Question

Suppose the government wants to reduce the total pollution emitted by three firms. Currently, each firm is creating 4 tons of pollution, for a total of 12 tons. The government is considering the following two methods to reduce total pollution to 6 tons:

1. The government sets regulation specifying that each of the three firms must cut its pollution in half.
2. The government allocates two tradable pollution permits to each of the three firms. Each permit allows the firm to emit 1 ton of pollution. Assume the negotiation and exchange of permits are costless.

The following table shows the cost each firm faces to eliminate each unit of pollution.


Cost of Eliminating: Firm X Firm Y Firm Z
First ton of pollution $950 $280 $600
Second ton of pollution $1,650 $300 $720
Third ton of pollution $2,500 $350 $880
Fourth ton of pollution $3,550 $450 $1,050

Suppose the owners of the three firms get together and agree on a trading price of $800 per permit.
Complete the following table with the action each firm will take at this permit price and the amount of pollution each firm will eliminate.



Firm Initial Pollution Permit Allocation (Tons of pollution) Action Final Amount of Pollution Eliminated (Tons of pollution)
Firm X 2
Firm Y 2
Firm Z 2

Determine the total cost of eliminating 6 tons of pollution under each method, and enter the amounts in the following table.

Method Total Cost of Eliminating 6 Tons of Pollution (Dollars)
Regulation
Tradable pollution permits

Answer 1

At a permit price of $800, Firm X will sell both permits and eliminate no pollution, Firm Y will eliminate two tons, and Firm Z will likely eliminate two tons. Regulation method costs total $5,400, while tradable permits lead to cost savings, totaling just $1,900 for pollution reduction.

Step-by-step explanation:

To determine the action each firm will take and the amount of pollution they will eliminate with a tradable pollution permits system at a trading price of $800 per permit, we need to compare the cost of eliminating pollution against the cost of buying or selling permits. Firms will choose the most cost-effective option between reducing pollution themselves or trading permits. The final amount of pollution each firm will eliminate depends on their costs of pollution reduction relative to the permit price.

• Firm X: Eliminating the first ton of pollution costs $950, which is more than $800, so they will sell one permit. Eliminating the second ton costs $1,650, which is also more than $800, so they sell another permit. Therefore, Firm X will sell both its permits and eliminate no pollution.
• Firm Y: The cost to eliminate the first and second tons of pollution is $280 and $300, respectively, which are both less than the price of a permit. Therefore, Firm Y will eliminate two tons of pollution and sell no permits.
• Firm Z: The cost to eliminate the first ton of pollution is $600, which is less than the price of a permit, so they will eliminate one ton. The cost to eliminate the second ton is $720, which is close to the trading price; they could choose to eliminate this pollution themselves, or sell their permit. For our calculations, we'll assume they eliminate this ton as well for a simpler analysis.

Under regulation, each firm must eliminate two tons of pollution, costing Firm X a total of ($950+$1,650), Firm Y a total of ($280+$300), and Firm Z a total of ($600+$720).

Tradable pollution permits allow firms to find the least expensive way to reduce pollution overall. Firm X sells both permits and eliminates no pollution, at no cost. Firm Y eliminates two tons at a cost of $580 total. Firm Z eliminates two tons at a cost of $1,320 total.

Adding up these costs provides the total cost of eliminating 6 tons of pollution for each method:

• Regulation: Firm X ($950 + $1,650) + Firm Y ($280 + $300) + Firm Z ($600 + $720) = $3,500 + $580 + $1,320 = $5,400
• Tradable Pollution Permits: Firm X ($0) + Firm Y ($580) + Firm Z ($1,320) = $1,900

Answer 2

The method cost of eliminating 6 is stated below in the explanation section while,The regulation = 4500, The tradable pollution permits = 2700

Step-by-step explanation:

Solution

Now,

Every Firm will remove the pollution until the cost of eliminating is lower than the cost of permit.

Thus,

Firm A will not eliminate any pollution as cost is higher than the permit cost, he will prefer to buy 2 more permits from other Firm

Firm B will eliminate 4 tons of pollution as cost is lower for elimination therefore will not require permit and thus sell his 2 permits to firm A.

Then

Firm C will eliminate 2 tons as after that cost is higher than the permit cost.

Firm A Action : Eliminate 2 tons and purchase 2 permits, Total tons eliminated 0

Firm B Action: Eliminate 4 tons and sell 2 permits, Total tons eliminated 4

Firm C Action : Eliminate 2 tons, Total Tons eliminated 2

If the government would have regulated then each firm would have to eliminate 2 tons each hence the cost would have been = 950+1650 + 280+300+600+720=4500

While with tradable permits cost is =280+300+350+450+600+720=2700