生產(chǎn)技術(shù)與利潤(rùn)最大化(1)-全文預(yù)覽
【正文】 of ReturnstoScale y a x a x a xn n? m i n { , , , }.1 1 2 2 ?The perfectplements production function is m in{ ( ), ( ), , ( )}( m in{ , , , }).a kx a kx a kxk a x a x a xkyn nn n1 1 2 21 1 2 2????The perfectplements production function exhibits constant returnstoscale. 28 28 Examples of ReturnstoScale y x x xa a na n? 1 21 2 ? .The CobbDouglas production function is ( ) ( ) ( ).kx kx kxk k k x x xk x x xk ya anaa a a a a aa a a a anaa ann nn nn1 21 21 21 2 1 21 2 1 21?? ???????? ? ?? ?29 29 Examples of ReturnstoScale The CobbDouglas technology’s returnstoscale is constant if a1+ … + a n = 1 increasing if a1+ … + a n 1 decreasing if a1+ … + a n 1 30 30 Question and answer Q: 在邊際產(chǎn)出遞減的情況下，是否能存在規(guī)模報(bào)酬遞增現(xiàn)象？ A: Yes. . y x x? 12 3 22 3/ / .31 31 ReturnstoScale MP x x1 1 1/ 3 22 323? ? /diminishes as x1 increases MP x x2 12 3 2 1/ 323? ?/diminishes as x1 increases ?所以，即使邊際產(chǎn)出是遞減的，規(guī)模報(bào)酬也可能是遞增的。 36 36 長(zhǎng)期和短期 y x x? 11/ 3 21/ 3 is the longrun production function (both x1 and x2 are variable). The shortrun production function when x2 ? 1 is .x1xy3/113/13/11 ??The shortrun production function when x2 ? 10 is .x15210xy 3/113/13/11 ???37 37 x1 y 3/13/11 10xy ?3/13/11 5xy ?3/13/11 2xy ?3/13/11 1xy ?長(zhǎng)期和短期 Four shortrun production functions. 38 38 ProfitMaximization Economic Profit 廠商用投入 j = 1…,m 生產(chǎn)產(chǎn)品 i = 1,…n. 產(chǎn)出水平 y1,…,y n，投入水平 x1,…,x m. 產(chǎn)品價(jià)格 p1,…,p n，投入價(jià)格 w1,…,w m. 廠商是價(jià)格接受者，即 p1,…,p n 和 w1,…,w m 給定。 A CobbDouglas Example 1 / 3 1 / 312y x x? 2 / 3 1 / 31 1 2113yM P x xx?????* 2 / 3 1 / 31 1 1 2 1()3pM R P p M P x x w?? ? ? ?3 / 2* 1 / 21213pxx
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