Exercise 4 A firm operates with production function q(L, K) = LK². The manager has been given the following production target: "Produce 8,000 units per day." He knows that the rental day price of capital is r = $400 per unit. The wage paid to each worker is w = $200. a) Currently, the firm is operating in the short run. They employ 80 workers per day (i.e., I = 80). Find the amount of capital the firm must rent to produce the firm's production target of 8,000 units per day. [Hint: Solve the firm's cost minimization problem (CMP) in the short run]. b) What is the firm's daily total cost if they rent just enough capital to produce the required output target in the short run? [Hint: Compute the total cost for the firm after solving the CMP in part (a)] c) Compare the marginal product per dollar sent on L and on K when the firm operates in the short run using the input choice found in part (a). What does this suggest about the way the firm might change their choice of L and K if they want to reduce the total cost in meeting production target?

Exercise 4 A firm operates with production function q(L, K) = LK². The manager has been given the following production target: "Produce 8,000 units per day." He knows that the rental day price of capital is r = $400 per unit. The wage paid to each worker is w = $200. a) Currently, the firm is operating in the short run. They employ 80 workers per day (i.e., I = 80). Find the amount of capital the firm must rent to produce the firm's production target of 8,000 units per day. [Hint: Solve the firm's cost minimization problem (CMP) in the short run]. b) What is the firm's daily total cost if they rent just enough capital to produce the required output target in the short run? [Hint: Compute the total cost for the firm after solving the CMP in part (a)] c) Compare the marginal product per dollar sent on L and on K when the firm operates in the short run using the input choice found in part (a). What does this suggest about the way the firm might change their choice of L and K if they want to reduce the total cost in meeting production target?

Economics:

10th Edition

ISBN:9781285859460

Author:BOYES, William

Publisher:BOYES, William

Chapter29: Resource Markets

Section: Chapter Questions

Problem 3E

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