Question

2. There are only two polluting sources in the region, each of which generates 10 units of pollution for a total of 20 units released into the environment, The government determines that emissions must be reduced by 12 units across the region to achieve the "socially desirable level of pollution". Each firm faces different abatement cost conditions modelled as follows: for Pol- luter 1, marginal abatement cost is MAC1-2.6Q1, while the total abate- ment cost is TAC1 1.3(Q1)2. For Polluter 2, marginal abatement cost is MAC2 0.52Q2, while the total abatement cost is TAC2 0.26(Q2)2. where Q1 is the amount of pollution controlled (abated) by Polluter 1, and Q2 is the amount of pollution controlled (abated) by Polluter2 (a) What is the cost effective abatement allocation across polluting sources? What is the total cost to achieve this goal? (b) Assume that the government implements the 12-units standard uni- formly, requiring each polluter to abate by 6 units. What is the total cost to achieve this goal? Is it more / less than the total cost from part a)? Comment on your findings.

Answer 1

Mac_1 = 2.6q_1 mac_2 = 0.52q_2 q_1 + q_2 = 12 optimal mac_1 = mac_2 2.6q_1 = 0.52q_2 q_2 = 2.6/0.52q_1 q_2 = 5q_1 1 implies q_1 + 5q_1 = 12 6q_1 = 12 q_1 = 2 q_2 = 5(2) q_2 = 10 total cost = tac_1 + tac_2 = 1.3(2)^2 + 0.26(10)^2 tc_a = 5.2 + 26 = 31.2 q_1 = 6, q_2 = 6 total cost = 1.3(6)^2 + 0.26(6)^2 tc_b = 56.16 tc_b > tc_a total cost is more than previous one because firm 1 have more marginal cost to producing extra unit compare to firm 2