Consider two firms are performing Cournot price competition in two differentiated goods markets. Firm 1 produces goods 1, and firm 2 produces goods 2, and two market demand functions are given by q1(p1,p2) = 12 - 2p1 +p2 and q2(p1,p2) = 15q2^2 + 45Q. Furthermore, assume that the two firms have the same cost function such that fixed cost is $20 and variable cost is zero.

(10pts) Calculate the equilibrium prices, quantities and profits for both firms.

(10pts) Assume the two firms collude and form a cartel. That is, they maximize their total profits by setting prices. What will be the new equilibrium prices, quantities, and profits?

(5pts) Assume two firms agree to set prices at the collusion equilibrium level given in (b), but one of the firm unilaterally deviates its price to the Cournot equilibrium level given in (a), what will be the quantities and profits for both firms in this case? Is this deviation profitable for this firm?

(5pts) Based on the information given in (a),(b),(c), draw out the payoff matrix for two firms which have two potential strategies: Collude or Deviate. Explain why this game is a prisoner dillema. (Hint: the strategy is what price the firm chooses; the payoff is the corresponding profit)