A market is characterized by a demand curve that can be expressed as P = 96 – (1/3) Q. Each of the two identical firms currently serving the market has a total cost function of the form C = 12 q. There are no fixed costs. If the 2 duopolists behave as independent, symmetric Cournot duopolists, what are the equilibrium price, quantity, and profits for each of the firms? Show work. If the 2 duopolists behave collusively, what are the equilibrium price, quantity, and profits for each of the firms? Show work. Now create a payoff matrix in which the two firms are deciding between producing the Cournot duopoly quantity that you found in part a and producing the collusive quantity that you also found in part a. In other words, each firm has 2 strategies: produce the Cournot quantity and produce the collusive quantity. The payoffs for two cells in the matrix are the profits you calculated in part a. Complete the other two cells in your payoff matrix; that is, find the profits for each of the firms when one of the firms produces the Cournot quantity and the other firm produces the collusive quantity. (You will need to calculate a new market price in order to find the profit payoffs for these two cells.) Show work. Find the Nash equilibrium for the game. Explain. Explain how your payoff matrix represents a prisoner’s dilemma.