2) A firm producing hockey sticks has a production function given by: 2\KL. Suppose Capital stock is fixed at K in the short-run. The rental rate for K is v, and the wage rate for L is w. a.) Show the firm's short-run total costs as a function of q, w, v, and K. b.) Given q, w, v, how should the capital stock be chosen to minimize total cost in the long run? c.) Use your results from part b to have the long-run total cost function. d.) For w = $4, v = $1, graph the long-run total cost curve for the firm. Show this is an envelope for the short-run curves computed in part a by examining values of K=100, %3D 200, 400. e.) For K =100, w=4, v =1, graph the SRATC and the SRMC curves for the firm. Where does the SRMC curve intersect the SRATC curve?

2) A firm producing hockey sticks has a production function given by: 2\KL. Suppose Capital stock is fixed at K in the short-run. The rental rate for K is v, and the wage rate for L is w. a.) Show the firm's short-run total costs as a function of q, w, v, and K. b.) Given q, w, v, how should the capital stock be chosen to minimize total cost in the long run? c.) Use your results from part b to have the long-run total cost function. d.) For w = $4, v = $1, graph the long-run total cost curve for the firm. Show this is an envelope for the short-run curves computed in part a by examining values of K=100, %3D 200, 400. e.) For K =100, w=4, v =1, graph the SRATC and the SRMC curves for the firm. Where does the SRMC curve intersect the SRATC curve?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

2) A firm producing hockey sticks has a production function given by: 2VKL.
Suppose Capital stock is fixed at K in the short-run. The rental rate for K is v, and the
wage rate for L is w.
a.) Show the firm's short-run total costs as a function of q, w, v, and K.
b.) Given q, w, v, how should the capital stock be chosen to minimize total cost in the
long run?
c.) Use your results from part b to have the long-run total cost function.
d.) For w = $4, v = $1, graph the long-run total cost curve for the firm. Show this is an
envelope for the short-run curves computed in part a by examining values of K=100,
200, 400.
e.) For K =100, w=4, v =1, graph the SRATC and the SRMC curves for the firm.
Where does the SRMC curve intersect the SRATC curve?

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A5
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