Suppose that Iran and Iraq are Cournot duopolists in the crude oil market and face the following market demand function:

P=100 - (q1 + q2);

Where q1 represents the output levels of the two countries with Iran being "I" and Iraq being "2" and P is the per-barrel price. The marginal revenue schedules facing the two countries are:

MR1 = 100 -2q1 -q2; and
MR2 = 100 - 2q2 - q1

Each country has a marginal cost curve of the form
MCi = qi;
Where i = 1, 2.

a) Describe 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 agreement?