1. Consider the problem of two polluting sources in the region,each of which generated 10 units of pollution for a total of 20units released into the environment. The government determined thatemissions must be reduced by 12 units across the region to achievethe ”socially desirable level of pollution”. Each firm facesdifferent abatement cost conditions modelled as follows: forPolluter 1, marginal abatement cost is MAC₁ =2.6Q₁, while the total abatement cost is TAC1 =1.3(Q1)². For Polluter 2, marginal abatement cost isMAC2 = 0.52Q₂, while the total abatement cost is TAC2 =0.26(Q2)², where Q₁ is the amount ofpollution controlled (abated) by Polluter 1, and Q₂ isthe amount of pollution controlled (abated) by Polluter 2.

(a) What is the cost effective abatement allocation acrosspolluting sources? What is the total cost to achieve this goal?

(b) Assume that the government implements the 12-units standarduniformly, requiring each polluter to abate by 6 units. What is thetotal cost to achieve this goal? Is it more / less than the totalcost from part a)? Comment on your findings.

Consider now other possible policies like a tradable emissionpermits (TEP’s) system and an emission tax as ways to achieve thecap of 8 units of emissions.

(c) Assume that the government imposes emission charge set at $4for each polluter. Show how each firm responses to tax. Does $4unit tax achieve the 12-unit abatement standard? If not, is $4 unittax too high or too low? Discuss.

(d) Assume that the government decides to issue permits ratherthan impose tax. It issues 8 permits, each of which allows thebearer to emit 1 unit of pollution. The government allocates 4permits to each polluter.

i. If the permits system does not allow for trading, what wouldbe each firm’s response - cost, abatement required to thisallocation?

ii. Assume now that trading is allowed and that two firms agreeon the purchase and sale of permit at a price of $8.00. What wouldbe each firm’s response - cost, abatement required, revenue to thisprice?

iii. Does the outcome from part (ii) represent the costeffective solution? If yes - why? If not, describe what happensnext.