
a
Socially optimal level of methane reduction
a

Answer to Problem 16.6P
Socially optimal level of R is 40.
Explanation of Solution
Given:
Marginal benefit (MB) from cow induced methane is given below:
Percentage reduction is represented by
Marginal cost (MC) to farmers of methane reduction is as follows:
Socially optimal level of methane is established by equating the social marginal benefit (MB) with marginal cost (MC) :
Socially optimal level of R is 40.
Introduction:
Social optimal level is attained when Marginal benefit is equal to Marginal cost.
Marginal benefit is the additional benefit derived when one more unit is consumed.
Marginal cost is the addition to total cost when one more unit of output is produced.
b)
Fee paid by farmers and optimal level
b)

Answer to Problem 16.6P
Fee should be
Explanation of Solution
Given:
Fee to be decided by the interaction of marginal benefit and marginal cost to society, optimal level of methane is 40 that equate the social marginal benefit and marginal cost abatement. Fee can be calculated by substituting the value of optimal level of methane either in social marginal benefit or marginal cost
Fee should be
Introduction:
Social optimal level is attained when Marginal benefit is equal to Marginal cost.
Marginal benefit is the additional benefit derived when one more unit is consumed.
Marginal cost is the addition to total cost when one more unit of output is produced.
c)
Reduction in methane cost and quantity
c)

Answer to Problem 16.6P
Reduction in methane quantity is 26.22
Explanation of Solution
Given:
Marginal benefit (MB)
Following is the condition for equilibrium:
Solve equations (1) and (2):
Substitute the value of
Total reduction is average two farms:
=
Introduction:
Marginal benefit is the additional benefit derived when one more unit is consumed.
Marginal cost is the addition to total cost when one more unit of output is produced.
d)
Adoption of methane fee
d)

Answer to Problem 16.6P
The overall reduction of methane is
Explanation of Solution
Given:
Equate the value of fee with marginal cost functions both farms:
The overall reduction of methane is
Introduction:
Marginal benefit is the additional benefit derived when one more unit is consumed.
Marginal cost is the addition to total cost when one more unit of output is produced.
e)
Difference in result part C and D
e)

Explanation of Solution
Both parts C and D yield different results. In the part C, the average of both farms is taken as the total reduction of methane. In part D, average of both farm is taken individually.
Introduction:
Marginal benefit is the additional benefit derived when one more unit is consumed.
Marginal cost is the addition to total cost when one more unit of output is produced.
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Chapter 16 Solutions
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