A firm producing hockey sticks has a production function given byq = 2VklIn the short run, the firm's amount of capital equipment is fixed at k = 100. The rental rate for k isr = 5, and the wage rate for r = $1, and the wage rate for l is w = $4.(a) Calculate the firm's short-run total cost curve. Calculate the short-run average cost curve.(b) What is the firm's short-run marginal cost function? What are the SC, SAC, and SMC for thefirm if it produces 25 hockey sticks? Fifty hockey sticks? One hundred hockey sticks? Twohundred hockey sticks?(c) Graph the SAC and the SMC curves for the firm. Indicate the points found in part (b).(d) Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will alwaysintersect the SAC curve at its lowest pointSuppose now that capital used for producing hockey sticks is fixed at ki in the short run.(e) Calculate the firm's total costs as a function of q, w, r, and k1.(f) Given q,w,and r, how should the capital stock be chosen to minimize total cost?(g) Use your results from part (f) to calculate the long-run total cost of hockey stick production.(h) For w = $4, r = $1, graph the long-run total cost curve for hockey stick production. Showthat this is an envelope for the short-run curves computed in part (e) by examining values ofki of 100, 200, and 400.2.

The total cost of production is the simple aggregate of the fixed cost and variable costs, in the…

A firm producing hockey sticks has a production function given by q = 2vkl In the short run, the firm's amount of capital equipment is fixed at k = 100. The rental rate for k is r = 5, and the wage rate for r = $1, and the wage rate for l is w = $4. (a) Calculate the firm's short-run total cost curve. Calculate the short-run average cost curve. (b) What is the firm's short-run marginal cost function? What are the SC, SAC, and SMC for the firm if it produces 25 hockey sticks? Fifty hockey sticks? One hundred hockey sticks? Two hundred hockey sticks? (c) Graph the SAC and the SMC curves for the firm. Indicate the points found in part (b). 2.

A firm producing hockey sticks has a production function given by q = 2vkl In the short run, the firm's amount of capital equipment is fixed at k = 100. The rental rate for k is r = 5, and the wage rate for r = $1, and the wage rate for l is w = $4. (a) Calculate the firm's short-run total cost curve. Calculate the short-run average cost curve. (b) What is the firm's short-run marginal cost function? What are the SC, SAC, and SMC for the firm if it produces 25 hockey sticks? Fifty hockey sticks? One hundred hockey sticks? Two hundred hockey sticks? (c) Graph the SAC and the SMC curves for the firm. Indicate the points found in part (b). 2.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.4P

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Question

A firm producing hockey sticks has a production function given by
q = 2Vkl
In the short run, the firm's amount of capital equipment is fixed at k = 100. The rental rate for k is
r = 5, and the wage rate for r = $1, and the wage rate for l is w = $4.
(a) Calculate the firm's short-run total cost curve. Calculate the short-run average cost curve.
(b) What is the firm's short-run marginal cost function? What are the SC, SAC, and SMC for the
firm if it produces 25 hockey sticks? Fifty hockey sticks? One hundred hockey sticks? Two
hundred hockey sticks?
(c) Graph the SAC and the SMC curves for the firm. Indicate the points found in part (b).
(d) Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will always
intersect the SAC curve at its lowest point
Suppose now that capital used for producing hockey sticks is fixed at ki in the short run.
(e) Calculate the firm's total costs as a function of q, w, r, and k1.
(f) Given q,w,and r, how should the capital stock be chosen to minimize total cost?
(g) Use your results from part (f) to calculate the long-run total cost of hockey stick production.
(h) For w = $4, r = $1, graph the long-run total cost curve for hockey stick production. Show
that this is an envelope for the short-run curves computed in part (e) by examining values of
ki of 100, 200, and 400.
2.

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