生產(chǎn)技術(shù)與利潤最大化(完整版)
【正文】 x’ x Input Level Output Level y’ 2x’ 2y’ Constant returnstoscale 21 21 Diminishing returnstoscale If, for any input bundle (x1,…,x n), f kx kx kx kf x x xn n( , , , ) ( , , , )1 2 1 2? ??then the technology exhibits diminishing returnstoscale. . (k = 2) doubling all input levels less than doubles the output level. 22 22 Diminishing returnstoscale y = f(x) x’ x Input Level Output Level f(x’) 2x’ f(2x’) 2f(x’) Decreasing returnstoscale 23 23 Increasing returnstoscale If, for any input bundle (x1,…,x n), f kx kx kx kf x x xn n( , , , ) ( , , , )1 2 1 2? ??then the technology exhibits increasing returnstoscale. . (k = 2) doubling all input levels more than doubles the output level. 24 24 Increasing returnstoscale y = f(x) x’ x Input Level Output Level f(x’) 2x’ f(2x’) 2f(x’) Increasing returnstoscale 25 25 ReturnstoScale y = f(x) x Input Level Output Level Decreasing returnstoscale Increasing returnstoscale 26 26 Examples of ReturnstoScale y a x a x a xn n? ? ? ?1 1 2 2 ? .The perfectsubstitutes production function is a kx a kx a kxk a x a x a xkyn nn n1 1 2 21 1 2 2( ) ( ) ( )( ).? ? ?? ? ? ????The perfectsubstitutes production function exhibits constant returnstoscale. 27 27 Examples 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
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