A firm employs a Cobb-Douglas production function of the form Y = K04L04. The output price is P and the input prices are r and w for K and L, respectively. a. Set up the firm's profit maximization problem and find the input demands for K and L b. Derive the firm's output supply function c. Derive the firm's profit function

A firm employs a Cobb-Douglas production function of the form Y = K04L04. The output price is P and the input prices are r and w for K and L, respectively. a. Set up the firm's profit maximization problem and find the input demands for K and L b. Derive the firm's output supply function c. Derive the firm's profit function

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 6E

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Each firm in a perfectly competitive industry has the following production function: q = K1/4L1/4 Each firm takes factor prices as given. Factor prices are r = 4, w = 16 Suppose firms in this industry face a recurring fixed cost FC=144, ie, firms face a fixed cost FC=144 in the long run. Rewrite long run MC(q) and AC(q) functions and then find the long run equilibrium price.
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Suppose the short-run cost function of a perfectly competitive firm is: C(q)= 193/8q - 1/2q2+ 2/3q3+100 In addition, there is a tax of t per unit produced. Solve for the firm's short-run supply function q(p,t). Be sure to show every step.
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Each firm in a perfectly competitive industry has the following production function: q = K1/4L1/4 Each firm takes factor prices as given. Factor prices are r = 4, w = 16 Suppose the market demand is given by QD = 900 − P How many firms are there in the industry in the long run?