Suppose the marginal cost of pollution reduction is ½ R, where R is the amount of pollution reduced given in percentage terms. The marginal benefit of pollution reduction is 90 - R. The government plans to auction off marketable permits in order to reduce pollution to the optimal level. How many permits should the Government issue? How much revenue will the auction raise?

Question

Suppose the marginal cost of pollution reduction is ½ R, where R is the amount of pollution reduced given in percentage terms. The marginal benefit of pollution reduction is 90 - R. The government plans to auction off marketable permits in order to reduce pollution to the optimal level. How many permits should the Government issue? How much revenue will the auction raise?

I don't even know where to begin with this question. Permits are a confusing matter for me. Would I set the MB and MC equal to each other? that would give me my optimum level of Pollution (R*)

Answer 1

see my later post.

Answer 2

Yes, to determine the optimal level of pollution reduction (R*), you would set the marginal cost (MC) of pollution reduction equal to the marginal benefit (MB) of pollution reduction. In this case, MC is ½R, and MB is 90 - R.

So, the equation would be: ½R = 90 - R

To solve for R, you would first simplify the equation: ½R + R = 90

Combining like terms, you would get: 1.5R = 90

Dividing both sides by 1.5, you would find: R = 60

Therefore, the optimal level of pollution reduction (R*) is 60%.

Now, to determine the number of permits the government should issue, you need to calculate the amount of pollution reduction (R*) in absolute terms. Since the total pollution reduction is given in percentage terms, you would find the absolute value of R* as a fraction of total pollution.

Let's assume the total amount of pollution reduction required is P. Then, 60% of P would be given by: (0.6)P

Therefore, the government should issue permits that allow for 60% of the total pollution reduction, or (0.6)P.

As for the revenue raised from the auction, you need to multiply the number of permits issued by the price of a single permit. The price of a permit can be determined through the auction process. If P is the price per permit, and x is the number of permits, the revenue (R) raised from the auction would be given by: R = P * x.

So, once you determine the number of permits (x), you would multiply that by the price per permit (P) to find the revenue raised from the auction.