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AEM 250 Spring 2008
HW #6 Solutions
1.
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View Full Document Note: why did I ask the above question: 1) to reiterate that MB for a public good are
added vertically, while the MC of abatement by firms will always be a private good
and
hence added horizontally. 2) to get you to think about MB and MC,
2.
The marginal control costs for each power plant are plotted in the graph below as
a function of the number of units of pollution reduction.
The marginal control
costs for Plant 2 are higher than those for Plant 1 as given by the MC
c
functions.
The total control costs for Plant 1 to reduce pollution by 5,000 tons are given by
the redhatched triangle in the graph above.
The area of the triangle is:
(0.5)*(5,000)*(100) = $250,000
The total control cost for Plant 2 to reduce their emissions by 5,000 tons is given
by the sum of the red and blue hatched triangles as:
(0.5)*(5,000)*(150) = $375,000
The total control costs for the plants are simply the sum of these two values, or
$625,000. The total pollution reduction is 10,000 tons.
b. With a pollution tax, each plant will reduce emissions as long as the tax amount
exceeds the marginal control costs.
We again plot each plant’s marginal control
costs in the graph below.
Plant 1 reduces its pollution by 6,000 tons until the marginal control costs equal
the tax level.
Note that we can solve the problem algebraically by finding when
the marginal control costs for Plant 1 equal the tax of $120 per unit:
120 = 0.02Q
Q = 6,000
The total control costs for Plant 1 is the sum of the purple and red areas in the
graph above, or:
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View Full Document (0.5)*(6,000)*(120) = $360,000
As Plant 1 is still producing 2,000 tons of pollution, it pays a total tax of
$240,000.
To solve for the pollution reduction by Plant 2, solve for a MC
c
of 120
as:
120 = 0.03Q
Q = 4,000
The total control costs are the purple and blue areas in the graph, or:
(0.5)*(4,000)*(120) = $240,000
As Plant 2 is still emitting 4,000 tons of pollution, it pays a tax of $480,000.
The
total control costs for the plants are $600,000 and the total tax revenues are
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This homework help was uploaded on 02/01/2009 for the course AEM 2500 taught by Professor Poe,g. during the Fall '07 term at Cornell University (Engineering School).
 Fall '07
 POE,G.

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