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# a2-w13-de_ans.pdf

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Department
Economics
Course
EC238
Professor
Karen Huff
Semester
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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