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Exam 26: Oligopoly

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Question 31

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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 = 200 - . Assuming Roach is aware of its competitors' costs, what price should Roach set for a used car?

A) $708.33
B) $575
C) $616.67
D) $604.17
E) $925

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Question 32

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Two firms decide to form a cartel and collude in a way that maximizes industry profits. Each firm has zero production costs and each firm is given a positive output quota by the cartel. Which of the following statements is not true?

A) Each firm would want to produce more than its quota if it knew that the other would continue to produce at its quota.
B) The price elasticity of demand will be 21 at the output level chosen.
C) Output would be lower than if the firms behaved as Cournot firms.
D) Output would be lower than if the firms behaved as competitors.
E) All of the other statements are false.

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Question 33

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The inverse demand function for fuzzy dice is p = 20 - q. There are constant returns to scale in this industry with unit costs of $8. Which of the following sets of statements is completely true?

There are two firms in the blastopheme industry. The demand curve for blastophemes is given by p = 3,600 - 4q. Each firm has one manufacturing plant and each firm i has a cost function C(q_i) = q²_i, where q_i is the output of firm i. The two firms form a cartel and arrange to split total industry profits equally. Under this cartel arrangement, they will maximize joint profits if

Suppose that the demand curve for an industry's output is a downward-sloping straight line and there is constant marginal cost. Then the larger the number of identical firms producing in Cournot equilibrium, the lower will be the price.

A duopoly faces the demand curve D(p) = 30 - .5p. Both firms in the industry have a total cost function given by C(q) = 4q. Suppose that firm 1 is a Stackelberg leader in choosing its quantity first. Firm 1's profit function can be written as

A Stackelberg leader will necessarily make at least as much profit as he would if he acted as a Cournot oligopolist.

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 5 + 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?

An industry has two firms each of which produces output at a constant unit cost of $10 per unit. The demand function for the industry is q = . The Cournot equilibrium price for this industry is

A duopoly faces the inverse demand curve p = 160 - 2q. Both firms in the industry have constant costs of $10 per unit of output. In a Cournot equilibrium how much output will each duopolist sell?

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 = $300 - .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 $45 and Grubb has marginal costs of $30. How much is Grinch's output in equilibrium?

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) = 56 - p.

A city has two newspapers. Demand for either paper depends on its own price and the price of its rival. Demand functions for papers A and B respectively, measured in tens of thousands of subscriptions, are 21 - 2P_a + P_b and 21 + P_a 2 2P_b. The marginal cost of printing and distributing an extra paper just equals the extra advertising revenue from another reader, so each paper treats marginal costs as zero. Each paper maximizes its revenue assuming that the other's price is independent of its own price. If the papers enter a joint operating agreement where they set prices to maximize total revenue, by how much will newspaper prices rise?

The demand for y is given by . Only two firms produce y. They have identical costs c(y) = y². If they agree to collude and maximize their joint profits, how much output will each firm produce?

The price elasticity of demand for melocotones is constant and equal to -2. The melocotone market is controlled by two Cournot duopolists who have different cost functions. One of the duopolists has a constant marginal cost of $975 per ton and produces 70% of the total number of melocotones sold. The equilibrium price of a ton of melocotones must be

In the Bertrand model of duopoly, each firm sets its price, believing that the other's price will not change. When both firms have identical production functions and produce with constant returns to scale, the Bertrand equilibrium price is equal to marginal cost.