1. General smokey is the only smoker in town, and he derives a utility u(q) = 2q 1 2 q 2 for consuming q cigars. Cigars are produced by Cubano, whose total cost of producing q cigars is C(q) = q 2 . That industry is perfectly competitive. The marginal second-hand smoking damage that Smokey creates is estimated at 1 2 + 1 2 q. (a) Given that the price of a cigar is p, maximize the net surplus of Smokey to nd his demand for cigars, i.e. the quantity of cigars he wishes to smoke when the unit price of a cigar is p. Compute the inverse demand. (b) Find the supply of cigar by Cubano qc(p), and compute the inverse supply pc(q). Graph the inverse demand, the inverse supply, and the social marginal benet. (c) Find the market equilibrium q m and p m. (d) What is the socially ecient amount of cigars q and p ? (e) The mayor of the town, Sengaku, cares about the wellbeing of the citizens and considers instauring a Pigouvian tax on cigars. What should that tax be?