A government study has concluded that the marginal benefits 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 achieve 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

Whereas the second has marginal costs given by

MC2 = 20 + 2R2

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

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

e. Explain why part c and part d yield different results.