Pollution Control Problem

Suppose a particular steel plant emits particulates that damage crops and affect human health. The relationship between emissions and environmental damage is represented by the marginal damage function,

MD=3.5e where e represents tons of emissions per month.

The cost to the firm (and society) of eliminating emissions is represented the marginal abatement cost function,

MAC=97.5-6.5e

Both MD and MAC are in dollars and cents.

A. If the steel firm were allowed to ignore the social cost of its emissions, what would be the firm’s monthly emission level?

B. What is the total damage to society if the firm ignores the social cost of pollution?

C.Calculate the socially efficient level of pollution.

D.What do both MAC and MD equal at this level?

E. Explain why the socially efficient level of emission is not zero.

F. Calculate the total environmental damage and the total abatement cost at the efficient emissions level. Do the two numbers sum to less than the total marginal damage calculated in part B?

G.By how much did total environmental damage decrease when the firm went to the efficient emissions level?

H.Calculate the total social cost of pollution if all emissions were eliminated. Is this cost also greater than the cost calculated at the efficient point?