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Chapter 17 Exercises 6-9. Oligopoly. Principles of Economics. G. Mankiw. 7th Edition
6. You and a classmate are assigned a project on which you will receive one 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 both 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
c. 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: She gets 50 units of happiness for a B, and 80 units of happiness for an A. If this classmate were your partner (but your preferences were unchanged), how would your answers to parts (a) and (b) change? Which of the two classmates would you prefer as a partner? Would she also want you as a partner?
d. Another classmate cares more about good grades: She gets 50 units of happiness for a B, and 80 units of happiness for an A. If this classmate were your partner (but your preferences were unchanged), how would your answers to parts (a) and (b) change? Which of the two classmates would you prefer as a partner? Would she 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 charges $300, it earns low profit if the other company also charges $300 and high profit if the other company charges $600. On the other hand, if the company charges $600, it earns very low profit if the other company charges $300 and medium profit if the other company also charges $600.
b. What is the Nash equilibrium in this game? Explain.
c. Is there an outcome that would be better than the Nash equilibrium for both airlines? How could it be achieved? Who would lose if it were achieved?
8. Two athletes of equal ability are competing for a prize of $10,000. Each is deciding whether to take a dangerous performance-enhancing drug. If one athlete takes the drug, and the other does not, the one who takes the drug wins the prize. If both or neither take the drug, they tie and split the prize. Taking the drug imposes health risks that are equivalent to a loss of X dollars.
a. Draw a 2 × 2 payoff matrix describing the decisions the athletes face
b. For what X is taking the drug the Nash equilibrium?
c. Does making the drug safer (that is, lowering X) make the athletes better or worse off? Explain.
9. Little Kona is a small coffee company that 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:
Does 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. Big 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 collude and agree on how to split the total profits, what outcome would they pick?