ECON 455 San Diego State University Marginal Abatement Costs Questionnaire


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ECON 455
San Diego State University
Fall 2022
Econ 455 – Problem Set 2
Please answer the following practice questions. For full credit, you must show your work
when asked. Partial credit may be given for incorrect answers with sensible work. You
must upload your files to Canvas. Late assignments will receive no credit.
Abatement, uniform standards, pollution taxes, and pollution permits
1. Suppose there are two power plants that release sulfur dioxide (SO2 ) into air at their
current production levels. Each firm currently emits 75 tons per year, thus emitting
150 tons total. Local authorities have decided they would like to reduce annual SO2
pollution to 100 tons per year (thus a 50 ton reduction).
The power plants have different marginal abatement costs given by the following equations:
M AC1 = 3q1 + 5
M AC2 = 2q2
(a) Suppose the local authorities decide to impose a uniform reduction of pollution by
both power plants. In order to achieve the 50 unit reduction under this plan, both
plants must reduce their emissions (abate pollution) by 25 units each. Find the
total cost of abatement under this uniform reduction policy.
(b) Find the efficient abatement amount for each power plant if you wanted to achieve
the 50 unit reduction at the most cost-efficient way possible (i.e. find the q1 and q2
that achieves the 50 unit reduction in the cheapest way). What is the total cost of
reducing pollution under this plan? How much must each plant pay?
(c) Now suppose the local authorities wanted to achieve this 50 ton reduction in annual
SO2 via a pollution tax. This tax is the same for for both power plants and must
be paid by each plant for every ton of SO2 emitted annually. Find the optimal tax
per ton of SO2 . How much does each plant pay in taxes? What is the total cost
for each plant from this policy (cost of tax payment and total abatement costs).
Which power plant pays more?
2. Suppose the local authorities wanted to achieve a more drastic reduction in total pollution of 75 tons in the scenario described above. They want to do so via the introduction
of a tradable pollution permits system whereby, each permit would allow a power plant
to emit one ton of SO2 annually at no cost, but a power plant’s emissions may not exceed
it’s permits. The authorities must will distribute 75 permits (to achieve the 150 – 75 =
75 ton reduction). Recall that prior to the policy, each plant is emitting 75 tons.
(a) If the regulator issues 35 permits to firm 1 and 40 permits to firm 2, without trading,
how much would each firm have to spend to comply with the regulation? Recall
that each firm must abate the pollution for which they do not hold permits. i.e.
q1 = 75 ? p1 where p1 is the number of permits firm 1 has.
(b) At this initial allocation, what is the marginal willingness to pay a permit for firm
1? What is the marginal willingness to accept to sell a permit for firm 2? Should
they trade?
(c) Find the efficient allocation of permits. How much must each firm spend on pollution control under the efficient permit allocation?
(d) Assume firms traded from the initial allocation (35, 40) to the efficient allocation
found above. Solve for the permit price, the total amount paid by firm 1 (and thus
received by firm 2). Can you show that trading made both firms better off than
they would have been under the initial allocation if permits were not tradable?
HINT: Compare the total costs in part (a) to the costs of abatement under the efficient allocation plus the costs/revenues from permit sales.
3. Assume you have three firms with different marginal abatement cost functions as follows:
M AC1 = 2q1
M AC2 = q2
M AC3 = q3
It has been determined that the total amount of pollution should be reduced by 35 units.
(a) Find the cost-effective allocation of pollution abatement for each firm.
(b) Find optimal emissions charge (pollution tax) that would result in a 35 unit total
reduction in pollution across the three firms.
Short Answer
4. Explain why regulators would likely prefer emissions charges or cap and trade policies
to emissions standards? Provide at least two reasons.
5. Imagine you are talking to a policy-maker enacting a tradable pollution permit policy
who makes the following statement:
We should be sure to give all firms the same number of permits. Otherwise,
we will not get cost-effective reduction in pollution.
Evaluate this statement.

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Uniform Standards

marginal abatement costs

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