Question

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​x2​ ​and marginal abatement cost of MAC​x(​ a​x)​ = 6*a​x.​ 2​ ● Utility Y has a total abatement cost of ​TAC​y(​ a​y)​ = 8*a​y​ 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.

Answer 1

a. Under the uniform standard, both the firms X and Y now need to abate 3 lbs of NO/MWh. Thus, the ax or the abatement by utility X is 6/2 or 3 lbs and similarly, utility Y will also abate 3 lbs of NO/MWh.
b. The marginal abatement cost for the last unit or from the 5th unit of abatement for Firm X is 6(3)=$18 while the marginal abatement cost from last or 5th unit of abatement for firm Y is 16*3=$48

c. total profits are revenue fo botn the firms mium the total costs of abatement by both the firms.

Total abatement cost of firm X is=3(3)^2=3*9=$27

Total abatement cost of firm Y is=8(3)^2=8*9=$72 (Please note that the formula for TACy is misprinted as it should be 8*ay^2)

Total profits= Revenue of firm X+Revenue of firm Y-TAC of X-TAC of Y=(100*1)+(100*1)-(27)-(72)=$101 (where revenue is price times the quantity produced).