Problem Set 8 1 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...

Problem

Set 8

1

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

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 (25

micrometers in diameter) referred to as PM25

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: MC_B
= 11A_B

TC_B
=055(A_B)²

National: MC_N
= 04A_N

TC_N
= 02(A_N)²

Assume that each

plant emits 40 units of PM25 for a total of 80 units In order for the Pittsburgh area to meet the

new standard, the EPA determines that thecombined 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 A_B
and A_N
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 thetotal

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 15B0 and answer the

question at the end of the second paragraph, “Does the same incentive hold for

CAC regulation…?” Explain your answer