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*)
I think you are on the right track. My interpretation of this question is to set MB=MC, solve for R*.
So, .5R = 90 - R, solve for R.
I get R=60, meaning the MB at the optimal R is 30, meaning the Goverment will sell 60 Rs at a price of 30 each.
To solve this problem, you will indeed need to set the marginal benefit (MB) and marginal cost (MC) equal to each other in order to find the optimum level of pollution reduction (R*).
The marginal benefit of pollution reduction is given by the equation MB = 90 - R. This represents the additional benefit society receives from reducing pollution by one percentage point.
The marginal cost of pollution reduction is given by the equation MC = 1/2 R. This represents the additional cost society incurs from reducing pollution by one percentage point.
To find the optimum level of pollution reduction (R*), we set MB equal to MC and solve for R:
90 - R = 1/2 R
To simplify the equation, we can multiply both sides by 2:
180 - 2R = R
Now, add 2R to both sides:
180 = 3R
Divide both sides by 3:
R = 60
So, the optimal level of pollution reduction (R*) is 60%.
Now, to determine how many permits the government should issue, we need to know the total amount of pollution in the economy. Let's assume that the total amount of pollution is 100 units.
Since the government plans to auction off marketable permits, it should issue permits that sum up to the total pollution reduction of R*. In this case, R* is 60%, which is 60 units of pollution reduction.
Thus, the government should issue 60 permits in total.
To calculate the revenue raised from the auction, we need to multiply the number of permits (60) with the market price of a single permit. Unfortunately, the market price of permits is not given in the question, so we cannot provide an exact value of the revenue raised. However, you can multiply the number of permits with the market price (if given) to find the revenue.
Remember, the revenue generated from the auction can be used by the government for various purposes such as funding additional pollution reduction projects or implementing environmental policies.