Question

The City Council wants to curb emissions by half and decides to auction off four permits, each of which entitles the bearer to emit 1 ton of smoke per day. No smoke may be emitted without a permit. Suppose the government conducts the auction by starting at $1 and asking how many permits each firm wants to buy at that price. If the total is more than four, it then raises the price by $1 and asks again, and so on, until the total quantity of demanded permits falls to four. How much will each permit sell for in this auction? Each permit will sell for $ . How many permits will each firm buy? Sludge Oil will purchase permit(s). Northwest Lumber will purchase permit(s). What will be the total cost to society of this reduction in pollution? Total cost of pollution reduction will be $ .

Answer 1

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Answer 2

The total cost to society of this reduction in pollution is $230.

How to calculate the pollution cost?

The government has started the auction at $1 ton per day. In this case, Sludge would have the first permit at 500 - 200 = $300, etc.

Northwest lumber would bid the first permit at ($2000 - 1000) = $1000, (1000-500) =$500 per ton for the second permit, etc

So Sludge would want 2 permits and Northwest wants 4 permits if the price is $80 but the government has only 4 permits. Therefore, the government will increase the price to $81 and then again auction till the permits are 4.

At $81, the permits by Sludge would be one, and that by Northwest would be three which would be a total of 4 and each permit would be sold at $81.

Sludge would have 1 permit and Northwest would have 3 permits.

The total cost to society for this reduction would be Sludge moving from 4 tons to 1 ton ie a cost of 200 - 50 = $150 and the cost of Northwest would be 180-100 = 80. The total cost to society would be $230 from the addition.

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