There are three industrial firms in Happy Vally.
Initial Cost of Reducing
Firm Pollution Level Pollution by 1 unit
A 70 units $20
B 80 units $25
C 50 units $10
The government wants to reduce pollution to 120 units, so it gives each firm 40 tradable pollution permits. Basically the government is allowing each firm to pollute up to 40 units and must remove the pollution for another over 40 units. By allowing the firm to trade (buy and sell) these permits to other firms in the industry, the firm can chose to sell its permits rather than use them.
a. Who sells permits and how many do they sell? Who buys permits and how many do they buy? Briefly explain why the sellers and buyers are each willing to do so. What is the total cost of pollution reduction in this situation? Show all calculations. (Hint: Each firm would be willing to sell permits if they can get more than the price of removing the pollution and each firm would be willing to buy permits if they could get them for less that the cost of removing the pollution.)
b. How much higher would the costs of pollution reduction be in the permits could not be traded? Show all calculations.
a. Firm A will sell 10 permits and Firm C will buy 10 permits. Firm A is willing to sell permits because they can get more than the cost of removing the pollution (20 x 10 = 200) and Firm C is willing to buy permits because they can get them for less than the cost of removing the pollution (10 x 10 = 100). The total cost of pollution reduction in this situation is 300 (200 + 100).
b. The costs of pollution reduction would be higher if the permits could not be traded. In this case, Firm A would have to reduce pollution by 40 units at a cost of $800 (40 x 20 = 800) and Firm C would have to reduce pollution by 10 units at a cost of $100 (10 x 10 = 100). The total cost of pollution reduction in this situation would be 900 (800 + 100).
a. In order to determine who sells and buys permits, we need to compare the cost of reducing pollution for each firm with the price they can sell or buy permits for.
For Firm A:
- Firm A's initial pollution level is 70 units.
- They are allowed to pollute up to 40 units, so they need to reduce their pollution by 30 units.
- The cost of reducing pollution by 30 units is $20 per unit, resulting in a total cost of 30 units * $20/unit = $600.
- However, Firm A can sell their permits for a price greater than $20/unit to make a profit.
- The other two firms, B and C, are in need of additional permits to meet the pollution reduction target.
- Assuming that the price for permits is negotiated, let's say Firm A sells 20 permits to Firm B for $30/unit and 10 permits to Firm C for $25/unit.
- The total revenue for Firm A from selling permits is 20 permits * $30/unit + 10 permits * $25/unit = $900 + $250 = $1,150.
- Therefore, Firm A sells 20 permits to Firm B and 10 permits to Firm C.
For Firm B:
- Firm B's initial pollution level is 80 units.
- They are allowed to pollute up to 40 units, so they need to reduce their pollution by 40 units.
- The cost of reducing pollution by 40 units is $25 per unit, resulting in a total cost of 40 units * $25/unit = $1,000.
- Firm B needs additional permits to meet the pollution reduction target.
- They can buy permits from Firm A or Firm C.
- Let's say Firm B buys 20 permits from Firm A for $30/unit.
- The total cost for Firm B is thus 20 permits * $30/unit = $600.
- Therefore, Firm B buys 20 permits from Firm A.
For Firm C:
- Firm C's initial pollution level is 50 units.
- They are allowed to pollute up to 40 units, so they need to reduce their pollution by 10 units.
- The cost of reducing pollution by 10 units is $10 per unit, resulting in a total cost of 10 units * $10/unit = $100.
- Firm C needs additional permits to meet the pollution reduction target.
- They can buy permits from Firm A or Firm B.
- Let's say Firm C buys 10 permits from Firm A for $25/unit.
- The total cost for Firm C is thus 10 permits * $25/unit = $250.
- Therefore, Firm C buys 10 permits from Firm A.
To summarize:
- Firm A sells 20 permits to Firm B and 10 permits to Firm C.
- Firm B buys 20 permits from Firm A.
- Firm C buys 10 permits from Firm A.
The total cost of pollution reduction in this situation is the sum of the costs for each firm, plus the revenue from selling permits:
- Total cost = Cost for Firm A + Cost for Firm B + Cost for Firm C
- Total cost = $600 + $1,000 + $100 = $1,700
b. If the permits could not be traded, the costs of pollution reduction would be significantly higher because each firm would need to solely rely on their own resources to reduce pollution. In this case, each firm would have to bear the entire burden of reducing pollution to meet the target.
Let's calculate the costs of pollution reduction without trading permits:
For Firm A:
- They need to reduce their pollution level from 70 units to 40 units, so they need to remove 30 units of pollution.
- The cost of reducing pollution by 30 units is $20 per unit, resulting in a total cost of 30 units * $20/unit = $600.
For Firm B:
- They need to reduce their pollution level from 80 units to 40 units, so they need to remove 40 units of pollution.
- The cost of reducing pollution by 40 units is $25 per unit, resulting in a total cost of 40 units * $25/unit = $1,000.
For Firm C:
- They need to reduce their pollution level from 50 units to 40 units, so they need to remove 10 units of pollution.
- The cost of reducing pollution by 10 units is $10 per unit, resulting in a total cost of 10 units * $10/unit = $100.
The total cost of pollution reduction without trading permits is the sum of the costs for each firm:
- Total cost = Cost for Firm A + Cost for Firm B + Cost for Firm C
- Total cost = $600 + $1,000 + $100 = $1,700
Therefore, the costs of pollution reduction would be the same, $1,700, even without the ability to trade permits.
a. To determine who sells permits and how many, we need to compare the cost of reducing pollution for each firm with the price of selling the permits.
Firm A: The cost of reducing pollution by 1 unit is $20. Since Firm A has been given 40 permits, it can effectively pollute up to 70 units (initial pollution) + 40 units (allowed permits) = 110 units. To achieve the government's target of 120 units, Firm A would need to reduce its pollution by 110 units - 120 units = 10 units. The cost of reducing 10 units of pollution is $20 * 10 units = $200.
Firm B: The cost of reducing pollution by 1 unit is $25. Firm B can effectively pollute up to 80 units (initial pollution) + 40 units (allowed permits) = 120 units. Since the government's target is 120 units, Firm B would not need to reduce any pollution. Therefore, the cost of reducing pollution for Firm B is $0.
Firm C: The cost of reducing pollution by 1 unit is $10. Firm C can effectively pollute up to 50 units (initial pollution) + 40 units (allowed permits) = 90 units. To meet the government's target of 120 units, Firm C would need to reduce its pollution by 90 units - 120 units = 30 units. The cost of reducing 30 units of pollution is $10 * 30 units = $300.
Now, let's compare these costs with the price of selling the permits. The total cost of pollution reduction in this situation is calculated by adding up the costs of each firm.
Total cost of pollution reduction = $200 + $0 + $300 = $500.
Since Firm B does not need to reduce any pollution, it can sell all its permits if the price is higher than $0.
Firm A: It can sell the excess permits (40 - 10 units) = 30 permits if the price is higher than $20 (cost of reducing 1 unit).
Firm C: It needs to buy 30 permits from other firms since it needs to reduce its pollution by 30 units. It will be willing to buy the permits if the price is lower than $10 (cost of reducing 1 unit).
b. If the permits could not be traded, each firm would have to bear the cost of reducing its pollution entirely on its own. Therefore, the total cost of pollution reduction would be the sum of the cost of reducing pollution for each firm separately.
Total cost of pollution reduction without trading permits = ($20 * 10) + ($25 * 0) + ($10 * 30) = $200 + $0 + $300 = $500.
Thus, the costs of pollution reduction would be the same whether the permits could be traded or not.