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2. (25 points) Two rms produce luxury sheepskin auto seat covers: Western Where (WW) and B. 8.8 Sheep (3835). Each firm has a cost function given by. C(q) = 10q + 0.5:]2 The market demand for these seat covers is represented by the inverse demand equation F = 100 20 where, Q = mm + am a. (4 points + 3 points+ 1 point + 2 points) Top managers of each of the firms recognizes the oligopolistic nature of the market and involve in Cournot competition. How much quantity does each firm produce under this strategy? Draw each firm's reaction function in a graph and show the equilibrium. What is the equilibrium price for seat covers in the market? How much prot does each rm earn? b. (3 points + 1 point 4- 1 point + 2 points) Suppose, the manager in 8885 guesses correctly that W is playing Cournot so 8385 starts playing Stackelberg. What are the equilibrium quantities each firm will be producing now? Does the market price increase or decrease compared to Coumot case? What happens to the prots of each firm? c. (2 points + 3 points + 3 points) it occurs to the managers that they could do a lot better by colluding. If the two firms collude, what will be the marginal cost function of the Cartel? Profit maximizing choice of output and the market price? The output and the profit for each rm in this case