There are two brands of cigarettes X, Y. The demand for each iss:

Q_X=80-2p

Q_Y=60-0.5p

Assume that the marginal cost of producing cigarette X is $10, the marginal cost of producing cigarette Y is $8, and that the market for both cigarettes is perfectly competitive. Assume that each pack of cigarette X smoked does $5 worth of health damage to the smoker, and a total of $4 worth of health damage to the smoker's neighbors via second-hand smoke. Each pack of cigarette Y smoked does $6 worth of health damage to the smoker, and $5 health damage to the smoker's neighbors.

(a) Plot the private demand curve and private supply curve for both cigarettes on separate axes.

(b) What is the privately efficient quantity demand of both cigarettes?

(c) Add the public supply curves to the graphs you plot in (a).

(d) What is the socially efficient quantity demand of both cigarettes?

(e) Explain why the public supply curves differ from the private supply curves, and how this represents the externality from second-hand smoke. Highlight the area(s) of your diagram that represent social loss.

(f) Calculate the social loss for both.

(g) Suppose the government decides to pursue a Pigouvian solution to eliminate social loss. What's the amount of tax or subsidy would the government implement? What's the resulting quantity of demand for both cigarettes.

(h) Besides the Pigouvian solution, what else solution do you have? What's the conditions in order to successfully implement this?