Economics 238OC: Written Assignment #2
Due Friday, February 15, 2013 Instructor: K. Hu▯
Written Assignment #2: Economics of the
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
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
MDC = 10 + 0:8E (1)
MAC = 110 ▯ 0:2E (2)
 (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
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)
0:2E0 = 110 (4)
E = 550 (5)
TDC = A+B
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.
10 ▯ 550 + ▯ (440 ▯ 550)
Total social cost of pollution in this case is the total damage cost of
 (b) What are the minimum social costs of pollution (total damage
costs plus total abatement costs) achievable? Show your calcula-
tions and very brie
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.
TAC = E
TDC = C+D
10 D MAC
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
 (c) Now calculate total social cost if the level of emissions is 300
tonnes. Show all your work and brie
At this level of emissions, MDC 6= MAC.
First, MAC at 300 is only $50 and MDC is $250.
TAC = E
110 TDC = C+D
10 E MAC
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.
 (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)
 Derive the industry MAC curve for this industry (see Lesson 4 page
for link to step by step derivation of aggregate industry MAC curve).
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
MAC = 0:5A (15)
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)
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)
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 T = MAC = 2 ▯ A T (24)
MAC T = A T (25)
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