EC465a:
Special Topics on Environmental Economics
Solution
to Fall 2002 Midterm
A bed-and-breakfast (B&B) owner in Vermont typically has
seven guests per weekend, who each pay $200 per room for the weekend. The B&B owner incurs costs of $700 if
she is open on a weekend, or she incurs costs of $0 if she is not open.
A local dairy farmer owns a large field which is upwind of
the B&B. For every additional 50 cows that the framer grazes in this field
over the weekend, he earns an additional $1000 in revenue from milk sales. The marginal cost of grazing the cows
increases with the addition of every additional 50 cows.
When the farmer grazes more than 50 cows in the
field, the resulting smell discourages guests from staying in the B&B. Specifically, for every additional 50 cows
in the field, the B&B owner loses another weekend guest.
Revenue and cost data for the dairy farmer and the B&B
owner are summarized here:
|
Dairy farmer |
B & B
owner |
|
||||
|
Herd size |
Marginal revenue |
Marginal Cost |
Total guest loss
(rooms) |
Marginal revenue
loss |
Marginal Cost
(with tax) |
|
|
50 |
$ 1,000 |
$
100 |
0 |
$ - |
$
100 |
|
|
100 |
$ 1,000 |
$
300 |
1 |
$ 200 |
$
500 |
|
|
150 |
$ 1,000 |
$
500 |
2 |
$ 200 |
$
700 |
|
|
200 |
$ 1,000 |
$
700 |
3 |
$ 200 |
$
900 |
|
|
250 |
$ 1,000 |
$
900 |
4 |
$ 200 |
$
1100 |
|
|
300 |
$ 1,000 |
$ 1,100 |
5 |
$ 200 |
$
1,300 |
|
1)
Describe the externality in this situation. Is it public or private, shiftable or
non-shiftable, pecuniary or technological?
Justify your answers.
This is a non-shiftable, pecuniary externality: the
B&B owner can not shift the cost onto someone else, and it affects her
directly though her production function (which is the equivalent of the cost
function), not through a change of process.
One can make a case that it is public or private, though it is, in
spirit, a public externality: others downwind may also be affected. See the definitions in Baumol and Oates.
2)
If a Pigouvian tax were imposed by the local
government, how much should it be and who should pay it? If such a tax were imposed, what would be
(a) the profit for the farmer, (b) the profit for the B&B owner, and (c)
the tax revenues for the government?
What would be society’s total net benefit?
We know that the Pigouvian tax should be equal to the marginal social damage, so in this case, the tax should be equal to $200 for every additional herd size of 50, after the initial level of 50, and it should be paid by the farmer. In this case, the marginal cost (with the tax) for the farmer would be as indicated above (second clumn from the right).
Now, the farmer would stop framing as soon as (P)MB >= (S)MC, which is at a herd size of 200. So, the farmer’s profits would be $4000 - $2200 = $1800. The B&B owner’s profits would be 4 guests X $200 = $800 - $700 = $100. The government would collect $600.
Society’s net benefit is $2500, the sum of the total profits and the tax revenues.
3)
If there were no tax, and the dairy farmer had the
‘property right’ in this situation, what would be his profit? What would be the B&B owner’s
profit? What would be society’s total
net benefit?
With no tax, the farmer would ignore the cost of the externality: so the farmers would have a herd size of 250, and the total profits would be $5000 - $2500 = $2500. The B&B owner would go out of business, since the revenues would be 3 guests X $200 = $600, which is leass than her $700 fixed cost.
Society’s net benefit is still $2500, the sum of the total profits.
4) If there were no tax, and the B&B owner had the ‘property right’ in this situation, what would be her profit? What would be the farmer’s profit? What would be society’s total net benefit?
The B&B owner could ask for any amount that is more than she normally would earn if the farmer was not there; that is, her regular profit of $700. The farmer would be willing to pay her some amount to not have guests, as long as he earns more than the amount he would earn if he was responsible for all of the marginal damage that he does – the $1800 we calculated above. So since the total pie is $2500, the B&B owner will get $700, and the farmer will get $1800. (Note: these will also be the respective profits if the farmer pays for the damages, as illustrated above)
5)
A new technology is available that can eliminate the
offending emissions from dairy cows, but in these circumstances it would cost
$500 per weekend to use. If the dairy
farmer had the ‘property right’ in this situation (again, with no tax), would
it be pareto-improving for the B&B owner to pay him $500 to adopt this
technology? If the B&B owner had
the ‘property right’ in this situation, would it be pareto-improving for the
farmer to pay $500 to adopt this technology?
Justify your answer.
[Note that with the introduction of the pareto-improving technology, the ’size of society’s pie’ is now $2700]
6)
In ‘real life’ Vermont, do you believe that dairy
farmers should be held liable for the externalities that they impose on the
neighbors (including soil erosion and watershed degradation)? Justify your answer.
Once can make a ‘polluter pays’ case that the polluter should be responsible. By contrast, one can make a Coasian case, which involves property rights. There is no right answer here; it just has to be well argued.
The Intergovernmental Panel on Climate Change (IPCC) has
determined that a $20 tax on each ton of carbon emissions would lead to the
stabilization of global warming. Two
firms (1 and 2) will now be subject to this tax. Prior to the imposition of the tax, Firm 1 was emitting 10,000
tons of carbon, and Firm 2 was emitting 12,000 tons of carbon.
After the imposition of the tax (or alternatively, the
permit-based regime described below), the following aspects of their
profit-maximizing behavior do not change: levels of output production,
the price of goods that they sell, and the costs of all other inputs.
The Marginal Abatement Cost (MAC) for Firm 1 is:
MAC = 0.02*A1 (where A1
is the number of units of abatement for Firm 1).
The MAC for Firm 2 is:
MAC = 0.01* A2 (where A2
is the number of units of abatement for Firm 2).
1) Under the new tax regime, how many tons of carbon will Firm 1 emit? What will be their total cost of abatement? What will be the total change in their profits since the imposition of the tax regime?
They will set MAC = to the tax
rate, so:
MAC = 0.02*A1 = 20
A1 = 1000
Since the starting amount of emissions are 10,000, the total emissions will be 9,000
The abetment cost will be the
triangular area under the MAC, as we showed in class:
Total costs = TAC + the tax
bill
Tax bill = $20 * 9000 = $180,000,
2) Under the new tax regime, how many tons of carbon will Firm 2 emit? What will be their total cost of abatement? What will be the total change in their profits since the imposition of the tax regime?
Following the same logic
MAC = 0.01*A2 = 20
A2 = 2000
Since the starting amount of emissions are 12,000, the total emissions will be 10,000
The abetment cost will be the
triangular area under the MAC, as we showed in class:
Total costs = TAC + the tax
bill
Tax bill = $20 * 10,000 =
$200,000,
Total costs = 220,000
Alternatively, instead of a tax, let’s say that the IPCC recommends a permit-based regime. They issue 9,500 permits to Firm 1 and 9,500 permits to Firm 2. The market price of permits quickly stabilizes to $20.
3) Under this permit regime, how many tons of carbon will Firm 1 emit? What will be their total cost of abatement? What will be the total change in their profits since the imposition of the permit regime (compared to the original, non-tax regime)?
Same amount of
emissions, since the price incentive is the same: tax = $20 or permit =
$20.
Therefore, same cost
of abatement: $10,000
But now, the total cost
= TAC - sale of permits (since they were issued 9.500, but only needed 9,000)
Thus, sale of permits
is $20*500 = 10,000. so that the net cost = 0
4) Under this permit regime, how many tons of carbon will Firm 2 emit? What will be their total cost of abatement? What will be the total change in their profits since the imposition of the permit regime (compared to the original, non-tax regime)?
Same amount of
emissions, since the price incentive is the same: tax = $20 or permit =
$20.
Therefore, same cost
of abatement: $20,000
But now, the total cost
= TAC + purchase of permits (since they were issued 9.500, but need 10,000)
Thus, purchase of
permits is $20*500 = 10,000. so that the net cost = $30,000
5) In the case of S02 reduction-policy, why did firms generally prefer a permit-based policy to a tax based-policy? Justify your answer.
A good answer would
note that cots are lower with permits, as well as some of the reasons discussed
in the IB policy by Goodstein and/of the Schmalansee article
Section II – Economic analysis and sustainability
(ANSWER ONE QUESTION IN THIS SECTION – IIA or IIB or
IIC)
A)
In ‘The Environmentalists are Wrong’ (The New York
Times, August 26, 2002), Bjorn Lomborg writes:
Traditionally, the developed nations of the West have shown greater concern for environmental sustainability, while the third world countries have a stronger desire for economic development. … The challenge in Johannesburg [the recent world summit on the environment] will be whether we are ready to put development ahead of sustainability. If the United States leads the way, the world may finally find the courage to do so.
Do you agree with this statement by Lomborg – should we put
development ‘ahead’ of sustainability?
Support your opinion with relevant material from our reading.
A good answer here would use some of the specific examples from our reading and discussions, including (but not limited to) Solow and the Shipbreakers.
B) In ‘The Economic Theory of a Common-Property
Resource,” (The Journal of Political
Economy 62(2):124-42), Scott Gordon writes:
Many [biologists] … have recognized that the ultimate question is not the ecology of life in the sea as such, but man’s use of these resources for his own economic purposes. Dr. Martin Burkenroad, for example, began a recent article on fishery management [by] saying that “the management of fisheries is intended for the benefit of man, not fish; therefore effect of management upon fishstocks cannot be regarded as beneficial per se.”
Do you agree with Gordon and Burkenroad – should the economic
benefits of humans guide the management of fisheries? Support your opinion with relevant material from our reading.
A good answer here would use some of the specific examples from our reading and discussions, including (but not limited to) Simpson and the Kurlansky.
C) In “A Tale of Two Fisheries” (The New York
Times, August 27, 2000), John Tierney quotes Rhode Island lobsterman
John Sorlien:
“If we get some kind of
environmental disruption that interferes with reproduction one year, we'll end
up with nothing to catch for a whole season. We just go from year to year not
knowing what to expect. I don't have a clue what kind of year this will be for
me. It's like we're backing up to the edge of a cliff blindfolded, and we don't
know if we're 50 feet away or have two wheels over the edge.”
How do Sorlien’s comments illustrate the weaknesses of
economic analysis as it applies to the management of ecosystems? Support your opinion with relevant material
from our reading.
A good answer here would use some of the specific examples from our reading and discussions, including (but not limited to) Simpson and Fullerton & Stavins.