A firm has the following Cobb-Douglas production function: q=(L^α)(K^1-α) 0<α < 1 is a parameter. Suppose 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 α and q). (b) Derive the average variable cost of the firm (expressed in terms of α and q). (c) Derive the cost function of the firm.
A firm has the following Cobb-Douglas production function: q=(L^α)(K^1-α) 0<α < 1 is a parameter. Suppose 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 α and q). (b) Derive the average variable cost of the firm (expressed in terms of α and q). (c) Derive the cost function of the firm.
Chapter11: Profit Maximization
Section: Chapter Questions
Problem 11.3P
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A firm has the following Cobb-Douglas production function: q=(L^α)(K^1-α)
0<α < 1 is a parameter. Suppose 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 α and q).
(b) Derive the
(c) Derive the cost function of the firm.
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