Question

The environment is one of many important correlates of health outcomes. Pollution has been a major public policy issue in the United States, mainly due to the negative externalities on health associated with a polluted environment.

Power production produces large amounts of air pollution.

Assume XYZ operates a power plant in the local market. XYZ’s marginal cost function is: MC(q) = 2+0.1q. XYZ can sell all the output he produces for $9 per unit. In generating power, XYZ also emits pollution that causes damage to the local community. The marginal external cost of his production is: MEC(q) = 0.05q.

What level of output will XYZ choose to maximize profits? Is this level of production efficient?

Determine the socially efficient price and quantity.

Calculate the optimal tax to resolve this problem.

Answer 1

(i) Profit is maximized when Price = MC.

2 + 0.1q = 9

0.1q = 7

q = 70

Since there is an external cost which is not being considered, this production level is inefficient.

(ii) Efficient output is achieved when Price = MC + MEC

2 + 0.1q + 0.05q = 9

0.15q = 7

q = 46.67

Efficient price ($) = 9 + MEC = 9 + (0.05 x 46.67) = 9 + 2.33 = 11.33

(iii) When q = 46.67,

MEC = 0.05 x 46.67 = $2.33

The optimal tax is $2.33 (= value of MEC when output is socially efficient).