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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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