Exam 26: Oligopoly

Suppose that the market demand curve for bean sprouts is given by P = 820 - 2Q, 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 $20 per unit of output. In equilibrium, total output by the two firms will be

Suppose that the inverse demand for bean sprouts is given by P(Y) = 370 - 4Y and the total cost of producing Y units for any firm is TC(Y) = 10Y. If the industry consists of two Cournot duopolists, then in equilibrium each firm's production is

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 $675 per ton and produces 50% of the total number of melocotones sold. The equilibrium price of a ton of melocotones must be

An industry has two firms. The inverse demand function for this industry is p = 74 - 4q. Both firms produce at a constant unit cost of $26 per unit. What is the Cournot equilibrium price for this industry?

Ann and Bruce each own a pizza store in Frostbite Falls, Minnesota. Demand for pizza is given by Q = 200 - 10P. 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 + 5Q. If Ann and Bruce behave as duopolists, each earns a profit of

An industry has two firms-a Stackelberg leader and a follower. The price of the industry output is given by P = 84 - Q, where Q is the total output of the two firms. The follower has a marginal cost of $0. The leader has a marginal cost of $21. How much should the leader produce in order to maximize profits?

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 - 3q, 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?

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 + 700Q + 5Q². The demand for used cars is Q = 300 - . Assuming Roach sets the market price so as to maximize its profit, how many cars will each of the follower firms supply?

Suppose that two airlines are Cournot duopolists serving the Peoria-Dubuque route, and the demand curve for tickets per day is Q = 230 - 2p (so p = 115 - ). Total costs of running a flight on this route are 450 + 40q, 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

An industry has two firms producing at a constant unit cost of $10 per unit. The inverse demand curve for the industry is p = 110 - .5q. Suppose that firm 1 is a Stackelberg leader in choosing its quantity (i.e., firm 1 chooses its quantity first, knowing that firm 2 will observe firm 1's quantity when it chooses its own output.) How much output will firm 2, the follower, produce?

Conjectural variation refers to the fact that in a single market there is variation among firms in their estimates of the demand function in future periods.

An industry has two firms-a Stackelberg leader and a follower. The price of the industry output is given by P = 36 - Q, where Q is the total output of the two firms. The follower has a marginal cost of $0. The leader has a marginal cost of $9. How much should the leader produce in order to maximize profits?

An industry has two firms. The inverse demand function for this industry is p = 263 - 6q. Both firms produce at a constant unit cost of $29 per unit. What is the Cournot equilibrium price for this industry?

A duopoly faces the inverse demand curve p = 160 - 2q. Firm 1's total cost function is given by C₁(q₁) = 8q₁ and firm 2's total cost function is given by C₂(q₂) = 10q₂. In a Cournot equilibrium,

There are two firms in the blastopheme industry. The demand curve for blastophemes is given by p = 4,200 - 3q. 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

North Bend currently has one McDonald's fast-food franchise. Demand for hamburgers in North Bend is given by Q = 300 - 10P. Any McDonald's franchise has costs of C = 70 + 2Q 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

One unit of zinc and one unit of copper are needed to produce a unit of brass. The world's supply of zinc and the world's supply of copper are owned by two different monopolists. For simplicity assume that it costs nothing to mine zinc and copper, that no other inputs are needed to produce brass, and that the brass industry operates competitively. Then the price of a unit of brass equals the cost of the inputs used to make it. The demand function for brass is q = 900 - 2p, where p is the price of brass. The zinc and copper monopolists each set a price, believing that the other monopolist will not change its price. What is the equilibrium price of brass?

The duopolists Carl and Simon face a demand function for pumpkins of Q = 8,200 - 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 $.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

Suppose that the inverse demand for bean sprouts is given by P(Y) = 750 - 2Y and the total cost of producing Y units for any firm is TC(Y) = 30Y. If the industry consists of two Cournot duopolists, then in equilibrium each firm's production is

An industry has two firms. Firm 1's cost function is c(y) = 2y + 500 and firm 2's cost function is c(y) = 2y + 400. The demand curve for the output of this industry is a downward-sloping straight line. In a Cournot equilibrium, where both firms produce positive amounts of output,