Economics of Law and Regulation Worksheet
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THE PENNSYLVANIA STATE UNIVERSITY
Department of Economics
Spring 2022
Economics 443
Due: April 25, 2022
This is an individual assignment in the sense that each individual must submit his or
her answers. However, you should feel free to work with another classmate to solve
the problems. Ultimately, it is important that each individual understand how to solve
these problems because questions similar to these will appear on exams. Turn in via
Canvas.
1
Market Structure
Participants:
The firms are assigned a number. Odd numbered firms differ from
even numbered firms in their abatement costs. Otherwise firms are the same.
Output market: The firms operate in the same country. Each firm produces the
same product. Total home country production is small relative to global production
so the firms take the market price of 40 per unit of output as given.
Production: Each firms production cost associated with Q units of output is C(Q) =
Q up to a capacity of 20 (all firms have the same cost function and same capacity
constraint). Marginal cost is constant at 1.
Pollution: Each unit of output produces one unit of pollution.
1
Pollution abatement: A firm can reduce its emissions by investing in pollution
abatement. For odd-numbered firms, the cost of reducing pollution by A units is
A
A
Codd
(A) = 3A2 . For even-numbered firms, the cost is Ceven
(A) = A2 . Thus, odd-
numbered firms have relatively higher abatement costs than even-numbered firms.
Marginal abatement costs are 6A for odd-numbered firms and 2A for even-numbered
firms.
Simplification:
There are the same number of odd and even firms. Thus, you can
assume that there are only two firms, Firm 1 and Firm 2, to answer the questions that
follow.
2
No regulation
Suppose there is no environmental regulation. What quantity will each firm produce? How
much will each firm choose to abate? What will be the profit of each firm?
3
Emission cap
Suppose the government of the firms home country institutes a cap on emissions of 10 units,
with each unit of pollution in excess of this limit fined at a rate of 70/unit. A firms pollution
associated with output Q is Q ? A. To avoid the fine, a firm must have Q ? A ? 10. What
quantity will each firm produce? How much will each firm choose to abate? What will be
the profit of each firm?
4
Cap and Trade
Consider a cap-and-trade policy whereby the government of the firms home country issues
tradable emission permits to the firms. Each firm is issued 10 permits. Each permit allows
a firm to emit one unit of pollution. Firms can buy or sell permits. A firms production
must equal permits on hand after trading plus abatement. A firm is fined $70 for each unit
of production that exceeds permits on hand plus abatement.
2
Consider five different production choices
1. Q1 = 14, Q2 = 10
2. Q1 = 10, Q2 = 14
3. Q1 = 16, Q2 = 20
4. Q1 = 20, Q2 = 16
5. Q1 = 20, Q2 = 20
For each of the five production choices above answer the following
1. Will Firm 2 sell to Firm 1 or will Firm 1 sell to Firm 2?
2. How many permits will be sold?
3. What will be the permit price?
4. How much will each firm choose to abate?
5. What will be the profit of each firm?
5
Summary
Fill in the following table. What quantities will the two firms choose under cap-and-trade.
Why does a cap-and-trade policy result in more total output, more total abatement, and
more total profit than an emission cap policy?
Senario
Q1
Q2
A1
A2
?1
?2
Px
No Regulation
na
Emission Cap
na
Cap and Trade
14
10
Cap and Trade
10
14
Cap and Trade
16
20
Cap and Trade
20
16
Cap and Trade
20
20
3
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Explanation & Answer:
Worksheet
Tags:
law
economics
regulation
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