CHAPTER 8 • Profit Maximization and Competitive Supply 315

(Hint: What is the inherent cost structure of the automo- are the steps by which a competitive market ensures
bile industry?) increased output? Will your answer change if the gov-
7. Because industry X is characterized by perfect com- ernment imposes a price ceiling?
petition, every firm in the industry is earning zero 13. The government passes a law that allows a substantial
economic profit. If the product price falls, no firm can subsidy for every acre of land used to grow tobacco.
survive. Do you agree or disagree? Discuss. How does this program affect the long-run supply
8. An increase in the demand for movies also increases curve for tobacco?
the salaries of actors and actresses. Is the long-run sup- 14. A certain brand of vacuum cleaners can be purchased
ply curve for films likely to be horizontal or upward from several local stores as well as from several cata-
sloping? Explain. logues or websites.
9. True or false: A firm should always produce at an output a. If all sellers charge the same price for the vacuum
at which long-run average cost is minimized. Explain. cleaner, will they all earn zero economic profit in
10. Can there be constant returns to scale in an industry the long run?
with an upward-sloping supply curve? Explain. b. If all sellers charge the same price and one local
11. What assumptions are necessary for a market to be seller owns the building in which he does busi-
perfectly competitive? In light of what you have ness, paying no rent, is this seller earning a positive
learned in this chapter, why is each of these assump- economic profit?
tions important? c. Does the seller who pays no rent have an incentive
12. Suppose a competitive industry faces an increase in to lower the price that he charges for the vacuum
demand (i.e., the demand curve shifts upward). What cleaner?

EXERCISES
1. The data in the table below give information about the $200. Assume that the price of the output remains at
price (in dollars) for which a firm can sell a unit of out- $60 per unit. What general conclusion can you reach
put and the total cost of production. about the effects of fixed costs on the firm’s output
a. Fill in the blanks in the table. choice?
b. Show what happens to the firm’s output choice and 3. Use the same information as in Exercise 1.
profit if the price of the product falls from $60 to $50. a. Derive the firm’s short-run supply curve. (Hint:
You may want to plot the appropriate cost curves.)
R P MC MR R MR P b. If 100 identical firms are in the market, what is the
industry supply curve?
q P P  60 C P  60 P  60 P  60 P  50 P  50 P  50 4. Suppose you are the manager of a watchmaking firm
operating in a competitive market. Your cost of pro-
0 60 100
duction is given by C ⫽ 200 ⫹ 2q2, where q is the level
1 60 150 of output and C is total cost. (The marginal cost of pro-
duction is 4q; the fixed cost is $200.)
2 60 178 a. If the price of watches is $100, how many watches
3 60 198 should you produce to maximize profit?
b. What will the profit level be?
4 60 212 c. At what minimum price will the firm produce a
5 60 230 positive output?
5. Suppose that a competitive firm’s marginal cost of pro-
6 60 250 ducing output q is given by MC(q) ⫽ 3 ⫹ 2q. Assume
that the market price of the firm’s product is $9.
7 60 272
a. What level of output will the firm produce?
8 60 310 b. What is the firm’s producer surplus?
c. Suppose that the average variable cost of the firm is
9 60 355
given by AVC(q) ⫽ 3 ⫹ q. Suppose that the firm’s fixed
10 60 410 costs are known to be $3. Will the firm be earning a
positive, negative, or zero profit in the short run?
11 60 475 6. A firm produces a product in a competitive industry
and has a total cost function C ⫽ 50 ⫹ 4q ⫹ 2q2 and
2. Using the data in the table, show what happens to
a marginal cost function MC ⫽ 4 ⫹ 4q. At the given
the firm’s output choice and profit if the fixed cost of
market price of $20, the firm is producing 5 units of
production increases from $100 to $150 and then to
 316 PART 2 • Producers, Consumers, and Competitive Markets

output. Is the firm maximizing its profit? What quan- *11. Suppose that a competitive firm has a total cost func-
tity of output should the firm produce in the long run? tion C(q) ⫽ 450 ⫹ 15q ⫹ 2q2 and a marginal cost function
7. Suppose the same firm’s cost function is C(q) ⫽ 4q2 ⫹ 16. MC(q) ⫽ 15 ⫹ 4q. If the market price is P ⫽ $115 per
a. Find variable cost, fixed cost, average cost, aver- unit, find the level of output produced by the firm. Find
age variable cost, and average fixed cost. (Hint: the level of profit and the level of producer surplus.
Marginal cost is given by MC ⫽ 8q.) *12. A number of stores offer film developing as a service to
b. Show the average cost, marginal cost, and average their customers. Suppose that each store offering this
variable cost curves on a graph. service has a cost function C(q) ⫽ 50 ⫹ 0.5q ⫹ 0.08q2 and
c. Find the output that minimizes average cost. a marginal cost MC ⫽ 0.5 ⫹ 0.16q.
d. At what range of prices will the firm produce a pos- a. If the going rate for developing a roll of film is $8.50,
itive output? is the industry in long-run equilibrium? If not, find
e. At what range of prices will the firm earn a nega- the price associated with long-run equilibrium.
tive profit? b. Suppose now that a new technology is developed
f. At what range of prices will the firm earn a positive which will reduce the cost of film developing by
profit? 25 percent. Assuming that the industry is in long-
*8. A competitive firm has the following short-run cost run equilibrium, how much would any one store be
function: C(q) ⫽ q3 − 8q2 ⫹ 30q ⫹ 5. willing to pay to purchase this new technology?
a. Find MC, AC, and AVC and sketch them on a graph. *13. Consider a city that has a number of hot dog stands
b. At what range of prices will the firm supply zero operating throughout the downtown area. Suppose that
output? each vendor has a marginal cost of $1.50 per hot dog
c. Identify the firm’s supply curve on your graph. sold and no fixed cost. Suppose the maximum number
d. At what price would the firm supply exactly 6 units of hot dogs that any one vendor can sell is 100 per day.
of output? a. If the price of a hot dog is $2, how many hot dogs
*9. a. Suppose that a firm’s production function is q ⫽ does each vendor want to sell?
9x1/2 in the short run, where there are fixed costs b. If the industry is perfectly competitive, will the
of $1000, and x is the variable input whose cost is price remain at $2 for a hot dog? If not, what will
$4000 per unit. What is the total cost of producing a the price be?
level of output q? In other words, identify the total c. If each vendor sells exactly 100 hot dogs a day and
cost function C(q). the demand for hot dogs from vendors in the city
b. Write down the equation for the supply curve. is Q ⫽ 4400 − 1200P, how many vendors are there?
c. If price is $1000, how many units will the firm pro- d. Suppose the city decides to regulate hot dog ven-
duce? What is the level of profit? Illustrate your dors by issuing permits. If the city issues only 20
answer on a cost-curve graph. permits and if each vendor continues to sell 100 hot
*10. Suppose you are given the following information dogs a day, what price will a hot dog sell for?
about a particular industry: e. Suppose the city decides to sell the permits. What
is the highest price that a vendor would pay for a
Q D = 6500 - 100P Market demand permit?
Q S = 1200P Market supply *14. A sales tax of $1 per unit of output is placed on a par-
ticular firm whose product sells for $5 in a competitive
q2
C(q) = 722 + Firm total cost function industry with many firms.
200 a. How will this tax affect the cost curves for the firm?
2q
MC(q) = Firm marginal cost function b. What will happen to the firm’s price, output, and
200 profit?
Assume that all firms are identical and that the market c. Will there be entry or exit in the industry?
is characterized by perfect competition. *15. A sales tax of 10 percent is placed on half the firms (the
a. Find the equilibrium price, the equilibrium quan- polluters) in a competitive industry. The revenue is
tity, the output supplied by the firm, and the profit paid to the remaining firms (the nonpolluters) as a 10
of each firm. percent subsidy on the value of output sold.
b. Would you expect to see entry into or exit from the a. Assuming that all firms have identical constant
industry in the long run? Explain. What effect will long-run average costs before the sales tax-subsidy
entry or exit have on market equilibrium? policy, what do you expect to happen (in both the
c. What is the lowest price at which each firm would short run and the long run), to the price of the
sell its output in the long run? Is profit positive, product, the output of firms, and industry output?
negative, or zero at this price? Explain. (Hint: How does price relate to industry input?)
d. What is the lowest price at which each firm would b. Can such a policy always be achieved with a bal-
sell its output in the short run? Is profit positive, anced budget in which tax revenues are equal to
negative, or zero at this price? Explain. subsidy payments? Why or why not? Explain.