II. Consider a market with only two firms that sell identical products. The market demand is Q = 1000.5p, where Q = 9 +92, and q and q2 are the quantities of firm 1 and firm 2, respectively. Suppose the two firms have identical marginal cost of $50. For simplicity, assume that each firm has no fixed cost. Assume the two firms act independently and simultaneously choose their prices as in the Bertrand model. Let p and p be the prices of firm 1 and firm 2, respectively. Show the basis and briefly explain what is going on as you answer each of the following questions. Your mark will depend upon the correctness of your basis and explanation. 1. What is the equation of the demand function faced by firm 1? 2. What is the equation of the demand function faced by firm 2? 3. Explain why is p = 50 and pa = 50 is a Nash-Bertrand equilibrium set of prices. 4. What are the Nash-Bertrand equilibrium quantities for the two firms. 5. If the two firms acted independently as in the Cournot model, what is the Nash-Cournot equilibrium price? 6. Show that the Nash-Bertrand equilibrium results to a welfare optimal market price- market quantity combination but not the Nash-Cournot equilibrium.