# Why might this be inefficient, using the defi-nition of efficiency developed in class?

EC 450: Economics of Environmental Policies
September 15, 2015
Due: September 24, 2015
Homework is due promptly at the beginning of class (12:40 PM). Late
assignments will not be accepted.
1. For each of the following social choice methods, which of Arrow’s
axioms (A1-6) are violated and why?
a. The Pareto criterion
b. plurality-rule voting (of several choices, the one with the most
c. majority-rule voting (between two alternatives)
d. pulling a choice out of a hat (random)
2. Assume there is a city of 1,000,000 people, 60 % of whom are willing
to pay \$1 maximum (each) to clean up pollution. The rest of the population
is wealthier and is willing to pay \$100 each to clean up pollution. Pollution
clean up will cost \$2,000,000. It has been proposed that each person be
taxed equally to pay for the pollution clean-up. Will that pass a majority
rule vote? Is it desirable from the point of view of the Pareto criterion?
Is it a good idea, using the compensation principle? Which social choice
mechanism do you think is best on intuitive grounds, and why?
3. Suppose you have a society of n identical individuals. Each individual
likes his or her material possessions as well as access to parks and wilderness
areas. In fact, the utility function for each individual is
U(x, H) = x + H ?
1
x
?
1
H
where x is consumption goods and H is environmental health. H attains its
highest level when it is pristine: H = 100 (ie, H is on a scale from 0 to 100
or 0 ? H ? 100 ). Consumption of goods degrades the environment, but
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the environment has some ability to heal itself. In fact, the environment has
health
Ht = Ht?1 + g(100 ? Ht?1) ? nx
where Ht
is today’s H and Ht?1 is yesterday’s H. Note that the environment’s
ability to cleanse itself, g, and the intensity of damage, n are both
fixed (are constants).
a. Simply focusing on the utility function (ignore the evolution of
H), discuss the extent to which the utility function is consistent
with biocentrism or anthropocentrism.
b. Suppose we start at H = 100. Assume g = 0.1 and n = 1.
Plot how H would evolve over three periods for x = 0.01, x = 0.1,
and x = 1. (Hint: You should have three graphs with time on the
horizontal axis and environmental health on the vertical axis).
c. Repeat part (b) except this time plot U instead of H. Can
you reach any conclusions about the level of consumption that
maximizes utility?
4. Suppose we have a small inhabited island with three residents and a
volcano that generates air pollution. Two people live upwind of the volcano
and one person lives downwind. For \$21,000 we can clean up the volcano
with a patented ”smoke guzzler.” The two upwind people wold pay \$1,000
each to get rid of the smoke whereas the downwind person would be willing
to pay \$15,000. Consider two plans to finance the ”smoke guzzler.” Plan
A calls for a head-tax of \$7,000. Plan B calls for the affected party (the
downwind person) to pay \$21,000 and everyone else nothing. Compare each
plan to the status quo and indicate society’s choice using (a) the Pareto
criterion (b) majority rule, and (c) potential Pareto improvement.
5. On a drawing of the following figure, find and label
a. a point D such that Z and Y are Pareto preferred to D, but
S is not.
b. a point E such that the arc BZ is the portion of the Pareto
frontier which includes points that are Pareto improvements on
E.
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6. In the following figure, the slope of the production possibility frontier
(the MRT of wine for garbage disposal) is increasing (getting steeper) as
garbage disposal decreases and wine increases. Does this make sense? Why?
7. Suppose an environmental regulation requires all polluters to reduce
emissions by 50%, even though the cost of pollution control differs widely
from one polluter to another. Why might this be inefficient, using the defi-
nition of efficiency developed in class?
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