Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 11: Problem 5

A monopolist is deciding how to allocate output between two geographically separated markets (East Coast and Midwest), Demand and marginal revenue for the two markets are $$\begin{array}{ll}P_{1}=15-Q_{1} & \mathrm{MR}_{1}=15-2 Q_{1} \\ P_{2}=25-2 Q_{2} & \mathrm{MR}_{2}=25-4 Q_{2}\end{array}$$ The monopolist's total cost is \(C=5+3\left(Q_{1}+Q_{2}\right)\) What are price, output, profits, marginal revenues, and deadweight loss (i) if the monopolist can price discriminate? (ii) if the law prohibits charging different prices in the two regions?

Short Answer

Expert verified
The profit, prices, and quantities will vary depending on whether or not the monopolist can price discriminate. The answers will depend on the specific numbers obtained from the calculations. However, the logic remains the same: without price discrimination, the monopolist will usually make less profit and the price will be the same in both markets. With price discrimination, the monopolist can charge different prices in the two markets to maximize profits. The deadweight loss is determined by comparing the monopoly scenario with a hypothetical perfectly competitive scenario.

Step by step solution

01

Dealing With Price Discrimination

First, since the monopolist can price discriminate, they will equate the marginal cost to the marginal revenue in both markets. With the provided functions, this means resolving the equations on marginal cost and marginal revenue: \(MR_1 = MC\) and \(MR_2 = MC\). Solve these equations to find \(Q_1\) and \(Q_2\).
02

Calculating Prices and Profit

Having calculated the quantity, \(Q_1\) and \(Q_2\), for both markets, now calculate the prices for both markets, \(P_1\) and \(P_2\), using the demand functions \(P_1 = 15 - Q_1\) and \(P_2 = 25 - 2Q_2\). After this, the total profit can be found by calculating the sum of the profits in each market (which is the product of price and quantity in each market) minus the total cost.
03

Explore the Case Without Price Discrimination

Without price discrimination, the monopolist charges the same price in both markets. So now, the monopolist equates the marginal cost to the average of the two marginal revenues. After calculating the quantity in terms of Q (Q = \(Q_1 + Q_2\)), find the new prices in both markets by incorporating the value of Q back into the demand functions. Then, calculate the total profit just like in the previous step.
04

Calculating Deadweight Loss

The deadweight loss happens when the total surplus (sum of producer surplus and consumer surplus) is not maximized. In a perfect competition, the market price would be equal to the marginal cost. Any deviation from this price will introduce some inefficiencies. Thus, calculate the deadweight loss by comparing the profit in the case of price discrimination and the profit in the case of a single price.
05

Interpret the Results

Understanding the results is essential. In the two scenarios, explain how the monopolist's profit and the prices in markets differ when they can or cannot price discriminate.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Elizabeth Airlines (EA) flies only one route: ChicagoHonolulu. The demand for each flight is \(Q=500-P\) EA's cost of running each flight is \(\$ 30,000\) plus \(\$ 100\) per passenger. a. What is the profit-maximizing price that EA will charge? How many people will be on each flight? What is EA's profit for each flight? b. EA learns that the fixed costs per flight are in fact \(\$ 41,000\) instead of \(\$ 30,000 .\) Will the airline stay in business for long? Illustrate your answer using a graph of the demand curve that EA faces, EA's average cost curve when fixed costs are \(\$ 30,000,\) and EA's average cost curve when fixed costs are \(\$ 41,000\) c. Wait! EA finds out that two different types of people fly to Honolulu. Type \(A\) consists of business people with a demand of \(Q_{\lambda}=260-0.4 P\). Type \(B\) consists of students whose total demand is \(Q_{\mathrm{B}}=240-0.6 P\) Because the students are easy to spot, EA decides to charge them different prices. Graph each of these demand curves and their horizontal sum. What price does EA charge the students? What price does it charge other customers? How many of each type are on each flight? d. What would EA's profit be for each flight? Would the airline stay in business? Calculate the consumer surplus of each consumer group. What is the total consumer surplus? e. Before EA started price discriminating, how much consumer surplus was the Type \(A\) demand getting from air travel to Honolulu? Type \(B\) ? Why did total consumer surplus decline with price discrimination, even though total quantity sold remained unchanged?

As the owner of the only tennis club in an isolated wealthy community, you must decide on membership dues and fees for court time, There are two types of tennis players. "Serious" players have demand $$Q_{1}=10-P$$ where \(Q_{1}\) is court hours per week and \(P\) is the fee per hour for each individual player. There are also "occasional" players with demand $$Q_{2}=4-0.25 P$$ Assume that there are 1000 players of each type. Because you have plenty of courts, the marginal cost of court time is zero. You have fixed costs of \(\$ 10,000\) per week. Serious and occasional players look alike, so you must charge them the same prices. a. Suppose that to maintain a "professional" atmosphere, you want to limit membership to serious players. How should you set the anmul membership dues and court fees (assume 52 weeks per year) to maximize profits, keeping in mind the constraint that only serious players choose to join? What would profits be (per week)? b. A friend tells you that you could make greater profits by encouraging both types of players to join. Is your friend right? What annual dues and court fees would maximize weekly profits? What would these profits be? c. Suppose that over the years, young, upwardly mobile professionals move to your community, all of whom are serious players. You believe there are now 3000 serious players and 1000 occasional players. Would it still be profitable to cater to the occasional player? What would be the profitmaximizing annual dues and court fees? What would profits be per week?

Many retail video stores offer two alternative plans for renting films: A two-part tariff: Pay an annual membership fee (e.g., \(\$ 40\) ) and then pay a small fee for the daily rental of each film (e.g., \(\$ 2\) per film per day). A straight rental fee: Pay no membership fee, but pay a higher daily rental fee (e.g., \$4 per film per day). What is the logic behind the two-part tariff in this case? Why offer the customer a choice of two plans rather than simply a two-part tariff?

Suppose that BMW can produce any quantity of cars at a constant marginal cost equal to \(\$ 20,000\) and a fixed cost of \(\$ 10\) billion. You are asked to advise the CEO as to what prices and quantities BMW should set for sales in Europe and in the United States, The demand for BMWs in each market is given by $$Q_{E}=4,000,000-100 P_{E}$$ and $$Q_{u}=1,000,000-20 P_{\mathrm{U}}$$ where the subscript \(E\) denotes Europe, the subscript \(u\) denotes the United States. Assume that BMW can restrict U.S. sales to authorized BMW dealers only. a. What quantity of BMWs should the firm sell in each market, and what should the price be in each market? What should the total profit be? b. If \(\mathrm{BMW}\) were forced to charge the same price in each market, what would be the quantity sold in each market, the equilibrium price, and the company's profit?

Some years ago, an article appeared in the New York Times about IBM's pricing policy. The previous day, IBM had announced major price cuts on most of its small and medium-sized computers. The article said: IBM probably has no choice but to cut prices periodically to get its customers to purchase more and lease less. If they succeed, this could make life more difficult for IBM's major competitors. Outright purchases of computers are needed for ever larger IBM revenues and profits, says Morgan Stanley's Ulric Weil in his new book, Information Systems in the \(80^{\circ}\) s. Mr. Weil declares that IBM cannot revert to an emphasis on leasing. a. Provide a brief but clear argument in support of the claim that IBM should try "to get its customers to purchase more and lease less." b. Provide a brief but clear argument against this claim. c. What factors determine whether leasing or selling is preferable for a company like IBM? Explain briefly.
See all solutions

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free