A decision to drive in Manhattan generates an externality: an extra car on the road provides a benefit to the driver but it also increases congestion and reduces welfare of everyone else. Assume that the price of driving a car on a given day (gasoline, depreciation, etc.) is given by 210. Given n cars already on the road, the private marginal benefit is 300 - n. At the same time, adding a car on the road when n are already present reduces welfare of the drivers already on the road by 2n.

(a) Plot a graph showing private marginal benefit, private marginal cost and social marginal benefit.

(b) Find the price and quantity in the private equilibrium (i.e., with no intervention of any kind).

(c) Find the socially efficient quantity and the deadweight loss.

(d) Suppose that we want to implement the efficient solution by imposing a constant fee for each car driving into Manhattan. What should the fee be?