## 9.7PROBLEMS

### Question 9.8

1. The accompanying table shows the demand schedule for vitamin D. Suppose that the marginal cost of producing vitamin D is zero.

 Price of vitamin D(per ton) Quantity of vitamin D demanded(tons) \$8 0 7 10 6 20 5 30 4 40 3 50 2 60 1 70
1. Assume that BASF is the only producer of vitamin D and acts as a monopolist. It currently produces 40 tons of vitamin D at \$4 per ton. If BASF were to produce 10 more tons, what would be the price effect for BASF? What would be the quantity effect? Would BASF have an incentive to produce those 10 additional tons?

2. Now assume that Roche enters the market by also producing vitamin D and the market is now a duopoly. BASF and Roche agree to produce 40 tons of vitamin D in total, 20 tons each. BASF cannot be punished for deviating from the agreement with Roche. If BASF, on its own, were to deviate from that agreement and produce 10 more tons, what would be the price effect for BASF? What would be the quantity effect for BASF? Would BASF have an incentive to produce those 10 additional tons?

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### Question 9.9

2. The market for olive oil in New York City is controlled by two families, the Sopranos and the Contraltos. Both families will ruthlessly eliminate any other family that attempts to enter the New York City olive oil market. The marginal cost of producing olive oil is constant and equal to \$40 per gallon. There is no fixed cost. The accompanying table gives the market demand schedule for olive oil.

 Price of olive oil(per gallon) Quantity of olive oil demanded(gallons) \$100 1,000 90 1,500 80 2,000 70 2,500 60 3,000 50 3,500 40 4,000 30 4,500 20 5,000 10 5,500
1. Suppose the Sopranos and the Contraltos form a cartel. For each of the quantities given in the table, calculate the total revenue for their cartel and the marginal revenue for each additional gallon. How many gallons of olive oil would the cartel sell in total and at what price? The two families share the market equally (each produces half of the total output of the cartel). How much profit does each family make?

2. Uncle Junior, the head of the Soprano family, breaks the agreement and sells 500 more gallons of olive oil than under the cartel agreement. Assuming the Contraltos maintain the agreement, how does this affect the price for olive oil and the profit earned by each family?

3. Anthony Contralto, the head of the Contralto family, decides to punish Uncle Junior by increasing his sales by 500 gallons as well. How much profit does each family earn now?

### Question 9.10

3. In France, the market for bottled water is controlled by two large firms, Perrier and Evian. Each firm has a fixed cost of €1 million and a constant marginal cost of €2 per liter of bottled water (€1 = 1 euro). The following table gives the market demand schedule for bottled water in France.

 Price of bottled water(per liter) Quantity of bottled waterdemanded (millions of liters) €10 0 9 1 8 2 7 3 6 4 5 5 4 6 3 7 2 8 1 9
1. Suppose the two firms form a cartel and act as a monopolist. Calculate marginal revenue for the cartel. What will the monopoly price and output be? Assuming the firms divide the output evenly, how much will each produce and what will each firm’s profit be?

2. Now suppose Perrier decides to increase production by 1 million liters. Evian doesn’t change its production. What will the new market price and output be? What is Perrier’s profit? What is Evian’s profit?

3. What if Perrier increases production by 3 million liters? Evian doesn’t change its production. What would its output and profit be relative to those in part b?

4. What do your results tell you about the likelihood of cheating on such agreements?

### Question 9.11

4. Over the last 40 years the Organization of Petroleum Exporting Countries (OPEC) has had varied success in forming and maintaining its cartel agreements. Explain how the following factors may contribute to the difficulty of forming and/or maintaining its price and output agreements.

1. New oil fields are discovered and increased drilling is undertaken in the Gulf of Mexico and the North Sea by nonmembers of OPEC.

2. Crude oil is a product that is differentiated by sulfur content: it costs less to refine low-sulfur crude oil into gasoline. Different OPEC countries possess oil reserves of different sulfur content.

### Question 9.12

5. Suppose you are an economist working for the Antitrust Division of the Department of Justice. In each of the following cases you are given the task of determining whether the behavior warrants an antitrust investigation for possible illegal acts or is just an example of undesirable, but not illegal, tacit collusion. Explain your reasoning.

1. Two companies dominate the industry for industrial lasers. Several people sit on the boards of directors of both companies.

2. Three banks dominate the market for banking in a given state. Their profits have been going up recently as they add new fees for customer transactions. Advertising among the banks is fierce, and new branches are springing up in many locations.

3. The two oil companies that produce most of the petroleum for the western half of the United States have decided to forgo building their own pipelines and to share a common pipeline, the only means of transporting petroleum products to that market.

4. The two major companies that dominate the market for herbal supplements have each created a subsidiary that sells the same product as the parent company in large quantities but with a generic name.

5. The two largest credit card companies, Passport and OmniCard, have required all retailers who accept their cards to agree to limit their use of rival credit cards.

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### Question 9.13

6. To preserve the North Atlantic fish stocks, it is decided that only two fishing fleets, one from the United States and the other from the European Union (EU), can fish in those waters. Suppose that this fisheries agreement breaks down, so that the fleets behave noncooperatively. Assume that the United States and the EU each can send out either one or two fleets. The more fleets in the area, the more fish they catch in total but the lower the catch of each fleet. The accompanying matrix shows the profit (in dollars) per week earned by each side.

1. What is the noncooperative Nash equilibrium? Will each side choose to send out one or two fleets?

2. Suppose that the fish stocks are being depleted. Each region considers the future and comes to a tit-for-tat agreement whereby each side will send only one fleet out as long as the other does the same. If either of them breaks the agreement and sends out a second fleet, the other will also send out two and will continue to do so until its competitor sends out only one fleet. If both play this tit-for-tat strategy, how much profit will each make every week?

### Question 9.14

7. Untied and Air “R” Us are the only two airlines operating flights between Collegeville and Bigtown. That is, they operate in a duopoly. Each airline can charge either a high price or a low price for a ticket. The accompanying matrix shows their payoffs, in profits per seat (in dollars), for any choice that the two airlines can make.

1. Suppose the two airlines play a one-shot game—that is, they interact only once and never again. What will be the Nash (noncooperative) equilibrium in this one-shot game?

2. Now suppose the two airlines play this game twice. And suppose each airline can play one of two strategies: it can play either always charge the low price or tit for tat—that is, it starts off charging the high price in the first period, and then in the second period it does whatever the other airline did in the previous period. Write down the payoffs to Untied from the following four possibilities:

1. Untied plays always charge the low price when Air “R” Us also plays always charge the low price.

2. Untied plays always charge the low price when Air “R” Us plays tit for tat.

3. Untied plays tit for tat when Air “R” Us plays always charge the low price.

4. Untied plays tit for tat when Air “R” Us also plays tit for tat.

### Question 9.15

8. Suppose that Coke and Pepsi are the only two producers of cola drinks, making them duopolists. Both companies have zero marginal cost and a fixed cost of \$100,000.

1. Assume first that consumers regard Coke and Pepsi as perfect substitutes. Currently both are sold for \$0.20 per can, and at that price each company sells 4 million cans per day.

1. How large is Pepsi’s profit?

2. If Pepsi were to raise its price to \$0.30 per can, and Coke did not respond, what would happen to Pepsi’s profit?

2. Now suppose that each company advertises to differentiate its product from the other company’s. As a result of advertising, Pepsi realizes that if it raises or lowers its price, it will sell less or more of its product, as shown by the demand schedule in the accompanying table.

 Price of Pepsi(per can) Quantity of Pepsi demanded(millions of cans) \$0.10 5 0.20 4 0.30 3 0.40 2 0.50 1

If Pepsi now were to raise its price to \$0.30 per can, what would happen to its profit?

3. Comparing your answer to part a(i) and to part b, what is the maximum amount Pepsi would be willing to spend on advertising?

### Question 9.16

9. Philip Morris and R.J. Reynolds spend huge sums of money each year to advertise their tobacco products in an attempt to steal customers from each other. Suppose each year Philip Morris and R.J. Reynolds have to decide whether or not they want to spend money on advertising. If neither firm advertises, each will earn a profit of \$2 million. If they both advertise, each will earn a profit of \$1.5 million. If one firm advertises and the other does not, the firm that advertises will earn a profit of \$2.8 million and the other firm will earn \$1 million.

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1. Use a payoff matrix to depict this problem.

2. Suppose Philip Morris and R.J. Reynolds can write an enforceable contract about what they will do. What is the cooperative solution to this game?

3. What is the Nash equilibrium without an enforceable contract? Explain why this is the likely outcome.

### Question 9.17

10. Use the three conditions for monopolistic competition discussed in the chapter to decide which of the following firms are likely to be operating as monopolistic competitors. If they are not monopolistically competitive firms, are they monopolists, oligopolists, or perfectly competitive firms?

1. A local band that plays for weddings, parties, and so on

2. Minute Maid, a producer of individual-serving juice boxes

4. A farmer who produces soybeans

### Question 9.18

11. You are thinking of setting up a coffee shop. The market structure for coffee shops is monopolistic competition. There are three Starbucks and two other coffee shops very much like Starbucks in your town already. In order for you to have some degree of market power, you may want to differentiate your coffee shop. Thinking about the three different ways in which products can be differentiated, explain how you would decide whether you should copy Starbucks or whether you should sell coffee in a completely different way.

WORK IT OUT

| interactive activity

### Question 9.19

12. Let’s revisit the fisheries agreement introduced in Problem 6 stating that to preserve the North Atlantic fish stocks, only two fishing fleets, one from the United States and the other from the European Union (EU), can fish in those waters. The accompanying table shows the market demand schedule per week for fish from these waters. The only costs are fixed costs, so fishing fleets maximize profit by maximizing revenue.

 Price of fish(per pound) Quantity of fish demanded(pounds) \$17 1,800 16 2,000 15 2,100 14 2,200 12 2,300
1. If both fishing fleets collude, what is the revenue-maximizing output for the North Atlantic fishery? What price will a pound of fish sell for?

2. If both fishing fleets collude and share the output equally, what is the revenue to the EU fleet? To the U.S. fleet?

3. Suppose the EU fleet cheats by expanding its own catch by 100 pounds per week. The U.S. fleet doesn’t change its catch. What is the revenue to the U.S. fleet? To the EU fleet?

4. In retaliation for the cheating by the EU fleet, the U.S. fleet also expands its catch by 100 pounds per week. What is the revenue to the U.S. fleet? To the EU fleet?