Firms A and B compete as Cournot duopolists in the cola market. The demand and marginal revenue are given by: p = 200 - Y, where Y = yA + yB is total output. Marginal revenue for each firm is
MRA = 200 - yB - 2yA, MRB = 200 - yA - 2yB.
The marginal cost of producing it is constant for both firms at $20 per case.
(a) Derive each firms best response function.
(b) Find the equilibrium price, quantities and profit for each firm.
(c) Why might these firms agree to form a cartel? If such a cartel is formed, use the prisoner's dilemma to describe why it may or may not survive. (Hint: prepare down a payoff matrix illustrating the prisoner's dilemma and find the Nash Equilibrium.)