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., L = 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? d) In the long run, how much L and K should the firm choose if they want to minimize the cost of producing 8,000 unis of output per day? [Hint: Solve the CMP in the long run in which the firm can decide how much of both inputs use] e) How much money is the firm sacrificing by not having the ability to choose its level of capital in the short run? [Hint: Compute the firm's total cost of production in the long run using the optimal input combination you found in part (d) and compare it against the total cost in the short run you found in part (b)]
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., L = 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? d) In the long run, how much L and K should the firm choose if they want to minimize the cost of producing 8,000 unis of output per day? [Hint: Solve the CMP in the long run in which the firm can decide how much of both inputs use] e) How much money is the firm sacrificing by not having the ability to choose its level of capital in the short run? [Hint: Compute the firm's total cost of production in the long run using the optimal input combination you found in part (d) and compare it against the total cost in the short run you found in part (b)]
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Show full answers and steps to part d) & e)
![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., L
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?
d) In the long run, how much L and K should the firm choose if they want to minimize the
cost of producing 8,000 unis of output per day? [Hint: Solve the CMP in the long run in
which the firm can decide how much of both inputs use]
e) How much money is the firm sacrificing by not having the ability to choose its level of
capital in the short run? [Hint: Compute the firm's total cost of production in the long run
using the optimal input combination you found in part (d) and compare it against the total
cost in the short run you found in part (b)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefc33442-7cfa-4638-8981-250e26e6d90c%2Fdc33e77e-1931-47a4-8a43-57ac86c6e03f%2Fiah33uxd_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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., L
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?
d) In the long run, how much L and K should the firm choose if they want to minimize the
cost of producing 8,000 unis of output per day? [Hint: Solve the CMP in the long run in
which the firm can decide how much of both inputs use]
e) How much money is the firm sacrificing by not having the ability to choose its level of
capital in the short run? [Hint: Compute the firm's total cost of production in the long run
using the optimal input combination you found in part (d) and compare it against the total
cost in the short run you found in part (b)]
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