Question

Suppose that at fixed input prices of W- a firm produces output with the differentiable and strictly convex cost function c(q,h), where q≥0 is its output level (whose price is p>0 ) and h is the level of a negative externality generated by the firm. The externality affects a single consumer, whose derived utility function takes the form ϕ(h)+w. The actions of the firm and consumer do not affect any market prices. (a) Derive the first-order condition for the firm's choice of q and h. (b) Derive the first-order conditions characterizing the Pareto optimal levels of q and h. (c) Suppose that the government taxes the firm's output level. Show that this cannot restore efficiency. Show that a direct tax on the externality can restore efficiency. (d) Show, however, that in the limiting case where h is necessarily produced in fixed proportions with q, so that h(q)=αq for some α>0, a tax on the firm's output can restore efficiency. What is the efficiency-restoring tax? RERWITE

Answer 1

Market prices for cigarettes reflect a private equilibrium at Pm and Qm, but do not account for the negative externality of second-hand smoke. The social optimal price and quantity, Pe and Qe, will be higher and lower respectively than the private equilibrium. A tax can help internalize the external cost and shift the market towards the social optimum.

Step-by-step explanation:

When analyzing the market prices for cigarettes in a scenario where there are no public smoking bans, we first identify the private market equilibrium where demand equals supply, labeling this private market price and quantity as Pm and Qm respectively. However, when accounting for the negative externality of second-hand smoke, the social costs are higher than the private costs. This means that the socially optimal output and price, labeled as Pe and Qe, would involve a lower quantity of cigarettes smoked to account for the harm caused by second-hand smoke. A graph of this market would show the demand curve intersecting with the higher social cost curve at the social optimum, resulting in a higher price and lower quantity than the private equilibrium. To illustrate the inefficiency in the private market equilibrium, one would shade the area between the social and private cost curves from Qm to Qe, which represents the deadweight loss associated with the negative externality of second-hand smoking. To address this negative externality, a tax on cigarettes could be imposed to shift the supply curve up, effectively increasing the market price to Pe and reducing the quantity to Qe, thus internalizing the external costs and restoring efficiency.