Question

Suppose that the social marginal benefit from reducing one unit of pollution is SMB = 975−50R, where R is the quantity of pollution that is reduced, and social marginal benefits are measured in dollars. Suppose that the marginal cost of reducing a unit of pollution is PMC1 = 25 · R. There are no other costs to reducing pollution. Thus, SMC1 = PMC1.

(a) Draw the market for pollution reduction.

(b) What is the socially efficient quantity regulation? What about the socially efficient tax on pollution?

(c) Now suppose it turns out to be more costly to reduce pollution than expected. The marginal cost of reducing pollution rises to PMC2 = SMC2 = 25 · R + 225. Draw the new market for pollution reduction.

(d) What is the new socially efficient quantity of reduction?

(e) Calculate the DWL under the prior corrective tax and and under the prior quantity regulation.

(f) What is the DWL under no pollution reduction?

(g) The IPCC wants to limit global warming to less than 2 degrees Celsius. It believes that further warming can lead to increasingly harmful consequences. What does this imply about how the marginal damage from carbon varies with the amount of carbon in the atmosphere? Over time, will the social cost of carbon stay the same, increase, or decrease?

Answer 1

a) The social marginal benefit of reducing 1 unit of pollution is given as

SMB= 975- 50R

The private marginal benefit is the demand curve and it is not equal to social marginal benefit. As benefit is obtained from pollution, the social marginal benefir curve lies above the private marginal benefit curve.

Since there is no cost of reducing pllution pollution the social marginal cost is equal t the supply curve, that is private marginal cost curve.

Thu, SMC= PMC= 25

Diagramatically it can be shown as,

b) The socilly efficient quantity of pollution that is to be reduced is determined by equating the social marginal cost and social marginal benefit

975- 20R= 25

20R= 950

R= 47.5

The socially efficient quantity of pollution that is to be reduced is 47.5

The socially efficient unit tax is equal to the social marginal benefit of reducing pollution, which is equal to

= 975- 20*47.5

=25