2 Problem 2 Monopoly and Duopoly: The country of Fruitopia is a closed economy; therefore, it does not trade any product with the rest of the world. In Fruitopia, Monsanto is the only producer of BBT, an important additive to fertilizers. The inverse demand for BBT in Fruitopia is P = 60 iQD, where C29 is measured in tons of BBT and P is the price per ton. The total cost of producing BBT is TC 2 10 + 622 and the marginal cost is MFG = %Q. a) What is Monsanto's marginal revenue function? b) Given that Monsanto is a monopolist, how much BBT will it sell? What price will it charge? c) Illustrate your answer to b) on a graph. Make sure you draw the inverse demand, the marginal revenue, and the marginal cost, and identify all the intercepts on the axes. Monsanto considers selling BBT in the world market, which is a perfectly competitive market. However, it will continue to be a monopolist in Fruitopia. d) What is the lowest world price of BBT at which Monsanto will consider exporting BBT? Explain. Assume that the current world price of BBT is $36 per ton. e) If Monsanto can price discriminate between its domestic and foreign customers, how much BBT will Monsanto export (that is, how much will it sell in the world market?)? How much BBT will it sell at home? \\Vhat price will it charge to its home customers? f) Are domestic customers better or worse off now that Monsanto can export BBT? Explain in fewer than three lines. Assume now that a second company, Boyer, enters the Fruitopia market. Also, assume that because Fruitopia does not allow any other country to sell BBT in Fruitopia, the rest of the world decides not to allow Fruitopia's rms to sell BBT on the world market. In other words, Boyer and Monsanto both sell in Fruitopia, but neither of them can sell in the rest of the world. Assume that Boyer is identical to Monsanto, that is, they have the same cost function. g) What is the (inverse) demand function that each rm faces? What is the marginal revenue of each rm? h) What are M onsanto's and Boyor's best-response functions (or reaction functions)? i) What is the optimal quantity that each rm will produce? What is the total quantity that will be placed on the market? At what price will BBT be sold? j) Complete the game below. (Hint: The game is symmetric.) Beyer _ _ N 248 340 32 Q = 48 1142, 1142 1233 , 1334 , Q = 40 1110 , 1190 , 1190 1270 , Q : 32 1014 , 1073 , 1142 , 1142 3 k) Does Memento have a dominant strategy? If so, which one? Does it have a dominated strategy? If so, which one(s)? Explain. 1) What is the Nash equilibrium of this game? Explain in words what a Nash equilibrium is. n1) Me or False: Duopolists do not choose their quantity by maximizing their prot. In fact, Beyer and M ensanto can earn higher prots by selling 40 units each. Explain in fewer than three lines