Question

Assume the following marginal abatement cost curves for polluters 1 and 2 : MAC1=10-e1 and MAC2=8-e1.

1. How much does polluter 1 and polluter 2 pollute without government intervention?

2. This level of pollution should be reduced by 50%. What are the marginal and total abatement costs of polluters 1 and 2 if a command and control policy is applied?

3. What is the optimal outcome, or which allocation of emissions minimize the abatement costs? Please calculate the total abatement costs for the economy.

Answer 1

1) when no intervention, at equilibrium

MAC = 0 , for each polluter

So, e1= 10

& e2= 8

Total pollution = 18

.

2) now constraint; e1+e2= 18/2= 9

Then, in command economy, e1'= 10/2= 5

e2'= 8/2= 4

Each polluter has to reduce pollution by 50%

So, MAC1= 10-5= 5

TAC1= .5*(10-5)*5= 12.5

MAC2= 8-4= 4

TAC2= .5*(8-4)*4=8

.

3) at optimal level

MAC1= MAC2, & e1+e2= 9

So, 10-e1= 8-e2

2= e1-e2

Put e1= 9-e2

So, 2= 9-2e2

2e2*= 7

e2*= 3.5, &

e1*= 9-3.5= 5.5

TAC1= .5*(10-5.5)*4.5= 10.125

TAC2= .5*(8-3.5)*4.5= 10.125

so TAC = 10.125*2= 20.25