22. Consider the following production function: Q = 8K³/4¹/2, with capital (K) and labour (L) as the two inputs. (a) Find the marginal products of capital and labour and comment on whether they reflect increasing, constant or decreasing marginal returns. What type of returns to scale does the production function exhibit? (b) What are the average products of capital and labour and what happens to them as inputs increase? How do the marginal and average products relate to each other? Provide an intuitive explanation as to whether this relationship is as you would expect. (c) Assuming that the prices of Labour and Capital are w and r respectively, find the optimal conditional input demands of capital and labour. (d) Suppose that the firm must keep output at the original level, Qo, but that the price of labour, w, falls. By drawing a diagram, illustrate and explain how the firm's optimal inputs would change and what this would mean for the firm's demand curve for labour.
22. Consider the following production function: Q = 8K³/4¹/2, with capital (K) and labour (L) as the two inputs. (a) Find the marginal products of capital and labour and comment on whether they reflect increasing, constant or decreasing marginal returns. What type of returns to scale does the production function exhibit? (b) What are the average products of capital and labour and what happens to them as inputs increase? How do the marginal and average products relate to each other? Provide an intuitive explanation as to whether this relationship is as you would expect. (c) Assuming that the prices of Labour and Capital are w and r respectively, find the optimal conditional input demands of capital and labour. (d) Suppose that the firm must keep output at the original level, Qo, but that the price of labour, w, falls. By drawing a diagram, illustrate and explain how the firm's optimal inputs would change and what this would mean for the firm's demand curve for labour.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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