【正文】 ctSubstitutes Technologies A perfectsubstitutes production function is of the form y a x a x a xn n? ? ? ?1 1 2 2 ? .y x x? ?1 23n a a n d a? ? ?2 1 31 2, .14 14 PerfectSubstitution Technologies 9 3 18 6 24 8 x1 x2 x1 + 3x2 = 9 x1 + 3x2 = 18 x1 + 3x2 = 24 y x x? ?1 2315 15 有限種投入比的技術 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 1x2xR1 X2:X1=8:1 R2 X2:X1=3:1 R3 X2:X1=1:1 R4 X2:X1=1:4 ?現(xiàn)有 6單位 x1和 3單位 x2 ?2單位 x1和 2單位 x2用于R3，生產產品 50單位； ?4單位 x1和 1單位 x2用于 R4，生產產品50單位 產量 100單位的等產量線 16 16 Marginal (Physical) Products The marginal product of input i is the rateofchange of the output level as the level of input i changes, holding all other input levels fixed. That is, y f x x n? ( , , )1 ?ii xyMP???17 17 Marginal (Physical) Products y f x x x x? ?( , ) /1 2 11/ 3 22 3MP yx x x1112 322 313? ????/ /MP yx x x2211/ 321/ 323? ???? .18 18 ReturnstoScale Marginal products describe the change in output level as a single input level changes. Returnstoscale describes how the output level changes as all input levels change in direct proportion (. all input levels doubled, or halved). 19 19 Constant 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 described by the production function f exhibits constant returnstoscale. . (k = 2) doubling all input levels doubles the output level. 20 20 Constant returnstoscale y = f(x) 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