Econ 101
PROBLEM SET 10
Wissink

1. Answer the question or critically evaluate the statement and explain whyor in what way the statement is true, false, or uncertain.

a) If OPEC could include all oil producing countries in their cartel and could strictly enforce price and quantity targets, then the price of gasoline would be unlimited.

b) Oligopolistic industries are both allocatively and productively efficient.

c) Given a fully described game, a dominant strategy for a player will also be a best response strategy for that player, furthermore, all best response strategies are dominant strategies.

d) The incentive to cheat in a cartel will be greater when the cartel produces a homogeneous good.

e) A member of a cartel has no incentive to violate the rules of the cartel since the cartel equates marginal revenue to marginal cost, thereby maximizing the profit of each member.

2. Graphically show the demand and marginal revenue curves for a: i) perfectly competitive firm; ii) monopolist; iii) monopolist that is able to perfectly price discriminate; iv) Sweezy oligopolist. How would a small increase in factor prices affect output and price in each case?

3. Consider each of the following games described below. For each game determine the dominant strategy equilibrium, Nash equilibrium, and/or maximin equilibrium, if they exist. In each case the numbers in parentheses refer to the payoffs for firm 1 and firm 2, respectively. Firm 1 can choose either A or B. Firm 2 can choose either C or D.

4. Suppose that Abe is a true believer in Cournot's model of oligopoly while Betty believes that Bertrand's oligopoly model is more accurate. How would Abe's and Betty's analyses of the "cola" market differ? Specifically, how would Abe and Betty compare the prevailing market prices and quantities of colas, as well as firm profitability, to what the prices, quantities, and profits would be if the cola market were perfectly competitive?

5. In a typical New York Times article (5/9/88) entitled, "April Output by OPEC UP," the International Energy Agency reported that "oil production by OPEC rose to 18.2 million barrels/day in April from 17.7 m. barrels in March." Part of this increase was attributed to Iraq's refusal to sign the group's production sharing program and its subsequent increase in output to 2.6 m. barrels/day. OPEC's other 12 members however cooperated with their agreements and produced close to their agreed upon quota.

a) Explain why oligopolists have an incentive to collude (i.e., what are the advantages to the oligopolists from cartelization?), and graphically describe how the cartel determines the cartel's profit maximizing level of output and target price. How are production quotas for the individual cartel members determined.

Suppose we could model this issue as a game between Iraq and the rest of OPEC. Each player has two strategies: Low quantities of oil production and high quantities of oil production. In "tree form" we can write this game as follows.

NOTE: The payoffs are written as (rest of OPEC's payoff, Iraq's payoff). Also note that the game is played simultaneously, that is neither the rest of OPEC nor IRAQ can observe the other country's strategy before choosing their own strategy.

b) Write the game in its "box" form, a.k.a. normal or matrix form.

c) Do there exist any dominant strategy equilibria to this game? Is so what are they?

d) Do there exist any Nash equilibria to this game? If so what are they?

e) If you were to advise the OPEC ministers, could you suggest an outcome that is better for the group than the outcome(s) you found above? Explain. What terms would you suggest be written into any contracts the two parties endorse. Is it necessary that these contracts be enforceable? Why or why not?

f) Presumably, contracts like the one you suggested in your answer to part (h) are written up and signed by the OPEC countries, eventually. Why is it then, that we consistently observe oil selling at prices below the OPEC target price?

6. Assume that Coke and Pepsi are the only two manufacturers of cola soft drinks. Assume they happen to be endowed with the following marginal cost schedules. Coke and Pepsi are thinking about colluding with each other in spite of its illegality and implementing the "multi-plant monopoly solution."

a) What is the cost minimizing way to allocate the production of 1 gallon of syrup between Coke and Pepsi? What is the marginal cost of producing this first gallon of syrup?

b) What is the cost minimizing way to allocate the production of 2 gallons of syrup between Coke and Pepsi? What is the marginal cost of producing the second gallon of syrup?

c) What is the cost minimizing way to allocate the production of 3 gallons of syrup between Coke and Pepsi? What is the marginal cost of producing this third gallon of syrup?

d) Based on your answers to a., b., and c., above, determine the cartel's marginal cost schedule and graph it.

e) Suppose you are given the following market demand information for cola syrup. Determine marginal revenue and graph it along with marginal cost and demand.

price: $15 $14 $13 $12 $11 $10 $9 $8 $7 $6 $5 $4 $3 $2 $1 $0

demand: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

f) What is the cartel's profit maximizing level of output. What price should the cartel set for its output? Show on your graph. What production quota should be given to the two members of the cartel? What is cartel profit? Without side payments, what is the profit of each cartel member?

g) Would your answer to part f. change if Coke and Pepsi were to horizontally merge into Coksi-cola? Explain.

h) Suppose industry output was set to be allocatively efficient. If so, what quantity should be produced? At what price should syrup be sold? How much syrup will each company produce?