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?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Show full answers and steps to part a) b) & c)
![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
2
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%2Fa3574180-5be7-46af-9f18-c1fbb9ec682c%2F1b05914c-8bfc-4de6-a0ce-99b7f7e5680b%2F6ype5u4_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
2
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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