Consider the following production function: q = (KL)ª, where a > 0. Answer the following questions: (a) Under what conditions (i.e. values of a) will the production function exhibit decreasing returns to scale? Under what conditions will it exhibit constant returns to scale? Under what circumstances will it exhibit increasing returns to scale? (b) Confirm that the marginal physical product of capital is homogenous of degree zero in the case in which the production function exhibits constant returns to scale. (c) Derive an expression for the cost function of a firm using the production function to produce output of a good.

Consider the following production function: q = (KL)ª, where a > 0. Answer the following questions: (a) Under what conditions (i.e. values of a) will the production function exhibit decreasing returns to scale? Under what conditions will it exhibit constant returns to scale? Under what circumstances will it exhibit increasing returns to scale? (b) Confirm that the marginal physical product of capital is homogenous of degree zero in the case in which the production function exhibits constant returns to scale. (c) Derive an expression for the cost function of a firm using the production function to produce output of a good.

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

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Chapter1: Making Economics Decisions

Section: Chapter Questions

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