5. Environmental standards versus tradable permits Aa Aa Suppose the government

ID: 1155394 • Letter: 5

Question

5. Environmental standards versus tradable permits Aa Aa Suppose the government wants to reduce the total pollution emitted by three firms in its area. Currently, each firm is creating 4 units of pollution in the area, for a total of 12 pollution units. The government wants to reduce total pollution in the area to 6 units. In order to do so, the government can choose between the following two methods Method 1: The government sets pollution standards Method 2: The government allocates tradable pollution permits Compare the two methods to determine the least-cost way of achieving the desired pollution quantity. Eliminating pollution can be more difficult (and thus more costly) for some kinds of firms than for others. The following table shows the cost of eliminating each unit of pollution for each of the three firms Cost of eliminating the first unit of pollution Cost of eliminating the second unit of pollution Cost of eliminating the third unit of pollution Cost of eliminating the fourth unit of pollution Firm X $500 $675 $1,100 $7,700 Firm Y $60 $80 $120 $600 Firm Z ?75 $100 $160 $960 Under method 1, the government sets pollution standards so that each firm must reduce its pollution by 2 units. Fill in the following table with the total cost to each firm of reducing its pollution by this amount. Firm X Firm Y Firm Z Total cost of eliminating 2 units of pollution $1,175 ? $140 $175 ? Adding up the costs to the three firms, you can see that the total cost of eliminating 6 units of pollution through regulatory standards is $1,490

Explanation / Answer

5. It is given that each firm emits 4 units of pollution and the total pollution is 4*3 = 12 units.

The Marginal Cost of abating pollution for each firm is given, from which the total abatement cost can be calculated as follows:

Cost of eliminating:

Firm X (MAC) $

Firm X (TC) $

Firm Y (MAC) $

Firm Y (TC) $

Firm Z (MAC) $

Firm Z (TC) $

1st unit of pollution

500

2nd unit of pollution

675

1175

140

100

175

3rd unit of pollution

1100

2275

120

260

160

335

4th unit of pollution

7700

9975

600

860

960

1295

Therefore Total Cost of eliminating 2 units of pollution are:

Firm X: $1,175

Firm Y: $140

Firm Z: $175

Adding up all three firms’ abatement costs, the total cost of eliminating pollution through regulatory standard is $1,175+$140+$175 = $1,490

When method 2 is used by allowing tradable pollution permits and each firm is allowed to pollute UP TO 2 units of pollution.

Therefore cost of eliminating 2 units of pollution is already $140 to firm Y. Now if firm Y emits 1 unit of pollution but reduces another unit, then cost of reducing the 3rd unit of pollution = $120. Thus, the price of 1 permit that Y sells to X will be greater than $120. However, since the cost of reducing the 3rd unit of pollution $160 to Firm Z, that firm will not allow to sell the permit anywhere below $160.

Thus the two options at which Y is willing to sell 1 permit to X but Z refuse to do so are:

$155 and $145

Suppose the price of each permit to be $158. Since Firm X has the highest cost of abating pollution, it will always opt to buy permits from Y or Z.

Initially every firm was polluting 4 units. Now every firm is allowed to pollute 2 units per head which means that with 2 permits, the cost of abating 2 units of pollution is the same as $1,490 which was shown above.

However, since the MAC of Firm Y for abating the 3rd unit of pollution is $120< the price of the permit $150, it can gain by reducing pollution by 3 units and selling 1 permit. Similarly, since the cost of abating the 3rd unit of pollution for Firm Z is $160>the price of the permit, it will opt not to sell any permit to X and will continue polluting 2 units. Therefore, the table can be completed as follows:

Firm X

Firm Y

Firm Z

Initial pollution permit allocation

2 units

Action

Buy 1 permit

Sell 1 permit`

Use its allocated share of 2 permits

Final Pollution amount

3 units

1 unit

2 units

Cost of pollution reduction

$500 (TC for abating 1 unit)

$260 (TC for abating 3 units)

$175 (TC for abating 2 units)

Therefore the total cost of eliminating 6 units of pollution = $500+$260+$175 = $935

(It is important to note that even after using pollution permits, the total pollution of all three firms = 3+1+2 = 6 units which was allocated through the permits)

On the basis of this example, eliminating pollution is more costly to the society when the government directs each firm to eliminate a certain amount of pollution than when it allocates pollution permits that can be bought and sold.