Let a firm’s production function be f(K,L) = √2K1/2L1/2. a) Solve for the contingent demand functions for Kand L. b) Substitute the contingent demand functions in the total cost that you minimized in part a) to obtain the total cost function. c) Find the minimal amount of Kand Lnecessary to produce Q= 8 when v= 2 and w= 1 (with minimal possible cost).
Let a firm’s production function be f(K,L) = √2K1/2L1/2. a) Solve for the contingent demand functions for Kand L. b) Substitute the contingent demand functions in the total cost that you minimized in part a) to obtain the total cost function. c) Find the minimal amount of Kand Lnecessary to produce Q= 8 when v= 2 and w= 1 (with minimal possible cost).
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.7P
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Question
Let a firm’s production function be f(K,L) = √2K1/2L1/2.
a) Solve for the contingent demand functions for Kand L.
b) Substitute the contingent demand functions in the total cost that you minimized in part
a) to obtain the total cost function.
c) Find the minimal amount of Kand Lnecessary to produce Q= 8 when v= 2 and
w= 1 (with minimal possible cost).
d) Suppose the price wincreases from 1 to 2. What happens to the demands for Kand
Land the total cost?
e) Explain the difference in results between your answers to part d) in this question and
the previous question. Why do the impacts on demands and costs differ?
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