16: In a small island there are only two consumers and two importing cars rms. One rm 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 rm with the lowest price. If both rms charge the same price, each one buys from a di ,Jerent firm. When a rm sells a car, it has to pay the import cost, which is equal to 10,000 e if the car comes from USA, or 8,000 e if from Europe. The rms cannot x prices with decimals, since the smaller coin in the island is 1 e . The rms mainly want to maximise prots, and if at the same prots, they prefer to sell as much as possible. (a) For the case where the two firms choose their prices simultaneously, write out the payo J functions for each of them (b) if the rm who sells American cars sets a price pA:10,000 e , what is the best response for the other rm? and if pA =5,000 e ? Note: If a rm is indi Jerent among many di Jerent prices, we assume that it sets a price equal to its import cost. (c) If the rm who sells European cars sets a price pE :15,000 e , what is the best response for the other rm? and if pA:1,000 e ? (d) Find the reaction functions for each rm, for all possible prices from its rival. Find the only Nash equilibrium in pure strategies. How many cars each rm sells, and at which price? Suppose now that the government of the island is worried about the prices of the cars, and decides to subsidise one (and only one} of the rms, paying 1,000 e 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 govemment give the subsidy? (f) Who is going to sell now? At which price? And how much the govemment will expend in subsidies