微观经济题求助

A Government study has concluded that the marginal benefit from controlling cow -induced methane production are given by : MB = 100-R

Where R represents the percentage reduction from unregulated levels. The Marginal cost to farmers of methane reduction (through better cow feed) is given by MC = 20+R

a. What is the socially optimal level of methane reduction?

b. If the government were to adopt a methane fee that farmers must pay for each percent of methane they do not reduce, how should this fee be set to achive the optimal level of R?

c. Suppose there are two farmers in this market with differing costs of methane reduction. The first has marginal costs given by MC1= 20+2/3R1 ,

Where the second has marginal costs given by MC2= 20+2R2

Total methane reduction is the average from these two farms. If the govermant mandates that each farm reduce methane by the optimal percentage calculated in part a), what will the overall reduction cost (assuming there are no fixed costs to reducing methane)?

d. Suppose, instead, that the government adopts the methane fee describe in part b. what will be the total reduction in methane and what will this reduction cost?

(1) MB=MC，推得R=40；