Unit 4: Perfect Competition – Problems
4.1: Perfect competition in the short run
CORE PROBLEMS
Problem 1
The table below shows costs over various output levels for a perfectly competitive firm in a market where the market price is $30
Q P TR MR TC MC
0 30 -- 10 --
1 30 20
2 30 40
3 30 65
4 30 100
5 30 140
6 30 200
a. Complete the table.
b. What is the profit-maximizing level of output for this firm? c. How much profit does the firm earn?
Problem 2
At its profit-maximizing output level, a firm has total revenue of $3500 per day but a total cost of $7000 per day.
Problem 3
The market demand for alfalfa sprouts is shown in the diagram on the left. The marginal cost curve for an individual producer is shown on the diagram on the right. The minimum level of average variable cost is zero, so there is no shut down. The market is perfectly competitive.
a. Show the amount of output produced by each firm as it depends on the price.
Price 𝒒𝑺 by each firm
$0
$50
$100
$200
$300
b. Show the quantity supplied in the market depending upon the number of firms.
Price 𝑸𝑺 with 20 firms 𝑸𝑺 with 30 firms 𝑸𝑺 with 80 firms
$0
$50
$100
$200
$300
c. On the left diagram, plot the three market supply curves – when there are 20 firms, 30 firms and 80 firms.
SUPPLEMENTARY PROBLEMS
Problem 4
A firm that operates in a perfectly competitive market has a cost schedule shown below.
Q TFC TVC TC AFC AVC ATC MC
0 2.00 2.00 -- -- -- --
1 2.00 2.75
2 2.00 4.00
3 2.00 6.00
4 2.00 12.00
a. Complete the table.
b. If the market price is $5.00, what is the firm’s profit-maximizing level of output and how much profit will it earn?
c. If the market price is $1.00, what is the firm’s profit-maximizing level of output and how much profit will it earn? Is it better to shut down or operate?
Problem 5
A firm operates in a perfectly competitive market where the market price is $5 per unit. Its cost schedule is shown below. Complete the table and find the profit-maximizing level of output.
Q P TR MR TC MC
0 5 -- 6 --
1 5 12
2 5 17
3 5 21
4 5 24
5 5 28
Problem 6
A firm operates in a perfectly competitive market where the market price is $50 per unit. Its cost schedule is shown below.
Q P TR MR TC MC
0 50 -- 5 --
1 50 35
2 50 15
3 50 35
4 50 55
a. Complete the table.
b. What is the firm’s profit-maximizing level of output? c. What price does the firm charge?
d. How much profit does the firm earn?
Problem 7
“My economics professor must be confused. First, he tells me that in perfect competition the demand curve is always completely elastic – horizontal. But then he draws a supply and demand diagram with a downward sloping demand curve.” Resolve this student’s confusion.
Problem 8
The diagram below shows the cost structure for a firm operating in a perfectly competitive market.
4.2: Perfect competition in the long run
CORE PROBLEMS
Problem 1
A firm that sells its output in a perfectly competitive market has the cost curves shown below.
a. When the market price is $50, what is the firm’s profit-maximizing level of output? How much profit does the firm earn?
b. Is $50 the long-run equilibrium price? If not, do you expect entry or exit?
c. When the market price is $25, what is the firm’s profit-maximizing level of output? How much profit does the firm earn?
d. Is $25 the long-run equilibrium price? If not, do you expect entry or exit?
e. When the market price is $15, what is the firm’s profit-maximizing level of output? f. Is $15 the long-run equilibrium price? If not, do you expect entry or exit?
A perfectly competitive firm has the cost schedule shown below.
Q TFC TVC TC AFC AVC ATC MC
0 20 0 -- -- -- --
1 20 10
2 20 26
3 20 46
4 20 72
5 20 110
a. Complete the table.
b. What is the short-run shut down price? c. What is the zero-profit price?
d. What is the long-run equilibrium price?
e. If the market price is $25, what is this firm’s profit-maximizing level of output? How much profit does the firm earn?
f. If the market price is $25, do you expect entry or exit for this industry?
Problem 3
Barack owns a farm. If he runs the farm himself, he’ll get $6000 in revenue but will have explicit costs equal to $2000. Instead of running the farm himself, Barack could rent the farm out to one of his friends (also farmers). George would be willing to pay $3000 to rent the farm, while Bill would be willing to pay $3500 to rent the farm. If Barack rents the farm out to either one of them, he does not earn the revenue from running the farm, but he doesn’t have to pay the explicit costs either. In addition to his rental income, if Barack rents the farm out, he has the opportunity to work as the President, which pays $1000.
a. What is Barack’s accounting profit from running the farm? b. What is Barack’s economic profit from running the farm?
SUPPLEMENTARY PROBLEMS
Problem 4
The table below gives the market supply and demand for potatoes at various prices. Quantities are in millions of pounds. The market is perfectly competitive.
Price (per pound)
Quantity Supplied
Quantity Demanded
$1.00 10 100
$1.25 15 90
$1.50 25 75
$1.75 40 63
$2.00 55 55
$2.25 65 40
Part of the total cost schedule for each firm producing potatoes is shown below.
Pounds Total Cost
60,000 $110,000
61,000 $111,000
62,000 $112,000
63,000 $115,000
a. Compute the marginal cost for the firm. b. What is the market price?
c. What is the profit-maximizing level of output for each firm? d. Is this market in long-run equilibrium?
Assume that the perfectly competitive market for boxed macaroni and cheese (an inferior good) is initially in long-run equilibrium. Consumer incomes suddenly rise.
a. What is the effect on the short-run market price?
b. What is the effect on the short-run level of output in the market? c. Will firms enter or exit the industry in the long-run?
Problem 6
The market for boats is perfectly competitive and initially in long-run equilibrium. The market diagram and the cost structure for each individual firm in the market are shown below. The initial equilibrium price is 𝑃∗. The initial market output and firm output are 𝑄∗ and 𝑞∗, respectively.
The government then imposes a “luxury tax” on each boat sold.
a. Draw the new average total cost curve after the tax is imposed and label it 𝐴𝑇𝐶′. b. Show the new short-run output produced by each firm and label it 𝑞∗.
c. Do firms earn a profit or a loss in the new short-run equilibrium? Shade on your diagram the level of profit or loss.
d. In the long-run, will there be entry or exit in this industry as a result of the tax?
e. Show the new long-run equilibrium in the market after the imposition of the tax. Label the new market price 𝑃∗ and the new market and firm output 𝑄∗ and 𝑞∗.
