Maintaining collusion vs competing in a Cournot duopoly

Now consider two major oil-producing companies in the US: Chevronand Exxon Mobil. Suppose that the two companies compete in a Cournot Duopoly in the US and the aggregate demand function faced by the companies is given by the equation Q = 18,000,000 - P where Q is the average number of barrels of oil demand per day in the US and P is the price of a barrel of oil. Further, you can assume that the marginal cost of extracting a barrel of oil is $36 for both companies.

a.Assume that the two companies begin colluding with each other and act like a monopoly. What would be the price of a barrel of oil charged by this monopoly and how many barrels of oil would this monopoly choose to produce?(10 pts)

b.Now assume that the two companies find colluding with each other very difficult and so begin deviating from the collusive agreement, ie: they stop acting like a monopoly. Find the Nash equilibrium of this duopolistic market. Make sure to illustrate the best response functions of the two companies and the Bash equilibrium for full credit.(10 pts)

c.Which outcome do you think would be preferable to Exxon Mobil and Chevron, the duopolistic competition or collusive agreement to act as a monopoly? What obstacles do the companies face when trying to maintain a collusive agreement?(5 pts)