Penn State College Environmental Economics Worksheet


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Homework 6, due date Tuesday, April 5th.
This homework is also a practice exam for midterm 2. After preparing for the exam, try the
practice exam as under exam conditions. Then, you can use your notes etc to prepare your
homework submission.
Econ 428, Patrik Guggenberger
Spring 2022
Practice Midterm Exam II
You have 75 minutes to work on the exam. Answer all questions for a total of 100 points. Closed
book exam: No notes, phones, textbooks… are allowed. Be precise in your statements. Don’t
forget to write your NAME.
True or false questions:
Question 1 (max 9): ____________
Question 2 (max 9):_____________
Question 3 (max 9): _____________
Essay questions:
Question 4 (max 12): _____________
Question 5 (max 12): _____________
Numerical questions:
Question 6 (max 19): ____________
Question 7 (max 20):_____________
Multiple choice questions:
Question 8 (max 5): _____________
Question 9 (max 5): _____________
Total (max 100): __________________
True or False: In each of the questions 1-3 say if the statement is true or false and explain why.
Credit is given for the thoroughness of the explanation.
Possible criticisms of a transfer system to incentivize countries to choose the emission
levels that are globally economically efficient are that a) they may not be stable if after
the formation of a coalition non-coalition members – rather than playing their individual
best response – also form a coalition and choose emission levels to maximize the
consumption of the collation and b) in order to calculate the transfers one would need to
know the precise values of various quantities that are hard to evaluate, including the
technologies of each country, the multiplicative constants that measure the damage
exposure of countries, and the nationally and globally optimal emission levels of each
2. To adapt Faustmann rule for efficient rotation to a model where there are also nontimber
forest benefits, we have to add the nontimber benefits to the marginal cost function (with
the interpretation of foregone benefits when the forest is harvested). Assuming positive
nontimber benefits the optimal rotation time will decrease.
3. Assume in the permit trading game played in class (nine firms with marginal cost of
abatement ranging from 2 to 10), the setup is modified by the one change that the EPA
decides to reduce the number of emission permits from 9 to 6 and gives one to each of the
six firms with the lowest marginal abatement cost. As the “willingness to pay” for
permits of these low abatement cost firms will decrease, the equilibrium price for permits
will be lower than in the version of the game played in class.
Essay questions.
When attempting to restore economic efficiency in the presence of negative externalities
from production, governments use regulation, taxes or cap and trade. Provide a detailed
discussion regarding the pros and cons of these methods. Name two other market
instruments governments could choose in an attempt to restore efficiency.
Regarding the model of combatting climate change in the international arena. A) Find
important aspects where the model oversimplifies reality. B) Discuss key features of
climate change that the model captures.
Numerical Problems
6. Assume F(X)=X-X2 describes the “growth of stock” when the size of the stock of fish
equals X. Furthermore, Y(X,E)=2XE describes the harvest when the stock of fish equals
X and the fishing effort (e.g. think of “number of fishing boats”) equals E.
a) In a steady state model, derive the harvest Y as a function of the fishing effort, i.e.
what is Y(E)?
b) For which stock level is the growth highest? Assume the marginal cost of fishing at
fishing effort E is given by MC(E)=$1 and the price p of one unit of harvest equals $2.
What is the economically efficient fishing effort EE, and what will be the fishing effort EO
under an open access policy? Interpret
c) Now assume that MC(E)=E (i.e. increasing marginal costs because (e.g.) the last boat
to go out to fish has to travel further out into the ocean). How do your answers to part b)
change for EE and EO?
d) In support of the struggling fishing industry many politicians advocated (and
implemented) subsidies (such as a fuel tax exemption) in the early 2000 when overfishing
had depleted the fish stock of many species. Discuss the impact of such subsidies in the
context of the model presented here.
7. Assume a firm’s marginal cost of abatement is given by 3a+1 when “a” units of
pollution are abated. Assume the current daily pollution emission of the firm is given by
two units. A new abatement technology becomes available that leads to a reduced
marginal cost of abatement given by 2a+.5. However, to purchase the equipment for the
new technology a one-time expense of $.5 is necessary. The firm minimizes total cost
over two periods (today and tomorrow) where expenses tomorrow are discounted by 5%.
A) Assume, in addition to the firm above, there are two other firms (both identical) that
also produce two units of pollution. Both these firms have already adopted the new
technology whereas the firm above has not. Under “cap and trade” with a daily cap of
5/3 units of pollution per firm, will the other firm also purchase the new abatement
technology? (Assume that the firms that sell pollution permits charge exactly the cost
that they face for the additional abatement and that the two low cost abaters share the
pollution permits sold to the high cost firm.)
B) Comparative statics: Ceteris paribus (i.e. everything else kept equal),
o if the discount rate was increased would it become more or less likely that the
firm adopts the new technology? Why?
o if there were more low cost firms participating in the cap and trade program
would it be come more or less likely that the firm adopts the new technology?
Multiple Choice: Circle the correct answer. Indicate clearly what your answer is.
8. A. By “marginal user cost” in the context of extraction of nonrenewable resources we mean
the difference between price of the resource and marginal extraction cost.
B. Hotelling rule implies that if the discount rate goes up then more of the resource should be
extracted today.
C. To maximize net present value of profits we have to pick extraction amounts such that the
last unit of the resource extracted today yields the same marginal profit as the net present
value of the profit of the last unit of the resource extracted tomorrow.
D. A-C
E. A and C
9. A. While all major developed countries ratified and participated in the Kyoto protocol from
2008-2012, many developing countries such as India and China did not have to reduce
their emissions under the rules of the protocol.
B. One key downside of the Kyoto protocol was that participation was essentially voluntary
with no real sanctions for countries that did not fulfill their obligations.
C. One key objective for fighting climate change is that a very large number of countries
participates. Otherwise, the cost to cap worldwide emissions at a given level is going to
be much higher. In that regard, the Kyoto protocol must be viewed as a failure as it
covered only about 2/3 of worldwide emissions of CO2 in 2012.
D. The Copenhagen (2009) agreement learned from the mistakes made in Kyoto by imposing
severe tariff penalties on each country that violates the emission cap imposed on it.
E. C and D.

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