A paper mill and an oil refinery both operation on the bank
of the Great Fish River. Both generate a
water pollutant called gunk that kills fish, thus reducing the profits of the
local fishery. The Environmental
Ministry is analyzing alternative regulations to address this pollution
problem, including implementing a pollution tax or a cap-and-trade system.
The
following table shows the marginal and total costs of to the polluters (mill
and refinery) for cleaning up gunk, as well as the marginal and total benefits
of cleanup to the fishery (measured as change in profit). Assume there is only one fishery affected.
GUNK REDUCED PAPER
MILL OIL REFINERY
Cost of
Reduction ($) Cost of Reduction ($)
(tons/day) Total Marginal Total Marginal
0 0 0 0 0
1 1.30 1.30 0.20 0.20
2 2.80 1.50 0.50 0.30
3 4.60 1.80 0.80 0.30
4 6.80 2.20 1.20 0.40
5 9.60 2.80 1.70 0.50
6 13.20 3.60 2.50 0.80
7 17.90 4.70 3.80 1.30
8 24.60 6.70 6.10 2.30
9 34.60 10.00 11.40 5.30
10 51.30 16.70 38.10 26.70
GUNK REDUCED FISHERY GUNK REDUCED FISHERY
Profit
from Reduction ($) Profit
from Reduction ($)
(tons/day) Total Marginal (tons/day) Total Marginal
0 54.10 0 11 178.30 5.40
1 70.90 16.80 12 182.60 4.30
2 86.60 15.70 13 186.00 3.40
3 101.20 14.60 14 188.80 2.80
4 114.80 13.60 15 191.00 2.20
5 127.40 12.60 16 192.80 1.80
6 139.30 11.90 17 194.20 1.40
7 149.70 10.40 18 195.30 1.10
8 158.70 9.00 19 196.30 1.00
9 166.40 7.70 20 197.00 0.70
10 172.90 6.50
Note that the fishery’s profits are a function of the TOTAL
pollution in the system, that is, the sum of the gunk produced by both the mill
and the refinery, while the cleanup costs for each polluter is a function only
of its own waste.
a. Understanding the table:
• What is
the marginal cost to the mill of cleaning up one additional ton of gunk if it
has already cleaned up 3 tons/day?
• What is
the marginal cost to the refinery of cleaning up one additional ton of gunk per
day if it is currently cleaning up 3 tons/day?
• If both
the mill and the refinery are cleaning up 3 tons/day, what is the marginal
benefit to the fishery of the refinery cleaning up one more ton per day?
b. Suppose that the Ministry imposes a
pollution tax of $3 per ton of gunk and that both the mill and the refinery
would emit 10 tons of gunk in the absence of any regulation.
• How much
gunk would the mill reduce if faced with this tax?
• How much
gunk would the refinery reduce?
• What
would total gunk emissions be? Remember
that your answers to the first two bullet points on this part are gunk
reduction from a level of 10 tons/day for each.
• What is
the fishery’s profit at this level of gunk reduction?
c. Suppose that instead of a tax, the
Ministry decides on a cap-and-trade system, limiting total pollution to 7
tons/day. To compensate the fishers for
damages, the Ministry gives the fishery all seven permits, allowing it to
either hold them or sell them. Thus no
pollution is allowed initially.
• How much
would the mill be willing to pay for one gunk permit? Keep in mind it is not allowed to pollute at
all without a permit.
• How much
would the refinery be willing to pay for one permit, given that it has zero
initially now?
• How much
would the fishery need to be paid to induce it to sell one gunk permit?
d. Follow the logic in part c to
determine if the fishery would be willing to sell the second, third, fourth and
so on permit for less than the mill or refinery would be willing to pay for
additional permits.
• What will
be the final distribution of the seven pollution permits? Be clear as to how many each party (mill,
refinery, fishery) holds after trading.
• If the
fishery sells just one permit at a time to the highest bidder, at approximately
what price (or what price range) will the final permit that changes hands sell
for?
e. How does the emissions reduction
distribution in part d compare to that in part b?
?
2. In July
1997, the EPA announced new air quality standards for small particulate matter
(2.5 micrometers in diameter) referred to as PM2.5. Previously particulate matter less than 10
microns in diameter were regulated.
Steel mills are a major source of these smaller particles and therefore
had to find ways to abate. Consider the
following hypothetical model of two steel plants, one owned by Bethlehem Steel
(B) and one owned by National Steel (N), both located in Pittsburgh,
Pennsylvania:
Bethlehem: MCB = 1.1AB
TCB
=0.55(AB)2
National: MCN = 0.4AN
TCN
= 0.2(AN)2
Assume that each plant emits 40 units of PM2.5 for a total
of 80 units. In order for the Pittsburgh
area to meet the new standard, the EPA determines that the combined abatement
for both plants must total 30 units.
a. Assuming
the new abatement standard is implemented uniformly between the two firms, find
the total cost of abatement for each firm and the overall total cost of
abatement. Show your work.
b. Mathematically
or graphically demonstrate that your answer to (a) is NOT cost effective.
c. Find the
cost effective solution for 30 total units of abatement. Show your work and clearly indicate both AB
and AN. Note that this is similar to
the “Puzzle” on page 317 but with MC as a function of abatement levels (level
of pollution reduced) rather than as a function of pollution. But see the solution to that puzzle if you
need help solving this problem.
d. Verify
that your solution in (c) is cost effective by showing that the marginal cost
of abatement is the same for both firms.
e. Under the
cost effective solution, which firm experiences increased total costs relative
to the uniform abatement policy?
Why? What happens to the total
costs for the other firm? Why?
f. Calculate
the total cost savings associated with the cost effective solution relative to
the uniform abatement standard. Show
your work.
?
3. Assume
that pollution reduction has marginal benefits measured in dollars equal to
20-2x, and marginal costs (in $) equal to 5 + (x/2), where x is the tons of
pollution reduced per week.
a. Graph the MB and MC curves. Show the value for x* (the efficient level of
pollution reduction) and for the dollar value of the MC and MB associated with
this level of x.
b. As a result of imperfect
information, regulators are considering two inefficient policies: a tax 10% below the efficient tax level and a
marketable permit system with the number of permits to be issued 10% below the
efficient reduction level. Which is more
efficient (or closest to the efficient outcome)? Explain or show graphically or
mathematically.
c. Suppose the regulators did not know
exactly what the MB was but did know that this pollutant was a threshold
pollutant. Should they use a tax or a
permit system if they are interested in efficient regulation? Explain why.
4. Answer
the following questions.
a. Under a pollution tax system, do
firms have the incentive to overstate or understate their costs of pollution
reduction? Explain why.
b. Under a pollution permit system, do
firms have the incentive to overstate or understate their costs of pollution
reduction? Explain why.
c. Read Application 15B.0 and answer
the question at the end of the second paragraph, “Does the same incentive hold
for CAC regulation…?” Explain your
answer.
