(a) Show that the production function Q = (Kα + Lα)β, where Q is output, K is capital input, L islabour input and α > 0 and β > 0 exhibits diminishing returns when α < 1 and increasing returns to scale when αβ > 1.

(a) Show that the production function Q = (Kα + Lα)β, where Q is output, K is capital input, L islabour input and α > 0 and β > 0 exhibits diminishing returns when α < 1 and increasing returns to scale when αβ > 1.

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 6E

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Question

(a) Show that the production function Q = (K^α + L^α)^β, where Q is output, K is capital input, L islabour input and α > 0 and β > 0 exhibits diminishing returns when α < 1 and increasing returns to scale when αβ > 1.
(b) Specify a translog cost function for two inputs and show that the input shares depend on input
prices.

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