EE 311 Homework 5

 

1. Suppose that Intel has a monopoly in the market for microprocessors in Brazil. During the year 2005, it faces a market demand curve given by P = 9 – Q, where Q is millions of microprocessors sold per year. Suppose you know nothing about Intel’s costs of production. Assuming that Intel acts as a profit-maximizing monopolist, would it ever sell 7 million microprocessors in Brazil in 2005?

 

 

2. A monopolist faces a demand curve P = 210 – 4Q and initially faces a constant marginal cost MC = 10.

a) Calculate the profit-maximizing monopoly quantity and compute the monopolist’s total revenue at the optimal price.

b) Suppose that the monopolist’s marginal cost increases to MC = 20. Verify that the monopolist’s total revenue goes down.

c) Suppose that all firms in a perfectly competitive equilibrium had a constant marginal cost MC = 10.

Find the long-run perfectly competitive industry price and quantity.

d) Suppose that all firms’ marginal costs increased to MC = 20. Verify that the increase in marginal cost causes total industry revenue to go up.

 

 

3. Suppose a monopolist has an inverse demand function given by P = 100Q-1/2. What is the monopolist’s optimal markup of price above marginal cost?

 

4. Imagine that Gillette has a monopoly in the market for razor blades in Mexico. The market demand curve for blades in Mexico is P = 968 – 20Q, where P is the price of blades in cents and Q is annual demand for blades expressed in millions. Gillette has two plants in which it can produce blades for the Mexican market: one in Los Angeles and one in Mexico City. In its L.A. plant, Gillette can produce any quantity of blades it wants at a marginal cost of 8 cents per blade. Letting Q1 and MC1 denote the output and marginal cost at the L.A. plant, we have MC1(Q1) = 8. The Mexican plant has a marginal cost function given by MC2(Q2) = 1 + 0.5Q2.

a) Find Gillette’s profit-maximizing price and quantity of output for the Mexican market overall. How will Gillette allocate production between its Mexican plant and its U.S. plant?

b) Suppose Gillette’s L.A. plant had a marginal cost of 10 cents rather than 8 cents per blade. How would your answer to part (a) change?

 

5. Market demand is P = 64 – (Q/7). A multiplant monopolist operates three plants, with marginal cost functions:

 

 

a) Find the monopolist’s profit-maximizing price and output at each plant. b) How would your answer to part (a) change if MC2 (Q2) = 4?

 

 

6. Suppose that a monopolist’s market demand is given by P = 100 – 2Q and that marginal cost is

given by MC = Q/2.

a) Calculate the profit-maximizing monopoly price and quantity.

b) Calculate the price and quantity that arise under perfect competition with a supply curve P = Q/2.

c) Compare consumer and producer surplus under monopoly versus marginal cost pricing. What is the deadweight loss due to monopoly?

d) Suppose market demand is given by P = 180 – 4Q. What is the deadweight loss due to monopoly now? Explain why this deadweight loss differs from that in part (c).

 

7. Which of the following are examples of first-degree, second-degree, or third-degree price discrimination?

a) The publishers of the Journal of Price Discrimination charge a subscription price of $75 per year to individuals and $300 per year to libraries.

b) The U.S. government auctions off leases on tracts of land in the Gulf of Mexico. Oil companies bid for the right to explore each tract of land and to extract oil.

c) Ye Olde Country Club charges golfers $12 to play the first 9 holes of golf on a given day, $9 to play an additional 9 holes, and $6 to play 9 more holes.

d) The telephone company charges you $0.10 per minute to make a long-distance call from Monday through Saturday and $0.05 per minute on Sunday.

e) You can buy one computer disk for $10, a pack of 3 for $27, or a pack of 10 for $75.

f) When you fly from New York to Chicago, the airline charges you $250 if you buy your ticket 14 days in advance, but $350 if you buy the ticket on the day of travel.

 

 

8. Suppose a profit-maximizing monopolist producing Q units of output faces the demand curve P = 20 – Q. Its total cost when producing Q units of output is TC = 24 + Q2. The fixed cost is sunk, and the marginal cost curve is MC = 2Q.

a) If price discrimination is impossible, how large will the profit be? How large will the producer surplus be?

b) Suppose the firm can engage in perfect first-degree price discrimination. How large will the profit be? How large is the producer surplus?

c) How much extra surplus does the producer capture when it can engage in first-degree price discrimination instead of charging a uniform price?

 

9. Fore! is a seller of golf balls that wants to increase its revenues by offering a quantity discount. For simplicity, assume that the firm sells to only one customer and that the demand for Fore!’s golf balls is P = 100 – Q. Its marginal cost is MC = 10. Suppose that Fore! sells the first block of Q1 golf balls at a price of P1 per unit.

a) Find the profit-maximizing quantity and price per unit for the second block if Q1 = 20 and P1 = 80.

b) Find the profit-maximizing quantity and price per unit for the second block if Q1 = 30 and P1 = 70.

c) Find the profit-maximizing quantity and price per unit for the second block if Q1 = 40 and P1 = 60.

d) Of the three options in parts (a) through (c), which block tariff maximizes Fore!’s total profits?

 

 

 

10. Suppose that Acme Pharmaceutical Company discovers a drug that cures the common cold. Acme has plants in both the United States and Europe and can manufacture the drug on either continent at a marginal cost of 10. Assume there are no fixed costs. In Europe, the demand for the drug is QE = 70 – PE, where QE is the quantity demanded when the price in Europe is PE. In the United States, the demand for the drug is QU = 110 – PU, where QU is the quantity demanded when the price in the United States is PU.

a) If the firm can engage in third-degree price discrimination, what price should it set on each continent to maximize its profit?

b) Assume now that it is illegal for the firm to price discriminate, so that it can charge only a single price P on both continents. What price will it charge, and what profits will it earn?

c) Will the total consumer and producer surplus in the world be higher with price discrimination or without price discrimination? Will the firm sell the drug on both continents?

 

 

11. You are the only European firm selling vacation trips to the North Pole. You know only three customers are in the market. You offer two services, round trip airfare and a stay at the Polar Bear Hotel. It costs you 300 euros to host a traveler at the Polar Bear and 300 euros for the airfare. If

EEE

 (60 10)50  2500 . Total profit will be   3400 .

b) If the firm can only sell the drug at one price, it will set the price to maximize total

  (P 10)Q UUU

you do not bundle the services, a customer might buy your airfare but not stay at the hotel. A customer could also travel to the North Pole in some other way (by private plane), but still stay at the Polar Bear. The customers have the following reservation prices for these services:

 

 

a) If you do not bundle the hotel and airfare, what are the optimal prices PA and PH, and what profits do you earn?

b) If you only sell the hotel and airfare in a bundle, what is the optimal price of the bundle PB, and what profits do you earn?

c) If you follow a strategy of mixed bundling, what are the optimal prices of the separate hotel, the separate airfare, and the bundle (PA, PH, and PB, respectively) and what profits do you earn?

 

 

12. You operate the only fast-food restaurant in town, selling burgers and fries. There are only two customers, one of whom is on the Atkins diet and the other on the Zone diet, whose willingness to pay for each item is displayed in the following table. For simplicity, assume you have zero fixed and marginal costs for each item.

a) If x = 1 and you do not bundle the two products, what are your profit-maximizing prices PB and PF? Calculate total surplus under this outcome.

b) Now assume only that x > 0. Instead, suppose that you hired an economist who tells you that the profit-maximizing bundle price (for a burger and fries) is $8, while if you sold the items individually (and did not offer a bundle) your profit-maximizing price for fries would be greater than $3. Using this information, what is the range of possible values for x?