A firm faces a production function given by q = √kl where q is the output, k is the firm's amount of capital equipment and I is the amount of labour-time employed. (a) In the short run, the amount of capital equipment is fixed at k 100. The rental rate for k is v= $1, and the wage rate for l is w = $2. Calculate the firm's short-run average cost (SAC) and short-run marginal cost (SMC) functions. Graph the SAC and the SMC curves for the firm. (b) (c) Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will always intersect the SAC curve at its lowest point. Calculate the long-run total cost of production. For w= $2, v = = $1, graph the long-run total cost curve. Show that this is an envelope for the short-run curves computed in part (a).
A firm faces a production function given by q = √kl where q is the output, k is the firm's amount of capital equipment and I is the amount of labour-time employed. (a) In the short run, the amount of capital equipment is fixed at k 100. The rental rate for k is v= $1, and the wage rate for l is w = $2. Calculate the firm's short-run average cost (SAC) and short-run marginal cost (SMC) functions. Graph the SAC and the SMC curves for the firm. (b) (c) Where does the SMC curve intersect the SAC curve? Explain why the SMC curve will always intersect the SAC curve at its lowest point. Calculate the long-run total cost of production. For w= $2, v = = $1, graph the long-run total cost curve. Show that this is an envelope for the short-run curves computed in part (a).
Chapter10: Cost Functions
Section: Chapter Questions
Problem 10.4P
Related questions
Question
Transcribed Image Text:A firm faces a production function given by
q = √kl
where q is the output, k is the firm's amount of capital equipment and I is the
amount of labour-time employed.
(a)
In the short run, the amount of capital equipment is fixed at k = 100.
The rental rate for k is v= $1, and the wage rate for is w = $2.
Calculate the firm's short-run average cost (SAC) and short-run
marginal cost (SMC) functions. Graph the SAC and the SMC curves for
the firm.
(b)
(c)
Where does the SMC curve intersect the SAC curve? Explain why the
SMC curve will always intersect the SAC curve at its lowest point.
Calculate the long-run total cost of production. For w $2, v = $1,
graph the long-run total cost curve. Show that this is an envelope for
the short-run curves computed in part (a).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 7 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Microeconomics: Principles & Policy
Economics
ISBN:
9781337794992
Author:
William J. Baumol, Alan S. Blinder, John L. Solow
Publisher:
Cengage Learning
Microeconomics: Principles & Policy
Economics
ISBN:
9781337794992
Author:
William J. Baumol, Alan S. Blinder, John L. Solow
Publisher:
Cengage Learning
Managerial Economics: Applications, Strategies an…
Economics
ISBN:
9781305506381
Author:
James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:
Cengage Learning
