Question

A firm has an industrial plant that emits pollutants into a town’s lake. The plant’s marginal abatement function is MAC= 200 – 0.5E and damages caused by its emissions are given by MD = 2E where emissions are in kg. per day.

What is the socially efficient level of emissions from this plant? Illustrate this in a graph.

Answer 1

The socially efficient level of emissions is 80 kg. per day where marginal abatement cost equals marginal damage. The firm will abate 30 pounds of pollutants to minimize costs when faced with a pollution tax, as abatement costs are less than the tax for this amount.

Step-by-step explanation:

The socially efficient level of emissions from the plant occurs where the marginal abatement cost (MAC) equals the marginal damage (MD). According to the provided functions, MAC = 200 – 0.5E and MD = 2E. Setting MAC equal to MD for equality, we have 200 – 0.5E = 2E, which simplifies to 200 = 2.5E and thus E = 80 kg. per day. This is the level of emissions where the cost of abating an additional kilogram of emissions equals the marginal damage that kilogram causes.

When faced with a pollution tax, the firm assesses whether to pay the tax or bear the cost of further abatement. Since the first three 10-pound increments of pollution abatement cost ($300, $500, $900) are each less than the $1,000 tax, the firm will abate to avoid the tax. However, for the fourth increment ($1,500), the cost of abatement exceeds the tax, so the firm will pay the tax instead. Thus, the firm will abate 30 pounds and pollute the remaining amount.