Problems And Applicatio

1. A large share of the world supply of diamonds Comes from Russia and South Africa. Suppose that the marginal cost of mining diamonds is constant at $1,00!) per diamond, and the demand for diamonds is described by the following schedule: Price Gusnt«y

7M0 6.0C0

6030 7,000

S030 S.OCO

4.030 9.000

3X00 10. COO ?O30 11.COO 1050 12.COO

a. If there were many suppliers of diamonds, what would be the price and quantity? L>. If there were only one supplier of diamonds, what would be the price anil quantity?

c. If Russia and South Africa formed a cartel, what would be the priceand quantity? If the countries split the market evenly, what would be South Africa's production and profit? What would happen to South Africa's profit if it increased its production by 1,000 while Russia stuck to the cartel agreement?

d. Use your answers to part (c) to explain why cartel agreements are often not successful.

2. The New Yort Times (Nov. 30. 1993) reported that "the inability of OPF.C to agree List week to cut production has sent the oil market into turmoil... [leading to) the lowest price for domestic crude oil since June 1990."

a. Why were the members of OI'F.C trying to agree to cut production?

b. Why do you suppose OPEC was unable lo agree on cutting production? Why did the oil market go into "turmoil" as a result?

c. The newspaper also noted OPEC's view "thai producing nations outside Ihe organization, like Norway and Britain, should do their share and ait production." What does the phrase "do their share" suggest about OPEC's de-sired relationship with Norway and Britain?

3. This chapter discussers companies thai are oligopolists in the market for the goods the-v sell. Many of the same ideas apply to companies that are oligopolists in the market for the inputs they buy.

a. If sellers who are oligopolists try to increase the price of goods they sell, what is the goal of buyers who are oligopolists?

b. Major league baseball te-am owners have an oligopoly in the market for baseball players. What is the owners' goal regarding players' salaries? Why is this goal difficult to achieve?

C. Baseball players went on strike in 199-1 because the)- would not accept the salary cap that the owners wanted to impose, If the owners were already colluding over salaries, why did the owners feel the need for a salary cap?

4. Consider trade relatkms between the United Stales and Mexico. Assume that the leaders of the two countries believe the payoffs to alternative trade policies are as follows:

I haM

«1« ruts a. What is the dominant strategy for the United Stales? For Mexico? Explain.

b. Define Masfr equilibrium. What is the Nash equilibrium for trade policy?

c. In 1993 the U.S. Congress ratified the North American Free Trade Agreement, in which the United States and Mexico agreed to reduce trade barriers simultaneously. the perceived payoffs shown here justify this approach to trade policy? Explain.

d. Based on your understanding of the gains from trade (discussed in Chapters 3 and 9), do you think that these payoffs actually reflect <1 nation's welfare under the four possible outcomes?

5. Synergy and Dynaco are the only two firms in a specific high-tech industry. They face the following payoff matrix as they decide upon the size of their research budget:

a. Does Synergy have a dominant strategy? Explain.

b Does Dynaco have a dominant strategy? Explain.

c. 1» there; a Nash equilibrium fur this scenario? Explain. (Hint: Look closely at the definition of Nash equilibrium.) 6. You and a classmate are assigned a project on which you will receive i>ne combined grade. You each want to receive a good grade-, but you also want to avoid hard work. In particular, here is the situation:

• If both of you work hard, you Kith get an A, which gives each of you 40 units of happiness.

• If only one of you works hard, you both get a B, which gives each of you 30 units of happiness.

• If neither of you works hard, you both get a D. which gives each of you 10 units of happiness.

• Working hard costs 25 units of happiness, a. Fill in the payoffs in the following decision box:

b. What is the likely outcome? Explain your answer.

e\ If you get this classmate as your partner on a series of projects throughout the year, rather than only once, how might that change the outcome you predicted in part (b)? d. Another classmate cares more about good grades: He gets 50 units of happiness for a B. and 80 units of happiness from an A. If this classmate were your partner (but your preferences were unchanged), how would your answers to parts (a) and lb) change-? Which of the two classmates would you prefer as a partner? Would he also want you as a partner?

7. A case study in the chapter describes a phone conversation between the presidents of American Airlines and Braniff Airways. Let's analyze the game between the two companies. Suppose that each company can charge either a high price for tickets or a low price. If one company chargers 5100, it earns low profits if the other company charges $100 also, and high profits if the other company charges $200. On the other hand, if the company charges 3200, it earns very low profits if the other company charges 5100, and medium profits if the other company charges $200 also.

a. Draw the decision box far this game.

b. What is the Nash equilibrium in this game? Explain.

c. Is there an outcome that would be better than the Nasi» equilibrium for both airlines? How could it be achieved? Who would lose if it were achieved?

8. Little Kona is a small coffee company thai is considering entering a market dominated by Big Brew. Each company's profit depends on whether Little Kona enters and whether Big Brew sets a high price or a low price:

Docs either player in this game have a dominant strategy?

b. Does your answer to part (a) help you figure out what the other player should do? What is the Nash equilibrium? Is there only one?

c. Dig Brew threatens Little Kona by saying, "If you enter, we're going to set a low price, so you had better stay out." Do you think Little Kona should believe the threat? Why or why not?

d. If the two firms could colludc and agree on how to split the total profits, what outcome would they pick?

9. Jeff and Steve are playing tennis. Every point comes down to whether Steve guesses correctly whether Jeff will hit the ball to Steve's left or right. The outcomes are:

Does either player have a dominant strategy? If Jeff chooses a particular strategy (Left or Right) and sticks with it, what will Steve do? Can you think of a better strategy for Jeff to follow?

10. Let's return to the chapter's discussion of lack and I ill's water duopoly. Suppose that lack and Jill are at the duopoly's Nash equilibrium (80 gallons) when a third person, John,discovers a water source and joins the market as a third producer.

a. Jack ami Jill pnipose- that the three* of them continue to produce a total of 80 gallons, splitting the market three ways. If John agrees to this, how much profit will he make?

b. After agreeing to the proposed deal, John is considering increasing his production by 10 gallons. If he does, and lack and lill stick to the agreement, how much profit will John make? What does this tell you about the proposed agreement?

c. What is the Nash equilibrium for this market with three? producers? How does it compare to the Nash equilibrium with two producers?

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