EBK INTERMEDIATE MICROECONOMICS AND ITS
EBK INTERMEDIATE MICROECONOMICS AND ITS
12th Edition
ISBN: 9781305176386
Author: Snyder
Publisher: YUZU
Question
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Chapter 16, Problem 16.6P

a

To determine

Socially optimal level of methane reduction

a

Expert Solution
Check Mark

Answer to Problem 16.6P

Socially optimal level of R is 40.

Explanation of Solution

Given:

  MC=20+R

  MB=100R

Marginal benefit (MB) from cow induced methane is given below:

  MB=100R

Percentage reduction is represented by R

Marginal cost (MC) to farmers of methane reduction is as follows:

  MC=20+R

Socially optimal level of methane is established by equating the social marginal benefit (MB) with marginal cost (MC) :

  MB=MC100R=20R2R=80R=802=40

Socially optimal level of R is 40.

Economics Concept Introduction

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)

To determine

Fee paid by farmers and optimal level

b)

Expert Solution
Check Mark

Answer to Problem 16.6P

Fee should be $60 to achieve the optimal level of methane

Explanation of Solution

Given:

  MC=20+R

  MB=100R

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

  MR=100R=10040=60

Fee should be $60 to achieve the optimal level of methane

Economics Concept Introduction

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)

To determine

Reduction in methane cost and quantity

c)

Expert Solution
Check Mark

Answer to Problem 16.6P

Reduction in methane quantity is 26.22

Explanation of Solution

Given:

  MC1=20+23R1MC2=20+2R2

  MB=100R

Marginal benefit (MB)

  MB=100RR=(R1+R2)

Following is the condition for equilibrium:

  MB=MC1=MC2100(R1+R2)=20+23R1100R1R2=20+23R1240=3R2+5R15R1+3R2=240.........(1)

  100(R1+R2)=20+2R2100R1R2=20+2R280=3R2+R1R1+3R2=80........(2)

Solve equations (1) and (2):

  5R1+3R2=2405R1+15R2=40012R2=160R2=16012=13.33

Substitute the value of R2 in equation (1):

  5R1+3R2=2405R1+3(13.33)=2405R1+39.99=240R1=40.002

Total reduction is average two farms:

  = ( 40.002+13.332)26.66

Economics Concept Introduction

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)

To determine

Adoption of methane fee

d)

Expert Solution
Check Mark

Answer to Problem 16.6P

The overall reduction of methane is 80(60+20) . The overall reduction is 80 and fee is also 40; hence, the total cost is $3,200 . Total reduction would be 40 if the average of two is taken. Thus, cost would be $1,600.

Explanation of Solution

Given:

  MC1=20+23R1MC2=20+2R2

  MB=100R

Equate the value of fee with marginal cost functions both farms:

  20+(23)R1=6060+2R1=180R1=1202=60

  20+2R2=60R2=402=20

The overall reduction of methane is 80(60+20) . The overall reduction is 80 and fee is also 40; hence, the total cost is $3,200 . Total reduction would be 40 if the average of two is taken. Thus, cost would be $1,600.

Economics Concept Introduction

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)

To determine

Difference in result part C and D

e)

Expert Solution
Check Mark

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.

Economics Concept Introduction

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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