Scenario: 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 TACx(ax) = 3ax2 and marginal abatement cost of MACx = 6ax
• Utility Y has a total abatement cost of TACx(ax) = 8ax2 and marginal abatement cost of MACx = 16ax

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

QUESTIONS THAT I HAVE ALREADY ANSWERED ARE IN FRONT OF THE QUESTION THAT I AM ASKING FOR HELP ON

QUESTIONS 1-2 ARE ALREADY ANSWERED

1.) Both firms are under a uniform standard, where they evenly split the total abatement.

For each firm, calculate:

• Abatement (ax and ay)

Due to the uniform standard, since the total abatement of NOx/MWh is 6 lbs, both firms x and y would now need to abate 3 lbs.

• MAC for the last unit of abatement

Both of there last units of abatement is the 3rd unit so you would plug 3 into their MAC equations:

Firm x:

1. MACx = 6ax
2. MACx = 6(3)
3. MACx = $18

Firm y:

1. MACx = 16ax
2. MACx = 16(3)
3. MACx = $48

• Total profits

Firm x:

1. TACx(ax) = 3ax2
2. TAC = 3(3)^2
3. TAC = 3*9
4. TAC = $27

Firm y:

1. TACx(ax) = 8ax2
2. TAC = 8(3)^2
3. TAC = 8*9
4. TAC = $72

TOTAL PROFITS:

1. TP = (Revenue of firm x) + (revenue of firm y) - (TAC of x) - (TAC of y)
2. TP = (100*1) + (100*1) - (27) - (72)
3. TP = $101

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:

• Abatement (ax and ay)

The total abatement quantity is 6lbs and before with the uniform standard we had firms x and y abate 3 each. Now they can trade so we're trying to figure out MACx = MACy

1. 6ax = 16ay
2. Also what is understood is that the total units of abatement have to equal up to 6 sooo ax + ay = 6, which means that we can plug in 6 - ax for ay
3. New equation: 6ax = 16(6 - ax)
4. 6ax = 96 - 16ax (distributed the 16 from before)
5. 22ax = 96
6. ax = 4.4 lbs
7. Then plug in 4.4 for 6(4.4)=16ay
8. Which gives you 1.6 = ay
9. The abatement for firm x should be 4.4 lbs and for y it should be 1.6 lbs

• MAC for the last unit of abatement

For firm x it is known that MACx = 6ax

1. We found out that x is abating 4.4
2. MACx = 6(4.4)
3. MACx = 26.4

For firm y it is known that MACy = 16ay

1. We found out that y is abating 1.6
2. MACy = 16ay
3. MACy = 16(1.6)
4. MACy = 25.6

MACx is $26.4 and MACy is $25.6

• Total profits

Total profits = (revenue firm x) + (revenue firm y) - (TACx) - (TACy)

1. TP = (100*1) + (100*1) - (3ax^2) - (8ay^2)
2. TP = 100 + 100 - 3(4.4^2) - 8(1.6^2)
3. TP = $121.44

THIS IS THE QUESTION THAT I AM ASKING

QUESTION #3 IS WHAT I NEED HELP ON

3.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)

1. What is the initial permit allocation that results in no need for trading? (hint: the regulator happens to get it right)
2. Which firm would prefer a uniform standard instead of a tradable permits program? Why would they have this preference?
3. 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