Let the production function be Q = 4∗K1/4L1/4 assume that both factors are variable. (a) Derive the contingent demand functions for K and L (b) Substitute the contingent demand functions in the total cost that you minimized in part a) to obtain the total cost function. (c) FindtheamountofKandLnecessarytoproduceQ=8whenv=16andw=1 (with minimal possible cost). (d) Find the average and marginal cost functions.
Let the production function be Q = 4∗K1/4L1/4 assume that both factors are variable. (a) Derive the contingent demand functions for K and L (b) Substitute the contingent demand functions in the total cost that you minimized in part a) to obtain the total cost function. (c) FindtheamountofKandLnecessarytoproduceQ=8whenv=16andw=1 (with minimal possible cost). (d) Find the average and marginal cost functions.
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.7P
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Question
Let the production function be Q = 4∗K1/4L1/4 assume that both factors are variable.
-
(a) Derive the contingent
demand functions for K and L -
(b) Substitute the contingent demand functions in the total cost that you minimized in part a) to obtain the total cost function.
-
(c) FindtheamountofKandLnecessarytoproduceQ=8whenv=16andw=1 (with minimal possible cost).
-
(d) Find the average and marginal cost functions.
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