Question

Suppose we have a market with a negative externality. Market demand is Q = 18 - P The private cost is Cp(Q) = Q and the cost of the externality is CzQ) = Q?. a. What is the marginal cost of the externality, MCg? b. What is the marginal cost to society of production MCs? c. What is the Socially Optimal quantity and price? d. Suppose the government wanted to tax a monopoly in this market with a negative externality. How much should a unit tax t be to arrive at the socially optimal quantity you calculated in part c?

Answer 1

Marginal social benefit is P = 18 - Q. Marginal private cost = Q and marginal external cost = 2Q. This indicates that marginal social cost = Q + 2Q = 3Q

A) the marginal cost of externality is the derivative of the cost of externality function dCE/dQ = 2Q.

B) marginal cost to the society is the sum of private marginal cost and marginal external cost = Q + 2Q = 3Q

C) socially optimal quantity is the one at which marginal social cost and marginal social benefit are equal to each other

18 - Q = 3Q

Q = 4.5 units

P = 13.5 per unit

D) the tax should be the difference between the marginal social cost and marginal private cost at socially optimal quantity = 3*4.5 - 1*4.5 = $9. The tax should be $9 per unit