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 q i 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:

MR₁ = 100 – 2q₁ – q₂ and

MR₂ = 100 – 2q₂ – q₁

Each country has a marginal cost curve of the form: 

MC_i = q_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?

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?