Returns to scale in production: Do the following production functions exhibitincreasing, constant, or decreasing returns to scale in K and L? (Assume Ais some fxed positive number.)(a) Y = K1/2L1/2(b) Y = K2/3L2/3(c) Y = K1/3L1/2(d) Y = K + L(e) Y = K + K1/3L1/3 (f ) Y = K 1/3L2/3 + A (g) Y = K 1/3L2/3 − A

Returns to scale in production: Do the following production functions exhibitincreasing, constant, or decreasing returns to scale in K and L? (Assume Ais some fxed positive number.)(a) Y = K1/2L1/2(b) Y = K2/3L2/3(c) Y = K1/3L1/2(d) Y = K + L(e) Y = K + K1/3L1/3 (f ) Y = K 1/3L2/3 + A (g) Y = K 1/3L2/3 − A

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 1.5CE

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Returns to scale in production: Recall that a production function F(K, L) exhibits constant returns to scale if doubling the inputs leads to a doubling of output. If it leads to more than doubling of output, there are increasing returns to scale; if it leads to less than doubling of output, there are decreasing returns to scale. The answers to parts (a) and (f) are worked out below. (a) Y = K1/2L1/2. If we double K and L, output is (2K) 1/2(2L) 1/2 = 21/221/2K1/2L1/2 = 21/2+1/2K1/2L1/2 = 2K1/2L1/2. So output exactly doubles, and there are constant returns to scale. (b) Y = K1/3L2/3 + . This production function says you get units of output “for free,” that is, even if there is no capital and no labor. Then you produce on top of that with a Cobb-Douglas production function. If we double K and L, output is Notice that the first term is doubled, but the output we got for free (the A) is left unchanged. Therefore, output is less than doubled, and this…
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