Chapter 16, Problem 16.8P

a.

To determine

To state:Whether the project would be undertaken and total net benefit as well as individual benefits and whether the total benefits are positive.

Answer to Problem 16.8P

The project will be undertaken.

Benefit to A would be $50

Benefit to B would be $40

Benefit to C would be ($50)

Total benefit would be positive

Explanation of Solution

If the project cost is $300 and it is divided equally amongst three people, A, B and C, each person will pay $100. This means that the profit/ loss to each party would be:

A:

  $\begin{array}{l}\text{Net}\text{benefits=Benefit-project}\text{cost}\\ \text{=\$(150-100)}\\ \text{=\$50}\end{array}$

B:

  $\begin{array}{l}\text{Net}\text{benefits=Benefit-project}\text{cost}\\ \text{=\$(140-100)}\\ \text{=\$40}\end{array}$

C:

  $\begin{array}{l}\text{Net}\text{benefits=Benefit-project}\text{cost}\\ \text{=\$(50-100)}\\ \text{=-\$50}\end{array}$

Since, two people gain from the project the project will be undertaken.

Net benefit from the project:

  $\begin{array}{l}\text{Net}\text{benefits=benefit}\text{to}\text{A+Benefit}\text{to}\text{B+Benefit}\text{to}\text{C}\\ \text{=\$(50+40-50)}\\ \text{=-}\text{\$40}\end{array}$

Economics Concept Introduction

Introduction:A project is selected only when the total benefits arising from it outweighs its cost. However, a project is selected on the basis that the aggregate benefits arising from the project is more than the individual losses.

b.

To determine

To state:Whether a majority would vote for the project and total net benefits would be positive.

Answer to Problem 16.8P

The project will be undertaken.

Benefit to A would be $25

Benefit to B would be $15

Benefit to C would be ($75)

Total benefit would be negative

Explanation of Solution

If the project cost is $375 and it is divided equally amongst three people, A, B and C, each person will pay $125. This means that the profit/ loss to each party would be:

A:

  $\begin{array}{l}\text{Net}\text{benefits=Benefit-project}\text{cost}\\ \text{=\$(150-125)}\\ \text{=\$25}\end{array}$

B:

  $\begin{array}{l}\text{Net}\text{benefits=Benefit-project}\text{cost}\\ \text{=\$(140-125)}\\ \text{=\$15}\end{array}$

C:

  $\begin{array}{l}\text{Net}\text{benefits=Benefit-project}\text{cost}\\ \text{=\$(50-125)}\\ \text{=-\$75}\end{array}$

Since, two people gain from the project the project will be undertaken.

Net benefit from the project:

  $\begin{array}{l}\text{Net}\text{benefits=benefit}\text{to}\text{A+Benefit}\text{to}\text{B+Benefit}\text{to}\text{C}\\ \text{=\$(25+15-75)}\\ \text{=-\$35}\end{array}$

Economics Concept Introduction

Introduction:A project is selected only when the total benefits arising from it outweighs its cost. However, a project is selected on the basis that the aggregate benefits arising from the project is more than the individual losses.

c.

To determine

To state:the type of results expected in part a and b when votes can be bought and sold in a free market.

Answer to Problem 16.8P

The project will be undertaken.

Benefit to A would be $50

Benefit to B would be $40

Benefit to C would be ($50)

Total benefit would be positive

Explanation of Solution

If the project cost is $300 and it is divided equally amongst three people, A, B and C, each person will pay $100. This means that the profit/ loss to each party would be:

A:

  $\begin{array}{l}\text{Net}\text{benefits=Benefit-project}\text{cost}\\ \text{=\$(150-100)}\\ \text{=\$50}\end{array}$

B:

  $\begin{array}{l}\text{Net}\text{benefits=Benefit-project}\text{cost}\\ \text{=\$(140-100)}\\ \text{=\$40}\end{array}$

C:

  $\begin{array}{l}\text{Net}\text{benefits=Benefit-project}\text{cost}\\ \text{=\$(50-100)}\\ \text{=-\$50}\end{array}$

Since, two people gain from the project the project will be undertaken.

Net benefit from the project:

  $\begin{array}{l}\text{Net}\text{benefits=benefit}\text{to}\text{A+Benefit}\text{to}\text{B+Benefit}\text{to}\text{C}\\ \text{=\$(50+40-50)}\\ =\text{\$40}\end{array}$

Economics Concept Introduction

Introduction:A project is selected only when the total benefits arising from it outweighs its cost. However, a project is selected on the basis that the aggregate benefits arising from the project is more than the individual losses.