The production function for a product is given by q= 10K^(1/2)L^(1/2) where K is capital, and Lis labor and q is output. a) Find the marginal product of labor and the marginal product of capital. b) Find the marginal rate of technical substitution between labor and capital. c) Denote the wage of labor by w and the rental of capital by r. What is the cost minimization condition for a firm? Show it diagrammatically. d) Now suppose w =30 and r= 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) Part A, B, C
The production function for a product is given by q= 10K^(1/2)L^(1/2) where K is capital, and Lis labor and q is output. a) Find the marginal product of labor and the marginal product of capital. b) Find the marginal rate of technical substitution between labor and capital. c) Denote the wage of labor by w and the rental of capital by r. What is the cost minimization condition for a firm? Show it diagrammatically. d) Now suppose w =30 and r= 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) Part A, B, C
Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter7: Production And Cost In The Firm
Section: Chapter Questions
Problem 19PAE
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The production function for a product is given by
q= 10K^(1/2)L^(1/2)
where K is capital, and
Lis labor and q is output.
a) Find the marginal product of labor and the marginal product of capital.
b) Find the marginal rate of technical substitution between labor and capital.
c) Denote the wage of labor by w and the rental of capital by r.
What is the cost
minimization condition for a firm? Show it diagrammatically.
d) Now suppose
w =30 and
r= 120. What is the minimum cost of producing
q=1000.
(You must show your work by clearly writing the equations that you use to derive the cost
minimizing levels of L and K.)
Part A, B, C
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