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 by 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 does 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 damage to society calculated in part B?
G.
Compare the total
environmental damage to the total abatement cost at the efficiency point. Which effect is taking precedence: the cost
to society in terms of lost benefits caused by the pollution, or the opportunity
cost to society of decreasing the pollution?
H.
By how much did total
environmental damage decrease when the firm went to the efficient emissions
level? How much did total abatement cost
increase?