A firm has the following Cobb-Douglas production function: q = LªK!-a, where 0 < a <1 is a parameter. Suppose that in the short run K = 1. The rental rate of a unit of K is $10, and the wage rate of a unit of L is $20. (a) Derive the marginal cost of the firm (expressed in terms of a and q). (b) Derive the average variable cost of the firm (expressed in terms of a and q). (c) Derive the cost function of the firm.

A firm has the following Cobb-Douglas production function: q = LªK!-a, where 0 < a <1 is a parameter. Suppose that in the short run K = 1. The rental rate of a unit of K is $10, and the wage rate of a unit of L is $20. (a) Derive the marginal cost of the firm (expressed in terms of a and q). (b) Derive the average variable cost of the firm (expressed in terms of a and q). (c) Derive the cost function of the firm.

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Problem 1QTC

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Question

2. A firm has the following Cobb-Douglas production function: q = LªK!-a, where 0 <
a <1 is a parameter. Suppose that in the short run K = 1. The rental rate of a unit of
K is $10, and the wage rate of a unit of L is $20.
(a) Derive the marginal cost of the firm (expressed in terms of a and q).
(b) Derive the average variable cost of the firm (expressed in terms of a and q).
(c) Derive the cost function of the firm.

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