Answer to Question #247181 in Microeconomics for Chilu

Question

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 ?

Answer 1

Solution:

a.). Socially optimal level of methane reduction:

Socially optimal level of methane is derived by equating the social marginal benefit with marginal cost:

MB = MC

100 – R = 20 + R

100 – 20 = R + R

80 = 2R

R = 40

The socially optimal level of methane reduction = 40

 

b.). The government should choose an appropriate environmental tax rate that will be beneficial to all parties, which will be charged on each percent of methane the farmers fail to reduce. This optimal tax rate will lead to a balance between marginal benefit and marginal cost.

 

c.). Set the optimal level of methane reduction to both farmers costs:

Farmer 1:

40 = 20 + $\frac{2}{3}$R₁

Multiply both sides by 3:

120 = 60 + 2R₁

120 – 60 = 2R₁

60 = 2R₁

R₁ = 30

Farmer 2:

40 = 20 + 2R₂

40 – 20 = 2R₂

20 = 2R₂

R₂ = 10

The overall reduction = 30 + 10 = 40

The reduction cost:

Farmer 1 = $20 + \frac{2}{3}(30) = 40$

Farmer 2 = 20 + 2(10) = 40

Total reduction cost = 40 + 40 = 80