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UNIVERSITY OF WASHINGTON
Department of Economics
Economics 200
Scott
Problem Set 4. Competitive Firm Behavior
Economic Profit:
1.
Undeterred by the statistics on the mortality rates of small businesses (more than half go out
of business in 18 months), a young chef opens his own restaurant. To do so, he quit his own
job at $8,000 per year, cashed in $20,000 worth of savings bonds yielding 5% to provide
capital for the business, and took over a store building owned by his wife which had
previously been rented out at $500 per month. His expenses during the first year amounted
to $50,000 for food, $15,000 for extra help, and $2,000 for gas, electricity, etc. His total
receipts for the first year are $78,000. Assume he is a profit maximizer and derives no
particular satisfaction from being his own boss, etc. Would you advise the young chef to
stay in business?
Competition:
2.
A purely competitive case:
Output
TFC
0
1
2
3
4
5
6
7
8
9
10
$300
300
300
300
300
300
300
300
300
300
300
$
TVC
TC
AFC
AVC
ATC
MC
0
100
150
210
290
400
540
720
950
1,240
1,600
$ 300
400
450
510
590
700
840
1,020
1,250
1,540
1,900
$ 300
150
100
75
60
50
43
38
33
30
$ 100
75
70
73
80
90
103
119
138
160
$ 400
225
170
148
140
140
146
156
171
190
$ 100
50
60
80
110
140
180
230
290
360
Assume that a purely competitive firm has the schedule of costs given in the table above.
Economics 200
Problem Set 4
2-1.
0
1
2
3
4
5
6
7
8
9
10
2-3.
Scott
Complete the table below showing the total revenue and total profit of the firm at each
level of output the firm might produce, assuming market prices of $55, $120, and $200.
Output
2-2.
2
Market Price = $55
Market Price = $120
Market Price = $200
Revenue
Revenue
Revenue
$
Profit
$
$
Profit
$
$
Profit
$
Indicate what output the firm would produce and what its profits would be at a:
a.
Price of $55: output of
and profit of
.
b.
Price of $120: output of
and profit of
.
c.
Price of $200: output of
and profit of
.
Complete the supply schedule of a firm in the table below and indicate what the profit of
the firm will be at each price.
Price
$360
290
230
180
140
110
80
60
Quantity Supplied
Profit
$
Economics 200
Problem Set 4
2-4.
3
Scott
If there are 100 firms in the industry and all have the same cost schedule:
a. Complete the market supply schedule in the table below.
Quantity Demanded
Price
400
500
600
700
800
900
1,000
b.
Quantity Supplied
$360
290
230
180
140
110
80
Using the demand schedule given in part a:
(1) What will the market price of the product be? $
(2) What quantity will the individual firm produce?
(3) How large will the firm’s profit be? $
(4) Will firms tend to enter or leave the industry in the long run?
Why?
2-5.
If the total costs assumed for the individual firm in problem 1 were long-run total costs
and if the industry were a constant-cost industry:
a.
What would be the market price of the product in the long run? $
b.
What output would each firm produce when the industry is in long-run
equilibrium?
c.
Approximately how many firms will there be in the industry in the long run, given
the present demand for the product?
d.
If the following were the market demand schedule for the product, how many
firms would there be in the long run in the industry?
Price
$
360
290
230
180
140
110
80
Quantity Demanded
500
600
700
800
900
1,000
1,100
Economics 200
Problem Set 4
e.
4
Scott
On the graph below, draw the long-run supply curve of this industry. Then draw a
long-run supply curve for an increasing-cost industry. Label them CC and IC.
P
Q
3. Cost Minimization. The diagram below, with intercepts 250 and 100 for the straightline, uses the standard
notation and depicts the cost-minimizing use of factors of production for a profit-maximizing firm. The price of
labor is $5.
K
250
K*
L*
100
L
Economics 200
Problem Set 4
5
Scott
a. What is the numerical value of the firm’s total cost? Explain.
b. What is the numerical value of the price of capital? Explain.
c. Given cost minimization, what is the marginal rate of technical substitution (give general definition and
numerical value for the cost-minimizing combination of K and L)? Explain.
4. Factor Substitution. Use isoquants and isocost curves to show:
(a) If capital and labor are perfect complements, factor intensity (the ratio of capital goods to labor) is
insensitive to changes in relative factor prices.
(b) If capital and labor a perfect substitutes, changing relative factor prices can cause dramatic shifts from
exclusive use of one factor of production to the other.
5. Analysis of a Lump-Sum Tax in Competitive Markets. The market for good X is in a competitive long-run
equilibrium for an industry with a unique size of firm that minimizes unit (i.e., average) cost. Then, the government
imposes a “lump-sum tax.” A lump-sum tax requires each firm in the market to pay a specified amount just for
being in business. No matter what the firm’s output or profit, it is now required to pay this new lump-sum tax. Such
a tax is sometimes called a franchise fee.
Analyze what happens in the market and to the typical firm in both the short run and the long run. What
happens to output and price in the short run – for the market and for the typical firm? What happens to output and
price in the long run – for the market and for the typical firm? Explain, illustrating your answer with the customary
diagrams for supply and demand in the market and for the typical firm’s cost and demand conditions.
6. LR and SR Costs, Isoquants and Isocosts. Draw the long-run average cost of a firm as the envelope of a few
short-run average cost schedules (see p. 143 of your text and your notes from lecture). “Talk through” the intuition,
using isoquant-isocost diagrams to illustrate your reasoning.
7. Marginal Product of Labor, Marginal Revenue Product of Labor, and Labor Demand. Using diagrams,
explain the equivalence between the condition “price equals marginal cost” and the condition “wage equals marginal
revenue product of labor” in the short run. Refer to your notes and to pages 182-183 in the text. Note that your text
calls marginal revenue produce the value of marginal product. How will an increase in the price of a good affect the
demand for labor used in the production of that good in the short-run?