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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter11: Profit Maximization

Section: Chapter Questions

Problem 11.3P

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