Q1. Shell and Mobile, due to a turbulence in gasoline prices, have to come up with new pricing strategies in order to stay competitive. For simplicity, let's assume that both firms can choose between setting the price at $3/gallon OR $2/gallon. They set their prices at the same time. Because most Shell and Mobile stations, for some reason, are always next to one another, whoever sets the lower price will get ALL the customers. If they set the same price the split the customers in half. Suppose the market demand for a small town, Economiville is given by P = 6 - 2Q Where Q is measured by millions of gallons, and consumers in Economiville only have access to Shell or Mobile. Shell and Mobile have no costs of producing the gas (assume they have a prior contract with OPEC (organization of petroleum exporting countries) and have already paid for the gas in stock). This allows us to consider them maximizing their revenue.
a. If Shell charges $3, and Mobile charges $2, what are the revenues for the two firms? (Hint: remember that since Mobil is cheaper, consumers will buy gas from Mobile only at $2/gallon.)
b. If Shell charges $3 and Mobile charges $3, what are the revenues?
c. What about if Shell charges $2, Mobile charges $2?
d. Finally, what about Shell charges $2, Mobiles charges $3?
e. In light of your answers in (a)-(d), what is the Nash equilibrium of this price setting game between Shell and Mobile?
f. Briefly discuss how this example compares with the idea in Prisoner's Dilemma we talked about in class. Is the Nash equilibrium the best outcome for the firms, in terms of revenues earned at the Nash equilibrium?
g. Is this oligopolistic competition good for consumers?
Q2. Assume that two stores occupy the Huntington Mall! These stores are facing a decision of whether or not to hire a security guard for the mall. The benefit, in the form of reduced theft, to each store of hiring the guard is 8. The cost of hiring a guard is $10. If either store hires a guard for the mall the other store will benefit just as much as if it had hired the guard (i.e. the guard is non-rival and non-excludable). Additionally, we will assume the one guard is just as good as two guards, thus, if both stores agree to hire a guard they will split the cost of one guard. The following payoff matrix reflects the payoffs of firms engaged in the game where the stores simultaneously select whether to hire.
a. Is it socially optimal (or the best solution) for the stores to hire the guard? Why or why not?
b. What is the Nash Equilibrium of the game? Is the solution a result of free riding? Explain (Free riding is the benefit one gets from a good or service without paying for it)
c. Now, solve the stores security guard problem (i.e. define a scheme you think would get them to the social optimum).
Q3. 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 $1,000 per diamond, and the demand for diamond is described by the following schedule.
a. If the market for diamonds was perfectly competitive, what would the price and quantity be?
b. If there were only one supplier of diamonds, what would the price and quantity be?
c. If Russia and South Africa formed a cartel (or a collusive oligopoly), what would be the price and quantity?
d. If the countries split the market evenly, what would be South Africa's production and profit?
e. What would happen to South Africa's profit if it increased its production by 1,000 while Russia stuck to the cartel agreement?
f. Use your answer to part (e) to explain why cartel agreements are often not successful
Q4. Ford and Lexus are competing in the market for SUV's. We assume there are no other rivals in the SUV market. The companies are planning to introduce a new model in this summer. They should decide whether to invest lots of money in advertisements or not. The profits of the two firms depend on the joint choice of both firms. The payoff matrix for the firms' interaction of strategies is shown below.
a) Compute Nash Equilibrium of this game. Dose either firm have a dominant strategy?
b) What would happen if the firms agreed ahead of time to advertise normally? Would either firm violate the agreement?
c) Under what conditions might the firms be able to cooperate and have normal advertisement? Explain.