1. 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 10 units across the region to achieve the "socially desirable level of pollution". Each firm faces different abatement cost conditions modeled as follows:
Polluter 1:
Marginal Control Cost: MCC1 = 2.5Q1
Total Control Cost: TCC1 = 1.25(Q1)²
Polluter 2: Marginal Control Cost: MCC2 = 0.625Q2
Total Control Cost: TCC1 = 0.3125(Q2)²
Where Q1 is the amount of pollution controlled (abated) by Polluter 1, and Q2 is the amount of
pollution controlled (abated) by Polluter 2.
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 10-units standard uniformly, requiring each polluter to abate by 5 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.
c) Now assume that the government imposes emission charge set at $4 for each polluter. Show how each firm responses to tax. Does $4 unit tax achieve the 10-unit abatement standard?
d) Government finally decides to issue permits rather than impose tax. It issues 10 permits, each of which allows the bearer to emit 1 unit of pollution. The government allocates 5 permits to each polluter.
(d.i) If the permits system does not allow for trading, what would be each firm's response - cost, abatement required to this allocation?
(d.ii) Assume now that trading is allowed and that two firms agree on the purchase and sale of permit at a price of $8.00. What would be each firm's response - cost, abatement required, revenue to this price?
(d.iii) Does the outcome from part (ii) represent the cost effective solution? If yes - why? If not, describe what happens next.
e) Compare and contrast outcomes from part b) - d). Which instrument would you recommend to government to achieve goal of emission reduction by 10 units?