ECON / ENVI 315 _ Emission Control
1. All environmental problems may be said to result from poorly defined property
Rights. [5 points]
False. Poorly defined property rights account for a great many environmental problems
From the over-exploitation of fisheries open access fisheries, to air and water
pollution problems. However, well-defined property rights does not guarantee dynamic
efficiency.
The best way to show this is to give examples.
For one, there need to be appropriate enforcement mechanisms. These, in turn,
can lead to enormous transaction costs, which could be prohibitive for finding an
efficient outcome.
Property rights could be fully specified and fully enforced yet inefficient (in the
modified Pareto sense). E.g., a glue factory could hold well-defined property
rights over an airshed that contained a city. It is easy to imagine that the
aggregate harm from the pollution might exceed the benefit from the glue
produced. Coasian negotiations would be unlikely to resolve a situation such as
this because the citizens of the city are unlikely to overcome their collective action
problem.
Extraction of natural resources will be dynamically inefficient if the resource
owner exercises market power.
2. Positive net benefits is both a necessary and sufficient condition for optimal
environmental policy. [5 points]
False. Positive net benefits is a necessary condition for optimal environmental policy,
but it is not sufficient. This is true for two reasons:
Optimal environmental policy will be set to equalize marginal benefits and
marginal costs.
Furthermore, society may (and does) choose to consider other criteria, such as
Distributional equity.
3. You can use graphs or simple algebra to answer this question; either way, be sure
to show all of your work and/or explain your reasoning.
Emission Control Problem_ 50 points
You can use graphs or simple algebra to answer this question; either way, be sure
to show all of your work and/or explain your reasoning.
Two firms can reduce emissions of a pollutant at the following marginal costs:
MC1 = $6 q1
MC2 = $2 q2
where q1 and q2 are, respectively, the amount of emissions reduced by the first
and second firms. Total pollution-control cost functions for the two firms are,
respectively:
TC1 = $5 + $3 (q1)2
TC2 = $5 + $1 (q2)2
Assume that with no control at all, each firm would be emitting 10 units of
emissions (for aggregate emissions of 20 tons), and assume that there are no
significant transaction costs.
a.
What are the total industry costs of pollution control (for both firms
combined) if a uniform emission standard is utilized to achieve an
aggregate reduction (for both firms combined) of 6 tons of emissions?
[5 points]
Each firm needs to reduce emissions by 3 tons.
TC1 = $5 + $3 (3)2 = $32
TC2 = $5 + $1 (3)2 = $14
TC = TC1 + TC2 = $32 + $14 = $46
b.
What are the marginal costs of pollution control for firm #1 and for firm
#2 under the standard considered in part a? [5 points]
MC1 = $6 (3) = $18
MC2 = $2 (3) = $6
c.
Compute the cost-effective reduction by each of the two firms if a total
reduction of 6 tons of emissions is necessary. [10 points]
We need solve a system of two equations:
(MC1 = MC2) and (q1 + q2 = 6)
MC1 = MC2
$6 q1 = $2 q2, where q2 = 6 - q1
$6 q1 = $2 (6 - q1)
q1 = 1.5
q2 = 6 - q1 = 4.5
d.
What is the total industry cost of reduction (for both firms combined) for
the scenario above in part (c)? [5 points]
TC1 = $5 + $3 (1.5)2 = $11.75
TC2 = $5 + $1 (4.5)2 = $25.25
TC = TC1 + TC2 = $11.75 + $22.25 = $37
e.
What is the cost-effective reduction by the two firms with a tradable
permit approach if both firm #1 and firm #2 are freely allocated 7 tons of
emissions permits? How will the cost-effective reduction be affected by a
change in the initial allocation? [5 points]
Total allocation of permits is 14 tons. With aggregate emissions of 20 tons, this implies
total emissions control of 6 tons. Tradable permits will result in the cost-effective
reduction by the two firms calculated in (c) above. In equilibrium,
q1 = 1.5
q2 = 4.5
Assuming no uncertainty and no transaction costs, a change in the initial allocation will
not affect the cost-effective reduction by individual firms.
f.
If the authority chose to reach its objective of 6 tons of aggregate
Reduction with an emission charge, what per-unit charge should be
Imposed? How much government revenue will the tax system generate, if
the tax is levied on all units of emission? [10 points]
Emissions charge = MC1 [ = MC2] = $6 (1.5) [ =$2 (4.5)] = $9
Tax revenue = $9 (20 - 1.5 - 4.5) = $9 (14) = $126
g.
Which policy instrument � taxes, tradable permits, or a uniform
standard � would you expect private industry as a whole to prefer
(assuming the same target for aggregate emission reductions in each
case)? Why? [10 points]
Private industry would prefer (freely allocated) tradable permits, since it minimizes the
cost to industry. Both permits and taxes lead to the cost-effective reduction, but taxes
require additional transfer payments from industry to government. A uniform standard
is not cost-effective.
Firm #2 alone would prefer the standard, since its total cost is lower than under the
permit system. However, the total cost to industry is minimized under the tradable
permit system.