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Suppose that Iran and Iraq are Cournot duopolists in the crude oil market and face the following market demand function: P qq = −+ 100 1 2 ( ), where qi represents the output levels of the two countries with Iran being 1 and Iraq being 2, and P is the per-barrel price. The marginal revenue schedules facing the two countries are: MR q q MR q q 1 1 2 2 2 1 100 2 100 2 = −− =−− and . Each country has a marginal cost curve of the form: MC q i i = , where i = 1, 2. a. Determine each country’s reaction function. b. Does a Cournot equilibrium exist? If so, find the outputs and prices of crude oil in the two countries. c. Suppose that the two countries collude and become a cartel. What will be the resulting price and outputs for crude oil for the two countries? [Note that the market marginal revenue is 100 − 2(q1 + q2).] d. Can it be said that because collusive profits are strictly greater, it is true that these countries should necessarily collude? Are there any potential pitfalls in such a collusive arrangement?