A firm's technology is characterized by a Cobb - Douglas production function of the form 1 1 y = f(K.L) = 2K² + 1² a. The output price is p, and the input prices are r and w for K and L, respectively. Set up the problem for a profit - maximizing firm and solve for the factor demand functions for K and L. b. Find the firm's supply function. c. Find the firm's profit function. d. Assume

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A firm's technology is characterized by a Cobb - Douglas production function of the form
1
1
y = f(K,L) = 2K² + 1² a. The output price is p, and the input prices are r and w for K and L,
respectively. Set up the problem for a profit - maximizing firm and solve for the factor demand
functions for K and L. b. Find the firm's supply function. c. Find the firm's profit function. d. Assume
now that p = 2, r = 1, and w = 1. Using the functions you have found in parts (a), (b) and (c),
calculate the profit - maximizing levels of the factors and (K* and L*), the profit - maximizing output
level (v) and the maximum profit of the firm (). Please solve it by explaining and explaining.
Transcribed Image Text:A firm's technology is characterized by a Cobb - Douglas production function of the form 1 1 y = f(K,L) = 2K² + 1² a. The output price is p, and the input prices are r and w for K and L, respectively. Set up the problem for a profit - maximizing firm and solve for the factor demand functions for K and L. b. Find the firm's supply function. c. Find the firm's profit function. d. Assume now that p = 2, r = 1, and w = 1. Using the functions you have found in parts (a), (b) and (c), calculate the profit - maximizing levels of the factors and (K* and L*), the profit - maximizing output level (v) and the maximum profit of the firm (). Please solve it by explaining and explaining.
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