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Economics

EC238

Karen Huff

Winter

Description

Economics 238OC: Written Assignment #2
Due Friday, February 15, 2013 Instructor: K. Hu▯
Written Assignment #2: Economics of the
Environment
This assignment involves:
1. Economic e▯ciency related to quantity of emis-
sions (rather than the quantity of some private
good being consumed)
2. Algebraically solving for the industry MAC
curve
3. Cost-bene▯t analysis in the case where there is
some uncertainty (ENPV analysis)
1. Suppose that the MDC and MAC curves for local air pollution are as
described below:
MDC = 10 + 0:8E (1)
MAC = 110 ▯ 0:2E (2)
[5] (a) What are the social costs of pollution (total damage costs plus to-
tal abatement costs) if ▯rms are not required to do any abatement.
Show your calculations and very brie
y explain.
E0is the level of emissions that obtains if ▯rms do no abatement.
That corresponds to an MAC of 0. Solving from equation 2 we get:
0 = 110 ▯ 0:2E (3)
0
0:2E0 = 110 (4)
E = 550 (5)
0
1 $
450 MDC
TDC = A+B
A
10
B 550
E
Trivially of course, TAC=0, but now we can determine the TDC from
our MDC curve. The MDC is $450 (10 + 0:8 ▯ 550) and TDC is
equal to the area under the MDC curve, $126,500.
1
10 ▯ 550 + ▯ (440 ▯ 550)
2
Total social cost of pollution in this case is the total damage cost of
$126,500.
[5] (b) What are the minimum social costs of pollution (total damage
costs plus total abatement costs) achievable? Show your calcula-
tions and very brie
y explain.
To ▯nd this we need to determine the level of emissions that equates
MAC and MDC.
110 ▯ 0:2E = 10 + 0:8E (6)
▯
100 = E (7)
Now we need to determine the total abatement cost (TAC) and total
damage costs (TDC). Note that MDC=MAC=$90.
2 $
MDC
450
TAC = E
TDC = C+D
110
90
C E
10 D MAC
100 550
E
TAC TAC equals the area of triangle E with base 450 (550-100) and
height $90. Thus TAC is $20,250.
TDC TDC equals the area of triangle C with height $80 high ($90-
$10) high and 100 wide, plus rectangle D which is 100 wide by
$10 high. The area of the triangle is $4,000, and that of the
rectangle is $1,000. Total damage cost is thus $5,000.
TSC Total social cost of pollution is thus $25,250. Choosing any
other level of emissions should yield a higher level of total social
cost.
[5] (c) Now calculate total social cost if the level of emissions is 300
tonnes. Show all your work and brie
y explain.
At this level of emissions, MDC 6= MAC.
First, MAC at 300 is only $50 and MDC is $250.
3 $
450 MDC
250
TAC = E
110 TDC = C+D
C
50
10 E MAC
D
300 550 E
Total abatement costs (TAC) is a triangle that is 250 wide (550▯300)
and $50 high. The area of that triangle is $6,250.
Total damage costs (TDC) are again made up of a triangle plus a
rectangle. This time the rectangle is 300 wide and $10 high, giving
an area of $3,000. The triangle is $240 tall (250 ▯ 10) and 300 wide
for an area of $36,000. TDC is thus $39,000.
Total social cost is thus $45,250, and as we have expected, it is
greater than the socially optimal level.
[5] (d) Rewrite the MAC curve as a function of abatement rather than
emissions. Be sure to show all the steps in the derivation.
The long way:
A = E ▯ E0 (8)
A = 550 ▯ E (9)
E = 550 ▯ A (10)
MAC = 110 ▯ 0:2(550 ▯ A) (11)
MAC = 0:2A (12)
4 2. Suppose that there are two polluting ▯rms (1 and 2) in an industry
with MAC curves as follows:
MAC 1 = 400 ▯ :5E 1 (13)
MAC 2 = 600 ▯ 2E 2 (14)
[10] Derive the industry MAC curve for this industry (see Lesson 4 page
for link to step by step derivation of aggregate industry MAC curve).
Brie
y explain what you are doing for each step of the derivation.
To answer this question, ▯rst rewrite each ▯rm’s MAC as a function of
abatement.
MAC = 0:5A (15)
1 1
MAC 2 = 2A 2 (16)
Then we need to use the cost-minimizing condition and the adding up con-
dition to determine the cost-minimizing allocation of abatement between
the sources and then use that to determine the total MAC curve. The ▯rst
condition requires MAC of each ▯rm to be equal while the second condition
states that the abatement done by each ▯rm must add up to total industry
abatement. So from the cost minimizing condition we can write:
MAC = MAC (17)
1 2
0:5A1 = 2A 2 (18)
A1 = 4A 2 (19)
Next using the adding up condition:
A + A = A (20)
1 2 T
4A2+ A 2 = A T (21)
5A2 = A T (22)
1
A = A (23)
2 5 T
Finally, to get the Industry MAC curve here we only need to realize that
when we are minimizing cost MA1 = MAC =2MAC , sT if we substitute
5 the expression obtained above into ▯rm 2’s MAC curve we will get the
MAC curve.
I
1
MAC T = MAC = 2 ▯ A T (24)
5
2
MAC T = A T (25)
5
3. The following question concerns bene▯t-cost analysis of some stylized
climate strategies. In this case, the costs of the strategies are known
with certainty, but the bene▯ts from action to

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