2454:
2069:
1245:
501:
1841:
2281:
1370:
35:. For a much more extensive discussion of various types of production functions and their properties, their relationships and origin, see Chambers (1988) and Sickles and Zelenyuk (2019, Chapter 6).
46:(L), mostly for heuristic purposes. These functions and their properties are easily generalizable to include additional factors of production (like land, natural resources, entrepreneurship, etc.)
1892:
1729:
1569:
1642:
853:
626:
379:
1022:
969:
1469:
2184:
940:
1883:
Cost
Function (because of the duality between cost and production functions, a specific technology can be represented equally well by either the cost or production function).
2138:
879:
2534:
Sickles, R., & Zelenyuk, V. (2019). Measurement of
Productivity and Efficiency: Theory and Practice. Cambridge: Cambridge University Press. doi:10.1017/9781139565981
783:
667:
220:
171:
122:
1012:
2220:
2486:
2274:
1870:
754:
2506:
2247:
2092:
1274:
390:
54:
There are three common ways to incorporate technology (or the efficiency with which factors of production are used) into a production function (here
1746:
2449:{\displaystyle x_{i}={\partial C \over \partial p_{i}}=b_{ii}y^{b_{yi}}+\textstyle \sum _{i\neq j}^{m}b_{ij}{\sqrt {p_{i}/p_{j}}}y^{b_{y}}}
1285:
1256:, a variation of the Cobb-Douglas production function that considers existence of a threshold factor requirement (represented by
2064:{\displaystyle C(p,y)=\sum _{i}b_{ii}\left(y^{b_{yi}}p_{i}+\sum _{j\,:\,j\neq i}b_{ij}{\sqrt {p_{i}p_{j}}}y^{b_{y}}\right)}
791:
534:
2533:
1659:
1486:
1586:
1253:
803:
2582:
Diewert, W. Erwin. "An application of the
Shephard duality theorem: A generalized Leontief production function."
1880:
38:
The production functions listed below, and their properties are shown for the case of two factors of production,
2524:
Chambers, R. G. (1988). Applied
Production Analysis: A Dual Approach. New York, NY: Cambridge University Press.
74:
546:
2602:
2545:
1240:{\displaystyle \ln(Y)=\ln(A)+a_{L}\ln(L)+a_{K}\ln(K)+b_{LL}\ln ^{2}(L)+b_{LK}\ln(L)\ln(K)+b_{KK}\ln ^{2}(K)}
252:
887:
234:
is a measure of how easily one factor can be substituted for another. With two factors of production, say,
2571:
Production economics: A dual approach to theory and applications: Applications of the theory of production
945:
1392:
2143:
899:
59:
2607:
2097:
858:
2556:
Nakamura, Shinichiro. "A nonhomothetic generalized
Leontief cost function based on pooled data."
759:
631:
178:
129:
80:
991:
2189:
2186:. This cost function reduces to the well-known Generalized Leontief function of Diewert when
1650:
Spillman
Production Function (This function is referenced in Agricultural Economics Research)
231:
2464:
2252:
1848:
697:
496:{\displaystyle \ slope=-{\frac {\partial F(K,L)/\partial K}{\partial F(K,L)/\partial L}}.}
8:
2226:
39:
19:
2491:
2232:
2077:
1259:
511:
43:
32:
28:
521:
Decreasing returns to scale: doubling all input usages less than doubles output.
518:
Increasing returns to scale: doubling all input usages more than doubles output.
2596:
1836:{\displaystyle Y=\min\{Y^{*},\beta _{1}+\beta _{2}L,\beta _{2}+\beta _{4}K\}}
985:
524:
Constant returns to scale: doubling all input usages exactly doubles output.
2546:
https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1744-7976.1977.tb02884.x
2544:
DECISION ASPECTS OF THE SPILLMAN PRODUCTION FUNCTION Janusz
Jaworski 1977
24:
981:
243:
1365:{\displaystyle Y=A\prod _{i=1}^{n}(x_{i}-z_{i})^{\alpha _{i}}}
1383:
Variable
Elasticity of Substitution Production Function (VES)
27:
literature. Production functions are a key part of modelling
384:
where "slope" denotes the slope of the isoquant, given by
2364:
2494:
2467:
2284:
2255:
2235:
2192:
2146:
2100:
2080:
1895:
1851:
1749:
1662:
1589:
1489:
1395:
1288:
1262:
1025:
994:
948:
902:
861:
806:
762:
700:
634:
549:
393:
255:
181:
132:
83:
1377:
242:, it is a measure of the curvature of a production
175:Solow-neutral technology, or "capital augmenting":
2500:
2480:
2448:
2268:
2241:
2214:
2178:
2132:
2086:
2063:
1864:
1835:
1724:{\displaystyle y=m-A\prod _{i=1}^{n}a_{i}^{x_{i}}}
1723:
1636:
1563:
1463:
1364:
1268:
1239:
1006:
963:
934:
873:
847:
777:
748:
661:
620:
495:
373:
214:
165:
126:Harrod-neutral technology, or "labor augmenting":
116:
2094:denotes the cost per unit output, the unit cost,
1872:is the maximal yield (considers capacity limits).
2594:
1756:
1564:{\displaystyle Y=Ae^{a_{1}K+a_{2}L}K^{1-b}L^{b}}
1637:{\displaystyle Y=AK^{\alpha }L^{1-\alpha }-mL}
848:{\displaystyle \ Y=AK^{\alpha }L^{1-\alpha }}
225:
1830:
1759:
70:is the amount of physical output produced):
2229:, we derive the demand function for input
688:Linear production (or perfect substitutes)
1990:
1986:
528:
2569:Fuss, Melvyn, and Daniel McFadden, eds.
621:{\displaystyle Y=A^{\frac {1}{\gamma }}}
230:The elasticity of substitution between
2595:
2558:The Review of Economics and Statistics
984:, a linear approximation of CES via a
792:Cobb–Douglas production function
374:{\displaystyle \ \epsilon =\left^{-1}}
677:which includes the special cases of:
1577:Constant Marginal Value Share (CMS)
964:{\displaystyle \gamma \to -\infty }
535:Constant elasticity of substitution
506:
13:
2309:
2301:
1477:Transcendental Production Function
1464:{\displaystyle Y=AK^{av}^{(1-a)v}}
958:
647:
481:
455:
447:
421:
300:
274:
246:. The mathematical definition is:
14:
2619:
2179:{\displaystyle \sum _{i}b_{ij}=1}
1378:Some Exotic Production Functions
935:{\displaystyle \ Y={\text{Min}}}
2576:
2563:
2550:
2538:
2527:
2518:
1911:
1899:
1737:von Liebig Production Function
1453:
1441:
1437:
1418:
1346:
1319:
1234:
1228:
1196:
1190:
1181:
1175:
1150:
1144:
1112:
1106:
1084:
1078:
1056:
1050:
1038:
1032:
952:
929:
917:
865:
743:
737:
725:
713:
656:
641:
604:
590:
578:
559:
473:
461:
439:
427:
317:
303:
295:
277:
209:
194:
160:
145:
111:
99:
66:is a production function, and
1:
2511:
2133:{\displaystyle b_{ij}=b_{ji}}
49:
2584:Journal of political economy
2488:denotes the amount of input
888:Leontief production function
874:{\displaystyle \gamma \to 0}
7:
778:{\displaystyle \ \gamma =1}
662:{\displaystyle \gamma \in }
215:{\displaystyle \ Y=F(AK,L)}
166:{\displaystyle \ Y=F(K,AL)}
117:{\displaystyle \ Y=AF(K,L)}
23:that have been used in the
10:
2624:
794:(or imperfect complements)
226:Elasticity of substitution
77:, or "factor augmenting":
1007:{\displaystyle \gamma =0}
2215:{\displaystyle b_{yi}=0}
890:(or perfect complements)
75:Hicks-neutral technology
2502:
2482:
2450:
2385:
2270:
2243:
2216:
2180:
2134:
2088:
2065:
1881:Generalized Ozaki (GO)
1866:
1837:
1725:
1698:
1638:
1565:
1465:
1366:
1318:
1270:
1241:
1008:
965:
936:
875:
849:
779:
750:
663:
622:
529:Some widely used forms
497:
375:
216:
167:
118:
2586:79.3 (1971): 481-507.
2503:
2483:
2481:{\displaystyle a_{i}}
2451:
2365:
2271:
2269:{\displaystyle x_{i}}
2244:
2217:
2181:
2135:
2089:
2066:
1867:
1865:{\displaystyle Y^{*}}
1838:
1726:
1678:
1639:
1566:
1466:
1367:
1298:
1271:
1242:
1009:
966:
937:
876:
850:
780:
751:
749:{\displaystyle \ Y=A}
664:
623:
498:
376:
232:factors of production
217:
168:
119:
2603:Production economics
2508:per unit of output.
2492:
2465:
2282:
2253:
2233:
2190:
2144:
2098:
2078:
1893:
1849:
1747:
1660:
1587:
1487:
1393:
1286:
1260:
1023:
992:
946:
900:
859:
804:
760:
698:
632:
547:
391:
253:
179:
130:
81:
20:production functions
1720:
2498:
2478:
2446:
2445:
2266:
2239:
2212:
2176:
2156:
2130:
2084:
2061:
2001:
1926:
1862:
1833:
1721:
1699:
1634:
1561:
1461:
1362:
1266:
1237:
1004:
961:
932:
871:
845:
775:
746:
659:
618:
493:
371:
212:
163:
114:
2573:. Elsevier, 2014.
2501:{\displaystyle i}
2426:
2323:
2242:{\displaystyle i}
2147:
2087:{\displaystyle c}
2037:
1978:
1917:
1269:{\displaystyle z}
986:Taylor polynomial
915:
905:
809:
765:
703:
615:
488:
396:
355:
321:
258:
184:
135:
86:
2615:
2587:
2580:
2574:
2567:
2561:
2560:(1990): 649-656.
2554:
2548:
2542:
2536:
2531:
2525:
2522:
2507:
2505:
2504:
2499:
2487:
2485:
2484:
2479:
2477:
2476:
2455:
2453:
2452:
2447:
2444:
2443:
2442:
2441:
2427:
2425:
2424:
2415:
2410:
2409:
2400:
2398:
2397:
2384:
2379:
2360:
2359:
2358:
2357:
2340:
2339:
2324:
2322:
2321:
2320:
2307:
2299:
2294:
2293:
2275:
2273:
2272:
2267:
2265:
2264:
2248:
2246:
2245:
2240:
2227:Shephard's lemma
2225:By applying the
2221:
2219:
2218:
2213:
2205:
2204:
2185:
2183:
2182:
2177:
2169:
2168:
2155:
2139:
2137:
2136:
2131:
2129:
2128:
2113:
2112:
2093:
2091:
2090:
2085:
2070:
2068:
2067:
2062:
2060:
2056:
2055:
2054:
2053:
2052:
2038:
2036:
2035:
2026:
2025:
2016:
2014:
2013:
2000:
1974:
1973:
1964:
1963:
1962:
1961:
1939:
1938:
1925:
1871:
1869:
1868:
1863:
1861:
1860:
1842:
1840:
1839:
1834:
1826:
1825:
1813:
1812:
1797:
1796:
1784:
1783:
1771:
1770:
1730:
1728:
1727:
1722:
1719:
1718:
1717:
1707:
1697:
1692:
1643:
1641:
1640:
1635:
1624:
1623:
1608:
1607:
1570:
1568:
1567:
1562:
1560:
1559:
1550:
1549:
1534:
1533:
1529:
1528:
1513:
1512:
1470:
1468:
1467:
1462:
1460:
1459:
1417:
1416:
1371:
1369:
1368:
1363:
1361:
1360:
1359:
1358:
1344:
1343:
1331:
1330:
1317:
1312:
1276:) of each output
1275:
1273:
1272:
1267:
1246:
1244:
1243:
1238:
1224:
1223:
1214:
1213:
1168:
1167:
1140:
1139:
1130:
1129:
1099:
1098:
1071:
1070:
1013:
1011:
1010:
1005:
970:
968:
967:
962:
941:
939:
938:
933:
916:
913:
903:
880:
878:
877:
872:
854:
852:
851:
846:
844:
843:
828:
827:
807:
784:
782:
781:
776:
763:
755:
753:
752:
747:
701:
668:
666:
665:
660:
627:
625:
624:
619:
617:
616:
608:
602:
601:
574:
573:
512:Returns to scale
507:Returns to scale
502:
500:
499:
494:
489:
487:
480:
453:
446:
419:
394:
380:
378:
377:
372:
370:
369:
361:
357:
356:
354:
337:
333:
324:
322:
320:
313:
298:
272:
256:
221:
219:
218:
213:
182:
172:
170:
169:
164:
133:
123:
121:
120:
115:
84:
2623:
2622:
2618:
2617:
2616:
2614:
2613:
2612:
2608:Economics lists
2593:
2592:
2591:
2590:
2581:
2577:
2568:
2564:
2555:
2551:
2543:
2539:
2532:
2528:
2523:
2519:
2514:
2493:
2490:
2489:
2472:
2468:
2466:
2463:
2462:
2437:
2433:
2432:
2428:
2420:
2416:
2411:
2405:
2401:
2399:
2390:
2386:
2380:
2369:
2350:
2346:
2345:
2341:
2332:
2328:
2316:
2312:
2308:
2300:
2298:
2289:
2285:
2283:
2280:
2279:
2260:
2256:
2254:
2251:
2250:
2234:
2231:
2230:
2222:for all inputs.
2197:
2193:
2191:
2188:
2187:
2161:
2157:
2151:
2145:
2142:
2141:
2121:
2117:
2105:
2101:
2099:
2096:
2095:
2079:
2076:
2075:
2048:
2044:
2043:
2039:
2031:
2027:
2021:
2017:
2015:
2006:
2002:
1982:
1969:
1965:
1954:
1950:
1949:
1945:
1944:
1940:
1931:
1927:
1921:
1894:
1891:
1890:
1856:
1852:
1850:
1847:
1846:
1821:
1817:
1808:
1804:
1792:
1788:
1779:
1775:
1766:
1762:
1748:
1745:
1744:
1713:
1709:
1708:
1703:
1693:
1682:
1661:
1658:
1657:
1613:
1609:
1603:
1599:
1588:
1585:
1584:
1555:
1551:
1539:
1535:
1524:
1520:
1508:
1504:
1503:
1499:
1488:
1485:
1484:
1440:
1436:
1409:
1405:
1394:
1391:
1390:
1380:
1354:
1350:
1349:
1345:
1339:
1335:
1326:
1322:
1313:
1302:
1287:
1284:
1283:
1261:
1258:
1257:
1219:
1215:
1206:
1202:
1160:
1156:
1135:
1131:
1122:
1118:
1094:
1090:
1066:
1062:
1024:
1021:
1020:
993:
990:
989:
947:
944:
943:
912:
901:
898:
897:
860:
857:
856:
833:
829:
823:
819:
805:
802:
801:
761:
758:
757:
699:
696:
695:
633:
630:
629:
607:
603:
597:
593:
569:
565:
548:
545:
544:
537:(CES) function:
531:
509:
476:
454:
442:
420:
418:
392:
389:
388:
362:
338:
329:
325:
323:
309:
299:
273:
271:
270:
266:
265:
254:
251:
250:
228:
180:
177:
176:
131:
128:
127:
82:
79:
78:
52:
33:national income
29:national output
12:
11:
5:
2621:
2611:
2610:
2605:
2589:
2588:
2575:
2562:
2549:
2537:
2526:
2516:
2515:
2513:
2510:
2497:
2475:
2471:
2459:
2458:
2457:
2456:
2440:
2436:
2431:
2423:
2419:
2414:
2408:
2404:
2396:
2393:
2389:
2383:
2378:
2375:
2372:
2368:
2363:
2356:
2353:
2349:
2344:
2338:
2335:
2331:
2327:
2319:
2315:
2311:
2306:
2303:
2297:
2292:
2288:
2277:
2263:
2259:
2238:
2223:
2211:
2208:
2203:
2200:
2196:
2175:
2172:
2167:
2164:
2160:
2154:
2150:
2127:
2124:
2120:
2116:
2111:
2108:
2104:
2083:
2072:
2059:
2051:
2047:
2042:
2034:
2030:
2024:
2020:
2012:
2009:
2005:
1999:
1996:
1993:
1989:
1985:
1981:
1977:
1972:
1968:
1960:
1957:
1953:
1948:
1943:
1937:
1934:
1930:
1924:
1920:
1916:
1913:
1910:
1907:
1904:
1901:
1898:
1885:
1884:
1876:
1875:
1874:
1873:
1859:
1855:
1843:
1832:
1829:
1824:
1820:
1816:
1811:
1807:
1803:
1800:
1795:
1791:
1787:
1782:
1778:
1774:
1769:
1765:
1761:
1758:
1755:
1752:
1739:
1738:
1734:
1733:
1732:
1731:
1716:
1712:
1706:
1702:
1696:
1691:
1688:
1685:
1681:
1677:
1674:
1671:
1668:
1665:
1652:
1651:
1647:
1646:
1645:
1644:
1633:
1630:
1627:
1622:
1619:
1616:
1612:
1606:
1602:
1598:
1595:
1592:
1579:
1578:
1574:
1573:
1572:
1571:
1558:
1554:
1548:
1545:
1542:
1538:
1532:
1527:
1523:
1519:
1516:
1511:
1507:
1502:
1498:
1495:
1492:
1479:
1478:
1474:
1473:
1472:
1471:
1458:
1455:
1452:
1449:
1446:
1443:
1439:
1435:
1432:
1429:
1426:
1423:
1420:
1415:
1412:
1408:
1404:
1401:
1398:
1385:
1384:
1379:
1376:
1375:
1374:
1373:
1372:
1357:
1353:
1348:
1342:
1338:
1334:
1329:
1325:
1321:
1316:
1311:
1308:
1305:
1301:
1297:
1294:
1291:
1278:
1277:
1265:
1250:
1249:
1248:
1247:
1236:
1233:
1230:
1227:
1222:
1218:
1212:
1209:
1205:
1201:
1198:
1195:
1192:
1189:
1186:
1183:
1180:
1177:
1174:
1171:
1166:
1163:
1159:
1155:
1152:
1149:
1146:
1143:
1138:
1134:
1128:
1125:
1121:
1117:
1114:
1111:
1108:
1105:
1102:
1097:
1093:
1089:
1086:
1083:
1080:
1077:
1074:
1069:
1065:
1061:
1058:
1055:
1052:
1049:
1046:
1043:
1040:
1037:
1034:
1031:
1028:
1015:
1014:
1003:
1000:
997:
978:
977:
976:
975:
974:
973:
972:
971:
960:
957:
954:
951:
931:
928:
925:
922:
919:
911:
908:
892:
891:
884:
883:
882:
881:
870:
867:
864:
842:
839:
836:
832:
826:
822:
818:
815:
812:
796:
795:
788:
787:
786:
785:
774:
771:
768:
745:
742:
739:
736:
733:
730:
727:
724:
721:
718:
715:
712:
709:
706:
690:
689:
681:
680:
679:
678:
672:
671:
670:
669:
658:
655:
652:
649:
646:
643:
640:
637:
614:
611:
606:
600:
596:
592:
589:
586:
583:
580:
577:
572:
568:
564:
561:
558:
555:
552:
539:
538:
530:
527:
526:
525:
522:
519:
508:
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504:
503:
492:
486:
483:
479:
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472:
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463:
460:
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452:
449:
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441:
438:
435:
432:
429:
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417:
414:
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405:
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399:
382:
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368:
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353:
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344:
341:
336:
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328:
319:
316:
312:
308:
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297:
294:
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288:
285:
282:
279:
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269:
264:
261:
227:
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211:
208:
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199:
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173:
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113:
110:
107:
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98:
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92:
89:
51:
48:
9:
6:
4:
3:
2:
2620:
2609:
2606:
2604:
2601:
2600:
2598:
2585:
2579:
2572:
2566:
2559:
2553:
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2535:
2530:
2521:
2517:
2509:
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2473:
2469:
2438:
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2329:
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2304:
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2206:
2201:
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2173:
2170:
2165:
2162:
2158:
2152:
2148:
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2122:
2118:
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2106:
2102:
2081:
2073:
2057:
2049:
2045:
2040:
2032:
2028:
2022:
2018:
2010:
2007:
2003:
1997:
1994:
1991:
1987:
1983:
1979:
1975:
1970:
1966:
1958:
1955:
1951:
1946:
1941:
1935:
1932:
1928:
1922:
1918:
1914:
1908:
1905:
1902:
1896:
1889:
1888:
1887:
1886:
1882:
1878:
1877:
1857:
1853:
1844:
1827:
1822:
1818:
1814:
1809:
1805:
1801:
1798:
1793:
1789:
1785:
1780:
1776:
1772:
1767:
1763:
1753:
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1741:
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1714:
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1596:
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1263:
1255:
1252:
1251:
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1220:
1216:
1210:
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1199:
1193:
1187:
1184:
1178:
1172:
1169:
1164:
1161:
1157:
1153:
1147:
1141:
1136:
1132:
1126:
1123:
1119:
1115:
1109:
1103:
1100:
1095:
1091:
1087:
1081:
1075:
1072:
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1063:
1059:
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1019:
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1016:
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906:
896:
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893:
889:
886:
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862:
840:
837:
834:
830:
824:
820:
816:
813:
810:
800:
799:
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797:
793:
790:
789:
772:
769:
766:
740:
734:
731:
728:
722:
719:
716:
710:
707:
704:
694:
693:
692:
691:
687:
686:
685:
684:
683:
682:
676:
675:
674:
673:
653:
650:
644:
638:
635:
612:
609:
598:
594:
587:
584:
581:
575:
570:
566:
562:
556:
553:
550:
543:
542:
541:
540:
536:
533:
532:
523:
520:
517:
516:
515:
513:
490:
484:
477:
470:
467:
464:
458:
450:
443:
436:
433:
430:
424:
415:
412:
409:
406:
403:
400:
397:
387:
386:
385:
366:
363:
358:
351:
348:
345:
342:
339:
334:
330:
326:
314:
310:
306:
292:
289:
286:
283:
280:
267:
262:
259:
249:
248:
247:
245:
241:
237:
233:
206:
203:
200:
197:
191:
188:
185:
174:
157:
154:
151:
148:
142:
139:
136:
125:
108:
105:
102:
96:
93:
90:
87:
76:
73:
72:
71:
69:
65:
61:
57:
47:
45:
41:
36:
34:
30:
26:
22:
21:
2583:
2578:
2570:
2565:
2557:
2552:
2540:
2529:
2520:
2460:
510:
383:
239:
235:
229:
67:
63:
60:scale factor
55:
53:
37:
17:
15:
1254:Stone-Geary
2597:Categories
2512:References
50:Technology
16:This is a
2374:≠
2367:∑
2310:∂
2302:∂
2149:∑
1995:≠
1980:∑
1919:∑
1858:∗
1819:β
1806:β
1790:β
1777:β
1768:∗
1680:∏
1673:−
1626:−
1621:α
1618:−
1605:α
1544:−
1448:−
1352:α
1333:−
1300:∏
1226:
1188:
1173:
1142:
1104:
1076:
1048:
1030:
996:γ
959:∞
956:−
953:→
950:γ
866:→
863:γ
841:α
838:−
825:α
767:γ
735:α
732:−
717:α
648:∞
645:−
639:∈
636:γ
613:γ
599:γ
588:α
585:−
571:γ
563:α
482:∂
456:∂
448:∂
422:∂
416:−
364:−
301:∂
275:∂
260:ϵ
42:(K), and
25:economics
982:Translog
244:isoquant
18:list of
628:, with
514:can be
40:capital
2461:Here,
2140:, and
2074:where
1845:where
988:about
904:
808:
764:
702:
395:
257:
183:
134:
85:
942:when
855:when
756:when
58:is a
44:labor
1879:The
238:and
31:and
1757:min
914:Min
2599::
2249:,
1217:ln
1185:ln
1170:ln
1133:ln
1101:ln
1073:ln
1045:ln
1027:ln
62:,
2496:i
2474:i
2470:a
2439:y
2435:b
2430:y
2422:j
2418:p
2413:/
2407:i
2403:p
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2326:=
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2276::
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2207:=
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2195:b
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2166:j
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2115:=
2110:j
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2071:.
2058:)
2050:y
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2041:y
2033:j
2029:p
2023:i
2019:p
2011:j
2008:i
2004:b
1998:i
1992:j
1988::
1984:j
1976:+
1971:i
1967:p
1959:i
1956:y
1952:b
1947:y
1942:(
1936:i
1933:i
1929:b
1923:i
1915:=
1912:)
1909:y
1906:,
1903:p
1900:(
1897:C
1854:Y
1831:}
1828:K
1823:4
1815:+
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1799:L
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1760:{
1754:=
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1667:=
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1594:=
1591:Y
1557:b
1553:L
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1541:1
1537:K
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1526:2
1522:a
1518:+
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1510:1
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1501:e
1497:A
1494:=
1491:Y
1457:v
1454:)
1451:a
1445:1
1442:(
1438:]
1434:K
1431:a
1428:b
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1419:[
1414:v
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1407:K
1403:A
1400:=
1397:Y
1356:i
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1341:i
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1320:(
1315:n
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1307:=
1304:i
1296:A
1293:=
1290:Y
1264:z
1235:)
1232:K
1229:(
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1208:K
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1191:(
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1079:(
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1054:A
1051:(
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1036:Y
1033:(
1002:0
999:=
930:]
927:L
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921:K
918:[
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729:1
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428:(
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304:(
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278:(
268:[
263:=
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207:L
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198:A
195:(
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189:=
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161:)
158:L
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152:,
149:K
146:(
143:F
140:=
137:Y
112:)
109:L
106:,
103:K
100:(
97:F
94:A
91:=
88:Y
68:Y
64:F
56:A
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