Assume that the production function for a certain production process is given by the following Cobb-Douglas production function: Q = f(K,L) KZL² a) What is the expression for the marginal product of K (capital) at the point (K, L)? = b) For small increases in K, holding L constant, does the marginal product of K increase, decrease or stay constant? c) What is the marginal product of L (labour)? d) Using your own words, briefly explain the definition of marginal rate of technical substitution. Calculate the marginal rate of technical substitution between K and L. e) Does the production function exhibit increasing, decreasing or constant returns to scale? Explain your answer.
Assume that the production function for a certain production process is given by the following Cobb-Douglas production function: Q = f(K,L) KZL² a) What is the expression for the marginal product of K (capital) at the point (K, L)? = b) For small increases in K, holding L constant, does the marginal product of K increase, decrease or stay constant? c) What is the marginal product of L (labour)? d) Using your own words, briefly explain the definition of marginal rate of technical substitution. Calculate the marginal rate of technical substitution between K and L. e) Does the production function exhibit increasing, decreasing or constant returns to scale? Explain your answer.
Microeconomics A Contemporary Intro
10th Edition
ISBN:9781285635101
Author:MCEACHERN
Publisher:MCEACHERN
Chapter7: Production And Cost In The Firm
Section7.A: Appendix: A Closer Look At Production And Cost
Problem 1AQ
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Part D E
Transcribed Image Text:Assume that the production function for a certain production process is given by the
following Cobb-Douglas production function:
Q = f(K,L) K²L²
a) What is the expression for the marginal product of K (capital) at the point (K, L)?
=
b) For small increases in K, holding L constant, does the marginal product of K
increase, decrease or stay constant?
c) What is the marginal product of L (labour)?
d) Using your own words, briefly explain the definition of marginal rate of technical
substitution. Calculate the marginal rate of technical substitution between K and L.
e) Does the production function exhibit increasing, decreasing or constant returns to
scale? Explain your answer.
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