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Economics

EC238

Karen Huff

Winter

Description

Economics 238OC: Written Assignment #3
Part 1 Due Friday, March 8, 2013
Part 2 Due Friday, March 22, 2013
Instructor: K. Hu▯
Written Assignment #3: Policy Related
Problems
This assignment is to be submitted in two
parts:
1. Part 1 includes questions 1-4.
2. Part 2 includes questions 5-8.
This entire assignment concerns achieving an abatement target in an in-
dustry with 3 di▯erent ▯rms (B;C;Z). Firms B and Z each have more
than one source of pollution. Firm C has just one source. The marginal
abatement (or control) costs of each source are di▯erent, as are the initial
emissions (E ) of each. Abatement for a given source cannot exceed that
0
source’s initial emissions. The initial emissions are in tonnes, and the MAC
are in dollars.
1 Firm B
Source E 0 Marginal Abatement Cost
B1 200 MAC B1 = 25
B2 700 MAC B2 = 8 + 0:50B2
B3 900 MAC B3 = 16
Firm C
Source E 0 Marginal Abatement Cost
C1 2,500 MAC C1 = 32
Firm Z
Source E 0 Marginal Abatement Cost
Z1 700 MAC Z1 = 15
Z2 500 MAC Z2 = 22
Z3 800 MAC = 10
Z3
Cost e▯ectiveness in the real world usually involves cost minimization at
several levels. In this example, it would imply a cost-e▯ective allocation of
abatement among the sources within each ▯rm and among the di▯erent ▯rms
within this industry. This assignment is intended to highlight this and show
how di▯erent regulatory tools can in
uence the pattern of abatement and
emissions as well as the ▯rms’ costs of compliance.
Before we look into any regulatory possibilities, we’ll consider the
shape of each of the ▯rms’ marginal abatement cost curves.
[20] 1. Explain in your own words the cost-minimizing strategy for ▯rm B to
satisfy any abatement target from zero to the maximum abatement it
can achieve. In other words, how would the ▯rm allocate abatement
responsibilities between its sources for each target.
The strategy for ▯rm B is more complex than for either of the other ▯rms
since it has three sources including one with an upward sloping MAC curve.
In the following diagram the MAC curves for the three sources are illus-
trated side by side.
2 $358
B1 B2 B3
$25 $16
$8
200 700 900
Firm B starts cleaning up at source B2 ▯rst because it has the lowest initial
MAC of $8. Since the next cheapest source is B3 with a constant MAC
of $16, the ▯rm will clean up all at B2 until it reaches a MAC of $16. At
$16, 16 tonnes of abatement will have taken place at B2. Next the ▯rm
will switch to cleaning up at source B3 with a constant MAC of $16. All
900 tonnes of emissions at B3 will be cleaned up before the ▯rm switches
back to abating at source B2. At this point, they will abate at B2 until
its MAC is equal to $25 since this is the next cheapest constant MAC at
B1. When B2’s MAC is equal to $25, total abatement from B2 will be
34 units, so with MAC rising from $16 to $25, an additional 18 tonnes of
abatement takes place at source B2 (since 16 tonnes have already been
abated there). Next the ▯rm will switch to abating at source B1. All 200
tonnes at B1 will be abated since its MAC is constant at $25. Finally, the
▯rm will switch back to abating at source B2 with MAC rising from $25
to $358 while cleaning up the remaining 666 units of emissions there.
So in order to minimize the cost of hitting a given ▯rm-wide abatement
target, ▯rm B would do the following:
0{16 tonnes Clean up 16 tonnes at source B2. MAC rises from $8 to
$16.
17{916 tonnes The ▯rm switches abatement activities to source B3.
MAC is constant at $16 and all 900 tonnes of emissions are cleaned
3 up.
917{934 tonnes The ▯rm switches abatement activities back to source
B2. MAC rises from $16 to $25. An additional 18 tonnes of emissions
at B2 are cleaned up.
935{1,134 tonnes The ▯rm switches abatement activities to source B1.
MAC is constant at $25. All 200 tonnes of emissions at B1 are cleaned
up.
1,135{1,800 tonnes The ▯rm switches back to abating at source B2.
MAC rises from $25 to $358 and the remaining 666 tonnes of emis-
sions at B2 are cleaned up.
[10] 2. Draw ▯rm B’s marginal abatement cost curve. Label the maximum
abatement achievable by ▯rm B as well as any jumps or kinks.
MAC B
358 MAC B
25
16
8 1134 1800
16 91634 A B
[5] 3. Explain in your own words the cost-minimizing strategy for ▯rm Z
to satisfy any abatement target from 0 to the maximum abatement it
can achieve. In other words, how would the ▯rm allocate abatement
responsibilities among its sources for each target.
The strategy for ▯rm Z is simpler than that for ▯rm B.
Firm Z starts cleaning up at source Z3 ▯rst, because its MAC is lowest
and constant at $10. Once Z3 is entirely cleaned up, the ▯rm switches
abatement activities to source Z1 with a constant MAC of $15. Finally,
▯rm Z will switch abatement to source Z2 with a constant MAC of $22.
4 0{800 tonnes clean up at source Z3, MAC is $10/t.
801{1,500 tonnes clean up source Z1, MAC is $15/t.
1,501{2,000 tonnes clean up source Z2, MAC is $22/t.
In this case, the logic is simple, we clean up the cheapest source ▯rst,
followed by the next cheapest and ▯nish at the costliest source.
[5] 4. Draw ▯rm Z’s marginal abatement cost curve. Be sure to label the
maximum abatement achievable by ▯rm Z and any jumps in its MAC.
MAC Z
MAC Z
22
15
10
800 1500 2000 A Z
5 [10] 5. Suppose that a uniform command and control (C&C) standard requires
each source to reduce emissions by 40%. Calculate the emissions, abate-
ment and abatement cost by source, ▯rm, and the industry as a whole.
Be sure to show your work.
Each row of the following table corresponds to a single source, and is
completed by ▯rst calculating the abatement target (40% 0f E for each
source). Then, E is0E less the abatement. Total abatement cost can then
be determined using the hints and can be thought of as the area under the
MAC curve.
Table 1: Summary Table for Uniform Standard
A E TAC TCC
B1 80.00 120.00 2000.00 2000.00
B2 280.00 420.00 21840.00 21840.00
B3 360.00 540.00 5760.00 5760.00
B 720.00 1080.00 29600.00 29600.00
C 1000.00 1500.00 32000.00 32000.00
Z1 280.00 420.00 4200.00 4200.00
Z2 200.00 300.00 4400.00 4400.00
Z3 320.00 480.00 3200.00 3200.00
Z 800.00 1200.00 11800.00 11800.00
I 2520.00 3780.00 73400.00 73400.00
Because this is a standard, polluters only need to pay their abatement costs
so TAC equals TCC.
[10] 6. Now suppose that ▯rms were allowed to take advantage of a ▯rm-wide
bubble. This is like a uniform standard, but it applies to the ▯rm,
rather than each source separately. Thus, each ▯rm has to reduce its
emissions by 40%, but could allocate the abatement among its sources
as it likes. Calculate the emissions, abatement, and abatement cost by
source and ▯rm.

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