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.
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*)
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