Question

Problem 1

Consider the environmental problem created by two chemical plants that release arsenic into a nearby river. The authorities set a standard for the waterway that requires a total abatement level (A) for arsenic of 16 units. Suppose that the two firms, firm 1 and firm 2, face the following marginal abatement cost equations: MAC₁ = 3A₁ and MAC₂ = A₂, where costs are measured in thousands of dollars.

1. If the state uses a uniform standard, show that such a ruling would not be cost-effective. Which firm should be abating more, and which firm should be abating less?
2. Now find the cost-effective solution.

Answer 1

A) now each is required to abate = 16/2 = 8 units

So then A1= A2 = 8

MAC1 = 3*8 = 24

MAC2 = 8

so as MAC1 not equals MAC2, so it is not cost effective solution.

so

higher MAC firm should abate less , which is firm 1

& Lower MAC firm should abate more , which is firm 2

B) at cost effective solution

MAC1 = MAC2

Marginal abatement costs are Equalized across all firms

So, 3A1 = A2

& A1+A2 = 16

Put A2 = 16-A1

So, 3A1 = 16-A1

4A1 =16

A1* = 4, A2* = 4*3 = 12