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.

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a. To determine who sells and buys permits, we need to compare the cost of reducing pollution for each firm to the price they can get from selling permits.

1. Firm A: The cost of reducing pollution by 1 unit is $20. Since Firm A's current pollution level is 70 units and they are allowed to pollute up to 40 units, they would need to reduce pollution by 30 units. The cost of reducing 30 units would be 30 * $20 = $600. Firm A can sell up to 40 permits. To cover the cost of reducing pollution, Firm A would be willing to sell all 40 permits if they can get more than $600.

2. Firm B: The cost of reducing pollution by 1 unit is $25. Firm B's current pollution level is 80 units, and they are allowed to pollute up to 40 units. They need to reduce pollution by 40 units. The cost of reducing 40 units would be 40 * $25 = $1000. Firm B can sell up to 40 permits. To cover the cost of reducing pollution, Firm B would be willing to sell all 40 permits if they can get more than $1000.

3. Firm C: The cost of reducing pollution by 1 unit is $10. Firm C's current pollution level is 50 units, and they are allowed to pollute up to 40 units. They do not need to reduce pollution as they are already within the allowed limit. Hence, Firm C would not sell any permits.

Now let's consider the buyers:

1. To reduce pollution to the government-mandated level of 120 units, the total reduction needed is (70 - 40) + (80 - 40) + (50 - 40) = 40 units.

2. Since Firm A and Firm B need to reduce pollution, they will want to buy permits if they can get them for less than the cost of reducing pollution.

Based on the information provided, Firm A would need to buy 30 permits (to cover the remaining 30 units of pollution reduction) and Firm B would need to buy 40 permits (to cover the entire 40 units of pollution reduction).

The sellers are Firm A (selling 40 permits) and Firm B (selling 40 permits).
The buyers are Firm A (buying 30 permits) and Firm B (buying 40 permits).

b. If permits could not be traded, each firm would have to reduce pollution by themselves.

1. Firm A: The cost of reducing 30 units of pollution is 30 * $20 = $600.
2. Firm B: The cost of reducing 40 units of pollution is 40 * $25 = $1000.
3. Firm C does not have to reduce pollution.

The total cost of pollution reduction without trading permits would be $600 + $1000 = $1600.