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ECOS3013Pigouvian Tax

创建日期：2024-06-14 15:02:42

所属分类：经济Economics

标签： ECOS3013

Pigouvian Tax

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ECOS3013 Tutorial 6

Question 1: Pigouvian Tax
Suppose that the marginal private cost of paper production isMPC(Q) = 3+9Q where Q is the industry
output. Suppose also that the marginal private benefit of paper products is MPB(Q) = 193− 10Q. The
paper production process is smelly and causes water pollution – a negative externality. Suppose that this
causes a constant amount of external harm E = $38 for each unit of paper produced.
A What level of paper production would there be in an unregulated market (call this Qm1)? What
would be the price pm1? What is the efficient quantity Q
∗? Draw a diagram of the paper market,
showing these quantities.
B Suppose that the government imposes a production tax of τ = $38 per unit of paper produced.
How much paper is produced?
C With the tax in place, what price do consumers pay? What price do producers receive, after they
remit the tax? How much tax revenue does the government raise? Show this on your diagram.
D Is society better or worse off after the tax (according to the Pareto criteria)?
Pre-question 2 (not assessed)
When thinking about reducing pollution there are two particularly important types of uncertainty. These
are uncertainty in how harmful pollution is (uncertain MD), and uncertainty in how expensive it will
be to reduce pollution (uncertain MAC). The more harmful pollution is, the more we want to reduce it.
The more expensive it is to reduce pollution, the less we want to reduce it so we can use those economic
resources that would have gone to pollution abatement for other purposes.
1
Think about how these types of uncertainty affect the environmental policy you’d recommend. If you
think MD are very uncertain, but MAC are relatively well known, does this affect policy? What if it was
the opposite, with relatively certain MD and relatively uncertain MAC? Do you expect these two types
of uncertainty to be symmetric? Or does one matter more?
Part of the answer to this won’t be clear until we do cap-and-trade
Question 2: Uncertainty in MD
A government is considering implementing a carbon tax, but the MD from climate change is unknown.
Suppose MAC from pollution emissions e are known, MAC(e) = 36 − 9e. However, marginal damages
are uncertain:
MDH(e) = 16e with probability 0.3
MDL(e) = 6e with probability 0.7
A What is the expected marginal damage function? Draw a diagram showing this function, along
with MDH(e) and MDL(e). Include the MAC (AKA marginal savings) function.
B What is the optimal Pigouvian tax rate, in expectation? Show it on your diagram. (Assume that
the regulator sets the tax based on expected MD and MAC, and is not trying to minimize the total
DWL under uncertainty, which might result in a different optimal tax rate.)
C If the tax rate you calculated in part 2 is imposed, what is the expected DWL?
Question 3: Uncertainty in MAC and MD
A government is considering implementing a carbon tax, but both the economic costs of reducing emis-
sions and the marginal damages may be uncertain. Draw four diagrams to illustrate this. In all four
diagrams assume the government sets the tax where the E[MD]=MAC, or the MD=E[MAC]. Like in
question 2, show the DWL triangles (two per diagram) that will result from this uncertainty.
you may find this easier to draw if you don’t worry about the MAC and MD lines intersecting at the
same point on the axes. Instead, just draw the uncertain MD or MAC lines within a diagram as parallel
lines.
2
A Show a certain MD and two uncertain (High and Low) MAC’s, using a relatively flat MD and two
steep MAC’s
B Show a certain MD and two uncertain (High and Low) MAC’s, using a relatively steep MD and
two flat MAC’s
C Show two uncertain MD (high and low) and a certain MAC, using relatively flat MD’s and a steep
MAC
D Show two uncertain MD (high and low) and a certain MAC, using relatively steep MD’s and a flat
MAC
E Explain how uncertainty in the MAC and MD curves affect the welfare losses of a carbon tax due
to uncertainty.

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