04 Jun Question EC: 434/534 Environmental Economics
Question
EC: 434/534 Environmental Economics
Homework 2
1). Suppose there is a town on the Yangtze River with two types of people: Farmers
and Students. Suppose further that there is an Apple Watch factory that generates pollution.
Pollution is non-rival and non-excludable. The total damage (or cost) to farmers
for each unit of pollution, p is given by T DF (p) = 3p
2
. The total damage to students is
T DS(p) = 6p. The total benefit to the factory from emitting p units of pollution is given
by B(p) = 10p ? p
2
.
a) Find the aggregate marginal damage/cost for pollution (also known as social marginal
cost). Hint: use calculus.
b) Graph the marginal benefit and social marginal cost curves as a function of pollution.
c) How much pollution does the factory choose in the absence of regulation or bargaining?
d) Calculate the social marginal benefit of abatement.
e) Calculate the marginal cost of abatement and the efficient amount of abatement.
f) Are questions of optimal pollution and optimal abatement equivalent? Explain.
2) Consider a factory that generates 5 tons of toxic waste. The factory chooses between
burying the waste on site or paying for recycling. These decisions do not affect output.
Burying a ton of waste costs the firm nothing, and given the nature of the production
process and the recycling industry, the marginal cost of recycling r tons is given by:
MCrecycling(r) = 2r
Toxic waste buried on site leaks into the water table that supplies a city. The estimated
marginal health damages from burying t tons is given by:
MHDtons(t) = 2 + t
In this problem, you can think of buried tons of waste (t) as “emissions” and the amount
of recycling r as “abatement.”
a). What is the equilibrium outcome? How many tons does the firm recycle?
1
b). How many tons would the social planner recycle to achieve efficiency?
c). What is the efficient flat tax on burying waste?
d). What is the change in surplus as a result of the tax (compared to the status-quo) for:
• The firm?
• water drinkers?
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