In the short run, the firm's amount of capital equipment is fixed at k = 100. The rental rate for k is v= $1, and the wage rate for I 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.
In the short run, the firm's amount of capital equipment is fixed at k = 100. The rental rate for k is v= $1, and the wage rate for I 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.
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.4P
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Transcribed Image Text:10.4
A firm producing hockey sticks has a production function given by
9= 2√kl.
364 Part 4: Production and Supply
In the short run, the firm's amount of capital equipment is fixed at k = 100. The rental rate for k is v= $1, and the wage rate
for I 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 k in the short run.
e. Calculate the firm's total costs as a function of q, w, v, and k.
f. Given q, w, and v, 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, v = $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 k of 100, 200, and 400.
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