CLASS QUESTIONS
for Summer School Course
EC240: Environmental Economics and Sustainable Development
Case Study: The costs of shale gas development
Please read the survey by Sovacool (2014) before class. Please discuss in groups:
a) The different costs of shale gas development
b) Which of those costs do you believe is the highest / most relevant? Why?
c) Why does this cost arise and will it be reflected in the market price for shale gas?
d) Can you think of a solution to the externality problem?
Question 1
Consider an airport that produces noise that decays as the distance (d), in kilometers, from the
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airport increases: 𝑁(𝑑) = 𝑑2. Luca works at the airport. Her damage from noise is $1 per unit of
noise and is associated with where Luca lives. Her costs of commuting are $1 per km (each way).
The closest she can live to the airport is d = 0.1 km.
a) Write an expression for Luca’s total costs (noise and transportation).
b) What is the distance Luca will live from the airport in the absence of compensation for the
noise? What are her total costs?
c) Suppose Luca is compensated for her damage, wherever she may live. How close to the
airport will she choose to live? How much will she be compensated?
d) If Luca could be compensated in a lump sum fashion for the noise externality, why would
this be non-distortionary?
Question 2
Individuals have to decide whether to make a journey or not. For each individual, the benefit
of making the journey is 15. The cost of making the journey, C, depends on the number of
𝑛
individuals making the journey, n, according to the function 𝐶 = 5 + 1000.
a) What is the equilibrium number of travelers, and what is the total benefit and total cost
accruing to all travelers at equilibrium?
b) What is the socially optimal number of travelers?
c) Explain the externality that arises in this example.
d) In view of this example, outline and evaluate two different policy measures that could be
applied to traffic congestion.
Question 3
Consider an air basin with only two consumers, Lisa and Solveig. Suppose Lisa’s demand for air
quality is given by 𝑞𝐿 = 1 − 𝑝 where p is Lisa’s marginal willingness to pay for air quality. Similarly,
Solveig’s demand is given by 𝑞𝑆 = 2 − 2𝑝. Air quality can be supplied according to 𝑞 = 𝑝 where p
is the marginal cost of supply.
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a) Graph the aggregate demand for air quality along with individual demands.
b) What is the efficient amount of air quality?
Question 4
Consider a pollution problem involving a paper mill located on a river and a commercial salmon
fishery operating on the same river. The fishery can operate at one of two locations upstream (above
the mill) or downstream (in the polluted part of the river). Pollution lowers profits for the fishery:
without pollution, profits are $300 upstream and $500 downstream; with pollution, profits are $200
upstream and $100 downstream. The mill earns $500 in profit, and the technology exists for it to
build a treatment plant at the site that completely eliminates the pollution, but at a cost of $200.
There are two possible assignments of property rights: (i) the fishery has the right to a clean river
and (ii) the mill has the right to pollute the river.
a) What is the efficient outcome?
b) What are the outcomes under the two different property regimes, when there is
no possibility of bargaining?
c) How does your answer to (b) change when the two firms can bargain without incurring any
costs?
Question 5
A beekeeper and a farmer with an apple orchard are neighbors. This is convenient for the orchard
owner since one hive of bees pollinate one acre of orchard. Unfortunately, there are not enough
bees next door to pollinate the whole orchard and pollination costs are $10 per acre. The
beekeeper has total costs of 𝑇𝐶 = 𝐻2 + 10𝐻 + 10, where H is the number of hives. Each hive
yields $20 worth of honey. Assume that the orchard owner already operated independently of the
beekeeper.
a) How many hives would the beekeeper maintain if operating independently of the farmer?
b) What is the socially efficient number of hives?
c) In the absence of transaction costs, what outcome do you expect to arise from bargaining
between the beekeeper and the farmer?
d) How high would total transaction costs have to be to erase all gains from bargaining?
Question 6
Air pollution through car emissions is quite a problem in Los Diablos. Fortunately, the local
government commanded a survey among car drivers which found out that practically all motorists
stated that they value cleaner air in the city with at least $1000 per year. The government then
offered to motorists a heavily subsidised catalytic converter for $300. After one year the
government had to concede that practically no motorist had bought a converter. How can you
explain this result? You should assume that motorists told the truth when asked in the survey.
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Question 7
Two firms can control emissions at the following marginal costs: 𝑀𝐶1 = 100𝑞1, 𝑀𝐶2 = 200𝑞2,
where 𝑞1 and 𝑞2 are, respectively, the amount of emissions reduced by the first and second firm.
Assume that with no control at all, each firm would be emitting 20 units of emissions or a total of 40
units for both firms.
a) Compute the cost-effective allocation of control responsibility if a total reduction of 21 units
of emissions is necessary.
b) Assume that the control authority wanted to reach its objective in a) by using an emission
charge system. What per unit charge should be imposed? How much revenue would the
control authority collect?
Question 8
The Fireyear and Goodstone rubber companies are two firms located in the rubber capital of the
world. These factories produce finished rubber and sell that rubber into a highly competitive world
market at the fixed price of £60 per ton. The process of producing a ton of rubber also results in a
ton of air pollution that affects the rubber capital of the world. This 1:1 relationship between rubber
output and pollution is fixed and immutable at both factories. Consider the following information
regarding the costs (in £) of producing rubber at the tow factories (𝑄𝐹 and 𝑄𝐺 ):
Fireyear: 𝐶 = 300 + 2𝑄𝐹2
Goodstone: 𝐶 = 500 + 𝑄𝐺2
Total pollution emissions generated are 𝐸𝐹 + 𝐸𝐺 = 𝑄𝐹 + 𝑄𝐺 . Marginal damage from pollution is
equal to £12.
a) In the absence of regulation, how much rubber would be produced by each firm? What is the
profit of each firm?
b) The local government decides to impose a Pigouvian tax on pollution in the community. What
is the efficient amount of such a tax per unit of emissions? What are the post-regulation levels
of rubber output and profits for each firm?
c) Suppose instead of the emission tax, the government observes the outcome in part a) and
decides to offer a subsidy to each firm for each unit of pollution abated. What is the efficient
per unit amount of such a subsidy? Again, calculate the levels of output and profit for each
firm.
d) Compare the output and profits for the two firms in part a) through c). Comment on the
differences, if any, and the possibility of one or both of the firms dropping out of the market.
Question 9
Two firms pollute the environment and thereby save money. Firm A’s savings function is given by
𝑆𝐴 = 100𝑒𝐴 − 2𝑒𝐴2. Firm B’s savings function is given by 𝑆𝐵 = 100𝑒𝐵 − 4𝑒𝐵2. If firm A is given two
emission permits and firm B is given four emission permits and they are allowed to trade, how many
permits will each firm end up with and what will be the price?
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Question 10
Assume that officials of the environmental protection agency know the MDC curve of reducing
emissions with certainty. However, there is uncertainty with respect to MAC curve. Assume for all
parts of this question that the true MAC curve lies below (to the left) of the expected MAC curve.
Prove, with the help of diagrams, the following statements. Make sure to label the respective areas
under the curves clearly. (For this exercise take the 45 degree line as a guideline. A line steeper than
the 45 degree line can be considered relatively steep, a line flatter than the 45 degree line can be
considered relatively flat).
a) If the MAC curve is steep and the MDC curve is neither steep nor flat, then taxes will lead to
a lower welfare loss than standards in case the agency comes to a wrong estimate of the
MAC curve.
b) If the MDC curve is flat and the MAC curve is neither steep nor flat, then taxes will lead to a
lower welfare loss than standards in case the agency comes to a wrong estimate of the MAC
curve.
c) If the MAC curve is flat and the MDC curve is neither steep nor flat, then taxes will lead to a
higher welfare loss than standards in case the agency comes to a wrong estimate of the MAC
curve.
d) If the MDC curve is steep and the MAX curve is neither steep nor flat, then taxes will lead to
a higher welfare loss than standards in case the agency come to a wrong estimate of the MAC
curve.
e) If the MAC curve is steep, but the MDC curve is steep as well, then there is no general rule
on whether taxes or standards will lead to a lower welfare loss in case the agency comes to
a wrong estimate of the MAC curve.
f) If the MAC curve is flat, but the MDC curve is flat as well, then there is no general rule on
whether taxes or standards will lead to a lower welfare loss in case the agency comes to a
wrong estimate of the MAC curve.
Question 11
An island has two lakes and 20 fishermen who can fish on either lake, and, with fishing organized by
a co-operative of fishermen, keep the average catch on the chosen lake. The total number of fish
caught on lakes X and Y when these are fished by 𝐿𝑋 and 𝐿𝑌 fishermen are 𝐹𝑋 and 𝐹𝑌 , according to
the following functions:
𝐹𝑋 = 10𝐿𝑋 − 0.5𝐿2𝑋
𝐹𝑌 = 5𝐿𝑌
a) If fishermen are free to choose on which lake they fish, then how many are on each lake and
what is the total number of fish caught?
b) What allocation of fishermen to lakes maximises the catch of fish? What is the total number
of fish caught, and what is the marginal product of fishermen on each lake? Why is this
equivalent to the efficient level of fish catch?
c) Identify precisely the externality in a).
d) If a fishing license were required for lake X, what value license (in terms of fish) would be
needed to achieve efficiency?
e) If a profit maximizing private owner of lake X were to hire fishermen at wage rate 5 fish, what
is the competitive equilibrium?
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Question 12
Assume that the relationship between growth of a fish population and the population size can be
expressed as 𝑔 = 4𝑃 − 0.1𝑃2, where 𝑔 is the growth in tons and 𝑃 is the size of the population (in
thousands of tons). Given a price of $100 per ton, the marginal benefit of smaller population sizes
(and hence larger catches) can be computed as 20𝑃 − 400.
a) Compute the population size that is compatible with the maximum sustainable yield. What
would be the size of the annual catch if the population were to be sustained at this level?
b) If the marginal cost of additional catches (expressed in terms of the population size) is 𝑀𝐶 =
2(160 − 𝑃), what is the population size which is compatible with the efficient sustainable
yield?
Question 13
Assume that a local fisheries council imposes an enforceable quota of 100 tons of fish on a particular
fishing ground for one year. Assume further that 100 tons per year is the efficient sustainable yield.
Once the 100th ton has been caught, the fishery would be closed for the remainder of the year.
a) Is this an efficient solution to the common-property problem? Why or why not?
b) Would you answer be different if the 100-ton quota were divided up into 100 transferable
quotas, each entitling the holder to catch one ton of fish, and distributed among the
fishermen in proportion to their historical catch? Why or why not?
Question 14
Show with the help of diagrams the effect of the inter-temporally efficient Hotelling price path and
the resource exhaustion date if the private discount rate used by resource owners is higher than the
correct social discount rate.
Question 15
Discuss, with diagrams, the consequences of the discovery of North Sea oil for
a) the price and output levels for the oil market
b) the date of exhaustion of oil reserves.
c) What will be the probable path over time of oil prices if there are frequent discoveries of oil?
Question 16
‘If the market puts a lower value on trees as preserved resources than as sources of timber for
construction, then those trees should be felled for timber.’ Discuss.
Question 17
‘Future generations can cast neither votes in current elections nor dollars in current market decisions.
Therefore, it should not come as a surprise to anyone that the interests in future generations are
ignored in a market economy’. Discuss.
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Question 18
‘Every molecule of a non-renewable resource used today precludes its use by future generations.
Therefore, from a sustainability perspective, the only defensible policy for any generation is to use
only renewable resources.’ Discuss.
Question 19
Suppose that an individual has the utility function 𝑈 = 𝐸 0.25 + 𝑌 0.75, where 𝐸 is some index of
environmental quality and 𝑌 is income. From an initial situation where 𝐸 = 1 and 𝑌 = 100, calculate
CS and ES for a decrease in 𝐸 to the level 0.5. Try to also illustrate CS and ES in a stylized diagram.
Question 20
Baked beans are an inferior good: The demand for baked beans decreases when income rises.
a) Show on an indifference curve diagram, with baked beans on the horizontal axis, and other
goods on the vertical axis, the effect on demand for baked beans of an increase in the price
of baked beans. Show the income and substitution effects. Show how you could use this
diagram to find the compensated and equivalent variation of the price increase.
b) Does the utility of the consumer increase or decrease when the price of baked beans
increases?
c) Show on the price-quantity diagram the uncompensated demand curve, and the two
compensated demand curves associated with the level of utility before and after the increase
in the price of baked beans.
d) Show on a different price-quantity diagram the equivalent variation, compensated variation
and change in consumer surplus of the increase in price of baked beans. Rank in order of size
the equivalent variation, compensated variation and change in consumer surplus. Are these
likely to differ greatly from each other in practice?
Question 21
The world consists of two countries, X which is poor and Y which is rich. The total benefits, 𝐵, and
total costs, 𝐶, of emission abatement, 𝐴, are given by the functions
𝐵𝑋 = 8(𝐴𝑋 + 𝐴𝑌 )
𝐵𝑌 = 5(𝐴𝑋 + 𝐴𝑌 )
𝐶𝑋 = 10 + 2𝐴𝑋 + 0.5𝐴2𝑋
𝐶𝑌 = 10 + 2𝐴𝑋 + 0.5𝐴2𝑌
a) Obtain the non-cooperative equilibrium levels of abatement for X and Y.
b) Obtain the cooperative equilibrium levels of abatement for X and Y.
c) Calculate the net benefits enjoyed by X and Y in the non-cooperative and cooperative
solutions. Does the cooperative solution deliver Pareto improvements for each country, or
would one have to give a side-payment to the other to obtain Pareto improvements for each
with cooperation?
d) Obtain the privately optimizing level of abatement for X, given that Y decides to emit at the
level of emissions that Y would emit in the cooperative equilibrium.
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e) You should find that the answer to d) is that X does the same amount of abatement that it
would have done in the non-cooperative case. What property or properties of the cost and
benefit function used in this example cause this particular result?
f) Suppose that Y acts as a ‘swing abater’, doing whatever (non-negative) amount of abatement
is required to make the combined world abatement equal to the combined total under a full
cooperative solution. X knows that Y acts as a ‘swing abater’ and can choose any (nonnegative) amount of abatement it likes. How much abatement is undertaken in the two
countries?
Question 22
In the early 1990s, the chief economist of the World Bank came under a great deal of criticism for
suggesting that developing countries take advantage of opportunities to import hazardous and nonhazardous wastes for storage and disposal. Why was he making this argument? What are the
arguments against his position?
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