Consider the us market for new cars. to keep things simple, assume that new cars constitute a homogeneous good (i. e. all new cars are perfect substitutes) and that the market for new cars is perfectly competitive. the demand for cars by us consumers is characterized by the following (inverse) demand curve: pd(q) = 36 ? q((for the remainder of this problem, assume that the quantities are enumerated in millions of units and that prices are denominated in thousands of us dollars.) the supply of cars by us producers is characterized by the following (inverse) supply curve: ps (q) = 6 + 2qsince us producers are operating under perfect competition, this function also represents the car industry�s marginal cost curve. cars are also produced and consumed in other countries around the world. again for simplicity, assume that the us car market is small relative to the world market, so that changes in the us car market do not affect the equilibrium price of cars on the world market. this world price therefore remains fixed at pw = 20.1. what would be the price of new cars in the us in autarky? 2. characterize the free trade equilibrium in the us new car market. what are the quantities of cars consumed, produced, and traded? are cars imported or exported? what are the levels of consumer surplus, producer surplus, and total social surplus generated in this equilibrium? 3. now assume that a specific tariff t is imposed (t thousand of dollars are collected for every car imported in the us). describe this new equilibrium 1 as a function of the tariff t. what is the new price of a car? compute the new equilibrium quantities and surpluses listed in part (2) (the revenue generated by the tariff should be included in the social surplus). how are producer and consumer surplus affected by the tariff? graph social surplus as a function of the tariff. what is the tariff level that maximizes social surplus? why? hint: separately consider the case when no cars are imported.4. you are now informed that the us car industry generates some beneficial spillovers to the rest of the us economy, due to the spillover of new production techniques and worker skills to other us manufacturing in- dustries. specifically, it is estimated that every car produced in the us generates a $6 (thousand) spillover to the rest of the us economy. note that this spillover represents an externality and that us car producers do not recoup any part of this benefit in the absence of government inter- vention. further note that imported cars do not generate this spillover. continue with the assumption that a tariff t is imposed on imported cars. what is the new level of social surplus generated by the us car market that takes this spillover into consideration (as a function of the tariff t)? graph this new social surplus as a function of the tariff. what is the tariff level that maximizes this new social surplus? is free trade (t = 0) the policy that maximizes welfare? why or why not? given this externality, would autarky be preferred from a welfare maximizing perspective to free trade? 5. now consider the effects of a production subsidy for the us car market that would replace the tariff. specifically, consider a subsidy s (in thousands of dollars) that would be paid by the us government to us car producers for every car produced. recall that a production subsidy reduces the marginal cost of every unit produced by us car manufacturers by the amount of the subsidy. continue to assume that car production in the us generates externalities as in () describe the new equilibrium as a function of the subsidy s, assuming that s is low enough that cars are still imported into the us. what is the new price of a car paid by us consumers? compute, as a function of the subsidy s, the new equilibrium quantities of cars produced, consumed, and traded. what is the threshold level of the subsidy 2 beyond which the us would become a car exporter? (continue with the assumption that s is below this ) what are the new levels of consumer surplus, producer surplus, and total social surplus, including the subsidy payment by the govern- ment? graph this social surplus as a function of the subsidy. what is the subsidy level that maximizes social surplus? could you have guessed this answer before computing the new social surplus? why? (c) compare the maximum level of social surplus under the subsidy with the maximum under the tariff. why is this level higher under the subsidy than under the tariff? also, compare the quantity of cars produced and consumed under both of these scenarios. without going through any additional calculations, consider the case when both subsidies and tariffs could be used to address the production externality. do you think that it would be beneficial from a welfare maximizing perspective to use both tariffs and subsidies to protect the car industry since both of these instruments, on their own, can raise welfare levels?