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Department
Economics
Course
EC238
Professor
Karen Huff
Semester
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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