Exam 26: Oligopoly

North Bend currently has one McDonald's fast-food franchise. Demand for hamburgers in North Bend is given by Q = 400 - 10P. Any McDonald's franchise has costs of C = 60 + 3Q for producing Q hamburgers. If a second McDonald's franchise were to move into North Bend (and both behaved as duopolists), the profit of the original McDonald's would fall from

A certain type of mushroom used to be produced on 50 farms, each of which had a cost function c(y) = y₂ + 1, where y > 0 and c(0) = 0. The firms operated as competitors. The demand curve for this kind of mushroom is given by D(p) = 52 - p. Marauding deviant Ninja turtles invaded many of the mushroom farms leaving absolute devastation and loathsome slime in their wake. (The turtles had no effect on the cost functions of farms that were not invaded.)

There are two major producers of corncob pipes in the world, both located in Herman, Missouri. Suppose that the inverse demand function for corncob pipes is described by p = 160 - 4q, where q is total industry output, and marginal costs are zero. What is the Cournot reaction function of firm 1 to the output, q₂, of firm 2?

In the Cournot model, each firm chooses its actions on the assumption that its rivals will react by changing their quantities in such a way as to maximize their own profits.

A Stackelberg leader chooses his actions on the assumption that his rival will adjust to the leader's actions in such a way as to maximize the rival's profits.

A duopoly in which two identical firms are engaged in Bertrand competition will not distort prices from their competitive levels.

An industry has two colluding firms that act so as to maximize total profit in the industry and then split the profits equally. Firm 1 has cost function c(y) = 8y. Firm 2 has cost function c(y) = y². Each firm produces an integer number of units. Market demand is given by Y(p) = 72 - p.

Roach Motors is the dominant used-car dealer in a small Midwestern city. After paying $50,000 for overhead, Roach Motors' cost per car is $500. There are 4 other small used-car lots in this town, but since they are not large enough to purchase cars through the same discount sources as Roach, each firm faces the cost function C = 5,000 + 600Q + 5Q². The demand for used cars is Q = 600 - . Assuming Roach sets the market price so as to maximize its profit, how many cars will each of the follower firms supply?

Suppose that the market demand curve for bean sprouts is given by P = 880 - 4Q, where P is the price and Q is the total industry output. Suppose that the industry has two firms, a Stackelberg leader and a follower. Each firm has a constant marginal cost of $80 per unit of output. In equilibrium, total output by the two firms will be

The duopolists Carl and Simon face a demand function for pumpkins of Q = 2,200 - 400P, where Q is the total number of pumpkins that reach the market and P is the price of pumpkins. Suppose further that each farmer has a constant marginal cost of $1.50 for each pumpkin produced. If Carl believes that Simon is going to produce Q_s pumpkins this year, then the reaction function tells us how many pumpkins Carl should produce in order to maximize his profits. Carl's reaction function is

A city has two major league baseball teams, A and B. The number of tickets sold by either team depends on the price of the team's own tickets and the price of the other team's tickets. If team A charges P_a for its tickets and team B charges P_b for its tickets, then ticket sales, measured in hundreds of thousands per season, are 10 - 2P_a + P_b for team A and 20 + P_a - 2P_b for team B. The marginal cost of an extra spectator is zero for both teams. Each team believes the other's price is independent of its own choice of price, and each team sets its own price so as to maximize its revenue. What price do they charge per ticket?

In Cournot equilibrium each firm chooses the quantity that maximizes its own profits assuming that the firm's rival will continue to sell at the same price as before.

Suppose that Grinch and Grubb go into the wine business in a small country where wine is difficult to grow. The demand for wine is given by p = $480 - .2Q, where p is the price and Q is the total quantity sold. The industry consists of just the two Cournot duopolists, Grinch and Grubb. Imports are prohibited. Grinch has constant marginal costs of $30 and Grubb has marginal costs of $60. How much is Grinch's output in equilibrium?

In Bertrand competition between two firms, each firm believes that if it changes its output, the rival firm will change its output by the same amount.

The cartel of copper exporting countries is called COPEC. As part of an international marketing agreement, the United States has agreed to buy all the copper that COPEC wants to sell the United States at a constant price of $100 per ton. COPEC also sells copper in Europe at a price of $150 per ton. COPEC acts just like a monopolist. If COPEC finds it profitable to sell in the United States at $100 per ton and simultaneously to sell in Europe for $150 a ton, what is the price elasticity of demand of COPEC's copper in the European market? (Hint: What is COPEC's marginal revenue in the U.S. market?)

Roach Motors is the dominant used-car dealer in a small Midwestern city. After paying $50,000 for overhead, Roach Motors' cost per car is $500. There are 5 other small used-car lots in this town, but since they are not large enough to purchase cars through the same discount sources as Roach, each firm faces the cost function C = 5,000 + 700Q + 5Q². The demand for used cars is Q = 500 - . Assuming Roach is aware of its competitors' costs, what price should Roach set for a used car?

Suppose that two airlines are Cournot duopolists serving the Peoria-Dubuque route, and the demand curve for tickets per day is Q = 220 - 2p (so p = 110 - ). Total costs of running a flight on this route are 1,400 + 20q, where q is the number of passengers on the flight. Each flight has a capacity of 80 passengers. In Cournot equilibrium, each duopolist will run one flight per day and will make a daily profit of

A Stackelberg leader and follower choose their outputs to maximize their own profits. Local property taxes which constitute a lump sum tax for each of them are reduced by $500 per year for the leader and by $200 a year for the follower. In consequence, the firms

Ann and Bruce each own a pizza store in Frostbite Falls, Minnesota. Demand for pizza is given by Q = 400 2 40P. Having the only two pizza stores in Frostbite Falls, they attempt to profitably split the market without violating the Sherman Antitrust Act. Each has the cost function C = 50 + 2Q. If Ann and Bruce behave as duopolists, each earns a profit of

Consider a market with one large firm and many small firms. The supply function of all of the small firms together is S(p) = 200 + p, the market demand curve is D(p) = 400 - p, and the cost function for the large firm is C(y) = 20y. The residual demand curve for the large firm, where D_L is the large firm's demand and y_L is the large firm's output, is