Greetings to the kind tutor who would mind checking my work regarding this game theory exercise about static games with continuous space.

Below the exercise and my answer to be checked.

16. In a small island there are only two consumers and two hnporting ears rms. lIC'lne rm imperis 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 rmschargethesameprice,eachonebuysfromadi'erentm When a rm sells a car, it has to pay the import cost, which is equal to El l],|llll[l ifthe ear comes 'om USA, or E8,\" if 'oem Europe. The rms cannot x prices with decimah, since the smaller coin in the island is El . The rms mainly want to maximize prots, and if at the same prots, they prefer to sell as much as presib le. [a]: For the ewe where the two rms choose their prices simultaneously, write the payoff mctions for each of them. [b] lfthe rm who sells American cars sets a price [pg] is E l,, what is the best response for the other rm? And if p4 = 51111111]? Note: If a rm is indifferent among many different prices, we assume that it sets a price equal to its import cost. {c} If the rm who sells European cars sets a price {pg} is El more, what is the best response for the other rm? And if 19;,- = Lill]? {d} Find the reaction flmctions for each rm, for all possible prices om 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 subsidize one {and only one} of the rms, paying El,[Hl of its imports costs for each car it sells. [e] If the government's objective is that the comumers buy the cars at the lowest possible price, to which rm should the government give the subsidy? (I) Who is going to sell now? At which price? And how much the government will