493,102264,1520],{},[1680,102266,1691],{},[1528,102268,100579],{"encoding":1530},[1065,102270,102272],{"id":102271},"cobb-douglasova-funkce-užitečnosti","Cobb-Douglasova funkce užitečnosti",[1030,102274,102275],{},"Nejčastěji používané funkce užitečnosti mají tvar",[1035,102277,102279],{"className":102278},[1480],[1482,102280,102281],{"xmlns":1484,"display":1485},[1487,102282,102283,102342],{},[19617,102284,102285],{"width":19619},[19621,102286,102287,102289,102335,102337],{},[19624,102288],{"width":19626},[19624,102290,102291],{},[1490,102292,102293,102295,102297,102303,102305,102311,102313,102315,102323,102325,102333],{},[1493,102294,1668],{},[1506,102296,1553],{"stretchy":1552},[1497,102298,102299,102301],{},[1493,102300,1520],{},[1680,102302,1682],{},[1506,102304,1559],{"separator":1041},[1497,102306,102307,102309],{},[1493,102308,1520],{},[1680,102310,1691],{},[1506,102312,1564],{"stretchy":1552},[1506,102314,1508],{},[1697,102316,102317,102319,102321],{},[1493,102318,1520],{},[1680,102320,1682],{},[1493,102322,1052],{},[1506,102324,1714],{},[1697,102326,102327,102329,102331],{},[1493,102328,1520],{},[1680,102330,1691],{},[1493,102332,2394],{},[1506,102334,1559],{"separator":1041},[19624,102336],{"width":19626},[19624,102338,102339],{},[1988,102340,102341],{},"(6.6)",[1528,102343,102344],{"encoding":1530},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^b, \\tag{6.6}",[1030,102346,20022,102347,102365,102366,102368,102369,102373,102374,102404,102405,102427],{},[1035,102348,102350],{"className":102349},[1480],[1482,102351,102352],{"xmlns":1484},[1487,102353,102354,102362],{},[1490,102355,102356,102358,102360],{},[1493,102357,1052],{},[1506,102359,1559],{"separator":1041},[1493,102361,2394],{},[1528,102363,102364],{"encoding":1530},"a, b"," jsou kladná čísla; nazývají se ",[1047,102367,87059],{}," (v příbuznosti s produkčními funkcemi — viz ",[1052,102370,102372],{"className":102371,"dataFsResolvedFilePath":1572,"href":1573},[1055],"kapitola 5","). Obvykle se volí ",[1035,102375,102377],{"className":102376},[1480],[1482,102378,102379],{"xmlns":1484},[1487,102380,102381,102401],{},[1490,102382,102383,102385,102387,102389,102391,102393,102395,102397,102399],{},[1493,102384,1052],{},[1506,102386,1559],{"separator":1041},[1493,102388,2394],{},[1506,102390,22378],{},[1506,102392,1553],{"stretchy":1552},[1680,102394,1871],{},[1506,102396,1559],{"separator":1041},[1680,102398,1682],{},[1506,102400,1564],{"stretchy":1552},[1528,102402,102403],{"encoding":1530},"a, b \\in (0, 1)",", často se klade ",[1035,102406,102408],{"className":102407},[1480],[1482,102409,102410],{"xmlns":1484},[1487,102411,102412,102424],{},[1490,102413,102414,102416,102418,102420,102422],{},[1493,102415,2394],{},[1506,102417,1508],{},[1680,102419,1682],{},[1506,102421,1888],{},[1493,102423,1052],{},[1528,102425,102426],{"encoding":1530},"b = 1 - a",", čímž (6.6) přejde na tvar",[1030,102429,102430],{},[18014,102431],{"alt":102432,"className":102433,"src":102434},"imek-cobb-douglas-3d-plus-ic",[1055,18018],"\u002Fwiki-assets\u002Fimek-cobb-douglas-3d-plus-ic.jpeg",[1035,102436,102438],{"className":102437},[1480],[1482,102439,102440],{"xmlns":1484,"display":1485},[1487,102441,102442,102492],{},[1490,102443,102444,102446,102448,102454,102456,102462,102464,102466,102474,102476,102490],{},[1493,102445,1668],{},[1506,102447,1553],{"stretchy":1552},[1497,102449,102450,102452],{},[1493,102451,1520],{},[1680,102453,1682],{},[1506,102455,1559],{"separator":1041},[1497,102457,102458,102460],{},[1493,102459,1520],{},[1680,102461,1691],{},[1506,102463,1564],{"stretchy":1552},[1506,102465,1508],{},[1697,102467,102468,102470,102472],{},[1493,102469,1520],{},[1680,102471,1682],{},[1493,102473,1052],{},[1506,102475,1714],{},[1697,102477,102478,102480,102482],{},[1493,102479,1520],{},[1680,102481,1691],{},[1490,102483,102484,102486,102488],{},[1680,102485,1682],{},[1506,102487,1888],{},[1493,102489,1052],{},[1493,102491,2632],{"mathvariant":1516},[1528,102493,102494],{"encoding":1530},"U(Q_1, Q_2) = Q_1^a \\cdot Q_2^{1-a}.",[1023,102496,102498,102549,102671,102805],{"className":102497,"dataCallout":66935},[1026,66934],[1030,102499,102501,102504,102505],{"className":102500},[1033],[1035,102502],{"className":102503,"ariaHidden":1041},[1038,66942,1040],"Příklad 6.3 — ověření vlastností pro ",[1035,102506,102508],{"className":102507},[1480],[1482,102509,102510],{"xmlns":1484},[1487,102511,102512,102546],{},[1490,102513,102514,102516,102518,102532],{},[1493,102515,1668],{},[1506,102517,1508],{},[1697,102519,102520,102522,102524],{},[1493,102521,1520],{},[1680,102523,1682],{},[1490,102525,102526,102528,102530],{},[1680,102527,1682],{},[1493,102529,1709],{"mathvariant":1516},[1680,102531,4007],{},[1697,102533,102534,102536,102538],{},[1493,102535,1520],{},[1680,102537,1691],{},[1490,102539,102540,102542,102544],{},[1680,102541,3201],{},[1493,102543,1709],{"mathvariant":1516},[1680,102545,4007],{},[1528,102547,102548],{"encoding":1530},"U = Q_1^{1\u002F4} Q_2^{3\u002F4}",[1035,102550,102552],{"className":102551},[1480],[1482,102553,102554],{"xmlns":1484,"display":1485},[1487,102555,102556,102668],{},[1490,102557,102558,102566,102568,102576,102592,102606,102608,102610,102612,102614,102622,102624,102632,102646,102662,102664,102666],{},[1697,102559,102560,102562,102564],{},[1493,102561,1668],{},[1680,102563,1682],{},[1506,102565,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,102567,1508],{},[1869,102569,102570],{"scriptlevel":1871,"displaystyle":1552},[1510,102571,102572,102574],{},[1680,102573,1682],{},[1680,102575,4007],{},[1697,102577,102578,102580,102582],{},[1493,102579,1520],{},[1680,102581,1682],{},[1490,102583,102584,102586,102588,102590],{},[1506,102585,1888],{},[1680,102587,3201],{},[1493,102589,1709],{"mathvariant":1516},[1680,102591,4007],{},[1697,102593,102594,102596,102598],{},[1493,102595,1520],{},[1680,102597,1691],{},[1490,102599,102600,102602,102604],{},[1680,102601,3201],{},[1493,102603,1709],{"mathvariant":1516},[1680,102605,4007],{},[1506,102607,2796],{},[1680,102609,1871],{},[1506,102611,1559],{"separator":1041},[1912,102613],{"width":2108},[1697,102615,102616,102618,102620],{},[1493,102617,1668],{},[1680,102619,1691],{},[1506,102621,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,102623,1508],{},[1869,102625,102626],{"scriptlevel":1871,"displaystyle":1552},[1510,102627,102628,102630],{},[1680,102629,3201],{},[1680,102631,4007],{},[1697,102633,102634,102636,102638],{},[1493,102635,1520],{},[1680,102637,1682],{},[1490,102639,102640,102642,102644],{},[1680,102641,1682],{},[1493,102643,1709],{"mathvariant":1516},[1680,102645,4007],{},[1697,102647,102648,102650,102652],{},[1493,102649,1520],{},[1680,102651,1691],{},[1490,102653,102654,102656,102658,102660],{},[1506,102655,1888],{},[1680,102657,1682],{},[1493,102659,1709],{"mathvariant":1516},[1680,102661,4007],{},[1506,102663,2796],{},[1680,102665,1871],{},[1506,102667,1559],{"separator":1041},[1528,102669,102670],{"encoding":1530},"U'_1 = \\tfrac{1}{4} Q_1^{-3\u002F4} Q_2^{3\u002F4} > 0, \\quad U'_2 = \\tfrac{3}{4} Q_1^{1\u002F4} Q_2^{-1\u002F4} > 0,",[1035,102672,102674],{"className":102673},[1480],[1482,102675,102676],{"xmlns":1484,"display":1485},[1487,102677,102678,102802],{},[1490,102679,102680,102692,102694,102696,102704,102720,102734,102736,102738,102740,102742,102754,102756,102758,102766,102780,102796,102798,102800],{},[1697,102681,102682,102684,102686],{},[1493,102683,1668],{},[1680,102685,8542],{},[1490,102687,102688,102690],{},[1506,102689,6927],{"mathvariant":1516},[1506,102691,6927],{"mathvariant":1516},[1506,102693,1508],{},[1506,102695,1888],{},[1869,102697,102698],{"scriptlevel":1871,"displaystyle":1552},[1510,102699,102700,102702],{},[1680,102701,3201],{},[1680,102703,9961],{},[1697,102705,102706,102708,102710],{},[1493,102707,1520],{},[1680,102709,1682],{},[1490,102711,102712,102714,102716,102718],{},[1506,102713,1888],{},[1680,102715,16580],{},[1493,102717,1709],{"mathvariant":1516},[1680,102719,4007],{},[1697,102721,102722,102724,102726],{},[1493,102723,1520],{},[1680,102725,1691],{},[1490,102727,102728,102730,102732],{},[1680,102729,3201],{},[1493,102731,1709],{"mathvariant":1516},[1680,102733,4007],{},[1506,102735,3961],{},[1680,102737,1871],{},[1506,102739,1559],{"separator":1041},[1912,102741],{"width":2108},[1697,102743,102744,102746,102748],{},[1493,102745,1668],{},[1680,102747,9923],{},[1490,102749,102750,102752],{},[1506,102751,6927],{"mathvariant":1516},[1506,102753,6927],{"mathvariant":1516},[1506,102755,1508],{},[1506,102757,1888],{},[1869,102759,102760],{"scriptlevel":1871,"displaystyle":1552},[1510,102761,102762,102764],{},[1680,102763,3201],{},[1680,102765,9961],{},[1697,102767,102768,102770,102772],{},[1493,102769,1520],{},[1680,102771,1682],{},[1490,102773,102774,102776,102778],{},[1680,102775,1682],{},[1493,102777,1709],{"mathvariant":1516},[1680,102779,4007],{},[1697,102781,102782,102784,102786],{},[1493,102783,1520],{},[1680,102785,1691],{},[1490,102787,102788,102790,102792,102794],{},[1506,102789,1888],{},[1680,102791,1752],{},[1493,102793,1709],{"mathvariant":1516},[1680,102795,4007],{},[1506,102797,3961],{},[1680,102799,1871],{},[1506,102801,1559],{"separator":1041},[1528,102803,102804],{"encoding":1530},"U''_{11} = -\\tfrac{3}{16} Q_1^{-7\u002F4} Q_2^{3\u002F4} \u003C 0, \\quad U''_{22} = -\\tfrac{3}{16} Q_1^{1\u002F4} Q_2^{-5\u002F4} \u003C 0,",[1030,102806,102807],{},"tedy podmínky (6.4) i (6.5) jsou splněny.",[1065,102809,102811],{"id":102810},"indiferenční-křivky-křivky-užitečnosti-a-jejich-vlastnosti","Indiferenční křivky (křivky užitečnosti) a jejich vlastnosti",[1030,102813,102814,102817],{},[1047,102815,102816],{},"Křivky užitečnosti"," (utility curves) jsou indiferenční křivky funkce užitečnosti. Jsou dány rovnicí",[1035,102819,102821],{"className":102820},[1480],[1482,102822,102823],{"xmlns":1484,"display":1485},[1487,102824,102825,102868],{},[19617,102826,102827],{"width":19619},[19621,102828,102829,102831,102861,102863],{},[19624,102830],{"width":19626},[19624,102832,102833],{},[1490,102834,102835,102837,102839,102845,102847,102853,102855,102857,102859],{},[1493,102836,1668],{},[1506,102838,1553],{"stretchy":1552},[1497,102840,102841,102843],{},[1493,102842,1520],{},[1680,102844,1682],{},[1506,102846,1559],{"separator":1041},[1497,102848,102849,102851],{},[1493,102850,1520],{},[1680,102852,1691],{},[1506,102854,1564],{"stretchy":1552},[1506,102856,1508],{},[1493,102858,8730],{},[1506,102860,1559],{"separator":1041},[19624,102862],{"width":19626},[19624,102864,102865],{},[1988,102866,102867],{},"(6.7)",[1528,102869,102870],{"encoding":1530},"U(Q_1, Q_2) = c, \\tag{6.7}",[1030,102872,20022,102873,102886],{},[1035,102874,102876],{"className":102875},[1480],[1482,102877,102878],{"xmlns":1484},[1487,102879,102880,102884],{},[1490,102881,102882],{},[1493,102883,8730],{},[1528,102885,8730],{"encoding":1530}," je kladná konstanta. Pro Cobb-Douglasovu funkci:",[1035,102888,102890],{"className":102889},[1480],[1482,102891,102892],{"xmlns":1484,"display":1485},[1487,102893,102894,102935],{},[19617,102895,102896],{"width":19619},[19621,102897,102898,102900,102928,102930],{},[19624,102899],{"width":19626},[19624,102901,102902],{},[1490,102903,102904,102912,102914,102922,102924,102926],{},[1697,102905,102906,102908,102910],{},[1493,102907,1520],{},[1680,102909,1682],{},[1493,102911,1052],{},[1506,102913,1714],{},[1697,102915,102916,102918,102920],{},[1493,102917,1520],{},[1680,102919,1691],{},[1493,102921,2394],{},[1506,102923,1508],{},[1493,102925,8730],{},[1493,102927,2632],{"mathvariant":1516},[19624,102929],{"width":19626},[19624,102931,102932],{},[1988,102933,102934],{},"(6.8)",[1528,102936,102937],{"encoding":1530},"Q_1^a \\cdot Q_2^b = c. \\tag{6.8}",[1030,102939,102940,102941,3397,102971,1656,102974,102987,102988,103023,103024,103041,103042,103072,103073,103076],{},"Body na téže křivce užitečnosti reprezentují kombinace ",[1035,102942,102944],{"className":102943},[1480],[1482,102945,102946],{"xmlns":1484},[1487,102947,102948,102968],{},[1490,102949,102950,102952,102958,102960,102966],{},[1506,102951,14314],{"stretchy":1552},[1497,102953,102954,102956],{},[1493,102955,1520],{},[1680,102957,1682],{},[1506,102959,1559],{"separator":1041},[1497,102961,102962,102964],{},[1493,102963,1520],{},[1680,102965,1691],{},[1506,102967,14323],{"stretchy":1552},[1528,102969,102970],{"encoding":1530},"[Q_1, Q_2]",[1047,102972,102973],{},"stejnou úrovní uspokojení",[1035,102975,102977],{"className":102976},[1480],[1482,102978,102979],{"xmlns":1484},[1487,102980,102981,102985],{},[1490,102982,102983],{},[1493,102984,8730],{},[1528,102986,8730],{"encoding":1530},". Křivky užitečnosti vznikají jako průsečnice plochy ",[1035,102989,102991],{"className":102990},[1480],[1482,102992,102993],{"xmlns":1484},[1487,102994,102995,103021],{},[1490,102996,102997,102999,103001,103003,103005,103011,103013,103019],{},[1493,102998,1668],{},[1506,103000,1508],{},[1493,103002,1668],{},[1506,103004,1553],{"stretchy":1552},[1497,103006,103007,103009],{},[1493,103008,1520],{},[1680,103010,1682],{},[1506,103012,1559],{"separator":1041},[1497,103014,103015,103017],{},[1493,103016,1520],{},[1680,103018,1691],{},[1506,103020,1564],{"stretchy":1552},[1528,103022,99394],{"encoding":1530}," s rovinami ",[1035,103025,103027],{"className":103026},[1480],[1482,103028,103029],{"xmlns":1484},[1487,103030,103031,103039],{},[1490,103032,103033,103035,103037],{},[1493,103034,1668],{},[1506,103036,1508],{},[1493,103038,8730],{},[1528,103040,98610],{"encoding":1530}," rovnoběžnými s rovinou ",[1035,103043,103045],{"className":103044},[1480],[1482,103046,103047],{"xmlns":1484},[1487,103048,103049,103069],{},[1490,103050,103051,103053,103059,103061,103067],{},[1506,103052,1553],{"stretchy":1552},[1497,103054,103055,103057],{},[1493,103056,1520],{},[1680,103058,1682],{},[1506,103060,1559],{"separator":1041},[1497,103062,103063,103065],{},[1493,103064,1520],{},[1680,103066,1691],{},[1506,103068,1564],{"stretchy":1552},[1528,103070,103071],{"encoding":1530},"(Q_1, Q_2)",". Jsou v příbuznosti s ",[1047,103074,103075],{},"izokvantami"," produkčních funkcí.",[1023,103078,103080,103087],{"className":103079,"dataCallout":66935},[1026,66934],[1030,103081,103083,103086],{"className":103082},[1033],[1035,103084],{"className":103085,"ariaHidden":1041},[1038,66942,1040],"Příklad 6.4 — rovnice křivek užitečnosti",[1030,103088,2364,103089,103151,103152,103196,103197,5153,103231,11074,103249,5153,103303,11074,103321,2632],{},[1035,103090,103092],{"className":103091},[1480],[1482,103093,103094],{"xmlns":1484},[1487,103095,103096,103148],{},[1490,103097,103098,103100,103102,103108,103110,103116,103118,103120,103134],{},[1493,103099,1668],{},[1506,103101,1553],{"stretchy":1552},[1497,103103,103104,103106],{},[1493,103105,1520],{},[1680,103107,1682],{},[1506,103109,1559],{"separator":1041},[1497,103111,103112,103114],{},[1493,103113,1520],{},[1680,103115,1691],{},[1506,103117,1564],{"stretchy":1552},[1506,103119,1508],{},[1697,103121,103122,103124,103126],{},[1493,103123,1520],{},[1680,103125,1682],{},[1490,103127,103128,103130,103132],{},[1680,103129,1682],{},[1493,103131,1709],{"mathvariant":1516},[1680,103133,4007],{},[1697,103135,103136,103138,103140],{},[1493,103137,1520],{},[1680,103139,1691],{},[1490,103141,103142,103144,103146],{},[1680,103143,3201],{},[1493,103145,1709],{"mathvariant":1516},[1680,103147,4007],{},[1528,103149,103150],{"encoding":1530},"U(Q_1, Q_2) = Q_1^{1\u002F4} Q_2^{3\u002F4}"," mají křivky užitečnosti rovnici ",[1035,103153,103155],{"className":103154},[1480],[1482,103156,103157],{"xmlns":1484},[1487,103158,103159,103193],{},[1490,103160,103161,103175,103189,103191],{},[1697,103162,103163,103165,103167],{},[1493,103164,1520],{},[1680,103166,1682],{},[1490,103168,103169,103171,103173],{},[1680,103170,1682],{},[1493,103172,1709],{"mathvariant":1516},[1680,103174,4007],{},[1697,103176,103177,103179,103181],{},[1493,103178,1520],{},[1680,103180,1691],{},[1490,103182,103183,103185,103187],{},[1680,103184,3201],{},[1493,103186,1709],{"mathvariant":1516},[1680,103188,4007],{},[1506,103190,1508],{},[1493,103192,8730],{},[1528,103194,103195],{"encoding":1530},"Q_1^{1\u002F4} Q_2^{3\u002F4} = c",". Umocněním na čtvrtou mocninu dostáváme ",[1035,103198,103200],{"className":103199},[1480],[1482,103201,103202],{"xmlns":1484},[1487,103203,103204,103228],{},[1490,103205,103206,103212,103220,103222],{},[1497,103207,103208,103210],{},[1493,103209,1520],{},[1680,103211,1682],{},[1697,103213,103214,103216,103218],{},[1493,103215,1520],{},[1680,103217,1691],{},[1680,103219,3201],{},[1506,103221,1508],{},[2315,103223,103224,103226],{},[1493,103225,8730],{},[1680,103227,4007],{},[1528,103229,103230],{"encoding":1530},"Q_1 Q_2^{3} = c^{4}",[1035,103232,103234],{"className":103233},[1480],[1482,103235,103236],{"xmlns":1484},[1487,103237,103238,103246],{},[1490,103239,103240,103242,103244],{},[1493,103241,8730],{},[1506,103243,1508],{},[1680,103245,1682],{},[1528,103247,103248],{"encoding":1530},"c = 1",[1035,103250,103252],{"className":103251},[1480],[1482,103253,103254],{"xmlns":1484},[1487,103255,103256,103300],{},[1490,103257,103258,103264,103266,103282,103284],{},[1497,103259,103260,103262],{},[1493,103261,1520],{},[1680,103263,1691],{},[1506,103265,1508],{},[1697,103267,103268,103270,103272],{},[1493,103269,1520],{},[1680,103271,1682],{},[1490,103273,103274,103276,103278,103280],{},[1506,103275,1888],{},[1680,103277,1682],{},[1493,103279,1709],{"mathvariant":1516},[1680,103281,3201],{},[1506,103283,1508],{},[1869,103285,103286],{"scriptlevel":1871,"displaystyle":1041},[1510,103287,103288,103290],{},[1680,103289,1682],{},[94023,103291,103292,103298],{},[1497,103293,103294,103296],{},[1493,103295,1520],{},[1680,103297,1682],{},[1680,103299,3201],{},[1528,103301,103302],{"encoding":1530},"Q_2 = Q_1^{-1\u002F3} = \\dfrac{1}{\\sqrt[3]{Q_1}}",[1035,103304,103306],{"className":103305},[1480],[1482,103307,103308],{"xmlns":1484},[1487,103309,103310,103318],{},[1490,103311,103312,103314,103316],{},[1493,103313,8730],{},[1506,103315,1508],{},[1680,103317,1691],{},[1528,103319,103320],{"encoding":1530},"c = 2",[1035,103322,103324],{"className":103323},[1480],[1482,103325,103326],{"xmlns":1484},[1487,103327,103328,103394],{},[1490,103329,103330,103336,103338,103350,103352,103368,103370],{},[1497,103331,103332,103334],{},[1493,103333,1520],{},[1680,103335,1691],{},[1506,103337,1508],{},[2315,103339,103340,103342],{},[1680,103341,1691],{},[1490,103343,103344,103346,103348],{},[1680,103345,4007],{},[1493,103347,1709],{"mathvariant":1516},[1680,103349,3201],{},[1506,103351,1714],{},[1697,103353,103354,103356,103358],{},[1493,103355,1520],{},[1680,103357,1682],{},[1490,103359,103360,103362,103364,103366],{},[1506,103361,1888],{},[1680,103363,1682],{},[1493,103365,1709],{"mathvariant":1516},[1680,103367,3201],{},[1506,103369,1508],{},[1869,103371,103372],{"scriptlevel":1871,"displaystyle":1041},[1510,103373,103374,103384],{},[1490,103375,103376,103378],{},[1680,103377,1691],{},[94023,103379,103380,103382],{},[1680,103381,1691],{},[1680,103383,3201],{},[94023,103385,103386,103392],{},[1497,103387,103388,103390],{},[1493,103389,1520],{},[1680,103391,1682],{},[1680,103393,3201],{},[1528,103395,103396],{"encoding":1530},"Q_2 = 2^{4\u002F3} \\cdot Q_1^{-1\u002F3} = \\dfrac{2 \\sqrt[3]{2}}{\\sqrt[3]{Q_1}}",[1304,103398,103400],{"id":103399},"čtyři-vlastnosti-křivek-užitečnosti","Čtyři vlastnosti křivek užitečnosti",[1030,103402,103403],{},[18014,103404],{"alt":103405,"className":103406,"src":103407},"imek-ic-4vlastnosti-anotovane",[1055,18018],"\u002Fwiki-assets\u002Fimek-ic-4vlastnosti-anotovane.jpeg",[1023,103409,103411,103418,103424,103471,103515,103521,103526],{"className":103410,"dataCallout":1155},[1026,1154],[1030,103412,103414,103417],{"className":103413},[1033],[1035,103415],{"className":103416,"ariaHidden":1041},[1038,1162,1040],"Čtyři základní vlastnosti indiferenčních křivek",[1030,103419,103420,103423],{},[1047,103421,103422],{},"1° Klesající."," Je-li nakoupeno méně jednoho zboží, je k dosažení stejného uspokojení třeba kompenzovat větším množstvím druhého zboží. Sklon tečny je",[1030,103425,103426],{},[1035,103427,103429],{"className":103428},[1480],[1482,103430,103431],{"xmlns":1484},[1487,103432,103433,103468],{},[1490,103434,103435,103438,103440,103442,103444,103446,103464,103466],{},[1493,103436,103437],{"mathvariant":1516},"tg",[1506,103439,7574],{},[1493,103441,34997],{},[1506,103443,1508],{},[1506,103445,1888],{},[1510,103447,103448,103456],{},[1697,103449,103450,103452,103454],{},[1493,103451,1668],{},[1680,103453,1682],{},[1506,103455,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1697,103457,103458,103460,103462],{},[1493,103459,1668],{},[1680,103461,1691],{},[1506,103463,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,103465,3961],{},[1680,103467,1871],{},[1528,103469,103470],{"encoding":1530},"\\operatorname{tg} \\alpha = -\\frac{U'_1}{U'_2} \u003C 0",[1030,103472,103473,103474,103514],{},"(derivace implicitně zadané funkce ",[1035,103475,103477],{"className":103476},[1480],[1482,103478,103479],{"xmlns":1484},[1487,103480,103481,103511],{},[1490,103482,103483,103485,103487,103493,103495,103501,103503,103505,103507,103509],{},[1493,103484,1668],{},[1506,103486,1553],{"stretchy":1552},[1497,103488,103489,103491],{},[1493,103490,1520],{},[1680,103492,1682],{},[1506,103494,1559],{"separator":1041},[1497,103496,103497,103499],{},[1493,103498,1520],{},[1680,103500,1691],{},[1506,103502,1564],{"stretchy":1552},[1506,103504,1888],{},[1493,103506,8730],{},[1506,103508,1508],{},[1680,103510,1871],{},[1528,103512,103513],{"encoding":1530},"U(Q_1, Q_2) - c = 0","). Ze záporné derivace plyne klesající průběh.",[1030,103516,103517,103520],{},[1047,103518,103519],{},"2° Neprotínají se."," V průsečíku by týž svazek ležel na dvou různých hladinách užitečnosti, což je spor.",[1030,103522,103523,2632],{},[1047,103524,103525],{},"3° Čím vzdálenější od počátku, tím vyšší užitečnost",[1030,103527,103528,103531,103532,103550,103551,103567,103568,103571],{},[1047,103529,103530],{},"4° Konvexní."," Pro každé dva body ",[1035,103533,103535],{"className":103534},[1480],[1482,103536,103537],{"xmlns":1484},[1487,103538,103539,103547],{},[1490,103540,103541,103543,103545],{},[1493,103542,3633],{},[1506,103544,1559],{"separator":1041},[1493,103546,11353],{},[1528,103548,103549],{"encoding":1530},"A, B"," na téže křivce leží vnitřní body úsečky ",[1035,103552,103554],{"className":103553},[1480],[1482,103555,103556],{"xmlns":1484},[1487,103557,103558,103564],{},[1490,103559,103560,103562],{},[1493,103561,3633],{},[1493,103563,11353],{},[1528,103565,103566],{"encoding":1530},"AB"," ve ",[1047,103569,103570],{},"vyšší"," hladině užitečnosti (tj. „nad\" křivkou) — vyjadřuje to preferenci smíšených svazků před krajními.",[1065,103573,103575],{"id":103574},"mezní-míra-komoditní-substituce-mrcs","Mezní míra komoditní substituce (MRCS)",[1030,103577,103578,1656,103581,7606,103594,103597],{},[1047,103579,103580],{},"Mezní míra komoditní substituce",[1035,103582,103584],{"className":103583},[1480],[1482,103585,103586],{"xmlns":1484},[1487,103587,103588,103592],{},[1490,103589,103590],{},[1988,103591,13960],{},[1528,103593,43799],{"encoding":1530},[1047,103595,103596],{},"marginal rate of commodity substitution",") je podíl mezních užitečností:",[1035,103599,103601],{"className":103600},[1480],[1482,103602,103603],{"xmlns":1484,"display":1485},[1487,103604,103605,103692],{},[19617,103606,103607],{"width":19619},[19621,103608,103609,103611,103685,103687],{},[19624,103610],{"width":19626},[19624,103612,103613],{},[1490,103614,103615,103617,103619,103621,103623,103629,103631,103637,103639,103641,103663,103665,103683],{},[1988,103616,13960],{},[1506,103618,1508],{},[1988,103620,13960],{},[1506,103622,1553],{"stretchy":1552},[1497,103624,103625,103627],{},[1493,103626,1520],{},[1680,103628,1682],{},[1506,103630,1559],{"separator":1041},[1497,103632,103633,103635],{},[1493,103634,1520],{},[1680,103636,1691],{},[1506,103638,1564],{"stretchy":1552},[1506,103640,1508],{},[1510,103642,103643,103653],{},[1490,103644,103645,103647],{},[1493,103646,1495],{},[1497,103648,103649,103651],{},[1493,103650,1668],{},[1680,103652,1682],{},[1490,103654,103655,103657],{},[1493,103656,1495],{},[1497,103658,103659,103661],{},[1493,103660,1668],{},[1680,103662,1691],{},[1506,103664,1508],{},[1510,103666,103667,103675],{},[1697,103668,103669,103671,103673],{},[1493,103670,1668],{},[1680,103672,1682],{},[1506,103674,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1697,103676,103677,103679,103681],{},[1493,103678,1668],{},[1680,103680,1691],{},[1506,103682,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1493,103684,2632],{"mathvariant":1516},[19624,103686],{"width":19626},[19624,103688,103689],{},[1988,103690,103691],{},"(6.9)",[1528,103693,103694],{"encoding":1530},"\\text{MRCS} = \\text{MRCS}(Q_1, Q_2) = \\frac{MU_1}{MU_2} = \\frac{U'_1}{U'_2}. \\tag{6.9}",[1030,103696,6707,103697,103731,103732,103764,103765,103800,103801,103814],{},[1035,103698,103700],{"className":103699},[1480],[1482,103701,103702],{"xmlns":1484},[1487,103703,103704,103728],{},[1490,103705,103706,103708],{},[1506,103707,1888],{},[1869,103709,103710],{"scriptlevel":1871,"displaystyle":1552},[1510,103711,103712,103720],{},[1697,103713,103714,103716,103718],{},[1493,103715,1668],{},[1680,103717,1682],{},[1506,103719,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1697,103721,103722,103724,103726],{},[1493,103723,1668],{},[1680,103725,1691],{},[1506,103727,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,103729,103730],{"encoding":1530},"-\\tfrac{U'_1}{U'_2}"," je derivace funkce ",[1035,103733,103735],{"className":103734},[1480],[1482,103736,103737],{"xmlns":1484},[1487,103738,103739,103761],{},[1490,103740,103741,103747,103749,103751,103753,103759],{},[1497,103742,103743,103745],{},[1493,103744,1520],{},[1680,103746,1691],{},[1506,103748,1508],{},[1493,103750,12889],{},[1506,103752,1553],{"stretchy":1552},[1497,103754,103755,103757],{},[1493,103756,1520],{},[1680,103758,1682],{},[1506,103760,1564],{"stretchy":1552},[1528,103762,103763],{"encoding":1530},"Q_2 = f(Q_1)"," zadané implicitně rovnicí ",[1035,103766,103768],{"className":103767},[1480],[1482,103769,103770],{"xmlns":1484},[1487,103771,103772,103798],{},[1490,103773,103774,103776,103778,103784,103786,103792,103794,103796],{},[1493,103775,1668],{},[1506,103777,1553],{"stretchy":1552},[1497,103779,103780,103782],{},[1493,103781,1520],{},[1680,103783,1682],{},[1506,103785,1559],{"separator":1041},[1497,103787,103788,103790],{},[1493,103789,1520],{},[1680,103791,1691],{},[1506,103793,1564],{"stretchy":1552},[1506,103795,1508],{},[1493,103797,8730],{},[1528,103799,26302],{"encoding":1530},". Protože je vždy záporná (křivka je klesající), bereme absolutní hodnotu a kladný ",[1035,103802,103804],{"className":103803},[1480],[1482,103805,103806],{"xmlns":1484},[1487,103807,103808,103812],{},[1490,103809,103810],{},[1988,103811,13960],{},[1528,103813,43799],{"encoding":1530}," chápeme jako velikost kompenzace.",[1023,103816,103818,103825],{"className":103817,"dataCallout":582},[1026,1186],[1030,103819,103821,103824],{"className":103820},[1033],[1035,103822],{"className":103823,"ariaHidden":1041},[1038,1193,1040],"Intuice — MRCS jako sklon indiferenční křivky",[1030,103826,103827,8994,103859,103897,103898,103915,103916,103933],{},[1035,103828,103830],{"className":103829},[1480],[1482,103831,103832],{"xmlns":1484},[1487,103833,103834,103856],{},[1490,103835,103836,103838,103840,103846,103848,103854],{},[1988,103837,13960],{},[1506,103839,1553],{"stretchy":1552},[1497,103841,103842,103844],{},[1493,103843,1520],{},[1680,103845,1682],{},[1506,103847,1559],{"separator":1041},[1497,103849,103850,103852],{},[1493,103851,1520],{},[1680,103853,1691],{},[1506,103855,1564],{"stretchy":1552},[1528,103857,103858],{"encoding":1530},"\\text{MRCS}(Q_1, Q_2)",[1047,103860,103861,103862,44574,103879,103896],{},"míra, jakou je spotřebitel ochoten zaměnit ",[1035,103863,103865],{"className":103864},[1480],[1482,103866,103867],{"xmlns":1484},[1487,103868,103869,103877],{},[1490,103870,103871],{},[1497,103872,103873,103875],{},[1493,103874,1520],{},[1680,103876,1682],{},[1528,103878,6702],{"encoding":1530},[1035,103880,103882],{"className":103881},[1480],[1482,103883,103884],{"xmlns":1484},[1487,103885,103886,103894],{},[1490,103887,103888],{},[1497,103889,103890,103892],{},[1493,103891,1520],{},[1680,103893,1691],{},[1528,103895,6683],{"encoding":1530}," při zachování užitečnosti"," — tedy kolik jednotek ",[1035,103899,103901],{"className":103900},[1480],[1482,103902,103903],{"xmlns":1484},[1487,103904,103905,103913],{},[1490,103906,103907],{},[1497,103908,103909,103911],{},[1493,103910,1520],{},[1680,103912,1691],{},[1528,103914,6683],{"encoding":1530}," „obětuje\" za jednu jednotku ",[1035,103917,103919],{"className":103918},[1480],[1482,103920,103921],{"xmlns":1484},[1487,103922,103923,103931],{},[1490,103924,103925],{},[1497,103926,103927,103929],{},[1493,103928,1520],{},[1680,103930,1682],{},[1528,103932,6702],{"encoding":1530}," navíc, aby zůstal na téže indiferenční křivce. Geometricky jde o absolutní hodnotu sklonu tečny k indiferenční křivce v daném bodě.",[1030,103935,103936,103937,45271],{},"Pro obecnou změnu ",[1035,103938,103940],{"className":103939},[1480],[1482,103941,103942],{"xmlns":1484},[1487,103943,103944,103954],{},[1490,103945,103946,103948],{},[1493,103947,3384],{"mathvariant":1516},[1497,103949,103950,103952],{},[1493,103951,1520],{},[1680,103953,1682],{},[1528,103955,103956],{"encoding":1530},"\\mathrm{d} Q_1",[1035,103958,103960],{"className":103959},[1480],[1482,103961,103962],{"xmlns":1484,"display":1485},[1487,103963,103964,104017],{},[19617,103965,103966],{"width":19619},[19621,103967,103968,103970,104010,104012],{},[19624,103969],{"width":19626},[19624,103971,103972],{},[1490,103973,103974,103976,103982,103984,103986,103992,103994,103996,103998,104000,104002,104008],{},[1493,103975,2976],{"mathvariant":1516},[1497,103977,103978,103980],{},[1493,103979,1520],{},[1680,103981,1691],{},[1506,103983,2343],{},[1493,103985,3384],{"mathvariant":1516},[1497,103987,103988,103990],{},[1493,103989,1520],{},[1680,103991,1691],{},[1506,103993,1508],{},[1506,103995,1888],{},[1988,103997,13960],{},[1506,103999,1714],{},[1493,104001,3384],{"mathvariant":1516},[1497,104003,104004,104006],{},[1493,104005,1520],{},[1680,104007,1682],{},[1506,104009,1559],{"separator":1041},[19624,104011],{"width":19626},[19624,104013,104014],{},[1988,104015,104016],{},"(6.10)",[1528,104018,104019],{"encoding":1530},"\\Delta Q_2 \\approx \\mathrm{d} Q_2 = -\\text{MRCS} \\cdot \\mathrm{d} Q_1, \\tag{6.10}",[1035,104021,104023],{"className":104022},[1480],[1482,104024,104025],{"xmlns":1484,"display":1485},[1487,104026,104027,104074],{},[19617,104028,104029],{"width":19619},[19621,104030,104031,104033,104067,104069],{},[19624,104032],{"width":19626},[19624,104034,104035],{},[1490,104036,104037,104039,104045,104047,104049,104055,104057,104059,104065],{},[1493,104038,3384],{"mathvariant":1516},[1497,104040,104041,104043],{},[1493,104042,1520],{},[1680,104044,1682],{},[1506,104046,1508],{},[1506,104048,1888],{},[1510,104050,104051,104053],{},[1680,104052,1682],{},[1988,104054,13960],{},[1988,104056,5016],{},[1493,104058,3384],{"mathvariant":1516},[1497,104060,104061,104063],{},[1493,104062,1520],{},[1680,104064,1691],{},[1493,104066,2632],{"mathvariant":1516},[19624,104068],{"width":19626},[19624,104070,104071],{},[1988,104072,104073],{},"(6.11)",[1528,104075,104076],{"encoding":1530},"\\mathrm{d} Q_1 = -\\frac{1}{\\text{MRCS}}\\, \\mathrm{d} Q_2. \\tag{6.11}",[1023,104078,104080,104086,104149,104266],{"className":104079,"dataCallout":66935},[1026,66934],[1030,104081,104083,45206],{"className":104082},[1033],[1035,104084],{"className":104085,"ariaHidden":1041},[1038,66942,1040],[1030,104087,2364,104088,45271],{},[1035,104089,104091],{"className":104090},[1480],[1482,104092,104093],{"xmlns":1484},[1487,104094,104095,104147],{},[1490,104096,104097,104099,104101,104107,104109,104115,104117,104119,104133],{},[1493,104098,1668],{},[1506,104100,1553],{"stretchy":1552},[1497,104102,104103,104105],{},[1493,104104,1520],{},[1680,104106,1682],{},[1506,104108,1559],{"separator":1041},[1497,104110,104111,104113],{},[1493,104112,1520],{},[1680,104114,1691],{},[1506,104116,1564],{"stretchy":1552},[1506,104118,1508],{},[1697,104120,104121,104123,104125],{},[1493,104122,1520],{},[1680,104124,1682],{},[1490,104126,104127,104129,104131],{},[1680,104128,1682],{},[1493,104130,1709],{"mathvariant":1516},[1680,104132,1691],{},[1697,104134,104135,104137,104139],{},[1493,104136,1520],{},[1680,104138,1691],{},[1490,104140,104141,104143,104145],{},[1680,104142,1682],{},[1493,104144,1709],{"mathvariant":1516},[1680,104146,1691],{},[1528,104148,45270],{"encoding":1530},[1030,104150,104151],{},[1035,104152,104154],{"className":104153},[1480],[1482,104155,104156],{"xmlns":1484},[1487,104157,104158,104264],{},[1490,104159,104160,104162,104164,104246,104248,104262],{},[1988,104161,13960],{},[1506,104163,1508],{},[1510,104165,104166,104206],{},[1490,104167,104168,104176,104192],{},[1869,104169,104170],{"scriptlevel":1871,"displaystyle":1552},[1510,104171,104172,104174],{},[1680,104173,1682],{},[1680,104175,1691],{},[1697,104177,104178,104180,104182],{},[1493,104179,1520],{},[1680,104181,1682],{},[1490,104183,104184,104186,104188,104190],{},[1506,104185,1888],{},[1680,104187,1682],{},[1493,104189,1709],{"mathvariant":1516},[1680,104191,1691],{},[1697,104193,104194,104196,104198],{},[1493,104195,1520],{},[1680,104197,1691],{},[1490,104199,104200,104202,104204],{},[1680,104201,1682],{},[1493,104203,1709],{"mathvariant":1516},[1680,104205,1691],{},[1490,104207,104208,104216,104230],{},[1869,104209,104210],{"scriptlevel":1871,"displaystyle":1552},[1510,104211,104212,104214],{},[1680,104213,1682],{},[1680,104215,1691],{},[1697,104217,104218,104220,104222],{},[1493,104219,1520],{},[1680,104221,1682],{},[1490,104223,104224,104226,104228],{},[1680,104225,1682],{},[1493,104227,1709],{"mathvariant":1516},[1680,104229,1691],{},[1697,104231,104232,104234,104236],{},[1493,104233,1520],{},[1680,104235,1691],{},[1490,104237,104238,104240,104242,104244],{},[1506,104239,1888],{},[1680,104241,1682],{},[1493,104243,1709],{"mathvariant":1516},[1680,104245,1691],{},[1506,104247,1508],{},[1510,104249,104250,104256],{},[1497,104251,104252,104254],{},[1493,104253,1520],{},[1680,104255,1691],{},[1497,104257,104258,104260],{},[1493,104259,1520],{},[1680,104261,1682],{},[1493,104263,2632],{"mathvariant":1516},[1528,104265,45387],{"encoding":1530},[1030,104267,45390,104268,18367,104311,45437,104313,104332],{},[1035,104269,104271],{"className":104270},[1480],[1482,104272,104273],{"xmlns":1484},[1487,104274,104275,104309],{},[1490,104276,104277,104279,104281,104283,104285,104287,104289,104291,104299,104301],{},[1988,104278,13960],{},[1506,104280,1553],{"stretchy":1552},[1680,104282,5231],{},[1506,104284,1559],{"separator":1041},[1680,104286,1796],{},[1506,104288,1564],{"stretchy":1552},[1506,104290,1508],{},[1869,104292,104293],{"scriptlevel":1871,"displaystyle":1552},[1510,104294,104295,104297],{},[1680,104296,1796],{},[1680,104298,5231],{},[1506,104300,1508],{},[1869,104302,104303],{"scriptlevel":1871,"displaystyle":1552},[1510,104304,104305,104307],{},[1680,104306,1752],{},[1680,104308,3201],{},[1528,104310,45434],{"encoding":1530},[1176,104312,12171],{},[1035,104314,104316],{"className":104315},[1480],[1482,104317,104318],{"xmlns":1484},[1487,104319,104320,104330],{},[1490,104321,104322],{},[1869,104323,104324],{"scriptlevel":1871,"displaystyle":1552},[1510,104325,104326,104328],{},[1680,104327,1752],{},[1680,104329,3201],{},[1528,104331,45457],{"encoding":1530}," jednotky, aby se užitečnost zachovala.",[1030,104334,104335,104336,104340],{},"(Paralelou je ",[1052,104337,104339],{"className":104338,"dataFsResolvedFilePath":1572,"href":1573},[1055],"mezní míra technické substituce MRTS"," z produkční teorie.)",[1065,104342,104344],{"id":104343},"_63-64-optimalizace-spotřebitele-přehled","6.3 – 6.4 Optimalizace spotřebitele — přehled",[1030,104346,104347,104348,104351],{},"Rámcově se v kapitole 6 studují ",[1047,104349,104350],{},"dvě vázané optimalizační úlohy"," s užitečností:",[1203,104353,104354,104490],{},[1206,104355,104356,104358,104359,26683,104390,1656,104393,104442,104443,2632],{},[1047,104357,43818],{}," — maximalizace ",[1035,104360,104362],{"className":104361},[1480],[1482,104363,104364],{"xmlns":1484},[1487,104365,104366,104388],{},[1490,104367,104368,104370,104372,104378,104380,104386],{},[1493,104369,1668],{},[1506,104371,1553],{"stretchy":1552},[1497,104373,104374,104376],{},[1493,104375,1520],{},[1680,104377,1682],{},[1506,104379,1559],{"separator":1041},[1497,104381,104382,104384],{},[1493,104383,1520],{},[1680,104385,1691],{},[1506,104387,1564],{"stretchy":1552},[1528,104389,32500],{"encoding":1530},[1047,104391,104392],{},"rozpočtovém omezení",[1035,104394,104396],{"className":104395},[1480],[1482,104397,104398],{"xmlns":1484},[1487,104399,104400,104440],{},[1490,104401,104402,104408,104410,104418,104424,104426,104434],{},[2315,104403,104404,104406],{},[1493,104405,1791],{},[1506,104407,2287],{},[1506,104409,1508],{},[1697,104411,104412,104414,104416],{},[1493,104413,1501],{},[1680,104415,1682],{},[1506,104417,2287],{},[1497,104419,104420,104422],{},[1493,104421,1520],{},[1680,104423,1682],{},[1506,104425,2162],{},[1697,104427,104428,104430,104432],{},[1493,104429,1501],{},[1680,104431,1691],{},[1506,104433,2287],{},[1497,104435,104436,104438],{},[1493,104437,1520],{},[1680,104439,1691],{},[1528,104441,33447],{"encoding":1530},". Výstupem je Marshallova poptávka ",[1035,104444,104446],{"className":104445},[1480],[1482,104447,104448],{"xmlns":1484},[1487,104449,104450,104488],{},[1490,104451,104452,104458,104460,104466,104468,104474,104476,104482,104484,104486],{},[1497,104453,104454,104456],{},[1493,104455,1520],{},[1493,104457,6277],{},[1506,104459,1508],{},[1497,104461,104462,104464],{},[1493,104463,3712],{},[1493,104465,6277],{},[1506,104467,1553],{"stretchy":1552},[1497,104469,104470,104472],{},[1493,104471,1501],{},[1680,104473,1682],{},[1506,104475,1559],{"separator":1041},[1497,104477,104478,104480],{},[1493,104479,1501],{},[1680,104481,1691],{},[1506,104483,1559],{"separator":1041},[1493,104485,1791],{},[1506,104487,1564],{"stretchy":1552},[1528,104489,51552],{"encoding":1530},[1206,104491,104492,43467,104494,43509,104540,104557,104558,2632],{},[1047,104493,4124],{},[1035,104495,104497],{"className":104496},[1480],[1482,104498,104499],{"xmlns":1484},[1487,104500,104501,104537],{},[1490,104502,104503,104505,104507,104515,104521,104523,104531],{},[1493,104504,2711],{},[1506,104506,1508],{},[1697,104508,104509,104511,104513],{},[1493,104510,1501],{},[1680,104512,1682],{},[1506,104514,2287],{},[1497,104516,104517,104519],{},[1493,104518,1520],{},[1680,104520,1682],{},[1506,104522,2162],{},[1697,104524,104525,104527,104529],{},[1493,104526,1501],{},[1680,104528,1691],{},[1506,104530,2287],{},[1497,104532,104533,104535],{},[1493,104534,1520],{},[1680,104536,1691],{},[1528,104538,104539],{"encoding":1530},"E = P_1^* Q_1 + P_2^* Q_2",[1035,104541,104543],{"className":104542},[1480],[1482,104544,104545],{"xmlns":1484},[1487,104546,104547,104555],{},[1490,104548,104549],{},[2315,104550,104551,104553],{},[1493,104552,1668],{},[1506,104554,2287],{},[1528,104556,43527],{"encoding":1530},". Výstupem je Hicksova poptávka ",[1035,104559,104561],{"className":104560},[1480],[1482,104562,104563],{"xmlns":1484},[1487,104564,104565,104603],{},[1490,104566,104567,104573,104575,104581,104583,104589,104591,104597,104599,104601],{},[1497,104568,104569,104571],{},[1493,104570,1520],{},[1493,104572,6277],{},[1506,104574,1508],{},[1497,104576,104577,104579],{},[1493,104578,3712],{},[1493,104580,6277],{},[1506,104582,1553],{"stretchy":1552},[1497,104584,104585,104587],{},[1493,104586,1501],{},[1680,104588,1682],{},[1506,104590,1559],{"separator":1041},[1497,104592,104593,104595],{},[1493,104594,1501],{},[1680,104596,1691],{},[1506,104598,1559],{"separator":1041},[1493,104600,1668],{},[1506,104602,1564],{"stretchy":1552},[1528,104604,33967],{"encoding":1530},[1030,104606,104607,104608,104611,104612,1656,104615,104654],{},"Obě úlohy se řeší ",[1052,104609,43532],{"className":104610,"dataFsResolvedFilePath":17265,"href":17266},[1055]," a vedou na ",[1047,104613,104614],{},"tentýž bod dotyku",[1035,104616,104618],{"className":104617},[1480],[1482,104619,104620],{"xmlns":1484},[1487,104621,104622,104652],{},[1490,104623,104624,104630,104632,104640,104642,104650],{},[2315,104625,104626,104628],{},[1493,104627,1520],{},[1506,104629,2287],{},[1506,104631,14314],{"stretchy":1552},[1697,104633,104634,104636,104638],{},[1493,104635,1520],{},[1680,104637,1682],{},[1506,104639,2287],{},[1506,104641,1559],{"separator":1041},[1697,104643,104644,104646,104648],{},[1493,104645,1520],{},[1680,104647,1691],{},[1506,104649,2287],{},[1506,104651,14323],{"stretchy":1552},[1528,104653,43893],{"encoding":1530}," indiferenční křivky a rozpočtové přímky (resp. přímky výdajů), v němž platí podmínka optimality",[1035,104656,104658],{"className":104657},[1480],[1482,104659,104660],{"xmlns":1484,"display":1485},[1487,104661,104662,104708],{},[1490,104663,104664,104666,104668,104686,104688,104706],{},[1988,104665,13960],{},[1506,104667,1508],{},[1510,104669,104670,104678],{},[1697,104671,104672,104674,104676],{},[1493,104673,1668],{},[1680,104675,1682],{},[1506,104677,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1697,104679,104680,104682,104684],{},[1493,104681,1668],{},[1680,104683,1691],{},[1506,104685,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,104687,1508],{},[1510,104689,104690,104698],{},[1697,104691,104692,104694,104696],{},[1493,104693,1501],{},[1680,104695,1682],{},[1506,104697,2287],{},[1697,104699,104700,104702,104704],{},[1493,104701,1501],{},[1680,104703,1691],{},[1506,104705,2287],{},[1493,104707,2632],{"mathvariant":1516},[1528,104709,104710],{"encoding":1530},"\\text{MRCS} = \\frac{U'_1}{U'_2} = \\frac{P_1^*}{P_2^*}.",[1030,104712,104713],{},"Poměr mezních užitečností se rovná poměru cen — sklon indiferenční křivky v optimu se rovná sklonu rozpočtové přímky.",[1023,104715,104717,104727],{"className":104716,"dataCallout":582},[1026,1186],[1030,104718,104720,104723,104724],{"className":104719},[1033],[1035,104721],{"className":104722,"ariaHidden":1041},[1038,1193,1040],"Pro detailní postup viz ",[1052,104725,774],{"className":104726,"dataFsResolvedFilePath":1841,"href":1842},[1055],[1030,104728,104729,104730,104733,104734,104761,104762,104796,104797,104831,104832,104875,104876,104879,104880,2632],{},"Kompletní odvození obou úloh Lagrangeovou metodou, geometrická interpretace, řešené ",[1047,104731,104732],{},"Příklady 6.5–6.8"," (MRCS pro Cobb-Douglase, maximalizace ",[1035,104735,104737],{"className":104736},[1480],[1482,104738,104739],{"xmlns":1484},[1487,104740,104741,104759],{},[1490,104742,104743,104745,104747,104753],{},[1493,104744,1668],{},[1506,104746,1508],{},[1497,104748,104749,104751],{},[1493,104750,1520],{},[1680,104752,1682],{},[1497,104754,104755,104757],{},[1493,104756,1520],{},[1680,104758,1691],{},[1528,104760,45550],{"encoding":1530}," s výsledkem ",[1035,104763,104765],{"className":104764},[1480],[1482,104766,104767],{"xmlns":1484},[1487,104768,104769,104793],{},[1490,104770,104771,104777,104779,104781,104783,104789,104791],{},[1497,104772,104773,104775],{},[1493,104774,1520],{},[1680,104776,1682],{},[1506,104778,1508],{},[1680,104780,2309],{},[1506,104782,1559],{"separator":1041},[1497,104784,104785,104787],{},[1493,104786,1520],{},[1680,104788,1691],{},[1506,104790,1508],{},[1680,104792,1775],{},[1528,104794,104795],{"encoding":1530},"Q_1 = 25, Q_2 = 10","; minimalizace výdajů s ",[1035,104798,104800],{"className":104799},[1480],[1482,104801,104802],{"xmlns":1484},[1487,104803,104804,104828],{},[1490,104805,104806,104812,104814,104816,104818,104824,104826],{},[1497,104807,104808,104810],{},[1493,104809,1520],{},[1680,104811,1682],{},[1506,104813,1508],{},[1680,104815,4007],{},[1506,104817,1559],{"separator":1041},[1497,104819,104820,104822],{},[1493,104821,1520],{},[1680,104823,1691],{},[1506,104825,1508],{},[1680,104827,1682],{},[1528,104829,104830],{"encoding":1530},"Q_1 = 4, Q_2 = 1","; obecná Hicksova poptávka pro ",[1035,104833,104835],{"className":104834},[1480],[1482,104836,104837],{"xmlns":1484},[1487,104838,104839,104873],{},[1490,104840,104841,104843,104845,104859],{},[1493,104842,1668],{},[1506,104844,1508],{},[1697,104846,104847,104849,104851],{},[1493,104848,1520],{},[1680,104850,1682],{},[1490,104852,104853,104855,104857],{},[1680,104854,1682],{},[1493,104856,1709],{"mathvariant":1516},[1680,104858,1691],{},[1697,104860,104861,104863,104865],{},[1493,104862,1520],{},[1680,104864,1691],{},[1490,104866,104867,104869,104871],{},[1680,104868,1682],{},[1493,104870,1709],{"mathvariant":1516},[1680,104872,1691],{},[1528,104874,5197],{"encoding":1530},"), odvození Marshallovy i Hicksovy funkce poptávky a Engelových funkcí, vztah dualita primární ↔ duální úlohy a úlohy ",[1047,104877,104878],{},"6.8–6.13"," jsou na stránce ",[1052,104881,43333],{"className":104882,"dataFsResolvedFilePath":1841,"href":1842},[1055],[1065,104884,104886],{"id":104885},"shrnutí-kapitoly-6","Shrnutí kapitoly 6",[1030,104888,104889,104890,104903,104904,104906,104907,104909,104910,104912,104913,104915,104916,104918,104919,104921,104922,1656,104924,104959,104960,104973,104974,104977,104978,104981,104982,2632],{},"Každá ",[1035,104891,104893],{"className":104892},[1480],[1482,104894,104895],{"xmlns":1484},[1487,104896,104897,104901],{},[1490,104898,104899],{},[1493,104900,7781],{},[1528,104902,7781],{"encoding":1530},"-tice množství jednotlivých zboží je ",[1047,104905,98746],{},". Přiřadíme-li každému svazku kladné číslo (jeho užitečnost), můžeme svazky uspořádat podle rostoucí užitečnosti; svazky se stejnou užitečností jsou indiferentní. Tím je definována ",[1047,104908,99232],{}," a současně ",[1047,104911,98749],{},". Její parciální derivace (podle jednotlivých množství) jsou ",[1047,104914,98754],{}," — přibližná změna užitečnosti při jednotkové změně příslušného zboží. Aby funkce mohla být funkcí užitečnosti, musejí být její první parciální derivace ",[1047,104917,66919],{}," (6.4) a druhé parciální derivace ",[1047,104920,101125],{}," (6.5 — zákon klesající mezní užitečnosti). ",[1047,104923,26265],{},[1035,104925,104927],{"className":104926},[1480],[1482,104928,104929],{"xmlns":1484},[1487,104930,104931,104957],{},[1490,104932,104933,104935,104937,104943,104945,104951,104953,104955],{},[1493,104934,1668],{},[1506,104936,1553],{"stretchy":1552},[1497,104938,104939,104941],{},[1493,104940,1520],{},[1680,104942,1682],{},[1506,104944,1559],{"separator":1041},[1497,104946,104947,104949],{},[1493,104948,1520],{},[1680,104950,1691],{},[1506,104952,1564],{"stretchy":1552},[1506,104954,1508],{},[1493,104956,8730],{},[1528,104958,26302],{"encoding":1530}," jsou klesající, neprotínající se, vzdálenější od počátku mají vyšší užitečnost a jsou konvexní. ",[1035,104961,104963],{"className":104962},[1480],[1482,104964,104965],{"xmlns":1484},[1487,104966,104967,104971],{},[1490,104968,104969],{},[1988,104970,13960],{},[1528,104972,43799],{"encoding":1530}," = podíl mezních užitečností udává náhradu jednoho zboží druhým při zachování užitečnosti. Na tento teoretický základ navazují optimalizační úlohy (",[1047,104975,104976],{},"maximalizace užitečnosti"," a duální ",[1047,104979,104980],{},"minimalizace výdajů",") řešené Lagrangeovou metodou — viz ",[1052,104983,774],{"className":104984,"dataFsResolvedFilePath":1841,"href":1842},[1055],[1065,104986,64217],{"id":64216},[1276,104988,104989,104992,104995,104998,105001,105004,105007,105010,105013,105016],{},[1206,104990,104991],{},"Co se zahrnuje pod termín užitečnost?",[1206,104993,104994],{},"Co se rozumí svazkem zboží? Které svazky zboží jsou indiferentní?",[1206,104996,104997],{},"Jak souvisejí hodnoty funkce užitečnosti s preferencí svazků?",[1206,104999,105000],{},"Jak se vypočítá mezní užitečnost?",[1206,105002,105003],{},"Jak lze ekonomicky interpretovat fakt, že mezní užitečnost určitého zboží se rovná 2,5?",[1206,105005,105006],{},"Jaké vlastnosti musí mít funkce více proměnných, aby mohla být funkcí užitečnosti?",[1206,105008,105009],{},"Které jsou nejčastěji používané funkce užitečnosti?",[1206,105011,105012],{},"Jakou rovnici mají křivky užitečnosti? Co platí v bodech ležících na téže křivce užitečnosti?",[1206,105014,105015],{},"Proč mají křivky užitečnosti záporný sklon?",[1206,105017,105018],{},"Jak se vypočte mezní míra komoditní substituce? Vysvětlete, co vypočtená hodnota vyjadřuje.",[1065,105020,105022],{"id":105021},"úlohy-teorie-užitečnosti-61-67","Úlohy — teorie užitečnosti (6.1 – 6.7)",[1030,105024,105025,105028,105029,95426,105071,1732,105099,1732,105127,105155],{},[1047,105026,105027],{},"6.1"," Užitečnost pro tři zboží — hudbu, čokoládu a sýr je dána vztahem ",[1035,105030,105032],{"className":105031},[1480],[1482,105033,105034],{"xmlns":1484},[1487,105035,105036,105068],{},[1490,105037,105038,105040,105042,105048,105050,105052,105058,105060,105062],{},[1493,105039,1668],{},[1506,105041,1508],{},[1497,105043,105044,105046],{},[1493,105045,1520],{},[1680,105047,1682],{},[1506,105049,2162],{},[1680,105051,77687],{},[1497,105053,105054,105056],{},[1493,105055,1520],{},[1680,105057,1691],{},[1506,105059,2162],{},[1680,105061,1691],{},[1497,105063,105064,105066],{},[1493,105065,1520],{},[1680,105067,3201],{},[1528,105069,105070],{"encoding":1530},"U = Q_1 + 1{,}5 Q_2 + 2 Q_3",[1035,105072,105074],{"className":105073},[1480],[1482,105075,105076],{"xmlns":1484},[1487,105077,105078,105096],{},[1490,105079,105080,105082,105084,105086,105088,105090,105092,105094],{},[1493,105081,1668],{},[1506,105083,1553],{"stretchy":1552},[1680,105085,4007],{},[1506,105087,1559],{"separator":1041},[1680,105089,1691],{},[1506,105091,1559],{"separator":1041},[1680,105093,1691],{},[1506,105095,1564],{"stretchy":1552},[1528,105097,105098],{"encoding":1530},"U(4, 2, 2)",[1035,105100,105102],{"className":105101},[1480],[1482,105103,105104],{"xmlns":1484},[1487,105105,105106,105124],{},[1490,105107,105108,105110,105112,105114,105116,105118,105120,105122],{},[1493,105109,1668],{},[1506,105111,1553],{"stretchy":1552},[1680,105113,1682],{},[1506,105115,1559],{"separator":1041},[1680,105117,4007],{},[1506,105119,1559],{"separator":1041},[1680,105121,1691],{},[1506,105123,1564],{"stretchy":1552},[1528,105125,105126],{"encoding":1530},"U(1, 4, 2)",[1035,105128,105130],{"className":105129},[1480],[1482,105131,105132],{"xmlns":1484},[1487,105133,105134,105152],{},[1490,105135,105136,105138,105140,105142,105144,105146,105148,105150],{},[1493,105137,1668],{},[1506,105139,1553],{"stretchy":1552},[1680,105141,1691],{},[1506,105143,1559],{"separator":1041},[1680,105145,3201],{},[1506,105147,1559],{"separator":1041},[1680,105149,1682],{},[1506,105151,1564],{"stretchy":1552},[1528,105153,105154],{"encoding":1530},"U(2, 3, 1)",". (b) Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků v (a).",[1030,105157,105158,105161,105162,105214,105215,1732,105241,1732,105267,1732,105293,1732,105319,1732,105345,1732,105371,105397],{},[1047,105159,105160],{},"6.2"," Je dána užitečnost ",[1035,105163,105165],{"className":105164},[1480],[1482,105166,105167],{"xmlns":1484},[1487,105168,105169,105211],{},[1490,105170,105171,105173,105175,105177,105191,105205],{},[1493,105172,1668],{},[1506,105174,1508],{},[1680,105176,1691],{},[1697,105178,105179,105181,105183],{},[1493,105180,1520],{},[1680,105182,1682],{},[1490,105184,105185,105187,105189],{},[1680,105186,1682],{},[1493,105188,1709],{"mathvariant":1516},[1680,105190,3201],{},[1697,105192,105193,105195,105197],{},[1493,105194,1520],{},[1680,105196,1691],{},[1490,105198,105199,105201,105203],{},[1680,105200,1682],{},[1493,105202,1709],{"mathvariant":1516},[1680,105204,1691],{},[1497,105206,105207,105209],{},[1493,105208,1520],{},[1680,105210,3201],{},[1528,105212,105213],{"encoding":1530},"U = 2 Q_1^{1\u002F3} Q_2^{1\u002F2} Q_3"," pro tři zboží. Rozhodněte o vzájemné preferenci, resp. indiferentnosti svazků ",[1035,105216,105218],{"className":105217},[1480],[1482,105219,105220],{"xmlns":1484},[1487,105221,105222,105238],{},[1490,105223,105224,105226,105228,105230,105232,105234,105236],{},[1506,105225,1553],{"stretchy":1552},[1680,105227,14846],{},[1506,105229,1559],{"separator":1041},[1680,105231,15165],{},[1506,105233,1559],{"separator":1041},[1680,105235,1775],{},[1506,105237,1564],{"stretchy":1552},[1528,105239,105240],{"encoding":1530},"(36, 27, 10)",[1035,105242,105244],{"className":105243},[1480],[1482,105245,105246],{"xmlns":1484},[1487,105247,105248,105264],{},[1490,105249,105250,105252,105254,105256,105258,105260,105262],{},[1506,105251,1553],{"stretchy":1552},[1680,105253,7466],{},[1506,105255,1559],{"separator":1041},[1680,105257,6138],{},[1506,105259,1559],{"separator":1041},[1680,105261,8436],{},[1506,105263,1564],{"stretchy":1552},[1528,105265,105266],{"encoding":1530},"(64, 8, 20)",[1035,105268,105270],{"className":105269},[1480],[1482,105271,105272],{"xmlns":1484},[1487,105273,105274,105290],{},[1490,105275,105276,105278,105280,105282,105284,105286,105288],{},[1506,105277,1553],{"stretchy":1552},[1680,105279,2309],{},[1506,105281,1559],{"separator":1041},[1680,105283,7466],{},[1506,105285,1559],{"separator":1041},[1680,105287,6138],{},[1506,105289,1564],{"stretchy":1552},[1528,105291,105292],{"encoding":1530},"(25, 64, 8)",[1035,105294,105296],{"className":105295},[1480],[1482,105297,105298],{"xmlns":1484},[1487,105299,105300,105316],{},[1490,105301,105302,105304,105306,105308,105310,105312,105314],{},[1506,105303,1553],{"stretchy":1552},[1680,105305,4007],{},[1506,105307,1559],{"separator":1041},[1680,105309,3021],{},[1506,105311,1559],{"separator":1041},[1680,105313,7508],{},[1506,105315,1564],{"stretchy":1552},[1528,105317,105318],{"encoding":1530},"(4, 125, 6)",[1035,105320,105322],{"className":105321},[1480],[1482,105323,105324],{"xmlns":1484},[1487,105325,105326,105342],{},[1490,105327,105328,105330,105332,105334,105336,105338,105340],{},[1506,105329,1553],{"stretchy":1552},[1680,105331,14365],{},[1506,105333,1559],{"separator":1041},[1680,105335,7380],{},[1506,105337,1559],{"separator":1041},[1680,105339,6797],{},[1506,105341,1564],{"stretchy":1552},[1528,105343,105344],{"encoding":1530},"(9, 40, 12)",[1035,105346,105348],{"className":105347},[1480],[1482,105349,105350],{"xmlns":1484},[1487,105351,105352,105368],{},[1490,105353,105354,105356,105358,105360,105362,105364,105366],{},[1506,105355,1553],{"stretchy":1552},[1680,105357,14365],{},[1506,105359,1559],{"separator":1041},[1680,105361,7466],{},[1506,105363,1559],{"separator":1041},[1680,105365,1752],{},[1506,105367,1564],{"stretchy":1552},[1528,105369,105370],{"encoding":1530},"(9, 64, 5)",[1035,105372,105374],{"className":105373},[1480],[1482,105375,105376],{"xmlns":1484},[1487,105377,105378,105394],{},[1490,105379,105380,105382,105384,105386,105388,105390,105392],{},[1506,105381,1553],{"stretchy":1552},[1680,105383,7466],{},[1506,105385,1559],{"separator":1041},[1680,105387,6138],{},[1506,105389,1559],{"separator":1041},[1680,105391,1775],{},[1506,105393,1564],{"stretchy":1552},[1528,105395,105396],{"encoding":1530},"(64, 8, 10)"," a uspořádejte je s neklesající užitečností.",[1030,105399,105400,105161,105403,105446,105447,105481,105482,22345,105512,105545,105546,105563,105564,105581],{},[1047,105401,105402],{},"6.3",[1035,105404,105406],{"className":105405},[1480],[1482,105407,105408],{"xmlns":1484},[1487,105409,105410,105444],{},[1490,105411,105412,105414,105416,105430],{},[1493,105413,1668],{},[1506,105415,1508],{},[1697,105417,105418,105420,105422],{},[1493,105419,1520],{},[1680,105421,1682],{},[1490,105423,105424,105426,105428],{},[1680,105425,1682],{},[1493,105427,1709],{"mathvariant":1516},[1680,105429,1691],{},[1697,105431,105432,105434,105436],{},[1493,105433,1520],{},[1680,105435,1691],{},[1490,105437,105438,105440,105442],{},[1680,105439,1682],{},[1493,105441,1709],{"mathvariant":1516},[1680,105443,1691],{},[1528,105445,5197],{"encoding":1530},". (a) Vypočtěte užitečnost pro ",[1035,105448,105450],{"className":105449},[1480],[1482,105451,105452],{"xmlns":1484},[1487,105453,105454,105478],{},[1490,105455,105456,105462,105464,105466,105468,105474,105476],{},[1497,105457,105458,105460],{},[1493,105459,1520],{},[1680,105461,1682],{},[1506,105463,1508],{},[1680,105465,2292],{},[1506,105467,1559],{"separator":1041},[1497,105469,105470,105472],{},[1493,105471,1520],{},[1680,105473,1691],{},[1506,105475,1508],{},[1680,105477,11232],{},[1528,105479,105480],{"encoding":1530},"Q_1 = 50, Q_2 = 80",". (b) Určete mezní užitečnosti ",[1035,105483,105485],{"className":105484},[1480],[1482,105486,105487],{"xmlns":1484},[1487,105488,105489,105509],{},[1490,105490,105491,105493,105499,105501,105503],{},[1493,105492,1495],{},[1497,105494,105495,105497],{},[1493,105496,1668],{},[1680,105498,1682],{},[1506,105500,1559],{"separator":1041},[1493,105502,1495],{},[1497,105504,105505,105507],{},[1493,105506,1668],{},[1680,105508,1691],{},[1528,105510,105511],{"encoding":1530},"MU_1, MU_2",[1035,105513,105515],{"className":105514},[1480],[1482,105516,105517],{"xmlns":1484},[1487,105518,105519,105543],{},[1490,105520,105521,105527,105529,105531,105533,105539,105541],{},[1497,105522,105523,105525],{},[1493,105524,1520],{},[1680,105526,1682],{},[1506,105528,1508],{},[1680,105530,2292],{},[1506,105532,1559],{"separator":1041},[1497,105534,105535,105537],{},[1493,105536,1520],{},[1680,105538,1691],{},[1506,105540,1508],{},[1680,105542,11232],{},[1528,105544,105480],{"encoding":1530}," a výsledky ekonomicky interpretujte. (d) Odhadněte změnu užitečnosti v důsledku změny ",[1035,105547,105549],{"className":105548},[1480],[1482,105550,105551],{"xmlns":1484},[1487,105552,105553,105561],{},[1490,105554,105555],{},[1497,105556,105557,105559],{},[1493,105558,1520],{},[1680,105560,1682],{},[1528,105562,6702],{"encoding":1530}," na 60 a poklesu ",[1035,105565,105567],{"className":105566},[1480],[1482,105568,105569],{"xmlns":1484},[1487,105570,105571,105579],{},[1490,105572,105573],{},[1497,105574,105575,105577],{},[1493,105576,1520],{},[1680,105578,1691],{},[1528,105580,6683],{"encoding":1530}," o 5 vzhledem k hladině dle (a) a porovnejte se skutečnou změnou užitečnosti.",[1030,105583,105584,105587,105588,105649,105650,2632],{},[1047,105585,105586],{},"6.4"," Je dána funkce ",[1035,105589,105591],{"className":105590},[1480],[1482,105592,105593],{"xmlns":1484},[1487,105594,105595,105647],{},[1490,105596,105597,105599,105601,105607,105609,105615,105617,105619,105633],{},[1493,105598,1668],{},[1506,105600,1553],{"stretchy":1552},[1497,105602,105603,105605],{},[1493,105604,1520],{},[1680,105606,1682],{},[1506,105608,1559],{"separator":1041},[1497,105610,105611,105613],{},[1493,105612,1520],{},[1680,105614,1691],{},[1506,105616,1564],{"stretchy":1552},[1506,105618,1508],{},[1697,105620,105621,105623,105625],{},[1493,105622,1520],{},[1680,105624,1682],{},[1490,105626,105627,105629,105631],{},[1680,105628,1682],{},[1493,105630,1709],{"mathvariant":1516},[1680,105632,1691],{},[1697,105634,105635,105637,105639],{},[1493,105636,1520],{},[1680,105638,1691],{},[1490,105640,105641,105643,105645],{},[1680,105642,1682],{},[1493,105644,1709],{"mathvariant":1516},[1680,105646,1691],{},[1528,105648,45270],{"encoding":1530},". (a) Ověřte, že tato funkce vykazuje vlastnosti funkce užitečnosti. (b) Najděte a načrtněte křivky ",[1035,105651,105653],{"className":105652},[1480],[1482,105654,105655],{"xmlns":1484},[1487,105656,105657,105747],{},[1490,105658,105659,105661,105663,105669,105671,105673,105675,105677,105679,105681,105687,105689,105691,105693,105695,105697,105699,105701,105703,105709,105711,105713,105715,105717,105719,105721,105727,105729,105731,105733,105735,105737,105739,105745],{},[1493,105660,1668],{},[1506,105662,1553],{"stretchy":1552},[1497,105664,105665,105667],{},[1493,105666,1520],{},[1680,105668,1682],{},[1506,105670,1559],{"separator":1041},[1680,105672,1682],{},[1506,105674,1564],{"stretchy":1552},[1506,105676,1559],{"separator":1041},[1493,105678,1668],{},[1506,105680,1553],{"stretchy":1552},[1497,105682,105683,105685],{},[1493,105684,1520],{},[1680,105686,1682],{},[1506,105688,1559],{"separator":1041},[1680,105690,1691],{},[1506,105692,1564],{"stretchy":1552},[1506,105694,1559],{"separator":1041},[1493,105696,1668],{},[1506,105698,1553],{"stretchy":1552},[1680,105700,1682],{},[1506,105702,1559],{"separator":1041},[1497,105704,105705,105707],{},[1493,105706,1520],{},[1680,105708,1691],{},[1506,105710,1564],{"stretchy":1552},[1506,105712,1559],{"separator":1041},[1493,105714,1668],{},[1506,105716,1553],{"stretchy":1552},[1680,105718,1691],{},[1506,105720,1559],{"separator":1041},[1497,105722,105723,105725],{},[1493,105724,1520],{},[1680,105726,1691],{},[1506,105728,1564],{"stretchy":1552},[1506,105730,1559],{"separator":1041},[1493,105732,1668],{},[1506,105734,1553],{"stretchy":1552},[1680,105736,3201],{},[1506,105738,1559],{"separator":1041},[1497,105740,105741,105743],{},[1493,105742,1520],{},[1680,105744,1691],{},[1506,105746,1564],{"stretchy":1552},[1528,105748,105749],{"encoding":1530},"U(Q_1, 1), U(Q_1, 2), U(1, Q_2), U(2, Q_2), U(3, Q_2)",[1030,105751,105752,105161,105755,105799,105800,105908,105909,1732,105934,1732,105959,106001,106002,1732,106031,106056],{},[1047,105753,105754],{},"6.5",[1035,105756,105758],{"className":105757},[1480],[1482,105759,105760],{"xmlns":1484},[1487,105761,105762,105796],{},[1490,105763,105764,105766,105768,105782],{},[1493,105765,1668],{},[1506,105767,1508],{},[1697,105769,105770,105772,105774],{},[1493,105771,1520],{},[1680,105773,1682],{},[1490,105775,105776,105778,105780],{},[1680,105777,1691],{},[1493,105779,1709],{"mathvariant":1516},[1680,105781,3201],{},[1697,105783,105784,105786,105788],{},[1493,105785,1520],{},[1680,105787,1691],{},[1490,105789,105790,105792,105794],{},[1680,105791,1682],{},[1493,105793,1709],{"mathvariant":1516},[1680,105795,3201],{},[1528,105797,105798],{"encoding":1530},"U = Q_1^{2\u002F3} Q_2^{1\u002F3}",". (a) Najděte rovnici křivek užitečnosti. (b) Určete a načrtněte křivky ",[1035,105801,105803],{"className":105802},[1480],[1482,105804,105805],{"xmlns":1484},[1487,105806,105807,105905],{},[1490,105808,105809,105811,105813,105819,105821,105827,105829,105831,105833,105835,105837,105839,105845,105847,105849,105851,105853,105855,105857,105863,105865,105867,105869,105871,105873,105875,105877,105879,105885,105887,105889,105891,105893,105895,105897,105903],{},[1493,105810,1668],{},[1506,105812,1553],{"stretchy":1552},[1497,105814,105815,105817],{},[1493,105816,1520],{},[1680,105818,1682],{},[1506,105820,1559],{"separator":1041},[1497,105822,105823,105825],{},[1493,105824,1520],{},[1680,105826,1691],{},[1506,105828,1564],{"stretchy":1552},[1506,105830,1508],{},[1680,105832,1691],{},[1506,105834,1559],{"separator":1041},[1493,105836,1668],{},[1506,105838,1553],{"stretchy":1552},[1497,105840,105841,105843],{},[1493,105842,1520],{},[1680,105844,1682],{},[1506,105846,1559],{"separator":1041},[1680,105848,3201],{},[1506,105850,1564],{"stretchy":1552},[1506,105852,1559],{"separator":1041},[1493,105854,1668],{},[1506,105856,1553],{"stretchy":1552},[1497,105858,105859,105861],{},[1493,105860,1520],{},[1680,105862,1682],{},[1506,105864,1559],{"separator":1041},[1680,105866,1691],{},[1506,105868,1564],{"stretchy":1552},[1506,105870,1559],{"separator":1041},[1493,105872,1668],{},[1506,105874,1553],{"stretchy":1552},[1680,105876,1691],{},[1506,105878,1559],{"separator":1041},[1497,105880,105881,105883],{},[1493,105882,1520],{},[1680,105884,1691],{},[1506,105886,1564],{"stretchy":1552},[1506,105888,1559],{"separator":1041},[1493,105890,1668],{},[1506,105892,1553],{"stretchy":1552},[1680,105894,3201],{},[1506,105896,1559],{"separator":1041},[1497,105898,105899,105901],{},[1493,105900,1520],{},[1680,105902,1691],{},[1506,105904,1564],{"stretchy":1552},[1528,105906,105907],{"encoding":1530},"U(Q_1, Q_2) = 2, U(Q_1, 3), U(Q_1, 2), U(2, Q_2), U(3, Q_2)",". Leží některé z bodů ",[1035,105910,105912],{"className":105911},[1480],[1482,105913,105914],{"xmlns":1484},[1487,105915,105916,105931],{},[1490,105917,105918,105920,105922,105924,105926,105929],{},[1493,105919,3633],{},[1506,105921,14314],{"stretchy":1552},[1680,105923,77687],{},[1506,105925,6065],{"separator":1041},[1680,105927,105928],{},"3,555",[1506,105930,14323],{"stretchy":1552},[1528,105932,105933],{"encoding":1530},"A[1{,}5; 3{,}555]",[1035,105935,105937],{"className":105936},[1480],[1482,105938,105939],{"xmlns":1484},[1487,105940,105941,105956],{},[1490,105942,105943,105945,105947,105949,105951,105954],{},[1493,105944,11353],{},[1506,105946,14314],{"stretchy":1552},[1680,105948,13279],{},[1506,105950,6065],{"separator":1041},[1680,105952,105953],{},"1,28",[1506,105955,14323],{"stretchy":1552},[1528,105957,105958],{"encoding":1530},"B[2{,}5; 1{,}28]",[1035,105960,105962],{"className":105961},[1480],[1482,105963,105964],{"xmlns":1484},[1487,105965,105966,105998],{},[1490,105967,105968,105970,105972,105974,105976,105978,105980,105986,105988,105990,105992,105994,105996],{},[1493,105969,1998],{},[1506,105971,14314],{"stretchy":1552},[1680,105973,1691],{},[1506,105975,6065],{"separator":1041},[1493,105977,1668],{},[1506,105979,1553],{"stretchy":1552},[1497,105981,105982,105984],{},[1493,105983,1520],{},[1680,105985,1682],{},[1506,105987,1559],{"separator":1041},[1680,105989,3201],{},[1506,105991,1564],{"stretchy":1552},[1506,105993,1508],{},[1680,105995,3201],{},[1506,105997,14323],{"stretchy":1552},[1528,105999,106000],{"encoding":1530},"C[2; U(Q_1, 3) = 3]"," (c) Leží některé z bodů ",[1035,106003,106005],{"className":106004},[1480],[1482,106006,106007],{"xmlns":1484},[1487,106008,106009,106028],{},[1490,106010,106011,106013,106015,106017,106019,106021,106023,106026],{},[1493,106012,3712],{},[1506,106014,14314],{"stretchy":1552},[1680,106016,3201],{},[1506,106018,6065],{"separator":1041},[1680,106020,1682],{},[1506,106022,6065],{"separator":1041},[1680,106024,106025],{},"0,832",[1506,106027,14323],{"stretchy":1552},[1528,106029,106030],{"encoding":1530},"D[3; 1; 0{,}832]",[1035,106032,106034],{"className":106033},[1480],[1482,106035,106036],{"xmlns":1484},[1487,106037,106038,106053],{},[1490,106039,106040,106042,106044,106046,106048,106051],{},[1493,106041,2711],{},[1506,106043,14314],{"stretchy":1552},[1680,106045,13279],{},[1506,106047,6065],{"separator":1041},[1680,106049,106050],{},"4,32",[1506,106052,14323],{"stretchy":1552},[1528,106054,106055],{"encoding":1530},"E[2{,}5; 4{,}32]"," na téže křivce užitečnosti? Když ano, určete ji.",[1030,106058,106059,105161,106062,106105,106106,22345,106119,106153,106154,106171,106172,106189],{},[1047,106060,106061],{},"6.6",[1035,106063,106065],{"className":106064},[1480],[1482,106066,106067],{"xmlns":1484},[1487,106068,106069,106103],{},[1490,106070,106071,106073,106075,106089],{},[1493,106072,1668],{},[1506,106074,1508],{},[1697,106076,106077,106079,106081],{},[1493,106078,1520],{},[1680,106080,1682],{},[1490,106082,106083,106085,106087],{},[1680,106084,1691],{},[1493,106086,1709],{"mathvariant":1516},[1680,106088,3201],{},[1697,106090,106091,106093,106095],{},[1493,106092,1520],{},[1680,106094,1691],{},[1490,106096,106097,106099,106101],{},[1680,106098,1682],{},[1493,106100,1709],{"mathvariant":1516},[1680,106102,3201],{},[1528,106104,105798],{"encoding":1530},". (a) Najděte mezní míru komoditní substituce ",[1035,106107,106109],{"className":106108},[1480],[1482,106110,106111],{"xmlns":1484},[1487,106112,106113,106117],{},[1490,106114,106115],{},[1988,106116,13960],{},[1528,106118,43799],{"encoding":1530},[1035,106120,106122],{"className":106121},[1480],[1482,106123,106124],{"xmlns":1484},[1487,106125,106126,106150],{},[1490,106127,106128,106134,106136,106138,106140,106146,106148],{},[1497,106129,106130,106132],{},[1493,106131,1520],{},[1680,106133,1682],{},[1506,106135,1508],{},[1680,106137,2916],{},[1506,106139,1559],{"separator":1041},[1497,106141,106142,106144],{},[1493,106143,1520],{},[1680,106145,1691],{},[1506,106147,1508],{},[1680,106149,5263],{},[1528,106151,106152],{"encoding":1530},"Q_1 = 100, Q_2 = 200"," a výsledek ekonomicky interpretujte. (c) Odhadněte, o kolik je třeba změnit ",[1035,106155,106157],{"className":106156},[1480],[1482,106158,106159],{"xmlns":1484},[1487,106160,106161,106169],{},[1490,106162,106163],{},[1497,106164,106165,106167],{},[1493,106166,1520],{},[1680,106168,1682],{},[1528,106170,6702],{"encoding":1530},", poklesne-li ",[1035,106173,106175],{"className":106174},[1480],[1482,106176,106177],{"xmlns":1484},[1487,106178,106179,106187],{},[1490,106180,106181],{},[1497,106182,106183,106185],{},[1493,106184,1520],{},[1680,106186,1691],{},[1528,106188,6683],{"encoding":1530}," o 5 vzhledem k hladině dle (b).",[1030,106191,106192,106195,106196,106213,106214,106231,106232,106264,106265,106290,106291,106304,106305,1732,106329,1732,106353,2632],{},[1047,106193,106194],{},"6.7"," Míra uspokojení z nákupu množství ",[1035,106197,106199],{"className":106198},[1480],[1482,106200,106201],{"xmlns":1484},[1487,106202,106203,106211],{},[1490,106204,106205],{},[1497,106206,106207,106209],{},[1493,106208,1520],{},[1680,106210,1682],{},[1528,106212,6702],{"encoding":1530}," nealko nápojů a množství ",[1035,106215,106217],{"className":106216},[1480],[1482,106218,106219],{"xmlns":1484},[1487,106220,106221,106229],{},[1490,106222,106223],{},[1497,106224,106225,106227],{},[1493,106226,1520],{},[1680,106228,1691],{},[1528,106230,6683],{"encoding":1530}," hamburgerů za týden je dána funkcí užitečnosti ",[1035,106233,106235],{"className":106234},[1480],[1482,106236,106237],{"xmlns":1484},[1487,106238,106239,106261],{},[1490,106240,106241,106243,106245],{},[1493,106242,1668],{},[1506,106244,1508],{},[2324,106246,106247],{},[1490,106248,106249,106255],{},[1497,106250,106251,106253],{},[1493,106252,1520],{},[1680,106254,1682],{},[1497,106256,106257,106259],{},[1493,106258,1520],{},[1680,106260,1691],{},[1528,106262,106263],{"encoding":1530},"U = \\sqrt{Q_1 Q_2}",". (a) Najděte vztah pro hodnoty ",[1035,106266,106268],{"className":106267},[1480],[1482,106269,106270],{"xmlns":1484},[1487,106271,106272,106288],{},[1490,106273,106274,106280,106282],{},[1497,106275,106276,106278],{},[1493,106277,1520],{},[1680,106279,1682],{},[1506,106281,1559],{"separator":1041},[1497,106283,106284,106286],{},[1493,106285,1520],{},[1680,106287,1691],{},[1528,106289,1826],{"encoding":1530},", pro něž je dosaženo užitečnosti 10 a uveďte několik takových dvojic hodnot. (b) Najděte ",[1035,106292,106294],{"className":106293},[1480],[1482,106295,106296],{"xmlns":1484},[1487,106297,106298,106302],{},[1490,106299,106300],{},[1988,106301,13960],{},[1528,106303,43799],{"encoding":1530}," na křivce nalezené v (a). (c) Ekonomicky interpretujte smysl ",[1035,106306,106308],{"className":106307},[1480],[1482,106309,106310],{"xmlns":1484},[1487,106311,106312,106326],{},[1490,106313,106314,106316,106318,106320,106322,106324],{},[1988,106315,13960],{},[1506,106317,1553],{"stretchy":1552},[1680,106319,1752],{},[1506,106321,1559],{"separator":1041},[1680,106323,8436],{},[1506,106325,1564],{"stretchy":1552},[1528,106327,106328],{"encoding":1530},"\\text{MRCS}(5, 20)",[1035,106330,106332],{"className":106331},[1480],[1482,106333,106334],{"xmlns":1484},[1487,106335,106336,106350],{},[1490,106337,106338,106340,106342,106344,106346,106348],{},[1988,106339,13960],{},[1506,106341,1553],{"stretchy":1552},[1680,106343,8436],{},[1506,106345,1559],{"separator":1041},[1680,106347,1752],{},[1506,106349,1564],{"stretchy":1552},[1528,106351,106352],{"encoding":1530},"\\text{MRCS}(20, 5)",[1035,106354,106356],{"className":106355},[1480],[1482,106357,106358],{"xmlns":1484},[1487,106359,106360,106374],{},[1490,106361,106362,106364,106366,106368,106370,106372],{},[1988,106363,13960],{},[1506,106365,1553],{"stretchy":1552},[1680,106367,1691],{},[1506,106369,1559],{"separator":1041},[1680,106371,2292],{},[1506,106373,1564],{"stretchy":1552},[1528,106375,106376],{"encoding":1530},"\\text{MRCS}(2, 50)",[1023,106378,106380,106387],{"className":106379,"dataCallout":1443},[1026,1442],[1030,106381,106383,106386],{"className":106382},[1033],[1035,106384],{"className":106385,"ariaHidden":1041},[1038,1450,1040],"Úlohy 6.8 – 6.13 (optimalizace, Lagrange, poptávka)",[1030,106388,106389,106390,2632],{},"Úlohy navázané na maximalizaci užitečnosti, minimalizaci výdajů a odvození Marshallových\u002FHicksových funkcí poptávky jsou na stránce ",[1052,106391,106394],{"className":106392,"dataFsResolvedFilePath":1841,"href":106393},[1055],"\u002Fwiki\u002Foptimalizace-spotrebitele#Úlohy k optimalizaci","Optimalizace spotřebitele — Úlohy",[1065,106396,31885],{"id":31884},[1203,106398,106399,106405,106410,106416,106469,106479,106525,106580,106643,106700,106755,106794],{},[1206,106400,106401,106404],{},[1047,106402,106403],{},"Užitečnost (utility)"," — ordinálně měřený ukazatel uspokojení spotřebitele ze svazku zboží.",[1206,106406,106407,106409],{},[1047,106408,98805],{}," — historická pojetí užitečnosti; v současnosti se preferuje ordinalistický.",[1206,106411,106412,106415],{},[1047,106413,106414],{},"Pět předpokladů chování spotřebitele"," — racionalita, ordinalita, konzistence a tranzitivita, rostoucí užitečnost, klesající mezní užitečnost.",[1206,106417,106418,106420,106421,106434,106435,2632],{},[1047,106419,99136],{}," — uspořádaná ",[1035,106422,106424],{"className":106423},[1480],[1482,106425,106426],{"xmlns":1484},[1487,106427,106428,106432],{},[1490,106429,106430],{},[1493,106431,7781],{},[1528,106433,7781],{"encoding":1530},"-tice ",[1035,106436,106438],{"className":106437},[1480],[1482,106439,106440],{"xmlns":1484},[1487,106441,106442,106466],{},[1490,106443,106444,106446,106452,106454,106456,106458,106464],{},[1506,106445,1553],{"stretchy":1552},[1497,106447,106448,106450],{},[1493,106449,1520],{},[1680,106451,1682],{},[1506,106453,1559],{"separator":1041},[1506,106455,26181],{},[1506,106457,1559],{"separator":1041},[1497,106459,106460,106462],{},[1493,106461,1520],{},[1493,106463,7781],{},[1506,106465,1564],{"stretchy":1552},[1528,106467,106468],{"encoding":1530},"(Q_1, \\dots, Q_n)",[1206,106470,106471,106474,106475,106478],{},[1047,106472,106473],{},"Relace preference"," — uspořádání svazků podle užitečnosti; ",[1047,106476,106477],{},"indiferentní svazky"," mají stejnou užitečnost.",[1206,106480,106481,1656,106484,106524],{},[1047,106482,106483],{},"Funkce užitečnosti",[1035,106485,106487],{"className":106486},[1480],[1482,106488,106489],{"xmlns":1484},[1487,106490,106491,106521],{},[1490,106492,106493,106495,106497,106499,106501,106507,106509,106511,106513,106519],{},[1493,106494,1668],{},[1506,106496,1508],{},[1493,106498,1668],{},[1506,106500,1553],{"stretchy":1552},[1497,106502,106503,106505],{},[1493,106504,1520],{},[1680,106506,1682],{},[1506,106508,1559],{"separator":1041},[1506,106510,26181],{},[1506,106512,1559],{"separator":1041},[1497,106514,106515,106517],{},[1493,106516,1520],{},[1493,106518,7781],{},[1506,106520,1564],{"stretchy":1552},[1528,106522,106523],{"encoding":1530},"U = U(Q_1, \\dots, Q_n)"," — vzorec (6.1); ekvivalentní až na monotónní transformaci.",[1206,106526,106527,1656,106530,106559,106560,1656,106563,106579],{},[1047,106528,106529],{},"Mezní užitečnost",[1035,106531,106533],{"className":106532},[1480],[1482,106534,106535],{"xmlns":1484},[1487,106536,106537,106557],{},[1490,106538,106539,106541,106547,106549],{},[1493,106540,1495],{},[1497,106542,106543,106545],{},[1493,106544,1668],{},[1493,106546,6277],{},[1506,106548,1508],{},[1697,106550,106551,106553,106555],{},[1493,106552,1668],{},[1493,106554,6277],{},[1506,106556,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1528,106558,98591],{"encoding":1530}," — vzorec (6.2); ",[1047,106561,106562],{},"totální diferenciál",[1035,106564,106566],{"className":106565},[1480],[1482,106567,106568],{"xmlns":1484},[1487,106569,106570,106576],{},[1490,106571,106572,106574],{},[1493,106573,3384],{"mathvariant":1516},[1493,106575,1668],{},[1528,106577,106578],{"encoding":1530},"\\mathrm{d} U"," — (6.3).",[1206,106581,106582,106584,106585,106609,106610,106642],{},[1047,106583,100780],{}," — (6.4) ",[1035,106586,106588],{"className":106587},[1480],[1482,106589,106590],{"xmlns":1484},[1487,106591,106592,106606],{},[1490,106593,106594,106602,106604],{},[1697,106595,106596,106598,106600],{},[1493,106597,1668],{},[1493,106599,6277],{},[1506,106601,6927],{"mathvariant":1516,"lspace":6926,"rspace":6926},[1506,106603,2796],{},[1680,106605,1871],{},[1528,106607,106608],{"encoding":1530},"U'_i > 0",", (6.5) ",[1035,106611,106613],{"className":106612},[1480],[1482,106614,106615],{"xmlns":1484},[1487,106616,106617,106639],{},[1490,106618,106619,106635,106637],{},[1697,106620,106621,106623,106629],{},[1493,106622,1668],{},[1490,106624,106625,106627],{},[1493,106626,6277],{},[1493,106628,6277],{},[1490,106630,106631,106633],{},[1506,106632,6927],{"mathvariant":1516},[1506,106634,6927],{"mathvariant":1516},[1506,106636,3961],{},[1680,106638,1871],{},[1528,106640,106641],{"encoding":1530},"U''_{ii} \u003C 0"," (zákon klesající mezní užitečnosti).",[1206,106644,106645,1656,106647,106678,106679,2632],{},[1047,106646,102272],{},[1035,106648,106650],{"className":106649},[1480],[1482,106651,106652],{"xmlns":1484},[1487,106653,106654,106676],{},[1490,106655,106656,106658,106660,106668],{},[1493,106657,1668],{},[1506,106659,1508],{},[1697,106661,106662,106664,106666],{},[1493,106663,1520],{},[1680,106665,1682],{},[1493,106667,1052],{},[1697,106669,106670,106672,106674],{},[1493,106671,1520],{},[1680,106673,1691],{},[1493,106675,2394],{},[1528,106677,2397],{"encoding":1530}," — (6.6), speciálně ",[1035,106680,106682],{"className":106681},[1480],[1482,106683,106684],{"xmlns":1484},[1487,106685,106686,106698],{},[1490,106687,106688,106690,106692,106694,106696],{},[1493,106689,2394],{},[1506,106691,1508],{},[1680,106693,1682],{},[1506,106695,1888],{},[1493,106697,1052],{},[1528,106699,102426],{"encoding":1530},[1206,106701,106702,1656,106705,106740,106741,106754],{},[1047,106703,106704],{},"Křivky užitečnosti (indiferenční)",[1035,106706,106708],{"className":106707},[1480],[1482,106709,106710],{"xmlns":1484},[1487,106711,106712,106738],{},[1490,106713,106714,106716,106718,106724,106726,106732,106734,106736],{},[1493,106715,1668],{},[1506,106717,1553],{"stretchy":1552},[1497,106719,106720,106722],{},[1493,106721,1520],{},[1680,106723,1682],{},[1506,106725,1559],{"separator":1041},[1497,106727,106728,106730],{},[1493,106729,1520],{},[1680,106731,1691],{},[1506,106733,1564],{"stretchy":1552},[1506,106735,1508],{},[1493,106737,8730],{},[1528,106739,26302],{"encoding":1530}," — (6.7), (6.8); čtyři vlastnosti: klesající, neprotínající se, vzdálenější od počátku = vyšší ",[1035,106742,106744],{"className":106743},[1480],[1482,106745,106746],{"xmlns":1484},[1487,106747,106748,106752],{},[1490,106749,106750],{},[1493,106751,1668],{},[1528,106753,1668],{"encoding":1530},", konvexní.",[1206,106756,106757,1656,106759,106793],{},[1047,106758,103580],{},[1035,106760,106762],{"className":106761},[1480],[1482,106763,106764],{"xmlns":1484},[1487,106765,106766,106790],{},[1490,106767,106768,106770,106772,106774,106780,106782,106784],{},[1988,106769,13960],{},[1506,106771,1508],{},[1493,106773,1495],{},[1497,106775,106776,106778],{},[1493,106777,1668],{},[1680,106779,1682],{},[1493,106781,1709],{"mathvariant":1516},[1493,106783,1495],{},[1497,106785,106786,106788],{},[1493,106787,1668],{},[1680,106789,1691],{},[1528,106791,106792],{"encoding":1530},"\\text{MRCS} = MU_1 \u002F MU_2"," — (6.9); vztahy (6.10), (6.11).",[1206,106795,106796,1656,106799,26303,106828,106831],{},[1047,106797,106798],{},"Podmínka optimality",[1035,106800,106802],{"className":106801},[1480],[1482,106803,106804],{"xmlns":1484},[1487,106805,106806,106826],{},[1490,106807,106808,106810,106812,106818,106820],{},[1988,106809,13960],{},[1506,106811,1508],{},[1497,106813,106814,106816],{},[1493,106815,1501],{},[1680,106817,1682],{},[1493,106819,1709],{"mathvariant":1516},[1497,106821,106822,106824],{},[1493,106823,1501],{},[1680,106825,1691],{},[1528,106827,43563],{"encoding":1530},[1052,106829,774],{"className":106830,"dataFsResolvedFilePath":1841,"href":1842},[1055]," pro plné odvození.",[1065,106833,17159],{"id":17158},[1203,106835,106836,106873,106914,106924],{},[1206,106837,106838,1656,106841,106844,106845,106858,106859,106872],{},[1047,106839,106840],{},"Navazující téma:",[1052,106842,1843],{"className":106843,"dataFsResolvedFilePath":1841,"href":1842},[1055]," (Lagrange, max ",[1035,106846,106848],{"className":106847},[1480],[1482,106849,106850],{"xmlns":1484},[1487,106851,106852,106856],{},[1490,106853,106854],{},[1493,106855,1668],{},[1528,106857,1668],{"encoding":1530},", min ",[1035,106860,106862],{"className":106861},[1480],[1482,106863,106864],{"xmlns":1484},[1487,106865,106866,106870],{},[1490,106867,106868],{},[1493,106869,2711],{},[1528,106871,2711],{"encoding":1530},", funkce poptávky, Příklady 6.5–6.8, úlohy 6.8–6.13).",[1206,106874,106875,1656,106878,27607,106881,98351,106884,106887,106888,106891,106892,34788,106910,106913],{},[1047,106876,106877],{},"Související pojmy:",[1052,106879,9472],{"className":106880,"dataFsResolvedFilePath":9470,"href":9471},[1055],[1052,106882,3506],{"className":106883,"dataFsResolvedFilePath":16621,"href":16622},[1055],[1052,106885,6836],{"className":106886,"dataFsResolvedFilePath":1572,"href":1573},[1055]," (paralela: MRCS ↔ MRTS, izokvanty ↔ indiferenční křivky, Cobb-Douglas), ",[1052,106889,17211],{"className":106890,"dataFsResolvedFilePath":3487,"href":3488},[1055]," (Marshallovy poptávkové funkce ",[1035,106893,106895],{"className":106894},[1480],[1482,106896,106897],{"xmlns":1484},[1487,106898,106899,106907],{},[1490,106900,106901],{},[1497,106902,106903,106905],{},[1493,106904,3712],{},[1493,106906,6277],{},[1528,106908,106909],{"encoding":1530},"D_i",[1052,106911,17267],{"className":106912,"dataFsResolvedFilePath":17265,"href":17266},[1055]," (vázaná optimalizace — nástroj pro navazující téma).",[1206,106915,106916,1656,106918,1732,106921],{},[1047,106917,51799],{},[1052,106919,17196],{"className":106920,"dataFsResolvedFilePath":17194,"href":17195},[1055],[1052,106922,17202],{"className":106923,"dataFsResolvedFilePath":17200,"href":17201},[1055],[1206,106925,106926,1656,106928],{},[1047,106927,17176],{},[1052,106929,1058],{"className":106930,"dataFsResolvedFilePath":1056,"href":1057},[1055],{"title":17269,"searchDepth":141,"depth":141,"links":106932},[106933,106934,106935,106938,106939,106942,106946,106947,106950,106951,106952,106953,106954,106955,106956],{"id":28491,"depth":141,"text":1042},{"id":98729,"depth":141,"text":98730},{"id":98788,"depth":141,"text":98789,"children":106936},[106937],{"id":98804,"depth":96,"text":98805},{"id":99115,"depth":141,"text":99116},{"id":99978,"depth":141,"text":99979,"children":106940},[106941],{"id":100530,"depth":96,"text":92358},{"id":100779,"depth":141,"text":100780,"children":106943},[106944],{"id":101356,"depth":96,"text":106945},"Příklad 6.2 — ověření vlastností a dopočet pro U=Q11\u002F2Q21\u002F3U = Q_1^{1\u002F2} Q_2^{1\u002F3}",{"id":102271,"depth":141,"text":102272},{"id":102810,"depth":141,"text":102811,"children":106948},[106949],{"id":103399,"depth":96,"text":103400},{"id":103574,"depth":141,"text":103575},{"id":104343,"depth":141,"text":104344},{"id":104885,"depth":141,"text":104886},{"id":64216,"depth":141,"text":64217},{"id":105021,"depth":141,"text":105022},{"id":31884,"depth":141,"text":31885},{"id":17158,"depth":141,"text":17159},{},"\u002Ftopics\u002Fuzitecnost",{"title":98514,"description":17269},[26098,32431],"topics\u002Fuzitecnost",[9,93,700,98,106,728],"lrl0AozL5aYHhzlz-gTrEXcvNMuZOKH0nUfguxqKRLs",{"id":106965,"title":19223,"body":106966,"course":9,"courses":17424,"created":19266,"description":107237,"extension":17426,"meta":107238,"navigation":17428,"path":107239,"seo":107240,"sources":107241,"stem":107242,"tags":107243,"type":19275,"updated":19276,"__hash__":107244},"topics\u002Ftopics\u002Fzaklady-matematicke-ekonomie.md",{"type":1016,"value":106967,"toc":107229},[106968,106971,106978,106985,106989,106999,107001,107035,107039,107082,107085,107143,107147,107177,107181,107201,107203],[1019,106969,19223],{"id":106970},"základy-matematické-ekonomie",[1030,106972,106973,106974,106977],{},"Úvodní pojmy a princip modelování v ",[1052,106975,32537],{"className":106976,"dataFsResolvedFilePath":1056,"href":1057},[1055],". Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",[1030,106979,106980],{},[18014,106981],{"alt":106982,"className":106983,"src":106984},"imek-model-promenne",[1055,18018],"\u002Fwiki-assets\u002Fimek-model-promenne.jpeg",[1065,106986,106988],{"id":106987},"co-je-matematická-ekonomie","Co je matematická ekonomie",[1030,106990,106991,106994,106995,106998],{},[1047,106992,106993],{},"Vědní disciplína",", která ekonomické vztahy vyjadřuje ",[1047,106996,106997],{},"exaktními (matematickými) prostředky"," a provádí jejich analýzu. Cílem není jen popis, ale i predikce a optimalizace.",[1065,107000,31885],{"id":31884},[1203,107002,107003,107009,107015,107021,107030],{},[1206,107004,107005,107008],{},[1047,107006,107007],{},"Model"," — zjednodušený obraz reálné situace nebo jevu. Vždy jde o redukci skutečnosti, ne její kopii.",[1206,107010,107011,107014],{},[1047,107012,107013],{},"Endogenní proměnné"," — zahrnuté do modelu, mohou se měnit (vysvětlované).",[1206,107016,107017,107020],{},[1047,107018,107019],{},"Exogenní proměnné"," — nejsou v modelu zahrnuté (potenciálně by mohly), berou se jako dané.",[1206,107022,107023,22970,107026,107029],{},[1047,107024,107025],{},"Ceteris paribus",[1176,107027,107028],{},"za jinak stejných podmínek",". Sledujeme změnu jedné proměnné, ostatní fixní.",[1206,107031,107032,107034],{},[1047,107033,64969],{}," — odezva endogenních proměnných na změnu některé exogenní.",[1065,107036,107038],{"id":107037},"ilustrace-funkce-poptávky","Ilustrace — funkce poptávky",[1030,107040,107041,107081],{},[1035,107042,107044],{"className":107043},[1480],[1482,107045,107046],{"xmlns":1484},[1487,107047,107048,107078],{},[1490,107049,107050,107052,107054,107056,107058,107060,107062,107064,107066,107068,107070,107072,107074,107076],{},[1493,107051,1520],{},[1506,107053,1508],{},[1493,107055,3712],{},[1506,107057,1553],{"stretchy":1552},[1493,107059,1501],{},[1506,107061,1559],{"separator":1041},[1493,107063,1791],{},[1506,107065,1559],{"separator":1041},[1493,107067,34441],{},[1506,107069,1559],{"separator":1041},[1493,107071,1668],{},[1506,107073,1559],{"separator":1041},[1506,107075,26181],{},[1506,107077,1564],{"stretchy":1552},[1528,107079,107080],{"encoding":1530},"Q = D(P, Y, N, U, \\ldots)"," — plná (vícefaktorová) funkce poptávky.",[1030,107083,107084],{},"Zjednodušení:",[1203,107086,107087,107115],{},[1206,107088,107089,1656,107092],{},[1047,107090,107091],{},"Jednofaktorový model:",[1035,107093,107095],{"className":107094},[1480],[1482,107096,107097],{"xmlns":1484},[1487,107098,107099,107113],{},[1490,107100,107101,107103,107105,107107,107109,107111],{},[1493,107102,1520],{},[1506,107104,1508],{},[1493,107106,3712],{},[1506,107108,1553],{"stretchy":1552},[1493,107110,1501],{},[1506,107112,1564],{"stretchy":1552},[1528,107114,19607],{"encoding":1530},[1206,107116,107117,1656,107120],{},[1047,107118,107119],{},"Inverzní zápis:",[1035,107121,107123],{"className":107122},[1480],[1482,107124,107125],{"xmlns":1484},[1487,107126,107127,107141],{},[1490,107128,107129,107131,107133,107135,107137,107139],{},[1493,107130,1501],{},[1506,107132,1508],{},[1493,107134,3712],{},[1506,107136,1553],{"stretchy":1552},[1493,107138,1520],{},[1506,107140,1564],{"stretchy":1552},[1528,107142,20356],{"encoding":1530},[1065,107144,107146],{"id":107145},"principy-řešení-ekonomických-úloh","Principy řešení ekonomických úloh",[1276,107148,107149,107158],{},[1206,107150,107151,107154,107155,16623],{},[1047,107152,107153],{},"Princip rovnováhy"," — hledáme stav, kdy se protichůdné síly vyrovnají (např. tržní rovnováha, viz ",[1052,107156,132],{"className":107157,"dataFsResolvedFilePath":3487,"href":3488},[1055],[1206,107159,107160,107163,107164,107167,107168,107171,107172,107176],{},[1047,107161,107162],{},"Princip optimalizace"," — hledáme extrém účelové funkce, případně vázaný omezujícími podmínkami (viz ",[1052,107165,102],{"className":107166,"dataFsResolvedFilePath":16621,"href":16622},[1055]," pro 1D, ",[1052,107169,32413],{"className":107170,"dataFsResolvedFilePath":9470,"href":9471},[1055]," pro 2D, ",[1052,107173,107175],{"className":107174,"dataFsResolvedFilePath":17265,"href":17266},[1055],"lagrangeova-metoda"," pro vázané extrémy).",[1065,107178,107180],{"id":107179},"konvence-z-přednášek","Konvence z přednášek",[1203,107182,107183,107189,107195],{},[1206,107184,6483,107185,107188],{},[107186,107187,2343],"code",{}," pro přibližné rovnosti (typicky linearizace přes diferenciál).",[1206,107190,107191,107192,2632],{},"Numerické výsledky ",[1047,107193,107194],{},"na 3 desetinná místa",[1206,107196,19315,107197,107200],{},[1176,107198,107199],{},"jednotková změna"," má standardní význam (změna o 1).",[1065,107202,17159],{"id":17158},[1203,107204,107205,107210,107218],{},[1206,107206,107207,107209],{},[1047,107208,19217],{}," —",[1206,107211,107212,1656,107214],{},[1047,107213,19228],{},[1052,107215,107217],{"className":107216,"dataFsResolvedFilePath":16621,"href":16622},[1055],"Derivace a diferenciál",[1206,107219,107220,1656,107222,1732,107225],{},[1047,107221,19236],{},[1052,107223,17190],{"className":107224,"dataFsResolvedFilePath":17188,"href":17189},[1055],[1052,107226,107228],{"className":107227,"dataFsResolvedFilePath":1056,"href":1057},[1055],"kurz ImeK",{"title":17269,"searchDepth":141,"depth":141,"links":107230},[107231,107232,107233,107234,107235,107236],{"id":106987,"depth":141,"text":106988},{"id":31884,"depth":141,"text":31885},{"id":107037,"depth":141,"text":107038},{"id":107145,"depth":141,"text":107146},{"id":107179,"depth":141,"text":107180},{"id":17158,"depth":141,"text":17159},"Úvodní pojmy a princip modelování v matematické ekonomii. Slouží jako vstupní bod pro celý kurz — bez těchto pojmů nedávají další kapitoly smysl.",{},"\u002Ftopics\u002Fzaklady-matematicke-ekonomie",{"title":19223,"description":107237},[19272],"topics\u002Fzaklady-matematicke-ekonomie",[9,712,510,520,412,642],"uqqF-7PfmmXvhN1ukMYX6DiVal_8HKB6FD0mzhBR8cg",{"id":107246,"title":107247,"body":107248,"course":9,"courses":17424,"created":26093,"description":17269,"extension":17426,"meta":111240,"navigation":17428,"path":111241,"seo":111242,"sources":111243,"stem":111244,"tags":111245,"type":19275,"updated":26102,"__hash__":111246},"topics\u002Ftopics\u002Fzdaneni-trhu.md","Zdanění trhu — dopady daně na rovnováhu",{"type":1016,"value":107249,"toc":111223},[107250,107253,107352,107356,107378,107392,107444,107446,107450,107513,107556,107575,107738,107741,107808,107812,107941,107980,108010,108122,108167,108233,108286,108362,108418,108420,108424,108488,108532,108552,108713,108716,108800,108803,108869,108873,108922,108948,109053,109117,109122,109218,109265,109267,109270,109292,109334,109341,109380,109382,109453,109507,109511,109600,109675,109942,109986,109988,109992,109995,110002,110313,110316,110374,110560,110589,110591,110595,110601,110739,110748,110750,110752,111177,111179,111181],[1019,107251,107247],{"id":107252},"zdanění-trhu-dopady-daně-na-rovnováhu",[1023,107254,107256,107262],{"className":107255,"dataCallout":582},[1026,1186],[1030,107257,107259,1042],{"className":107258},[1033],[1035,107260],{"className":107261,"ariaHidden":1041},[1038,1193,1040],[1030,107263,57180,107264,107277,107278,107281,107282,107284,107285,107288,107289,107310,107311,107334,107335,107338,107339,2632],{},[1035,107265,107267],{"className":107266},[1480],[1482,107268,107269],{"xmlns":1484},[1487,107270,107271,107275],{},[1490,107272,107273],{},[1493,107274,5289],{},[1528,107276,5289],{"encoding":1530}," uložená na každou prodanou jednotku zboží posouvá jednu z křivek — ",[1047,107279,107280],{},"nabídku"," (je-li daň uložena výrobci) nebo ",[1047,107283,98796],{}," (je-li uložena spotřebiteli). Výsledné ",[1047,107286,107287],{},"daňové břemeno"," se dělí mezi obě strany trhu na ",[1035,107290,107292],{"className":107291},[1480],[1482,107293,107294],{"xmlns":1484},[1487,107295,107296,107308],{},[1490,107297,107298],{},[1497,107299,107300,107302],{},[1493,107301,5289],{},[1490,107303,107304,107306],{},[1493,107305,25906],{},[1493,107307,1030],{},[1528,107309,57233],{"encoding":1530}," (spotřebitel) a ",[1035,107312,107314],{"className":107313},[1480],[1482,107315,107316],{"xmlns":1484},[1487,107317,107318,107332],{},[1490,107319,107320],{},[1497,107321,107322,107324],{},[1493,107323,5289],{},[1490,107325,107326,107328,107330],{},[1493,107327,25950],{},[1493,107329,3052],{},[1493,107331,7740],{},[1528,107333,57257],{"encoding":1530}," (výrobce). Klíčovým zjištěním je ",[1047,107336,107337],{},"ekvivalence obou přístupů",": rovnovážné množství i čistá cena pro výrobce jsou v obou režimech totožné; liší se pouze nominální cena na trhu o ",[1035,107340,107342],{"className":107341},[1480],[1482,107343,107344],{"xmlns":1484},[1487,107345,107346,107350],{},[1490,107347,107348],{},[1493,107349,5289],{},[1528,107351,5289],{"encoding":1530},[1065,107353,107355],{"id":107354},"dvě-formy-zdanění","Dvě formy zdanění",[1030,107357,107358,107359,107377],{},"Uvažujme jednotkovou daň ",[1035,107360,107362],{"className":107361},[1480],[1482,107363,107364],{"xmlns":1484},[1487,107365,107366,107374],{},[1490,107367,107368,107370,107372],{},[1493,107369,5289],{},[1506,107371,2796],{},[1680,107373,1871],{},[1528,107375,107376],{"encoding":1530},"T > 0"," (Kč na kus), kterou stát ukládá na každou prodanou jednotku zboží. Daň může být uložena buď:",[1203,107379,107380,107386],{},[1206,107381,107382,107385],{},[1047,107383,107384],{},"(a) výrobci"," — výrobce ji musí odvést státu z každé prodané jednotky,",[1206,107387,107388,107391],{},[1047,107389,107390],{},"(b) spotřebiteli"," — spotřebitel ji platí navíc k ceně, kterou si účtuje prodejce.",[1030,107393,107394,107395,107408,107409,107412,107413,2632],{},"V obou případech dochází k posunu jedné z křivek o ",[1035,107396,107398],{"className":107397},[1480],[1482,107399,107400],{"xmlns":1484},[1487,107401,107402,107406],{},[1490,107403,107404],{},[1493,107405,5289],{},[1528,107407,5289],{"encoding":1530}," svisle (buď nabídky nahoru, nebo poptávky dolů) a k rozdělení ",[1047,107410,107411],{},"daňového břemene"," mezi spotřebitele a výrobce. Výchozí rovnovážný bod bez daně označujeme ",[1035,107414,107416],{"className":107415},[1480],[1482,107417,107418],{"xmlns":1484},[1487,107419,107420,107442],{},[1490,107421,107422,107424,107426,107432,107434,107440],{},[1493,107423,2711],{},[1506,107425,14314],{"stretchy":1552},[2315,107427,107428,107430],{},[1493,107429,1520],{},[1493,107431,2711],{},[1506,107433,1559],{"separator":1041},[2315,107435,107436,107438],{},[1493,107437,1501],{},[1493,107439,2711],{},[1506,107441,14323],{"stretchy":1552},[1528,107443,56005],{"encoding":1530},[1246,107445],{},[1065,107447,107449],{"id":107448},"daň-uložená-výrobci","Daň uložená výrobci",[1030,107451,107452,107453,107466,107467,107484,107485,107512],{},"Je-li daň ",[1035,107454,107456],{"className":107455},[1480],[1482,107457,107458],{"xmlns":1484},[1487,107459,107460,107464],{},[1490,107461,107462],{},[1493,107463,5289],{},[1528,107465,5289],{"encoding":1530}," uložena výrobci, pak z podmínky, že výrobce za každou prodanou jednotku obdrží ",[1035,107468,107470],{"className":107469},[1480],[1482,107471,107472],{"xmlns":1484},[1487,107473,107474,107482],{},[1490,107475,107476,107478,107480],{},[1493,107477,1501],{},[1506,107479,1888],{},[1493,107481,5289],{},[1528,107483,55774],{"encoding":1530}," (hrubá cena mínus odvod), plyne z rovnice ",[1035,107486,107488],{"className":107487},[1480],[1482,107489,107490],{"xmlns":1484},[1487,107491,107492,107510],{},[1490,107493,107494,107496,107498,107500,107502,107504,107506,107508],{},[1493,107495,1501],{},[1506,107497,1888],{},[1493,107499,5289],{},[1506,107501,1508],{},[1493,107503,2001],{},[1506,107505,1553],{"stretchy":1552},[1493,107507,1520],{},[1506,107509,1564],{"stretchy":1552},[1528,107511,55803],{"encoding":1530}," nová funkce nabídky:",[1035,107514,107516],{"className":107515},[1480],[1482,107517,107518],{"xmlns":1484,"display":1485},[1487,107519,107520,107554],{},[1490,107521,107522,107524,107526,107532,107534,107536,107538,107540,107542,107544,107546,107548,107550,107552],{},[1493,107523,1501],{},[1506,107525,1508],{},[1497,107527,107528,107530],{},[1493,107529,2001],{},[1680,107531,1682],{},[1506,107533,1553],{"stretchy":1552},[1493,107535,1520],{},[1506,107537,1564],{"stretchy":1552},[1506,107539,1508],{},[1493,107541,2001],{},[1506,107543,1553],{"stretchy":1552},[1493,107545,1520],{},[1506,107547,1564],{"stretchy":1552},[1506,107549,2162],{},[1493,107551,5289],{},[1493,107553,2632],{"mathvariant":1516},[1528,107555,55848],{"encoding":1530},[1030,107557,107558,107559,1656,107572,107574],{},"Nabídka se tedy posouvá o ",[1035,107560,107562],{"className":107561},[1480],[1482,107563,107564],{"xmlns":1484},[1487,107565,107566,107570],{},[1490,107567,107568],{},[1493,107569,5289],{},[1528,107571,5289],{"encoding":1530},[1047,107573,55881],{}," (ekvivalentně doleva). Poptávka se nemění.",[1030,107576,107577,107578,107618,107619,1586,107647,107675,107676,107695,107696,107720,107721,16623],{},"Nový rovnovážný bod ",[1035,107579,107581],{"className":107580},[1480],[1482,107582,107583],{"xmlns":1484},[1487,107584,107585,107615],{},[1490,107586,107587,107593,107595,107603,107605,107613],{},[1497,107588,107589,107591],{},[1493,107590,2711],{},[1680,107592,1682],{},[1506,107594,14314],{"stretchy":1552},[1697,107596,107597,107599,107601],{},[1493,107598,1520],{},[1680,107600,1682],{},[1493,107602,2711],{},[1506,107604,1559],{"separator":1041},[1697,107606,107607,107609,107611],{},[1493,107608,1501],{},[1680,107610,1682],{},[1493,107612,2711],{},[1506,107614,14323],{"stretchy":1552},[1528,107616,107617],{"encoding":1530},"E_1[Q_1^E, P_1^E]"," splňuje ",[1035,107620,107622],{"className":107621},[1480],[1482,107623,107624],{"xmlns":1484},[1487,107625,107626,107644],{},[1490,107627,107628,107636,107638],{},[1697,107629,107630,107632,107634],{},[1493,107631,1520],{},[1680,107633,1682],{},[1493,107635,2711],{},[1506,107637,3961],{},[2315,107639,107640,107642],{},[1493,107641,1520],{},[1493,107643,2711],{},[1528,107645,107646],{"encoding":1530},"Q_1^E \u003C Q^E",[1035,107648,107650],{"className":107649},[1480],[1482,107651,107652],{"xmlns":1484},[1487,107653,107654,107672],{},[1490,107655,107656,107664,107666],{},[1697,107657,107658,107660,107662],{},[1493,107659,1501],{},[1680,107661,1682],{},[1493,107663,2711],{},[1506,107665,2796],{},[2315,107667,107668,107670],{},[1493,107669,1501],{},[1493,107671,2711],{},[1528,107673,107674],{"encoding":1530},"P_1^E > P^E",". Spotřebitel platí ",[1035,107677,107679],{"className":107678},[1480],[1482,107680,107681],{"xmlns":1484},[1487,107682,107683,107693],{},[1490,107684,107685],{},[1697,107686,107687,107689,107691],{},[1493,107688,1501],{},[1680,107690,1682],{},[1493,107692,2711],{},[1528,107694,62192],{"encoding":1530},", výrobci ale zůstává pouze čistá cena ",[1035,107697,107699],{"className":107698},[1480],[1482,107700,107701],{"xmlns":1484},[1487,107702,107703,107717],{},[1490,107704,107705,107713,107715],{},[1697,107706,107707,107709,107711],{},[1493,107708,1501],{},[1680,107710,1682],{},[1493,107712,2711],{},[1506,107714,1888],{},[1493,107716,5289],{},[1528,107718,107719],{"encoding":1530},"P_1^E - T"," (ta je nižší než původní rovnovážná ",[1035,107722,107724],{"className":107723},[1480],[1482,107725,107726],{"xmlns":1484},[1487,107727,107728,107736],{},[1490,107729,107730],{},[2315,107731,107732,107734],{},[1493,107733,1501],{},[1493,107735,2711],{},[1528,107737,56102],{"encoding":1530},[1304,107739,59642],{"id":107740},"příklad-29",[1030,107742,107743,56206,107745,56241,107769,107789,107790,107807],{},[1047,107744,1263],{},[1035,107746,107748],{"className":107747},[1480],[1482,107749,107750],{"xmlns":1484},[1487,107751,107752,107766],{},[1490,107753,107754,107756,107758,107760,107762,107764],{},[1493,107755,1501],{},[1506,107757,1508],{},[1680,107759,6797],{},[1506,107761,1888],{},[1680,107763,1691],{},[1493,107765,1520],{},[1528,107767,107768],{"encoding":1530},"P = 12 - 2Q",[1035,107770,107772],{"className":107771},[1480],[1482,107773,107774],{"xmlns":1484},[1487,107775,107776,107786],{},[1490,107777,107778,107780,107782,107784],{},[1493,107779,1501],{},[1506,107781,1508],{},[1680,107783,4007],{},[1493,107785,1520],{},[1528,107787,107788],{"encoding":1530},"P = 4Q",". Na výrobce je uložena jednotková daň ",[1035,107791,107793],{"className":107792},[1480],[1482,107794,107795],{"xmlns":1484},[1487,107796,107797,107805],{},[1490,107798,107799,107801,107803],{},[1493,107800,5289],{},[1506,107802,1508],{},[1680,107804,7508],{},[1528,107806,55920],{"encoding":1530}," Kč.",[1030,107809,107810],{},[1047,107811,52997],{},[1030,107813,107814,107817,107818,21333,107844,21352,107864,1732,107886,107916,107917,2632],{},[1176,107815,107816],{},"Bez daně."," Z rovnosti ",[1035,107819,107821],{"className":107820},[1480],[1482,107822,107823],{"xmlns":1484},[1487,107824,107825,107841],{},[1490,107826,107827,107829,107831,107833,107835,107837,107839],{},[1680,107828,6797],{},[1506,107830,1888],{},[1680,107832,1691],{},[1493,107834,1520],{},[1506,107836,1508],{},[1680,107838,4007],{},[1493,107840,1520],{},[1528,107842,107843],{"encoding":1530},"12 - 2Q = 4Q",[1035,107845,107847],{"className":107846},[1480],[1482,107848,107849],{"xmlns":1484},[1487,107850,107851,107861],{},[1490,107852,107853,107855,107857,107859],{},[1680,107854,7508],{},[1493,107856,1520],{},[1506,107858,1508],{},[1680,107860,6797],{},[1528,107862,107863],{"encoding":1530},"6Q = 12",[1035,107865,107867],{"className":107866},[1480],[1482,107868,107869],{"xmlns":1484},[1487,107870,107871,107883],{},[1490,107872,107873,107879,107881],{},[2315,107874,107875,107877],{},[1493,107876,1520],{},[1493,107878,2711],{},[1506,107880,1508],{},[1680,107882,1691],{},[1528,107884,107885],{"encoding":1530},"Q^E = 2",[1035,107887,107889],{"className":107888},[1480],[1482,107890,107891],{"xmlns":1484},[1487,107892,107893,107913],{},[1490,107894,107895,107901,107903,107905,107907,107909,107911],{},[2315,107896,107897,107899],{},[1493,107898,1501],{},[1493,107900,2711],{},[1506,107902,1508],{},[1680,107904,4007],{},[1506,107906,1714],{},[1680,107908,1691],{},[1506,107910,1508],{},[1680,107912,6138],{},[1528,107914,107915],{"encoding":1530},"P^E = 4 \\cdot 2 = 8",". Rovnovážný bod ",[1035,107918,107920],{"className":107919},[1480],[1482,107921,107922],{"xmlns":1484},[1487,107923,107924,107938],{},[1490,107925,107926,107928,107930,107932,107934,107936],{},[1493,107927,2711],{},[1506,107929,14314],{"stretchy":1552},[1680,107931,1691],{},[1506,107933,1559],{"separator":1041},[1680,107935,6138],{},[1506,107937,14323],{"stretchy":1552},[1528,107939,107940],{"encoding":1530},"E[2, 8]",[1030,107942,107943,107946,107947,107979],{},[1176,107944,107945],{},"S daní uloženou výrobci."," Nová nabídka je ",[1035,107948,107950],{"className":107949},[1480],[1482,107951,107952],{"xmlns":1484},[1487,107953,107954,107976],{},[1490,107955,107956,107962,107964,107966,107968,107970,107972,107974],{},[1497,107957,107958,107960],{},[1493,107959,2001],{},[1680,107961,1682],{},[1506,107963,1274],{},[1493,107965,1501],{},[1506,107967,1508],{},[1680,107969,4007],{},[1493,107971,1520],{},[1506,107973,2162],{},[1680,107975,7508],{},[1528,107977,107978],{"encoding":1530},"S_1: P = 4Q + 6",". Z rovnice",[1035,107981,107983],{"className":107982},[1480],[1482,107984,107985],{"xmlns":1484,"display":1485},[1487,107986,107987,108007],{},[1490,107988,107989,107991,107993,107995,107997,107999,108001,108003,108005],{},[1680,107990,6797],{},[1506,107992,1888],{},[1680,107994,1691],{},[1493,107996,1520],{},[1506,107998,1508],{},[1680,108000,4007],{},[1493,108002,1520],{},[1506,108004,2162],{},[1680,108006,7508],{},[1528,108008,108009],{"encoding":1530},"12 - 2Q = 4Q + 6",[1030,108011,108012,108013,21352,108033,1732,108057,108093,108094,2632],{},"plyne ",[1035,108014,108016],{"className":108015},[1480],[1482,108017,108018],{"xmlns":1484},[1487,108019,108020,108030],{},[1490,108021,108022,108024,108026,108028],{},[1680,108023,7508],{},[1493,108025,1520],{},[1506,108027,1508],{},[1680,108029,7508],{},[1528,108031,108032],{"encoding":1530},"6Q = 6",[1035,108034,108036],{"className":108035},[1480],[1482,108037,108038],{"xmlns":1484},[1487,108039,108040,108054],{},[1490,108041,108042,108050,108052],{},[1697,108043,108044,108046,108048],{},[1493,108045,1520],{},[1680,108047,1682],{},[1493,108049,2711],{},[1506,108051,1508],{},[1680,108053,1682],{},[1528,108055,108056],{"encoding":1530},"Q_1^E = 1",[1035,108058,108060],{"className":108059},[1480],[1482,108061,108062],{"xmlns":1484},[1487,108063,108064,108090],{},[1490,108065,108066,108074,108076,108078,108080,108082,108084,108086,108088],{},[1697,108067,108068,108070,108072],{},[1493,108069,1501],{},[1680,108071,1682],{},[1493,108073,2711],{},[1506,108075,1508],{},[1680,108077,4007],{},[1506,108079,1714],{},[1680,108081,1682],{},[1506,108083,2162],{},[1680,108085,7508],{},[1506,108087,1508],{},[1680,108089,1775],{},[1528,108091,108092],{"encoding":1530},"P_1^E = 4 \\cdot 1 + 6 = 10",". Nový rovnovážný bod ",[1035,108095,108097],{"className":108096},[1480],[1482,108098,108099],{"xmlns":1484},[1487,108100,108101,108119],{},[1490,108102,108103,108109,108111,108113,108115,108117],{},[1497,108104,108105,108107],{},[1493,108106,2711],{},[1680,108108,1682],{},[1506,108110,14314],{"stretchy":1552},[1680,108112,1682],{},[1506,108114,1559],{"separator":1041},[1680,108116,1775],{},[1506,108118,14323],{"stretchy":1552},[1528,108120,108121],{"encoding":1530},"E_1[1, 10]",[1030,108123,108124,108127,108128,108152,108153,108166],{},[1176,108125,108126],{},"Rozklad daňového břemene."," Spotřebitel platí ",[1035,108129,108131],{"className":108130},[1480],[1482,108132,108133],{"xmlns":1484},[1487,108134,108135,108149],{},[1490,108136,108137,108145,108147],{},[1697,108138,108139,108141,108143],{},[1493,108140,1501],{},[1680,108142,1682],{},[1493,108144,2711],{},[1506,108146,1508],{},[1680,108148,1775],{},[1528,108150,108151],{"encoding":1530},"P_1^E = 10"," Kč namísto původních ",[1035,108154,108156],{"className":108155},[1480],[1482,108157,108158],{"xmlns":1484},[1487,108159,108160,108164],{},[1490,108161,108162],{},[1680,108163,6138],{},[1528,108165,6138],{"encoding":1530},", navýšení je",[1035,108168,108170],{"className":108169},[1480],[1482,108171,108172],{"xmlns":1484,"display":1485},[1487,108173,108174,108230],{},[1490,108175,108176,108186,108188,108196,108198,108204,108206,108208,108210,108212,108214,108216,108218,108228],{},[1497,108177,108178,108180],{},[1493,108179,5289],{},[1490,108181,108182,108184],{},[1493,108183,25906],{},[1493,108185,1030],{},[1506,108187,1508],{},[1697,108189,108190,108192,108194],{},[1493,108191,1501],{},[1680,108193,1682],{},[1493,108195,2711],{},[1506,108197,1888],{},[2315,108199,108200,108202],{},[1493,108201,1501],{},[1493,108203,2711],{},[1506,108205,1508],{},[1680,108207,1775],{},[1506,108209,1888],{},[1680,108211,6138],{},[1506,108213,1508],{},[1680,108215,1691],{},[1988,108217,10922],{},[1490,108219,108220,108222],{},[1988,108221,1504],{},[2178,108223,108224,108226],{"accent":1041},[1988,108225,8730],{},[1506,108227,8576],{},[1493,108229,2632],{"mathvariant":1516},[1528,108231,108232],{"encoding":1530},"T_{sp} = P_1^E - P^E = 10 - 8 = 2\\ \\text{Kč}.",[1030,108234,108235,108236,108152,108272,108285],{},"Výrobci zůstává čistá cena ",[1035,108237,108239],{"className":108238},[1480],[1482,108240,108241],{"xmlns":1484},[1487,108242,108243,108269],{},[1490,108244,108245,108253,108255,108257,108259,108261,108263,108265,108267],{},[1697,108246,108247,108249,108251],{},[1493,108248,1501],{},[1680,108250,1682],{},[1493,108252,2711],{},[1506,108254,1888],{},[1493,108256,5289],{},[1506,108258,1508],{},[1680,108260,1775],{},[1506,108262,1888],{},[1680,108264,7508],{},[1506,108266,1508],{},[1680,108268,4007],{},[1528,108270,108271],{"encoding":1530},"P_1^E - T = 10 - 6 = 4",[1035,108273,108275],{"className":108274},[1480],[1482,108276,108277],{"xmlns":1484},[1487,108278,108279,108283],{},[1490,108280,108281],{},[1680,108282,6138],{},[1528,108284,6138],{"encoding":1530},", pokles je",[1035,108287,108289],{"className":108288},[1480],[1482,108290,108291],{"xmlns":1484,"display":1485},[1487,108292,108293,108359],{},[1490,108294,108295,108307,108309,108315,108317,108319,108327,108329,108331,108333,108335,108337,108339,108341,108343,108345,108347,108357],{},[1497,108296,108297,108299],{},[1493,108298,5289],{},[1490,108300,108301,108303,108305],{},[1493,108302,25950],{},[1493,108304,3052],{},[1493,108306,7740],{},[1506,108308,1508],{},[2315,108310,108311,108313],{},[1493,108312,1501],{},[1493,108314,2711],{},[1506,108316,1888],{},[1506,108318,1553],{"stretchy":1552},[1697,108320,108321,108323,108325],{},[1493,108322,1501],{},[1680,108324,1682],{},[1493,108326,2711],{},[1506,108328,1888],{},[1493,108330,5289],{},[1506,108332,1564],{"stretchy":1552},[1506,108334,1508],{},[1680,108336,6138],{},[1506,108338,1888],{},[1680,108340,4007],{},[1506,108342,1508],{},[1680,108344,4007],{},[1988,108346,10922],{},[1490,108348,108349,108351],{},[1988,108350,1504],{},[2178,108352,108353,108355],{"accent":1041},[1988,108354,8730],{},[1506,108356,8576],{},[1493,108358,2632],{"mathvariant":1516},[1528,108360,108361],{"encoding":1530},"T_{vyr} = P^E - (P_1^E - T) = 8 - 4 = 4\\ \\text{Kč}.",[1030,108363,108364,108365,108417],{},"Kontrola: ",[1035,108366,108368],{"className":108367},[1480],[1482,108369,108370],{"xmlns":1484},[1487,108371,108372,108414],{},[1490,108373,108374,108384,108386,108398,108400,108402,108404,108406,108408,108410,108412],{},[1497,108375,108376,108378],{},[1493,108377,5289],{},[1490,108379,108380,108382],{},[1493,108381,25906],{},[1493,108383,1030],{},[1506,108385,2162],{},[1497,108387,108388,108390],{},[1493,108389,5289],{},[1490,108391,108392,108394,108396],{},[1493,108393,25950],{},[1493,108395,3052],{},[1493,108397,7740],{},[1506,108399,1508],{},[1680,108401,1691],{},[1506,108403,2162],{},[1680,108405,4007],{},[1506,108407,1508],{},[1680,108409,7508],{},[1506,108411,1508],{},[1493,108413,5289],{},[1528,108415,108416],{"encoding":1530},"T_{sp} + T_{vyr} = 2 + 4 = 6 = T",". Spotřebitel nese třetinu daně, výrobce dvě třetiny.",[1246,108419],{},[1065,108421,108423],{"id":108422},"daň-uložená-spotřebiteli","Daň uložená spotřebiteli",[1030,108425,107452,108426,108439,108440,108458,108459,108487],{},[1035,108427,108429],{"className":108428},[1480],[1482,108430,108431],{"xmlns":1484},[1487,108432,108433,108437],{},[1490,108434,108435],{},[1493,108436,5289],{},[1528,108438,5289],{"encoding":1530}," uložena spotřebiteli, pak spotřebitel platí celkem ",[1035,108441,108443],{"className":108442},[1480],[1482,108444,108445],{"xmlns":1484},[1487,108446,108447,108455],{},[1490,108448,108449,108451,108453],{},[1493,108450,1501],{},[1506,108452,2162],{},[1493,108454,5289],{},[1528,108456,108457],{"encoding":1530},"P + T"," (cena prodejce plus daň). Z podmínky ",[1035,108460,108462],{"className":108461},[1480],[1482,108463,108464],{"xmlns":1484},[1487,108465,108466,108484],{},[1490,108467,108468,108470,108472,108474,108476,108478,108480,108482],{},[1493,108469,1501],{},[1506,108471,2162],{},[1493,108473,5289],{},[1506,108475,1508],{},[1493,108477,3712],{},[1506,108479,1553],{"stretchy":1552},[1493,108481,1520],{},[1506,108483,1564],{"stretchy":1552},[1528,108485,108486],{"encoding":1530},"P + T = D(Q)"," plyne nová funkce poptávky:",[1035,108489,108491],{"className":108490},[1480],[1482,108492,108493],{"xmlns":1484,"display":1485},[1487,108494,108495,108529],{},[1490,108496,108497,108499,108501,108507,108509,108511,108513,108515,108517,108519,108521,108523,108525,108527],{},[1493,108498,1501],{},[1506,108500,1508],{},[1497,108502,108503,108505],{},[1493,108504,3712],{},[1680,108506,1691],{},[1506,108508,1553],{"stretchy":1552},[1493,108510,1520],{},[1506,108512,1564],{"stretchy":1552},[1506,108514,1508],{},[1493,108516,3712],{},[1506,108518,1553],{"stretchy":1552},[1493,108520,1520],{},[1506,108522,1564],{"stretchy":1552},[1506,108524,1888],{},[1493,108526,5289],{},[1493,108528,2632],{"mathvariant":1516},[1528,108530,108531],{"encoding":1530},"P = D_2(Q) = D(Q) - T.",[1030,108533,108534,108535,1656,108548,108551],{},"Poptávka se tedy posouvá o ",[1035,108536,108538],{"className":108537},[1480],[1482,108539,108540],{"xmlns":1484},[1487,108541,108542,108546],{},[1490,108543,108544],{},[1493,108545,5289],{},[1528,108547,5289],{"encoding":1530},[1047,108549,108550],{},"svisle dolů",". Nabídka se nemění.",[1030,108553,107577,108554,107618,108594,1586,108622,108650,108651,108670,108671,108695,108696,16623],{},[1035,108555,108557],{"className":108556},[1480],[1482,108558,108559],{"xmlns":1484},[1487,108560,108561,108591],{},[1490,108562,108563,108569,108571,108579,108581,108589],{},[1497,108564,108565,108567],{},[1493,108566,2711],{},[1680,108568,1691],{},[1506,108570,14314],{"stretchy":1552},[1697,108572,108573,108575,108577],{},[1493,108574,1520],{},[1680,108576,1691],{},[1493,108578,2711],{},[1506,108580,1559],{"separator":1041},[1697,108582,108583,108585,108587],{},[1493,108584,1501],{},[1680,108586,1691],{},[1493,108588,2711],{},[1506,108590,14323],{"stretchy":1552},[1528,108592,108593],{"encoding":1530},"E_2[Q_2^E, P_2^E]",[1035,108595,108597],{"className":108596},[1480],[1482,108598,108599],{"xmlns":1484},[1487,108600,108601,108619],{},[1490,108602,108603,108611,108613],{},[1697,108604,108605,108607,108609],{},[1493,108606,1520],{},[1680,108608,1691],{},[1493,108610,2711],{},[1506,108612,3961],{},[2315,108614,108615,108617],{},[1493,108616,1520],{},[1493,108618,2711],{},[1528,108620,108621],{"encoding":1530},"Q_2^E \u003C Q^E",[1035,108623,108625],{"className":108624},[1480],[1482,108626,108627],{"xmlns":1484},[1487,108628,108629,108647],{},[1490,108630,108631,108639,108641],{},[1697,108632,108633,108635,108637],{},[1493,108634,1501],{},[1680,108636,1691],{},[1493,108638,2711],{},[1506,108640,3961],{},[2315,108642,108643,108645],{},[1493,108644,1501],{},[1493,108646,2711],{},[1528,108648,108649],{"encoding":1530},"P_2^E \u003C P^E",". Výrobce obdrží ",[1035,108652,108654],{"className":108653},[1480],[1482,108655,108656],{"xmlns":1484},[1487,108657,108658,108668],{},[1490,108659,108660],{},[1697,108661,108662,108664,108666],{},[1493,108663,1501],{},[1680,108665,1691],{},[1493,108667,2711],{},[1528,108669,62253],{"encoding":1530},", spotřebitel platí celkem ",[1035,108672,108674],{"className":108673},[1480],[1482,108675,108676],{"xmlns":1484},[1487,108677,108678,108692],{},[1490,108679,108680,108688,108690],{},[1697,108681,108682,108684,108686],{},[1493,108683,1501],{},[1680,108685,1691],{},[1493,108687,2711],{},[1506,108689,2162],{},[1493,108691,5289],{},[1528,108693,108694],{"encoding":1530},"P_2^E + T"," (tato částka je vyšší než původní ",[1035,108697,108699],{"className":108698},[1480],[1482,108700,108701],{"xmlns":1484},[1487,108702,108703,108711],{},[1490,108704,108705],{},[2315,108706,108707,108709],{},[1493,108708,1501],{},[1493,108710,2711],{},[1528,108712,56102],{"encoding":1530},[1030,108714,108715],{},"Daňové břemeno:",[1035,108717,108719],{"className":108718},[1480],[1482,108720,108721],{"xmlns":1484,"display":1485},[1487,108722,108723,108797],{},[1490,108724,108725,108735,108737,108739,108747,108749,108751,108753,108755,108761,108763,108765,108777,108779,108785,108787,108795],{},[1497,108726,108727,108729],{},[1493,108728,5289],{},[1490,108730,108731,108733],{},[1493,108732,25906],{},[1493,108734,1030],{},[1506,108736,1508],{},[1506,108738,1553],{"stretchy":1552},[1697,108740,108741,108743,108745],{},[1493,108742,1501],{},[1680,108744,1691],{},[1493,108746,2711],{},[1506,108748,2162],{},[1493,108750,5289],{},[1506,108752,1564],{"stretchy":1552},[1506,108754,1888],{},[2315,108756,108757,108759],{},[1493,108758,1501],{},[1493,108760,2711],{},[1506,108762,1559],{"separator":1041},[1912,108764],{"width":1914},[1497,108766,108767,108769],{},[1493,108768,5289],{},[1490,108770,108771,108773,108775],{},[1493,108772,25950],{},[1493,108774,3052],{},[1493,108776,7740],{},[1506,108778,1508],{},[2315,108780,108781,108783],{},[1493,108782,1501],{},[1493,108784,2711],{},[1506,108786,1888],{},[1697,108788,108789,108791,108793],{},[1493,108790,1501],{},[1680,108792,1691],{},[1493,108794,2711],{},[1493,108796,2632],{"mathvariant":1516},[1528,108798,108799],{"encoding":1530},"T_{sp} = (P_2^E + T) - P^E, \\qquad T_{vyr} = P^E - P_2^E.",[1304,108801,59722],{"id":108802},"příklad-210",[1030,108804,108805,108807,108808,56241,108831,108850,108851,108868],{},[1047,108806,1263],{}," Pokračuje z Příkladu 2.9 — stejný trh, poptávka ",[1035,108809,108811],{"className":108810},[1480],[1482,108812,108813],{"xmlns":1484},[1487,108814,108815,108829],{},[1490,108816,108817,108819,108821,108823,108825,108827],{},[1493,108818,1501],{},[1506,108820,1508],{},[1680,108822,6797],{},[1506,108824,1888],{},[1680,108826,1691],{},[1493,108828,1520],{},[1528,108830,107768],{"encoding":1530},[1035,108832,108834],{"className":108833},[1480],[1482,108835,108836],{"xmlns":1484},[1487,108837,108838,108848],{},[1490,108839,108840,108842,108844,108846],{},[1493,108841,1501],{},[1506,108843,1508],{},[1680,108845,4007],{},[1493,108847,1520],{},[1528,108849,107788],{"encoding":1530},". Daň ",[1035,108852,108854],{"className":108853},[1480],[1482,108855,108856],{"xmlns":1484},[1487,108857,108858,108866],{},[1490,108859,108860,108862,108864],{},[1493,108861,5289],{},[1506,108863,1508],{},[1680,108865,7508],{},[1528,108867,55920],{"encoding":1530}," Kč je tentokrát uložena na spotřebitele.",[1030,108870,108871],{},[1047,108872,52997],{},[1030,108874,108875,108876,107979],{},"Nová poptávka je ",[1035,108877,108879],{"className":108878},[1480],[1482,108880,108881],{"xmlns":1484},[1487,108882,108883,108919],{},[1490,108884,108885,108891,108893,108895,108897,108899,108901,108903,108905,108907,108909,108911,108913,108915,108917],{},[1497,108886,108887,108889],{},[1493,108888,3712],{},[1680,108890,1691],{},[1506,108892,1274],{},[1493,108894,1501],{},[1506,108896,1508],{},[1680,108898,6797],{},[1506,108900,1888],{},[1680,108902,1691],{},[1493,108904,1520],{},[1506,108906,1888],{},[1680,108908,7508],{},[1506,108910,1508],{},[1680,108912,7508],{},[1506,108914,1888],{},[1680,108916,1691],{},[1493,108918,1520],{},[1528,108920,108921],{"encoding":1530},"D_2: P = 12 - 2Q - 6 = 6 - 2Q",[1035,108923,108925],{"className":108924},[1480],[1482,108926,108927],{"xmlns":1484,"display":1485},[1487,108928,108929,108945],{},[1490,108930,108931,108933,108935,108937,108939,108941,108943],{},[1680,108932,7508],{},[1506,108934,1888],{},[1680,108936,1691],{},[1493,108938,1520],{},[1506,108940,1508],{},[1680,108942,4007],{},[1493,108944,1520],{},[1528,108946,108947],{"encoding":1530},"6 - 2Q = 4Q",[1030,108949,108012,108950,21352,108969,1732,108993,108093,109025,2632],{},[1035,108951,108953],{"className":108952},[1480],[1482,108954,108955],{"xmlns":1484},[1487,108956,108957,108967],{},[1490,108958,108959,108961,108963,108965],{},[1680,108960,7508],{},[1493,108962,1520],{},[1506,108964,1508],{},[1680,108966,7508],{},[1528,108968,108032],{"encoding":1530},[1035,108970,108972],{"className":108971},[1480],[1482,108973,108974],{"xmlns":1484},[1487,108975,108976,108990],{},[1490,108977,108978,108986,108988],{},[1697,108979,108980,108982,108984],{},[1493,108981,1520],{},[1680,108983,1691],{},[1493,108985,2711],{},[1506,108987,1508],{},[1680,108989,1682],{},[1528,108991,108992],{"encoding":1530},"Q_2^E = 1",[1035,108994,108996],{"className":108995},[1480],[1482,108997,108998],{"xmlns":1484},[1487,108999,109000,109022],{},[1490,109001,109002,109010,109012,109014,109016,109018,109020],{},[1697,109003,109004,109006,109008],{},[1493,109005,1501],{},[1680,109007,1691],{},[1493,109009,2711],{},[1506,109011,1508],{},[1680,109013,4007],{},[1506,109015,1714],{},[1680,109017,1682],{},[1506,109019,1508],{},[1680,109021,4007],{},[1528,109023,109024],{"encoding":1530},"P_2^E = 4 \\cdot 1 = 4",[1035,109026,109028],{"className":109027},[1480],[1482,109029,109030],{"xmlns":1484},[1487,109031,109032,109050],{},[1490,109033,109034,109040,109042,109044,109046,109048],{},[1497,109035,109036,109038],{},[1493,109037,2711],{},[1680,109039,1691],{},[1506,109041,14314],{"stretchy":1552},[1680,109043,1682],{},[1506,109045,1559],{"separator":1041},[1680,109047,4007],{},[1506,109049,14323],{"stretchy":1552},[1528,109051,109052],{"encoding":1530},"E_2[1, 4]",[1030,109054,109055,109056,109092,109093,107807],{},"Spotřebitel platí celkem ",[1035,109057,109059],{"className":109058},[1480],[1482,109060,109061],{"xmlns":1484},[1487,109062,109063,109089],{},[1490,109064,109065,109073,109075,109077,109079,109081,109083,109085,109087],{},[1697,109066,109067,109069,109071],{},[1493,109068,1501],{},[1680,109070,1691],{},[1493,109072,2711],{},[1506,109074,2162],{},[1493,109076,5289],{},[1506,109078,1508],{},[1680,109080,4007],{},[1506,109082,2162],{},[1680,109084,7508],{},[1506,109086,1508],{},[1680,109088,1775],{},[1528,109090,109091],{"encoding":1530},"P_2^E + T = 4 + 6 = 10"," Kč; výrobce obdrží ",[1035,109094,109096],{"className":109095},[1480],[1482,109097,109098],{"xmlns":1484},[1487,109099,109100,109114],{},[1490,109101,109102,109110,109112],{},[1697,109103,109104,109106,109108],{},[1493,109105,1501],{},[1680,109107,1691],{},[1493,109109,2711],{},[1506,109111,1508],{},[1680,109113,4007],{},[1528,109115,109116],{"encoding":1530},"P_2^E = 4",[1030,109118,109119],{},[1176,109120,109121],{},"Rozklad daňového břemene:",[1035,109123,109125],{"className":109124},[1480],[1482,109126,109127],{"xmlns":1484,"display":1485},[1487,109128,109129,109215],{},[1490,109130,109131,109141,109143,109145,109147,109149,109151,109153,109155,109157,109159,109161,109163,109173,109175,109177,109189,109191,109193,109195,109197,109199,109201,109203,109213],{},[1497,109132,109133,109135],{},[1493,109134,5289],{},[1490,109136,109137,109139],{},[1493,109138,25906],{},[1493,109140,1030],{},[1506,109142,1508],{},[1506,109144,1553],{"stretchy":1552},[1680,109146,4007],{},[1506,109148,2162],{},[1680,109150,7508],{},[1506,109152,1564],{"stretchy":1552},[1506,109154,1888],{},[1680,109156,6138],{},[1506,109158,1508],{},[1680,109160,1691],{},[1988,109162,10922],{},[1490,109164,109165,109167],{},[1988,109166,1504],{},[2178,109168,109169,109171],{"accent":1041},[1988,109170,8730],{},[1506,109172,8576],{},[1506,109174,1559],{"separator":1041},[1912,109176],{"width":1914},[1497,109178,109179,109181],{},[1493,109180,5289],{},[1490,109182,109183,109185,109187],{},[1493,109184,25950],{},[1493,109186,3052],{},[1493,109188,7740],{},[1506,109190,1508],{},[1680,109192,6138],{},[1506,109194,1888],{},[1680,109196,4007],{},[1506,109198,1508],{},[1680,109200,4007],{},[1988,109202,10922],{},[1490,109204,109205,109207],{},[1988,109206,1504],{},[2178,109208,109209,109211],{"accent":1041},[1988,109210,8730],{},[1506,109212,8576],{},[1493,109214,2632],{"mathvariant":1516},[1528,109216,109217],{"encoding":1530},"T_{sp} = (4 + 6) - 8 = 2\\ \\text{Kč}, \\qquad T_{vyr} = 8 - 4 = 4\\ \\text{Kč}.",[1030,109219,109220,109221,2632],{},"Opět ",[1035,109222,109224],{"className":109223},[1480],[1482,109225,109226],{"xmlns":1484},[1487,109227,109228,109262],{},[1490,109229,109230,109240,109242,109254,109256,109258,109260],{},[1497,109231,109232,109234],{},[1493,109233,5289],{},[1490,109235,109236,109238],{},[1493,109237,25906],{},[1493,109239,1030],{},[1506,109241,2162],{},[1497,109243,109244,109246],{},[1493,109245,5289],{},[1490,109247,109248,109250,109252],{},[1493,109249,25950],{},[1493,109251,3052],{},[1493,109253,7740],{},[1506,109255,1508],{},[1680,109257,7508],{},[1506,109259,1508],{},[1493,109261,5289],{},[1528,109263,109264],{"encoding":1530},"T_{sp} + T_{vyr} = 6 = T",[1246,109266],{},[1065,109268,57210],{"id":109269},"daňové-břemeno",[1030,109271,109272,7606,109274,109277,109278,109291],{},[1047,109273,57210],{},[1176,109275,109276],{},"tax burden",") je rozdělení zaplacené daně ",[1035,109279,109281],{"className":109280},[1480],[1482,109282,109283],{"xmlns":1484},[1487,109284,109285,109289],{},[1490,109286,109287],{},[1493,109288,5289],{},[1528,109290,5289],{"encoding":1530}," mezi spotřebitele a výrobce:",[1035,109293,109295],{"className":109294},[1480],[1482,109296,109297],{"xmlns":1484,"display":1485},[1487,109298,109299,109331],{},[1490,109300,109301,109303,109305,109315,109317,109329],{},[1493,109302,5289],{},[1506,109304,1508],{},[1497,109306,109307,109309],{},[1493,109308,5289],{},[1490,109310,109311,109313],{},[1493,109312,25906],{},[1493,109314,1030],{},[1506,109316,2162],{},[1497,109318,109319,109321],{},[1493,109320,5289],{},[1490,109322,109323,109325,109327],{},[1493,109324,25950],{},[1493,109326,3052],{},[1493,109328,7740],{},[1493,109330,2632],{"mathvariant":1516},[1528,109332,109333],{"encoding":1530},"T = T_{sp} + T_{vyr}.",[1030,109335,109336],{},[18014,109337],{"alt":109338,"className":109339,"src":109340},"imek-dan-rozklad-bremene-sklony",[1055,18018],"\u002Fwiki-assets\u002Fimek-dan-rozklad-bremene-sklony.jpeg",[1023,109342,109344,109351],{"className":109343,"dataCallout":582},[1026,1186],[1030,109345,109347,109350],{"className":109346},[1033],[1035,109348],{"className":109349,"ariaHidden":1041},[1038,1193,1040],"Intuice — proč se daňové břemeno dělí",[1030,109352,109353,109354,1586,109367,2632],{},"Kdyby byla poptávka dokonale elastická (vodorovná), spotřebitelé by při jakémkoliv navýšení ceny úplně přestali nakupovat — celou daň by musel zaplatit výrobce. Naopak při dokonale neelastické poptávce (svislá křivka) spotřebitelé nakupují stále stejné množství a celou daň přenesou na ně. V realitě jsou obě křivky nějak skloněné a daňové břemeno se dělí v poměru, který je dán relativními sklony ",[1035,109355,109357],{"className":109356},[1480],[1482,109358,109359],{"xmlns":1484},[1487,109360,109361,109365],{},[1490,109362,109363],{},[1493,109364,3712],{},[1528,109366,3712],{"encoding":1530},[1035,109368,109370],{"className":109369},[1480],[1482,109371,109372],{"xmlns":1484},[1487,109373,109374,109378],{},[1490,109375,109376],{},[1493,109377,2001],{},[1528,109379,2001],{"encoding":1530},[1304,109381,17903],{"id":17902},[1030,109383,109384,109385,109406,109407,109420,109421,109438,109439,109452],{},"V grafu ",[1035,109386,109388],{"className":109387},[1480],[1482,109389,109390],{"xmlns":1484},[1487,109391,109392,109404],{},[1490,109393,109394,109396,109398,109400,109402],{},[1506,109395,1553],{"stretchy":1552},[1493,109397,1520],{},[1506,109399,1559],{"separator":1041},[1493,109401,1501],{},[1506,109403,1564],{"stretchy":1552},[1528,109405,65513],{"encoding":1530}," je svislá vzdálenost mezi původní a posunutou křivkou právě ",[1035,109408,109410],{"className":109409},[1480],[1482,109411,109412],{"xmlns":1484},[1487,109413,109414,109418],{},[1490,109415,109416],{},[1493,109417,5289],{},[1528,109419,5289],{"encoding":1530},". Vedeme-li v novém rovnovážném bodě vodorovnou přímku na úrovni původní rovnovážné ceny ",[1035,109422,109424],{"className":109423},[1480],[1482,109425,109426],{"xmlns":1484},[1487,109427,109428,109436],{},[1490,109429,109430],{},[2315,109431,109432,109434],{},[1493,109433,1501],{},[1493,109435,2711],{},[1528,109437,56102],{"encoding":1530},", rozdělí se úsečka ",[1035,109440,109442],{"className":109441},[1480],[1482,109443,109444],{"xmlns":1484},[1487,109445,109446,109450],{},[1490,109447,109448],{},[1493,109449,5289],{},[1528,109451,5289],{"encoding":1530}," na dvě části:",[1203,109454,109455,109480],{},[1206,109456,109457,109458,109479],{},"horní část odpovídá ",[1035,109459,109461],{"className":109460},[1480],[1482,109462,109463],{"xmlns":1484},[1487,109464,109465,109477],{},[1490,109466,109467],{},[1497,109468,109469,109471],{},[1493,109470,5289],{},[1490,109472,109473,109475],{},[1493,109474,25906],{},[1493,109476,1030],{},[1528,109478,57233],{"encoding":1530}," (o kolik vzrostla cena placená spotřebitelem),",[1206,109481,109482,109483,109506],{},"dolní část odpovídá ",[1035,109484,109486],{"className":109485},[1480],[1482,109487,109488],{"xmlns":1484},[1487,109489,109490,109504],{},[1490,109491,109492],{},[1497,109493,109494,109496],{},[1493,109495,5289],{},[1490,109497,109498,109500,109502],{},[1493,109499,25950],{},[1493,109501,3052],{},[1493,109503,7740],{},[1528,109505,57257],{"encoding":1530}," (o kolik klesla cena přijímaná výrobcem).",[1304,109508,109510],{"id":109509},"sklony-křivek-a-rozklad","Sklony křivek a rozklad",[1030,109512,109513,109514,109517,109518,7606,109541,109558,109559,7606,109582,109599],{},"Platí obecně: ",[1047,109515,109516],{},"čím strmější křivka (menší elasticita), tím větší část daně nese daná strana trhu."," Pro lineární poptávku ",[1035,109519,109521],{"className":109520},[1480],[1482,109522,109523],{"xmlns":1484},[1487,109524,109525,109539],{},[1490,109526,109527,109529,109531,109533,109535,109537],{},[1493,109528,1501],{},[1506,109530,1508],{},[1493,109532,1052],{},[1493,109534,1520],{},[1506,109536,2162],{},[1493,109538,2394],{},[1528,109540,52158],{"encoding":1530},[1035,109542,109544],{"className":109543},[1480],[1482,109545,109546],{"xmlns":1484},[1487,109547,109548,109556],{},[1490,109549,109550,109552,109554],{},[1493,109551,1052],{},[1506,109553,3961],{},[1680,109555,1871],{},[1528,109557,57642],{"encoding":1530},") a lineární nabídku ",[1035,109560,109562],{"className":109561},[1480],[1482,109563,109564],{"xmlns":1484},[1487,109565,109566,109580],{},[1490,109567,109568,109570,109572,109574,109576,109578],{},[1493,109569,1501],{},[1506,109571,1508],{},[1493,109573,8730],{},[1493,109575,1520],{},[1506,109577,2162],{},[1493,109579,3384],{},[1528,109581,55008],{"encoding":1530},[1035,109583,109585],{"className":109584},[1480],[1482,109586,109587],{"xmlns":1484},[1487,109588,109589,109597],{},[1490,109590,109591,109593,109595],{},[1493,109592,8730],{},[1506,109594,2796],{},[1680,109596,1871],{},[1528,109598,55026],{"encoding":1530},") lze rozklad odvodit pomocí multiplikátorů a platí",[1035,109601,109603],{"className":109602},[1480],[1482,109604,109605],{"xmlns":1484,"display":1485},[1487,109606,109607,109672],{},[1490,109608,109609,109633,109635,109645,109647,109670],{},[1510,109610,109611,109621],{},[1497,109612,109613,109615],{},[1493,109614,5289],{},[1490,109616,109617,109619],{},[1493,109618,25906],{},[1493,109620,1030],{},[1497,109622,109623,109625],{},[1493,109624,5289],{},[1490,109626,109627,109629,109631],{},[1493,109628,25950],{},[1493,109630,3052],{},[1493,109632,7740],{},[1506,109634,1508],{},[1510,109636,109637,109639],{},[1493,109638,8730],{},[1490,109640,109641,109643],{},[1506,109642,1888],{},[1493,109644,1052],{},[1506,109646,1508],{},[1510,109648,109649,109660],{},[1490,109650,109651,109653,109656,109658],{},[1493,109652,8620],{"mathvariant":1516},[1988,109654,109655],{},"sklon ",[1493,109657,2001],{},[1493,109659,8620],{"mathvariant":1516},[1490,109661,109662,109664,109666,109668],{},[1493,109663,8620],{"mathvariant":1516},[1988,109665,109655],{},[1493,109667,3712],{},[1493,109669,8620],{"mathvariant":1516},[1493,109671,2632],{"mathvariant":1516},[1528,109673,109674],{"encoding":1530},"\\frac{T_{sp}}{T_{vyr}} = \\frac{c}{-a} = \\frac{|\\text{sklon } S|}{|\\text{sklon } D|}.",[1023,109676,109678,109685],{"className":109677,"dataCallout":1443},[1026,1442],[1030,109679,109681,109684],{"className":109680},[1033],[1035,109682],{"className":109683,"ariaHidden":1041},[1038,1450,1040],"Postup výpočtu rozkladu",[1276,109686,109687,109722,109775,109854],{},[1206,109688,109689,109690,109721],{},"Spočti rovnovážný bod ",[1035,109691,109693],{"className":109692},[1480],[1482,109694,109695],{"xmlns":1484},[1487,109696,109697,109719],{},[1490,109698,109699,109701,109703,109709,109711,109717],{},[1493,109700,2711],{},[1506,109702,14314],{"stretchy":1552},[2315,109704,109705,109707],{},[1493,109706,1520],{},[1493,109708,2711],{},[1506,109710,1559],{"separator":1041},[2315,109712,109713,109715],{},[1493,109714,1501],{},[1493,109716,2711],{},[1506,109718,14323],{"stretchy":1552},[1528,109720,56005],{"encoding":1530}," bez daně.",[1206,109723,109724,109725,16846,109750,16623],{},"Urči posunutou křivku (",[1035,109726,109728],{"className":109727},[1480],[1482,109729,109730],{"xmlns":1484},[1487,109731,109732,109748],{},[1490,109733,109734,109740,109742,109744,109746],{},[1497,109735,109736,109738],{},[1493,109737,2001],{},[1680,109739,1682],{},[1506,109741,1508],{},[1493,109743,2001],{},[1506,109745,2162],{},[1493,109747,5289],{},[1528,109749,57306],{"encoding":1530},[1035,109751,109753],{"className":109752},[1480],[1482,109754,109755],{"xmlns":1484},[1487,109756,109757,109773],{},[1490,109758,109759,109765,109767,109769,109771],{},[1497,109760,109761,109763],{},[1493,109762,3712],{},[1680,109764,1691],{},[1506,109766,1508],{},[1493,109768,3712],{},[1506,109770,1888],{},[1493,109772,5289],{},[1528,109774,57337],{"encoding":1530},[1206,109776,109777,109778,19330,109797,28611,109816,19330,109835,16623],{},"Vyřeš novou rovnovážnou rovnici — získáš ",[1035,109779,109781],{"className":109780},[1480],[1482,109782,109783],{"xmlns":1484},[1487,109784,109785,109795],{},[1490,109786,109787],{},[1697,109788,109789,109791,109793],{},[1493,109790,1520],{},[1680,109792,1682],{},[1493,109794,2711],{},[1528,109796,62171],{"encoding":1530},[1035,109798,109800],{"className":109799},[1480],[1482,109801,109802],{"xmlns":1484},[1487,109803,109804,109814],{},[1490,109805,109806],{},[1697,109807,109808,109810,109812],{},[1493,109809,1520],{},[1680,109811,1691],{},[1493,109813,2711],{},[1528,109815,62233],{"encoding":1530},[1035,109817,109819],{"className":109818},[1480],[1482,109820,109821],{"xmlns":1484},[1487,109822,109823,109833],{},[1490,109824,109825],{},[1697,109826,109827,109829,109831],{},[1493,109828,1501],{},[1680,109830,1682],{},[1493,109832,2711],{},[1528,109834,62192],{"encoding":1530},[1035,109836,109838],{"className":109837},[1480],[1482,109839,109840],{"xmlns":1484},[1487,109841,109842,109852],{},[1490,109843,109844],{},[1697,109845,109846,109848,109850],{},[1493,109847,1501],{},[1680,109849,1691],{},[1493,109851,2711],{},[1528,109853,62253],{"encoding":1530},[1206,109855,109856,109857,1586,109878,109901,109902,2632],{},"Dopočítej ",[1035,109858,109860],{"className":109859},[1480],[1482,109861,109862],{"xmlns":1484},[1487,109863,109864,109876],{},[1490,109865,109866],{},[1497,109867,109868,109870],{},[1493,109869,5289],{},[1490,109871,109872,109874],{},[1493,109873,25906],{},[1493,109875,1030],{},[1528,109877,57233],{"encoding":1530},[1035,109879,109881],{"className":109880},[1480],[1482,109882,109883],{"xmlns":1484},[1487,109884,109885,109899],{},[1490,109886,109887],{},[1497,109888,109889,109891],{},[1493,109890,5289],{},[1490,109892,109893,109895,109897],{},[1493,109894,25950],{},[1493,109896,3052],{},[1493,109898,7740],{},[1528,109900,57257],{"encoding":1530}," z definice, vždy ověř ",[1035,109903,109905],{"className":109904},[1480],[1482,109906,109907],{"xmlns":1484},[1487,109908,109909,109939],{},[1490,109910,109911,109921,109923,109935,109937],{},[1497,109912,109913,109915],{},[1493,109914,5289],{},[1490,109916,109917,109919],{},[1493,109918,25906],{},[1493,109920,1030],{},[1506,109922,2162],{},[1497,109924,109925,109927],{},[1493,109926,5289],{},[1490,109928,109929,109931,109933],{},[1493,109930,25950],{},[1493,109932,3052],{},[1493,109934,7740],{},[1506,109936,1508],{},[1493,109938,5289],{},[1528,109940,109941],{"encoding":1530},"T_{sp} + T_{vyr} = T",[1023,109943,109945,109952],{"className":109944,"dataCallout":1155},[1026,1154],[1030,109946,109948,109951],{"className":109947},[1033],[1035,109949],{"className":109950,"ariaHidden":1041},[1038,1162,1040],"Pozor — zákonný vs. ekonomický nositel daně",[1030,109953,109954,109955,109958,109959,1586,109972,109985],{},"I když zákon ukládá daň formálně pouze jedné straně (výrobci nebo spotřebiteli), ",[1047,109956,109957],{},"ekonomicky ji vždy nesou obě strany",". Skutečné rozdělení určují sklony ",[1035,109960,109962],{"className":109961},[1480],[1482,109963,109964],{"xmlns":1484},[1487,109965,109966,109970],{},[1490,109967,109968],{},[1493,109969,3712],{},[1528,109971,3712],{"encoding":1530},[1035,109973,109975],{"className":109974},[1480],[1482,109976,109977],{"xmlns":1484},[1487,109978,109979,109983],{},[1490,109980,109981],{},[1493,109982,2001],{},[1528,109984,2001],{"encoding":1530},", nikoli paragrafové znění zákona. Kupující a prodávající tak fakticky platí daň bez ohledu na to, na koho je uvalena.",[1246,109987],{},[1065,109989,109991],{"id":109990},"ekvivalence-obou-přístupů","Ekvivalence obou přístupů",[1030,109993,109994],{},"Porovnáním Příkladu 2.9 (daň výrobci) a Příkladu 2.10 (daň spotřebiteli) zjistíme:",[1030,109996,109997],{},[18014,109998],{"alt":109999,"className":110000,"src":110001},"imek-dan-ekvivalence-vyrobce-spotrebitel",[1055,18018],"\u002Fwiki-assets\u002Fimek-dan-ekvivalence-vyrobce-spotrebitel.jpeg",[1073,110003,110004,110016],{},[1076,110005,110006],{},[1079,110007,110008,110010,110013],{},[1082,110009,68477],{},[1082,110011,110012],{},"(a) daň výrobci",[1082,110014,110015],{},"(b) daň spotřebiteli",[1092,110017,110018,110073,110140,110200],{},[1079,110019,110020,110023,110048],{},[1097,110021,110022],{},"Rovnovážné množství",[1097,110024,110025],{},[1035,110026,110028],{"className":110027},[1480],[1482,110029,110030],{"xmlns":1484},[1487,110031,110032,110046],{},[1490,110033,110034,110042,110044],{},[1697,110035,110036,110038,110040],{},[1493,110037,1520],{},[1680,110039,1682],{},[1493,110041,2711],{},[1506,110043,1508],{},[1680,110045,1682],{},[1528,110047,108056],{"encoding":1530},[1097,110049,110050],{},[1035,110051,110053],{"className":110052},[1480],[1482,110054,110055],{"xmlns":1484},[1487,110056,110057,110071],{},[1490,110058,110059,110067,110069],{},[1697,110060,110061,110063,110065],{},[1493,110062,1520],{},[1680,110064,1691],{},[1493,110066,2711],{},[1506,110068,1508],{},[1680,110070,1682],{},[1528,110072,108992],{"encoding":1530},[1079,110074,110075,110078,110103],{},[1097,110076,110077],{},"Cena placená spotřebitelem",[1097,110079,110080],{},[1035,110081,110083],{"className":110082},[1480],[1482,110084,110085],{"xmlns":1484},[1487,110086,110087,110101],{},[1490,110088,110089,110097,110099],{},[1697,110090,110091,110093,110095],{},[1493,110092,1501],{},[1680,110094,1682],{},[1493,110096,2711],{},[1506,110098,1508],{},[1680,110100,1775],{},[1528,110102,108151],{"encoding":1530},[1097,110104,110105],{},[1035,110106,110108],{"className":110107},[1480],[1482,110109,110110],{"xmlns":1484},[1487,110111,110112,110138],{},[1490,110113,110114,110122,110124,110126,110128,110130,110132,110134,110136],{},[1697,110115,110116,110118,110120],{},[1493,110117,1501],{},[1680,110119,1691],{},[1493,110121,2711],{},[1506,110123,2162],{},[1493,110125,5289],{},[1506,110127,1508],{},[1680,110129,4007],{},[1506,110131,2162],{},[1680,110133,7508],{},[1506,110135,1508],{},[1680,110137,1775],{},[1528,110139,109091],{"encoding":1530},[1079,110141,110142,110145,110175],{},[1097,110143,110144],{},"Cena přijímaná výrobcem",[1097,110146,110147],{},[1035,110148,110150],{"className":110149},[1480],[1482,110151,110152],{"xmlns":1484},[1487,110153,110154,110172],{},[1490,110155,110156,110164,110166,110168,110170],{},[1697,110157,110158,110160,110162],{},[1493,110159,1501],{},[1680,110161,1682],{},[1493,110163,2711],{},[1506,110165,1888],{},[1493,110167,5289],{},[1506,110169,1508],{},[1680,110171,4007],{},[1528,110173,110174],{"encoding":1530},"P_1^E - T = 4",[1097,110176,110177],{},[1035,110178,110180],{"className":110179},[1480],[1482,110181,110182],{"xmlns":1484},[1487,110183,110184,110198],{},[1490,110185,110186,110194,110196],{},[1697,110187,110188,110190,110192],{},[1493,110189,1501],{},[1680,110191,1691],{},[1493,110193,2711],{},[1506,110195,1508],{},[1680,110197,4007],{},[1528,110199,109116],{"encoding":1530},[1079,110201,110202,110205,110259],{},[1097,110203,110204],{},"Rozklad břemene",[1097,110206,110207,1732,110232],{},[1035,110208,110210],{"className":110209},[1480],[1482,110211,110212],{"xmlns":1484},[1487,110213,110214,110230],{},[1490,110215,110216,110226,110228],{},[1497,110217,110218,110220],{},[1493,110219,5289],{},[1490,110221,110222,110224],{},[1493,110223,25906],{},[1493,110225,1030],{},[1506,110227,1508],{},[1680,110229,1691],{},[1528,110231,57528],{"encoding":1530},[1035,110233,110235],{"className":110234},[1480],[1482,110236,110237],{"xmlns":1484},[1487,110238,110239,110257],{},[1490,110240,110241,110253,110255],{},[1497,110242,110243,110245],{},[1493,110244,5289],{},[1490,110246,110247,110249,110251],{},[1493,110248,25950],{},[1493,110250,3052],{},[1493,110252,7740],{},[1506,110254,1508],{},[1680,110256,4007],{},[1528,110258,57557],{"encoding":1530},[1097,110260,110261,1732,110286],{},[1035,110262,110264],{"className":110263},[1480],[1482,110265,110266],{"xmlns":1484},[1487,110267,110268,110284],{},[1490,110269,110270,110280,110282],{},[1497,110271,110272,110274],{},[1493,110273,5289],{},[1490,110275,110276,110278],{},[1493,110277,25906],{},[1493,110279,1030],{},[1506,110281,1508],{},[1680,110283,1691],{},[1528,110285,57528],{"encoding":1530},[1035,110287,110289],{"className":110288},[1480],[1482,110290,110291],{"xmlns":1484},[1487,110292,110293,110311],{},[1490,110294,110295,110307,110309],{},[1497,110296,110297,110299],{},[1493,110298,5289],{},[1490,110300,110301,110303,110305],{},[1493,110302,25950],{},[1493,110304,3052],{},[1493,110306,7740],{},[1506,110308,1508],{},[1680,110310,4007],{},[1528,110312,57557],{"encoding":1530},[1030,110314,110315],{},"Výsledek je v obou režimech reálně totožný — liší se pouze to, kterou cenu nazveme \"tržní\":",[1035,110317,110319],{"className":110318},[1480],[1482,110320,110321],{"xmlns":1484,"display":1485},[1487,110322,110323,110371],{},[1490,110324,110325,110333,110335,110343,110345,110347,110355,110357,110359,110361,110369],{},[1697,110326,110327,110329,110331],{},[1493,110328,1520],{},[1680,110330,1682],{},[1493,110332,2711],{},[1506,110334,1508],{},[1697,110336,110337,110339,110341],{},[1493,110338,1520],{},[1680,110340,1691],{},[1493,110342,2711],{},[1506,110344,1559],{"separator":1041},[1912,110346],{"width":1914},[1697,110348,110349,110351,110353],{},[1493,110350,1501],{},[1680,110352,1682],{},[1493,110354,2711],{},[1506,110356,1888],{},[1493,110358,5289],{},[1506,110360,1508],{},[1697,110362,110363,110365,110367],{},[1493,110364,1501],{},[1680,110366,1691],{},[1493,110368,2711],{},[1493,110370,2632],{"mathvariant":1516},[1528,110372,110373],{"encoding":1530},"Q_1^E = Q_2^E, \\qquad P_1^E - T = P_2^E.",[1023,110375,110377,110384,110401,110555],{"className":110376,"dataCallout":1443},[1026,1442],[1030,110378,110380,110383],{"className":110379},[1033],[1035,110381],{"className":110382,"ariaHidden":1041},[1038,1450,1040],"Věta o ekvivalenci zdanění",[1030,110385,110386,110387,110400],{},"Nezávisle na tom, zda je jednotková daň ",[1035,110388,110390],{"className":110389},[1480],[1482,110391,110392],{"xmlns":1484},[1487,110393,110394,110398],{},[1490,110395,110396],{},[1493,110397,5289],{},[1528,110399,5289],{"encoding":1530}," uložena výrobci, nebo spotřebiteli, se po jejím uložení rovnají:",[1203,110402,110403,110435,110471,110508],{},[1206,110404,110405,110406,1559],{},"rovnovážná množství obou režimů, ",[1035,110407,110409],{"className":110408},[1480],[1482,110410,110411],{"xmlns":1484},[1487,110412,110413,110433],{},[1490,110414,110415,110423,110425],{},[1697,110416,110417,110419,110421],{},[1493,110418,1520],{},[1680,110420,1682],{},[1493,110422,2711],{},[1506,110424,1508],{},[1697,110426,110427,110429,110431],{},[1493,110428,1520],{},[1680,110430,1691],{},[1493,110432,2711],{},[1528,110434,57460],{"encoding":1530},[1206,110436,110437,110438,1559],{},"čistá cena přijímaná výrobcem, ",[1035,110439,110441],{"className":110440},[1480],[1482,110442,110443],{"xmlns":1484},[1487,110444,110445,110469],{},[1490,110446,110447,110455,110457,110459,110461],{},[1697,110448,110449,110451,110453],{},[1493,110450,1501],{},[1680,110452,1682],{},[1493,110454,2711],{},[1506,110456,1888],{},[1493,110458,5289],{},[1506,110460,1508],{},[1697,110462,110463,110465,110467],{},[1493,110464,1501],{},[1680,110466,1691],{},[1493,110468,2711],{},[1528,110470,57494],{"encoding":1530},[1206,110472,110473,110474,1559],{},"celková cena placená spotřebitelem, ",[1035,110475,110477],{"className":110476},[1480],[1482,110478,110479],{"xmlns":1484},[1487,110480,110481,110505],{},[1490,110482,110483,110491,110493,110501,110503],{},[1697,110484,110485,110487,110489],{},[1493,110486,1501],{},[1680,110488,1682],{},[1493,110490,2711],{},[1506,110492,1508],{},[1697,110494,110495,110497,110499],{},[1493,110496,1501],{},[1680,110498,1691],{},[1493,110500,2711],{},[1506,110502,2162],{},[1493,110504,5289],{},[1528,110506,110507],{"encoding":1530},"P_1^E = P_2^E + T",[1206,110509,110510,110511,1586,110532,2632],{},"rozklad daňového břemene ",[1035,110512,110514],{"className":110513},[1480],[1482,110515,110516],{"xmlns":1484},[1487,110517,110518,110530],{},[1490,110519,110520],{},[1497,110521,110522,110524],{},[1493,110523,5289],{},[1490,110525,110526,110528],{},[1493,110527,25906],{},[1493,110529,1030],{},[1528,110531,57233],{"encoding":1530},[1035,110533,110535],{"className":110534},[1480],[1482,110536,110537],{"xmlns":1484},[1487,110538,110539,110553],{},[1490,110540,110541],{},[1497,110542,110543,110545],{},[1493,110544,5289],{},[1490,110546,110547,110549,110551],{},[1493,110548,25950],{},[1493,110550,3052],{},[1493,110552,7740],{},[1528,110554,57257],{"encoding":1530},[1030,110556,110557,110558,2632],{},"Z hlediska reálných dopadů na trh (objem transakcí, reálné platby stran) jsou tedy obě formy zdanění ",[1047,110559,50300],{},[1030,110561,110562,110563,1586,110576,16623],{},"Ekvivalence má zásadní politickou implikaci: otázka, \"kdo má platit daň\", je z hlediska trhu formální — skutečné rozdělení určuje struktura trhu (sklony ",[1035,110564,110566],{"className":110565},[1480],[1482,110567,110568],{"xmlns":1484},[1487,110569,110570,110574],{},[1490,110571,110572],{},[1493,110573,3712],{},[1528,110575,3712],{"encoding":1530},[1035,110577,110579],{"className":110578},[1480],[1482,110580,110581],{"xmlns":1484},[1487,110582,110583,110587],{},[1490,110584,110585],{},[1493,110586,2001],{},[1528,110588,2001],{"encoding":1530},[1246,110590],{},[1065,110592,110594],{"id":110593},"úlohy","Úlohy",[1030,110596,110597,110598,18579],{},"Z kapitoly 2 se zdanění týkají zejména následující úlohy (zadání v hub-page ",[1052,110599,132],{"className":110600,"dataFsResolvedFilePath":3487,"href":3488},[1055],[1203,110602,110603,110633,110664],{},[1206,110604,110605,110608,110609,110632],{},[1047,110606,110607],{},"Úloha 2.4"," — Poptávka ",[1035,110610,110612],{"className":110611},[1480],[1482,110613,110614],{"xmlns":1484},[1487,110615,110616,110630],{},[1490,110617,110618,110620,110622,110624,110626,110628],{},[1493,110619,1501],{},[1506,110621,1508],{},[1680,110623,6797],{},[1506,110625,1888],{},[1680,110627,1691],{},[1493,110629,1520],{},[1528,110631,107768],{"encoding":1530},"; najděte novou poptávku po uložení daně 6 Kč na kupujícího.",[1206,110634,110635,110638,110639,110663],{},[1047,110636,110637],{},"Úloha 2.9"," — Nabídka ",[1035,110640,110642],{"className":110641},[1480],[1482,110643,110644],{"xmlns":1484},[1487,110645,110646,110660],{},[1490,110647,110648,110650,110652,110654,110656,110658],{},[1493,110649,1501],{},[1506,110651,1508],{},[1680,110653,3687],{},[1493,110655,1520],{},[1506,110657,2162],{},[1680,110659,9787],{},[1528,110661,110662],{"encoding":1530},"P = 0{,}5Q + 15","; najděte novou nabídku po uložení daně 5 Kč na výrobce.",[1206,110665,110666,110669,110670,1586,110696,110720,110721,110738],{},[1047,110667,110668],{},"Úloha 2.13"," — Komplexní úloha se zadáním ",[1035,110671,110673],{"className":110672},[1480],[1482,110674,110675],{"xmlns":1484},[1487,110676,110677,110693],{},[1490,110678,110679,110681,110683,110685,110687,110689,110691],{},[1493,110680,1501],{},[1506,110682,1508],{},[1506,110684,1888],{},[1680,110686,4007],{},[1493,110688,1520],{},[1506,110690,2162],{},[1680,110692,11232],{},[1528,110694,110695],{"encoding":1530},"P = -4Q + 80",[1035,110697,110699],{"className":110698},[1480],[1482,110700,110701],{"xmlns":1484},[1487,110702,110703,110717],{},[1490,110704,110705,110707,110709,110711,110713,110715],{},[1493,110706,1501],{},[1506,110708,1508],{},[1680,110710,3201],{},[1493,110712,1520],{},[1506,110714,2162],{},[1680,110716,1775],{},[1528,110718,110719],{"encoding":1530},"P = 3Q + 10",": rovnováha, daň ",[1035,110722,110724],{"className":110723},[1480],[1482,110725,110726],{"xmlns":1484},[1487,110727,110728,110736],{},[1490,110729,110730,110732,110734],{},[1493,110731,5289],{},[1506,110733,1508],{},[1680,110735,16580],{},[1528,110737,62150],{"encoding":1530}," Kč uložená postupně výrobci i spotřebiteli, rozklad daňového břemene a analýza ekvivalence.",[1030,110740,110741,110742,110744,110745,110747],{},"Související úvodní příklady posunu křivek při zdanění: ",[1047,110743,59567],{}," (posun poptávky při zdanění kupujícího) a ",[1047,110746,59601],{}," (posun nabídky při zdanění výrobce).",[1246,110749],{},[1065,110751,31885],{"id":31884},[1203,110753,110754,110773,110831,110888,110971,111017,111060,111105,111171],{},[1206,110755,110756,1656,110759,110772],{},[1047,110757,110758],{},"Jednotková daň",[1035,110760,110762],{"className":110761},[1480],[1482,110763,110764],{"xmlns":1484},[1487,110765,110766,110770],{},[1490,110767,110768],{},[1493,110769,5289],{},[1528,110771,5289],{"encoding":1530}," — fixní částka na každou prodanou jednotku zboží",[1206,110774,110775,110777,110778,110816,110817,110830],{},[1047,110776,107449],{}," — posun nabídky ",[1035,110779,110781],{"className":110780},[1480],[1482,110782,110783],{"xmlns":1484},[1487,110784,110785,110813],{},[1490,110786,110787,110793,110795,110797,110799,110801,110803,110805,110807,110809,110811],{},[1497,110788,110789,110791],{},[1493,110790,2001],{},[1680,110792,1682],{},[1506,110794,1553],{"stretchy":1552},[1493,110796,1520],{},[1506,110798,1564],{"stretchy":1552},[1506,110800,1508],{},[1493,110802,2001],{},[1506,110804,1553],{"stretchy":1552},[1493,110806,1520],{},[1506,110808,1564],{"stretchy":1552},[1506,110810,2162],{},[1493,110812,5289],{},[1528,110814,110815],{"encoding":1530},"S_1(Q) = S(Q) + T"," (o ",[1035,110818,110820],{"className":110819},[1480],[1482,110821,110822],{"xmlns":1484},[1487,110823,110824,110828],{},[1490,110825,110826],{},[1493,110827,5289],{},[1528,110829,5289],{"encoding":1530}," svisle nahoru)",[1206,110832,110833,110835,110836,110816,110874,110887],{},[1047,110834,108423],{}," — posun poptávky ",[1035,110837,110839],{"className":110838},[1480],[1482,110840,110841],{"xmlns":1484},[1487,110842,110843,110871],{},[1490,110844,110845,110851,110853,110855,110857,110859,110861,110863,110865,110867,110869],{},[1497,110846,110847,110849],{},[1493,110848,3712],{},[1680,110850,1691],{},[1506,110852,1553],{"stretchy":1552},[1493,110854,1520],{},[1506,110856,1564],{"stretchy":1552},[1506,110858,1508],{},[1493,110860,3712],{},[1506,110862,1553],{"stretchy":1552},[1493,110864,1520],{},[1506,110866,1564],{"stretchy":1552},[1506,110868,1888],{},[1493,110870,5289],{},[1528,110872,110873],{"encoding":1530},"D_2(Q) = D(Q) - T",[1035,110875,110877],{"className":110876},[1480],[1482,110878,110879],{"xmlns":1484},[1487,110880,110881,110885],{},[1490,110882,110883],{},[1493,110884,5289],{},[1528,110886,5289],{"encoding":1530}," svisle dolů)",[1206,110889,110890,22970,110893,56364,110932],{},[1047,110891,110892],{},"Rovnovážný bod s daní",[1035,110894,110896],{"className":110895},[1480],[1482,110897,110898],{"xmlns":1484},[1487,110899,110900,110930],{},[1490,110901,110902,110908,110910,110918,110920,110928],{},[1497,110903,110904,110906],{},[1493,110905,2711],{},[1680,110907,1682],{},[1506,110909,14314],{"stretchy":1552},[1697,110911,110912,110914,110916],{},[1493,110913,1520],{},[1680,110915,1682],{},[1493,110917,2711],{},[1506,110919,1559],{"separator":1041},[1697,110921,110922,110924,110926],{},[1493,110923,1501],{},[1680,110925,1682],{},[1493,110927,2711],{},[1506,110929,14323],{"stretchy":1552},[1528,110931,107617],{"encoding":1530},[1035,110933,110935],{"className":110934},[1480],[1482,110936,110937],{"xmlns":1484},[1487,110938,110939,110969],{},[1490,110940,110941,110947,110949,110957,110959,110967],{},[1497,110942,110943,110945],{},[1493,110944,2711],{},[1680,110946,1691],{},[1506,110948,14314],{"stretchy":1552},[1697,110950,110951,110953,110955],{},[1493,110952,1520],{},[1680,110954,1691],{},[1493,110956,2711],{},[1506,110958,1559],{"separator":1041},[1697,110960,110961,110963,110965],{},[1493,110962,1501],{},[1680,110964,1691],{},[1493,110966,2711],{},[1506,110968,14323],{"stretchy":1552},[1528,110970,108593],{"encoding":1530},[1206,110972,110973,7606,110975,110977,110978],{},[1047,110974,57210],{},[1176,110976,109276],{},") — rozklad ",[1035,110979,110981],{"className":110980},[1480],[1482,110982,110983],{"xmlns":1484},[1487,110984,110985,111015],{},[1490,110986,110987,110989,110991,111001,111003],{},[1493,110988,5289],{},[1506,110990,1508],{},[1497,110992,110993,110995],{},[1493,110994,5289],{},[1490,110996,110997,110999],{},[1493,110998,25906],{},[1493,111000,1030],{},[1506,111002,2162],{},[1497,111004,111005,111007],{},[1493,111006,5289],{},[1490,111008,111009,111011,111013],{},[1493,111010,25950],{},[1493,111012,3052],{},[1493,111014,7740],{},[1528,111016,57396],{"encoding":1530},[1206,111018,111019,111042,111043,1564],{},[1047,111020,111021],{},[1035,111022,111024],{"className":111023},[1480],[1482,111025,111026],{"xmlns":1484},[1487,111027,111028,111040],{},[1490,111029,111030],{},[1497,111031,111032,111034],{},[1493,111033,5289],{},[1490,111035,111036,111038],{},[1493,111037,25906],{},[1493,111039,1030],{},[1528,111041,57233],{"encoding":1530}," — část daně nesená spotřebitelem (navýšení ceny nad ",[1035,111044,111046],{"className":111045},[1480],[1482,111047,111048],{"xmlns":1484},[1487,111049,111050,111058],{},[1490,111051,111052],{},[2315,111053,111054,111056],{},[1493,111055,1501],{},[1493,111057,2711],{},[1528,111059,56102],{"encoding":1530},[1206,111061,111062,111087,111088,1564],{},[1047,111063,111064],{},[1035,111065,111067],{"className":111066},[1480],[1482,111068,111069],{"xmlns":1484},[1487,111070,111071,111085],{},[1490,111072,111073],{},[1497,111074,111075,111077],{},[1493,111076,5289],{},[1490,111078,111079,111081,111083],{},[1493,111080,25950],{},[1493,111082,3052],{},[1493,111084,7740],{},[1528,111086,57257],{"encoding":1530}," — část daně nesená výrobcem (pokles čisté přijímané ceny pod ",[1035,111089,111091],{"className":111090},[1480],[1482,111092,111093],{"xmlns":1484},[1487,111094,111095,111103],{},[1490,111096,111097],{},[2315,111098,111099,111101],{},[1493,111100,1501],{},[1493,111102,2711],{},[1528,111104,56102],{"encoding":1530},[1206,111106,111107,22970,111109,1732,111138],{},[1047,111108,64808],{},[1035,111110,111112],{"className":111111},[1480],[1482,111113,111114],{"xmlns":1484},[1487,111115,111116,111136],{},[1490,111117,111118,111126,111128],{},[1697,111119,111120,111122,111124],{},[1493,111121,1520],{},[1680,111123,1682],{},[1493,111125,2711],{},[1506,111127,1508],{},[1697,111129,111130,111132,111134],{},[1493,111131,1520],{},[1680,111133,1691],{},[1493,111135,2711],{},[1528,111137,57460],{"encoding":1530},[1035,111139,111141],{"className":111140},[1480],[1482,111142,111143],{"xmlns":1484},[1487,111144,111145,111169],{},[1490,111146,111147,111155,111157,111159,111161],{},[1697,111148,111149,111151,111153],{},[1493,111150,1501],{},[1680,111152,1682],{},[1493,111154,2711],{},[1506,111156,1888],{},[1493,111158,5289],{},[1506,111160,1508],{},[1697,111162,111163,111165,111167],{},[1493,111164,1501],{},[1680,111166,1691],{},[1493,111168,2711],{},[1528,111170,57494],{"encoding":1530},[1206,111172,111173,111176],{},[1047,111174,111175],{},"Zákonný vs. ekonomický nositel daně"," — rozdíl mezi formálním ustanovením zákona a skutečným rozdělením břemene",[1246,111178],{},[1065,111180,17159],{"id":17158},[1203,111182,111183,111191,111209,111216],{},[1206,111184,111185,1656,111188],{},[1047,111186,111187],{},"Kontext (hub):",[1052,111189,3489],{"className":111190,"dataFsResolvedFilePath":3487,"href":3488},[1055],[1206,111192,111193,1656,111195,111198,111199,34788,111201,111204,111205,111208],{},[1047,111194,65057],{},[1052,111196,28281],{"className":111197,"dataFsResolvedFilePath":17231,"href":17232},[1055]," (daň vyvolává ztrátu blahobytu — ",[1176,111200,69214],{},[1052,111202,3506],{"className":111203,"dataFsResolvedFilePath":16621,"href":16622},[1055]," (sklony křivek, rovnovážný bod jako řešení soustavy), ",[1052,111206,17218],{"className":111207,"dataFsResolvedFilePath":3807,"href":3808},[1055]," (kvantifikace, jak se daňové břemeno dělí podle citlivosti stran trhu)",[1206,111210,111211,1656,111213],{},[1047,111212,65092],{},[1052,111214,17190],{"className":111215,"dataFsResolvedFilePath":17188,"href":17189},[1055],[1206,111217,111218,1656,111220],{},[1047,111219,17176],{},[1052,111221,1058],{"className":111222,"dataFsResolvedFilePath":1056,"href":1057},[1055],{"title":17269,"searchDepth":141,"depth":141,"links":111224},[111225,111226,111229,111232,111236,111237,111238,111239],{"id":107354,"depth":141,"text":107355},{"id":107448,"depth":141,"text":107449,"children":111227},[111228],{"id":107740,"depth":96,"text":59642},{"id":108422,"depth":141,"text":108423,"children":111230},[111231],{"id":108802,"depth":96,"text":59722},{"id":109269,"depth":141,"text":57210,"children":111233},[111234,111235],{"id":17902,"depth":96,"text":17903},{"id":109509,"depth":96,"text":109510},{"id":109990,"depth":141,"text":109991},{"id":110593,"depth":141,"text":110594},{"id":31884,"depth":141,"text":31885},{"id":17158,"depth":141,"text":17159},{},"\u002Ftopics\u002Fzdaneni-trhu",{"title":107247,"description":17269},[26098,19272],"topics\u002Fzdaneni-trhu",[9,341,434,436,810,132],"jkJm0ohc_XEz8a90Ecl-kSuUbr1GjWopTekn334zpFM",[111248],{"slug":9,"path":1057,"title":10,"snippet":111249},"… urzu v definičním tvaru, se zdrojem a intuicí. Referenční list pro přípravu na zkoušku. - \u003C\u003Cimek-zkouska-priprava>> — plná řešení všech 32 zkouškových úloh (Q1 rozhodovací, Q2 definice + interpretace, Q3 o …",[111251,111254,111258,111261,111262],{"slug":111252,"title":111253,"path":17170,"sharedTags":96},"imek-vzorce-prehled","ImeK — kompletní přehled vzorců se zdroji a intuicí",{"slug":111255,"title":111256,"path":111257,"sharedTags":96},"imek-kniha","Kniha — *Úvod do matematické ekonomie pro ekonomy*","\u002Fwiki\u002Fimek-kniha",{"slug":111259,"title":111260,"path":17189,"sharedTags":141},"imek-blok-01","ImeK — Kalkul a mikroekonomie",{"slug":112,"title":28483,"path":7755,"sharedTags":141},{"slug":111263,"title":111264,"path":111265,"sharedTags":141},"imek-detail-predmetu","Matematická ekonomie — Detail předmětu","\u002Fwiki\u002Fimek-detail-predmetu",1777320342953]