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1. Suppose that the demand for oil is given by P = 120 – Q, where Q is the total market

demand for oil and is measured in barrels of oil. Assume that there are no costs of

producing oil in OPEC countries. Assume that costs of producing oil in non-OPEC

countries is $10 per barrel (AC=MC=10). Non-OPEC producers always produce 20

barrels as long as price remains above their average production costs and they shut

down otherwise. [General hint for what you have so far: Write Q = Q c + Q o , where

Q c is the competitive fringe supply by non-OPEC countries and Q o is quantity

produced by OPEC. Q c is always 20 as long as P > $10.]

i) Given that price is above $10, what is the profit maximizing quantity and

price for OPEC? How much profit does OPEC make?

ii) The oil minister for Kuwait claims that OPEC would make more profit by

lowering price and forcing non-OPEC producers to shut down. Demonstrate

whether this claim is correct or not.

iii) Suppose that Iraq’s quota for OPEC is 1/5 of the total. If Iraq is sure that the

other members of the cartel are going to abide by the cartel agreement, show

that Iraq can gain more profit by expanding output. [Hint: Find the profit

maximizing level of production for Iraq.]

iv) Explain what measures OPEC members can take to keep Iraq (or any other

member of the cartel) from cheating on the cartel agreement.

(35) 2. Suppose there are two firms in an industry that has a demand curve given by the

equation P = 60 − Q, where P is industry price, and Q the industry output. Assume

that costs of production are zero.

i) Solve for the cartel level of output and profit for each firm. (Assume a 50-50

split of output and profit.)

ii) Solve for the profit maximizing level of production for a firm if it decides to

cheat on the cartel agreement given that the other firm abides by the cartel

agreement. Find the level of profits for each firm. [Hint: Write the profit

maximization problem for the firm that cheats and remember that the output

level of the firm that abides by the cartel agreement is fixed at the level you

found in part i).]

iii) Find the level of profit for each firm if they both produce at the level of a

cheating firm solved for in part ii) above.

iv) Use the results from parts i) through iii) to derive a payoff matrix where each

player has two strategies: a) cooperate and stick with the agreement; or b)

cheat on the agreement.

v) What are the likely outcomes of this game? Be sure to explain how your

answer would vary with different assumptions you choose to make.

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