Problem 1) Firm Profit Maximization:
Consider the market for textiles in the United States, which we will treat as perfectly competitive. The market demand for textiles is expressed as:
P = 250 – 0.5Q
and the supply of textiles is expressed as:
P = Q/10
where P represents price per bolt of cloth and Q represents the number of bolts of cloth produced in the entire industry each day. The typical firm in this market has total cost
TC = 50 + 5q2
where q represents the number of bolts of cloth produced by a single firm each day. Thus, marginal cost is given by:
MC = 10q.
a) Determine the equilibrium market price and quantity in the market for textiles.
b) At the equilibrium market price computed in (a) above, what is the quantity produced by a typical firm?
c) At the equilibrium market price computed in (a) above, what is the profit of a typical firm?
d) If all firms in the market have the same cost structure, how many firms would compete at the equilibrium price computed in (a) above?
e) If all firms in the market have the same cost structure, then as the market moves to long-run equilibrium, will there be entry, exit or no change in the number of firms? Explain.
Problem 2) Firm Profit Maximization:
For this question, refer to the following table of short-run costs for a firm participating in a perfectly competitive market. Assume that there are only two inputs, capital and labor. The fixed input is capital and the variable input is labor.
You are not being asked to fill out this table. However, you might need to fill out parts of the table to answer the questions below.
|
Output
Q
|
Total Cost
C
|
Variable Cost
VC
|
Fixed Cost
FC
|
Marginal Cost
MC
|
Average Cost
AC
|
Average Variable Cost
AVC
|
Average Fixed Cost
AFC
|
|
0
|
20
|
|
|
|
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|
1
|
24
|
|
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|
|
|
|
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2
|
30
|
|
|
|
|
|
|
|
3
|
38
|
|
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|
|
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|
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4
|
50
|
|
|
|
|
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|
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5
|
65
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6
|
85
|
|
|
|
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|
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7
|
120
|
|
|
|
|
|
|
a) Suppose the firm shuts down. What will be the firm’s profit?
b) Suppose that the price of the firm’s output is $12. What is the profit-maximizing level of output for this firm? Explain why. What is the firm’s profit? Show your calculations.
c) Suppose that fixed cost is $40 instead of what is represented in the table. How does your answer to part b change? Explain.
Problem 3) Extensions of Firm Theory
Answer each of the following in a few complete sentences.
From time immemorial, moralists have been fond of counseling that, “anything worth doing is worth doing well.”
a) Indicate how the theory of the firm can be adapted to shed light on whether this advice is correct. [Hint: Think of the firm’s profit-maximizing rule.]
b) Consider cleanliness, which some say is second only to godliness. Use your answer in part (a) to explain why people settle for a lower level of cleanliness in car garages than hospital operating rooms.
c) TRUE, FALSE or UNCERTAIN and explain why: If people are unwilling to pay a higher price for higher quality, then the quality of products will never improve.