Q1 Bertrand capacity constrained duopoly model: Suppose two rms produce identical goods. The market demand curve is given by P = 100 Q Each firm has a total cost function given by TC( (Cl '1) = 4'11 (a) Suppose that there is only one rm in the market, i.e., the firm is a monopolist. Suppose conSumers react to price quotations rather than quantities. Determine the profit-maximizing price and market quantity for the firm. Calculate the firm's prot. (b) Now assume that there are only two fin-ms in the market: F1 and F2. Determine the Bertrand Nash equilibrium of game. Explain your reSult. (c) Now suppose that both rms have limited capacities and that each can produce a maximum of 48 units at 154/ unit. Find the range over which prices uctuate, that is, the maximum and the minimum price that either competitor will charge for the product. In three steps explain why rms are willing to let prices uctuate over this range. Q2 Subgame Perfect Nash Equilibrium There are two players Alpha and Beta. Alpha chooses whether to go either up (U) or down (D) and Beta must decide whether to go left (L), middle (M) or right (R). (9.) Suppose that each player chooses its own strategy before it can observe the other player's choice. The payoff table for this sirnultaneousmove game is given below: PAYOFF MATRIX \"WEB BETA (B) L M R U 3, 6 1, 4 0, 0 ALPHA\") D -1, 9 3, 11 mm Determine the Nash equilibria of this simultaneous-move game. For each possible candidate for Nash equilibria PROVE that they are indeed a Nash equilibrium. (b) Now suppose Alpha moves rst, choosing either U or D. Beta observes Alpha's choice and then decides whether to go left (L), middle (M) or right (R). Suppose that the payoffs of this sequentialmove game correspond to those of the simultaneous-move game described in part (21). Draw the game three and determine the subgame perfect equilibrium of this sequential-move game