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A plant's production function is Q = 2KL. For this production function, MPK = 2L and MPL = 2K. The price of labor, w, is $4 and of capital, r, is $6 per unit. a) In the short run, the plant's capital is fixed at R = 5. Find the amount of labor it must employ to produce Q = 300 units of output. b) How much money is the firm losing by not having the ability to choose its level of capital optimally? Hint: Solve the long run cost minimization problem (where the firm can choose its level of both capital and labor) and compare the cost of the solution with the cost of the inputs used in the answer to part a.

A plant's production function is Q = 2KL. For this production function, MPK = 2L and MPL = 2K. The price of labor, w, is $4 and of capital, r, is $6 per unit. a) In the short run, the plant's capital is fixed at R = 5. Find the amount of labor it must employ to produce Q = 300 units of output. b) How much money is the firm losing by not having the ability to choose its level of capital optimally? Hint: Solve the long run cost minimization problem (where the firm can choose its level of both capital and labor) and compare the cost of the solution with the cost of the inputs used in the answer to part a.

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Mainly concerned with how to answer part b.

A plant’s production function is \( Q = 2KL \). For this production function, \( MP_K = 2L \) and \( MP_L = 2K \). The price of labor, \( w \), is $4 and of capital, \( r \), is $6 per unit. a) In the short run, the plant’s capital is fixed at \( \overline{K} = 5 \). Find the amount of labor it must employ to produce \( Q = 300 \) units of output. b) How much money is the firm losing by not having the ability to choose its level of capital optimally? *Hint: Solve the long-run cost minimization problem (where the firm can choose its level of both capital and labor) and compare the cost of the solution with the cost of the inputs used in the answer to part a.*
Transcribed Image Text:A plant’s production function is \( Q = 2KL \). For this production function, \( MP_K = 2L \) and \( MP_L = 2K \). The price of labor, \( w \), is $4 and of capital, \( r \), is $6 per unit. a) In the short run, the plant’s capital is fixed at \( \overline{K} = 5 \). Find the amount of labor it must employ to produce \( Q = 300 \) units of output. b) How much money is the firm losing by not having the ability to choose its level of capital optimally? *Hint: Solve the long-run cost minimization problem (where the firm can choose its level of both capital and labor) and compare the cost of the solution with the cost of the inputs used in the answer to part a.*
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