Microeconomics
Microeconomics
2nd Edition
ISBN: 9781464187025
Author: Austan Goolsbee, Steven Levitt, Chad Syverson
Publisher: Worth Publishers
Question
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Chapter 17, Problem 18P

 (a)

To determine

The total marginal benefit (MBT).

 (a)

Expert Solution
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Explanation of Solution

The total marginal benefit (MB) is the sum total of individual marginal benefits. There are two consumers of mosquito abatement, such as D and L, where the marginal benefit of consumer D is MBD=100Q and the marginal benefit of consumer L is MBL=60Q. Therefore, the total marginal benefit can be calculated as follows:

MBT=MBD+MBL=100Q+60Q=1602Q

Therefore, the total marginal benefit is MBT=1602Q.

Economics Concept Introduction

Marginal benefit: Marginal benefit can be defined as the additional utility derived from the additional consumption of one or more unit of goods and services.

 (b)

To determine

The optimal level of mosquito abatement.

 (b)

Expert Solution
Check Mark

Explanation of Solution

The optimal level of mosquito abatement is determined at the point where the total marginal benefit is equal to the marginal cost (MC).

The total marginal benefit is MBT=1602Q.

The total marginal cost is given as MC=2Q.

Now, set the two expressions to get the value of optimal quantity:

1602Q=2Q160=4QQ=1604=40

Therefore, the optimal level of mosquito abatement is 40.

Economics Concept Introduction

Marginal benefit: Marginal benefit can be defined as the additional utility derived from the additional consumption of one or more unit of goods and services.

Marginal cost (MC): Marginal benefit refers to the amount of additional cost incurred in the process of increasing one more unit of output.

 (c)

To determine

The individual total benefit at the optimal level of mosquito abatement.

 (c)

Expert Solution
Check Mark

Explanation of Solution

Figure 1 illustrates the MB, MC, and the optimal quantity of the mosquito abatement of consumer D as follows:

Microeconomics, Chapter 17, Problem 18P , additional homework tip  1

In Figure1, the vertical axis shows the MB and MC of the mosquito abatement and the horizontal axis shows the quantity of mosquito abatement, where the interaction between the total marginal benefit with MC curve determines the optimal quantity of mosquito abatement.

The MB of consumer D can be calculated by substituting the respective value in the MB function of D as follows:

  MBD=(10040)=60

Therefore, 60 is the MB of consumer D.

The MB of consumer L can be calculated by substituting the respective value in the MB function of L as follows:

MBL=(6040)=20

Therefore, 20 is the MB of consumer D.

Therefore, the total benefit is 80(60+20).

Now, the total benefit (TB) for consumer D can be calculated using the formula given below:

TB=Optimal quantity×MBD+12×Optimal quantity×(MBDMBL) (1)

Now, substitute the respective values in Equation (1) to get the value of total benefit of consumer D.

TB=40×60+12×40×(6020)=3,200

Therefore, the total benefit of consumer D is 3,200.

Figure 2 illustrates the MB, MC, and the optimal quantity of the mosquito abatement of consumer L as follows:

Microeconomics, Chapter 17, Problem 18P , additional homework tip  2

In Figure2, the vertical axis measures the MB and MC of the mosquito abatement and the horizontal axis measures the quantity of mosquito abatement, where the interaction between the total marginal benefit with MC curve determines the optimal quantity of mosquito abatement.

The total benefit (TB) for consumer L can be calculated using the formula given below:

TB=Optimal quantity×MBL+12×Optimal quantity×(MBDMBL) (2)

Now, substitute the respective values in Equation (2) to get the value of total benefit of consumer L.

TB=40×20+12×40×(6020)=1,600

Therefore, the total benefit of consumer L is 1,600.

Economics Concept Introduction

Marginal benefit: Marginal benefit can be defined as the additional utility derived from the additional consumption of one or more unit of goods and services.

Marginal cost (MC): Marginal benefit refers to the amount of additional cost incurred in the process of increasing one more unit of output.

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