In a small island there are only two consumers and two importing cars firms. One firm imports American cars while the other imports European cars. Right now, both consumers are without a car, and since there is no public transport services in the island, each of them is going to buy a car, no matter the price. But they don't want to expend too much, so they both are going to buy from the firm with the lowest price. If both firms charge the same price, each one buys from a different firm. When a firm sells a car, it has to pay the import cost, which is equal to 10,000 if the car comes from USA, or 8,000 if from Europe. The firms cannot fix prices with decimals, since the smaller coin in the island is 1. The firms mainly want to maximize profits, and if at the same profits, they prefer to sell as much as possible. (a) For the case where the two firms choose their prices simultaneously, write the payoff functions for each of them? b) If the firm who sells American cars sets a price (A) is 10,000, what is the best response for the other firm? And if = 5.000? Note: If a firm is indifferent among many different prices, we assume that it sets a price equal to its import cost. (c) If the firm who sells European cars sets a price (pE) is 15,000, what is the best response for the other firm? And if pE = 1.000? (d) Find the reaction functions for each firm, for all possible prices from its rival. Find the only Nash equilibrium in pure strategies. How many cars each firm sells, and at which price? Suppose now that the government of the island is worried about the prices of the cars, and decides to subsidize one (and only one) of the firms, paying 1,000 of its imports costs for each car it sells. (e) If the government's objective is that the consumers buy the cars at the lowest possible price, to which firm should the government give the subsidy? (f) Who is going to sell now? At which price? And how much the government will expend in subsidies?