Question

Suppose the marginal cost for mineral water production in a small isolated country is 20 + Q, and the demand for mineral water is P = 80 – 2Q, where P is the dollar price and Q is the tons of mineral water produced. Suppose the processing procedure in mineral water production generates pollution, which incurs damage to the environment described by a marginal function of MEC = Q. (The externality does not directly harm producers or consumers.)

Question: If the government intends to impose a production tax to reach the socially optimal level of pollution, how much should the tax be? (how much per unit, assuming a constant per-unit tax: not total tax revenue)

Answer 1

First find the socially optimum output level. Here we find social marginal cost which is private MC + MEC. This

gives Social MC = 20 + Q + Q or 20 + 2Q. Demand is P = 80 - 2Q. At the socially optimum level they are equal:

20 + 2Q = 80 - 2Q

4Q = 60

Q = 15 units

Price = 80 - 2*15 = $50 per unit

At this quantity, private MC is 20 + 15 = $35

Hence the required production tax is social MC - Private MC at equilibrium Q = 50 - 35 = $15 per unit.