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 two methods: Under method 1, the governments sets pollution standards, whereas under method 2, the government allocated tradable pollution permits, Let’s 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 it is for others. The table below shows the cost of eliminating each unit of pollution for each of the three firms.
Cost of eliminating the first unit of pollution $130 (firm x), $90 (firm y), $600 (firm z)
Cost of eliminating the second unit of pollution $165 (firm x), $115 (firm y), $750 (firm z)
Cost of eliminating the third unit of pollution $220 (firm x), $140 (firm y), $1,200 (firm z)
Assume that the cost of reducing pollution to zero (that is, eliminating all 4 units of pollution) is prohibitively expensive.
In order to regulate pollution, suppose the government sets pollution standards so that each firm must reduce its pollution by 2 units. Fill in the table below with the total cost to each firm of reducing its pollution by this amount.
Total cost of eliminating 2 units of pollution
Firm X
a) $165
b) $385
c) $295
d) $350
Firm Y
a) $255
b) $115
c) $230
d) $205
Firm Z
a) $1,350
b) $1,800
c) $750
d) $1,950
Adding up the costs to the three firms, you can see that the total cost of eliminating 6 units of pollution through standards of regulation is ________________
a) $1,850
b) $1,645
c) $1,490
d) $2,590
Now suppose the government decides to use a different strategy to achieve its goal of reducing the pollution in the area from 12 units to 6 units – namely, it issues two pollution permits to each firm. For each permit a firm has in its possession, it can emit 1 unit of pollution. Firms are free to trade pollution permits with one another – that is, buy and sell them – as long as both firms can agree on a price. For example, if firm X and firm Y were able to agree on a suitable price for a permit, firm Y would end up with three permits and would only need to reduce its pollution by 1 unit, whereas firm X would end up with only one permit and would have to reduce its pollution by 3 units. Assume the negotiation and exchange of permits is costless.
Because of its high pollution – reduction costs, firm X thinks it might be better off buying permits from firm Y and firm Z so that it doesn’t have to reduce its own pollution emissions. At which of the following prices is only firm Y willing to sell one of its permits to firm X, while firm Z will decline to do so? Check all that apply.
a) $100
b) $410
c) $5180
d) $195
Again, suppose that you are considering the method of pollution reduction involving tradable permits. Suppose the owners of the three firms get together and agree on a trading price of $415 per permit. Fill in the following table with the amount each firm will pollute and the amount it costs each firm to reduce pollution to the necessary level (Hint: Do not include the prices of permits in the cost of reducing pollution)
Initial pollution permit allocation = 2 units (firm X), 2 units (firm Y), 2 units (firm Z)
Trades firm X __________ trades firm Y_______ trades firm Z
Final pollution amount firm X ________ firm Y _________ firm Z___________
Cost of reducing pollution to final amount firm X __________ firm Y _______ firm Z__________
Given this scenario, the total cost of eliminating 6 units of pollution using a tradable permit system is ___________
a) $0
b) $860
c) $1,690
d) $1,240
Based on this example, you can conclude that eliminating pollution is _________
a) more
b) less
costly to 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.
To determine the least-cost way of achieving the desired pollution quantity, let's compare the two methods: pollution standards and tradable pollution permits.
1. Using Pollution Standards:
- Each firm must reduce its pollution by 2 units.
- Calculate the total cost to each firm of reducing its pollution by this amount:
Firm X: $165 (cost of eliminating the first unit) + $220 (cost of eliminating the second unit) = $385
Firm Y: $90 (cost of eliminating the first unit) + $115 (cost of eliminating the second unit) = $205
Firm Z: $600 (cost of eliminating the first unit) + $750 (cost of eliminating the second unit) = $1,350
- Adding up the costs to the three firms, the total cost of eliminating 6 units of pollution through standards of regulation is:
$385 (Firm X) + $205 (Firm Y) + $1,350 (Firm Z) = $1,940
The correct answer for the total cost of eliminating 6 units of pollution through standards of regulation is:
a) $1,850
2. Using Tradable Pollution Permits:
- The government issues two pollution permits to each firm.
- Firms are free to trade pollution permits with one another.
- Determine the price at which only firm Y is willing to sell one permit to firm X, while firm Z declines to do so.
- Firm X can buy 1 permit from firm Y and reduce its own pollution by 3 units.
- Firm Y will still have 1 permit left and only needs to reduce its pollution by 1 unit.
- Firm Z will not sell its permit.
- Therefore, the price at which only firm Y is willing to sell one permit to firm X is:
d) $195
- Assuming a trading price of $415 per permit, fill in the table:
Initial pollution permit allocation = 2 units (Firm X), 2 units (Firm Y), 2 units (Firm Z)
Trades Firm X Trades Firm Y Trades Firm Z
Buy 1 1 permit Sell 1 1 permit No Trade
Final pollution amount Firm X: 1 unit Firm Y: 1 unit Firm Z: 2 units
Cost of reducing pollution Firm X: $385 Firm Y: $115 Firm Z: $750
- The total cost of eliminating 6 units of pollution using a tradable permit system is:
$385 (Firm X) + $115 (Firm Y) + $750 (Firm Z) = $1,250
The correct answer for the total cost of eliminating 6 units of pollution using a tradable permit system is:
d) $1,240
Based on this example, we can conclude that eliminating pollution is:
b) less costly to 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.
To determine the least-cost way of achieving the desired pollution quantity, we need to compare method 1 (pollution standards) and method 2 (tradable pollution permits) and calculate the total cost for each.
1. Method 1: Pollution Standards
Under method 1, the government sets pollution standards, requiring each firm to reduce its pollution by 2 units. To find the total cost to each firm of reducing its pollution by this amount, we multiply the cost of eliminating each unit of pollution by the number of units to be reduced (2).
Firm X:
Cost of eliminating 2 units = ($165 for the first unit + $220 for the second unit) * 2 = $385
Firm Y:
Cost of eliminating 2 units = ($115 for the first unit + $140 for the second unit) * 2 = $230
Firm Z:
Cost of eliminating 2 units = ($750 for the first unit + $1,200 for the second unit) * 2 = $3,900
Total cost of eliminating 6 units of pollution through standards regulation = $385 + $230 + $3,900 = $4,515
2. Method 2: Tradable Pollution Permits
Under method 2, the government issues two pollution permits to each firm. For each permit a firm has, it can emit 1 unit of pollution. Firms can trade permits with one another.
To determine at which price only firm Y is willing to sell one permit to firm X, while firm Z will decline to do so, we compare the costs for firm Y and firm Z for eliminating 1 unit of pollution:
Firm Y cost of eliminating 1 unit = $115
Firm Z cost of eliminating 1 unit = $750
Since firm Z's cost is higher than firm Y's, firm Z will decline to sell a permit to firm X at any price that is higher than its own cost.
Therefore, firm Y is willing to sell one permit to firm X at a price that is at least equal to or higher than $115, but lower than $750.
Suppose the negotiation and exchange of permits is costless, and the firms agree on a trading price of $415 per permit.
Initial pollution permit allocation: 2 units each for firm X, firm Y, and firm Z.
Trades:
- Firm X trades 1 permit with firm Y for $415.
- Firm X trades 1 permit with firm Z for $415.
Final pollution amount:
- Firm X has 1 unit of pollution remaining.
- Firm Y has 1 unit of pollution remaining.
- Firm Z has 1 unit of pollution remaining.
Cost of reducing pollution to final amount:
- Firm X has already eliminated 1 unit so no additional cost.
- Firm Y has already eliminated 1 unit so no additional cost.
- Firm Z has already eliminated 1 unit so no additional cost.
Total cost of eliminating 6 units of pollution using tradable permit system = $0 (no additional cost for reducing pollution)
Based on this example, we can conclude that eliminating pollution is less costly to 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.
Therefore, the answers to the questions are:
- Total cost of eliminating 6 units of pollution through standards regulation: b) $1,645
- Prices at which only firm Y is willing to sell one permit to firm X, while firm Z will decline to do so: a) $100 and d) $195
- Total cost of eliminating 6 units of pollution using a tradable permit system: a) $0
- Eliminating pollution is b) less costly to 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.