Industry demand is: The market is supplied by a duopoly, where each firm has MC = 200 with no fixed costs. P = 1,000 0.10 Q therefore, MR = 1,000 -0.20 Q a). Find the cartel outcome (i.e. assume the firms cooperate to maximize joint profit): b). price, firm-level quantity, revenue, costs and profit, plus joint profit. Find the competitive outcome. c). Is the cartel outcome likely to occur, in a single-period game? Assume for what follows that the firms must change production in blocks of 500 units. Show that each firm has an incentive to deviate from the cartel outcome and produce another 500 units. d). Write the payoff matrix for the above duopoly, where the first row/column has each firm producing the cartel (joint monopoly) quantity, and the second assumes the extra 500 units are added. What is the Nash equilibrium? e). Show that the Nash equilibrium is stable - that is, calculate what happens to profit if a firm deviates (Up OR Down) from the N.E.