Exam 23: Monopoly

The town council of Frostbite, Ontario, is trying to decide whether to build an outdoor skating rink which would cost $1 million and last for only one season. Operating costs would be zero. Yearly passes would be sold to anyone who wanted to use the rink. If p is the price of the pass in dollars, the number demanded would be q = 1200 - .6p. The council has asked you to advise them on building the rink. You should tell them that

A monopolist faces the demand function Q = . If she charges a price of p, her marginal revenue will be

The demand for a monopolist's output is , where p is its price. It has constant marginal costs equal to $6 per unit. What price will it charge to maximize its profits?

The demand for a monopolist's output is , where p is the price it charges. At a price of $3, the elasticity of demand for the monopolist's output is

A monopolist enjoys a monopoly over the right to sell automobiles on a certain island. He imports automobiles from abroad at a cost of $10,000 each and sells them at the price that maximizes profits. One day, the island's government annexes a neighboring island and extends the monopolist's monopoly rights to this island. People on the annexed island have the same tastes and incomes and there are just as many people as on the first.

A monopolist faces the demand curve q = 90 - , where q is the number of units sold and p is the price in dollars. He has quasi-fixed costs, C, and constant marginal costs of $20 per unit of output. Therefore his total costs are C + 20q if q > 0 and 0 if q = 0. What is the largest value of C for which he would be willing to produce positive output?

A profit-maximizing monopolist has the cost schedule c(y) = 20y. The demand for her product is given by , where p is her price. Suppose that the government tries to get her to increase her output by giving her a subsidy of $15 for every unit that she sells. Giving her the subsidy would make her

A firm has discovered a new kind of nonfattening, non-habit-forming dessert called zwiffle. It doesn't taste very good, but some people like it and it can be produced from old newspapers at zero marginal cost. Before any zwiffle could be produced, the firm would have to spend a fixed cost of $F. Demand for zwiffle is given by the equation q = 12 - p. The firm has a patent on zwiffle, so it can have a monopoly in this market.

A firm has invented a new beverage called Slops. It doesn't taste very good, but it gives people a craving for Lawrence Welk's music and Professor Johnson's jokes. Some people are willing to pay money for this effect, so the demand for Slops is given by the equation q = 10 - p. Slops can be made at zero marginal cost from old-fashioned macroeconomics books dissolved in bathwater. But before any Slops can be produced, the firm must undertake a fixed cost of $30. Since the inventor has a patent on Slops, it can be a monopolist in this new industry.

The Cleveland Visitors Bureau is the exclusive national marketer of weekend getaway vacations in Cleveland, Ohio. At current market prices, the price elasticity of demand is -.50. To maximize profits, the bureau should

The Cleveland Visitors Bureau is the exclusive national marketer of weekend getaway vacations in Cleveland, Ohio. At current market prices, the price elasticity of demand is -1. To maximize profits, the bureau should

A profit-maximizing monopoly faces an inverse demand function described by the equation p(y) = 30 - y and its total costs are c(y) = 5y, where prices and costs are measured in dollars. In the past it was not taxed, but now it must pay a tax of 2 dollars per unit of output. After the tax, the monopoly will

A monopolist faces the inverse demand function described by p = 23 - 5q, where q is output. The monopolist has no fixed cost and his marginal cost is $6 at all levels of output. Which of the following expresses the monopolist's profits as a function of his output?

The Fabulous 50s Decor Company is the only producer of pink flamingo lawn statues. While business is not as good as it used to be, in recent times the annual demand has been Q = 700 - 5P. Flamingo lawn statues are handcrafted by artisans using the process Q = min{L, } where L is hours of labor and P is pounds of pink plastic. P_L = 20 and P_P = 2. What would be the profit-maximizing output and price?

The demand for copies of the software package Macrosoft Doors is given by Q = 10,000P^-2. The cost to produce Doors is C = 100,000 + 5Q. If Macrosoft practices cost plus pricing, what would be the profit-maximizing markup?

A firm has invented a new beverage called Slops. It doesn't taste very good, but it gives people a craving for Lawrence Welk's music and Professor Johnson's jokes. Some people are willing to pay money for this effect, so the demand for Slops is given by the equation q = 14 - p. Slops can be made at zero marginal cost from old-fashioned macroeconomics books dissolved in bathwater. But before any Slops can be produced, the firm must undertake a fixed cost of $54. Since the inventor has a patent on Slops, it can be a monopolist in this new industry.