1. Consider a world with two countries: Italy (1) and France (F). The supply and demand functions for cars in Italy and France are given respectively by the following: D = 300 - 10pl S' = - 20 + 10P/ DF = 200 - 20PF SF = - 40 + 40PF a) (10 points) Assume that these countries trade freely with each other. Calculate (i) the equilibrium price of cars, (ii) the quantity exported and imported by each country, and (iii) the total welfare of the importing country. Answer with exact numbers. b) (15 points) The importing country decides to impose a tariff of E4 per imported car. Calculate (i) the new price in the importing country (ii) the new price in the exporting country, (iii) the total welfare in the importing country, (iv) The change in welfare, compared with answer in section a), in the importing country due to the introduction of the tariff. Answer with exact numbers. c) (15 points) Now assume that both Italy and France sign a free trade agreement with the rest of the world for the car industry. The two countries are relatively small when compared with the rest of the world. The international equilibrium price of cars is E7. Calculate the welfare of the importing country under the following two scenarios (i) the importing country maintains the E4 tariff and (ii) the importing country removes the tariff. (iii) What will be the optimal rate in this case? (iv) Is the optimal tariff different from the situation in point a), i.e. free trade only between the two countries. Why or why not