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Consider two utilities X and Y, which are subject to pollution control regulation.

They try to maximize their own profit. 

·      The price for electricity generation received by each utility is ​$100/MWh. 

·      Assume that each firm produces ​1 MWh​ of power regardless of regulation. 

·      Each utility separately emits ​10.0 lbs​ of NOx/MWh in the absence of regulation.

·      The regulator wishes to limit total emissions to ​14.0 lbs​ of NOx/MWh. 

·       In other words, the goal is total abatement of ​6.0 lbs​ of NOx/MWh ( because 10 + 10 - 14 = 6).

·      Utility X has a total abatement cost of ​TAC​x​(a​x​) = 3*a​x​2​ and marginal abatement cost of MAC​x​(a​x​) = 6*a​x​.

·      Utility Y has a total abatement cost of ​TAC​y​(a​y​) = 8*a​y​2​ and marginal abatement cost of MAC​y​(a​y​) = 16*a​y​. 

 Keep in mind that profit is equal to total revenue minus total cost.

1.      Both firms are under a ​uniform standard ​ , where they evenly split the total abatement. For each firm, calculate:

a.      Abatement (a​x​ and a​y​)

b.      MAC for the last unit of abatement

c.       Total profits

2.      Now, assume both firms are under a ​tradable permits program ​ , where firms may trade permits to pollute according to their marginal abatement costs. Calculate:

a.       Abatement (a​x​ and a​y​)

b.       MAC for the last unit of abatement

c.       Total profits

d.       Using specific numbers, explain why this policy is more efficient than the other.

3.      [challenging] ​Recall from class that the initial allocation of permits does not influence the total profit or total abatement, but it can change how individual firms are affected. Assume that permits exist in continuous quantities. (i.e. they don't have to be whole numbers) 

a.      What is the initial permit allocation that results in no need for trading? (hint: the regulator happens to get it right)

b.      Which firm would prefer a uniform standard instead of a tradable permits program? Why would they have this preference?

c.      How many permits would this firm have to receive initially in order to be indifferent between the two? (You may assume that the equilibrium permit price is where the MAC curves cross)

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