Exam 23: Monopoly

A baseball teams attendance depends on the number of games it wins per season and on the price of its tickets. The demand function it faces is Q = N(20 - p), where Q is the number of tickets (in hundred thousands) sold per year, p is the price per ticket, and N is the fraction of its games that the team wins. The team can increase the number of games it wins by hiring better players. If the team spends C million dollars on players, it will win .7 - of its games. Over the relevant range, the marginal cost of selling an extra ticket is zero. a. Write an expression for the firms profits as a function of ticket price and expenditure on players. b. Find the ticket price that maximizes revenue. c. Find the profit-maximizing expenditure on players and the profit-maximizing fraction of games to win.

If the interest rate is 10%, a monopolist will choose a markup of price over marginal cost of at least 10%.

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?

The Hard Times Concrete Company is a monopolist in the concrete market. It uses two inputs, cement and gravel, which it buys in competitive markets. The company's production function is q, where q is its output, c is the amount of cement it uses, and g is the amount of gravel it uses. If the price of cement goes up, the firm's demand for cement

Charlie can work as many hours as he wishes at a local fast-food restaurant for a wage of $4 per hour. Charlie also does standup comedy. Since Charlie lives in a quiet, rather solemn Midwestern town, he is the town's only comedian and has a local monopoly for standup comedy. The demand for comedy is Q = 40 - P, where Q is the number of hours of comedy performed per week and P is the price charged per hour of comedy. When Charlie maximizes his utility, he spends at least 1 hour per week working at the restaurant and he gets at least 1 hour of leisure time. His utility depends only on income and leisure. How many hours per week does he perform standup comedy?

In a market with the inverse demand curve P = 10 - Q, Brand X is a monopolist with no fixed costs and with a marginal cost of $2. If marginal cost rises to $4, by how much will the price of Brand X rise?

A monopolist faces a downward-sloping demand curve and has fixed costs so large that when she maximizes profits with a positive amount of output, she earns exactly zero profits. At this positive, profit-maximizing output,

A monopolist faces a constant marginal cost of $1 per unit. If at the price he is charging, the price elasticity of demand for the monopolist's output is -0.5, then

A major software developer has estimated the demand for its new personal finance software package to be Q = 1,000,000P^-1.40 while the total cost of the package is C = 100,000 + 20Q. If this firm wishes to maximize profit, what percentage markup should it place on this product?

In some parts of the world, Red Lizzard Wine is alleged to increase one's longevity. It is produced by the process Q = min{ ( )L, R}, where L is the number of spotted red lizards and R is gallons of rice wine. P_L = P_R = $1. Demand for Red Lizzard Wine in the United States is Q = . If the advertising budget is $144, the quantity of wine which should be imported into the United States is

A monopolist has decreasing average costs as output increases. If the monopolist sets price equal to average cost, it will

A monopolist will always equate marginal revenue and marginal cost when maximizing profit.

An industry has two firms, a leader and a follower. The demand curve for the industry's output is given by p = 456 - 6q, where q is total industry output. Each firm has zero marginal cost. The leader chooses his quantity first, knowing that the follower will observe the leader's choice and choose his quantity to maximize profits, given the quantity produced by the leader. The leader will choose an output of

A monopoly has the demand curve q = 10,000 - 100p. Its total cost function is c(q) = 1,000 + 10q. The government plans to tax the monopoly's profits at a rate of 50%. If it does so, the monopoly will

A monopolist has the total cost function c(q) = 800 + 8q. The inverse demand function is 80 - 6q, where prices and costs are measured in dollars. If the firm is required by law to meet demand at a price equal to its marginal costs,

A natural monopoly occurs when a firm gains ownership of the entire stock of some natural resource and thus is able to exclude other producers.

A monopolist faces the inverse demand curve p = 64 - 2q. At what level of output is his total revenue maximized?

A profit-maximizing monopolist sets

Peter Morgan sells pigeon pies from his pushcart in Central Park. Due to the abundant supplies of raw materials, his costs are zero. The demand schedule for his pigeon pies is p(y) = . What level of output will maximize Peter's profits?

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 = 400 - 6P. 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 = 15 and P_P = 3. What would be the profit-maximizing output and price?