Chapter 20, Problem 1SPA

(a)

To determine

Identify the expected income.

Explanation of Solution

In the given case, there is a 50% chance to make $4,000 in a month and another 50% chance to make nothing. Therefore, the expected income of L can be calculated as follows:

$\begin{array}{c}\text{Expected income}=\left({\text{Probaility}}_1\times {\text{Income}}_1\right)+\left({\text{Probaility}}_2\times {\text{Income}}_2\right)\\ =\left(0.5\times \$4,000\right)+\left(0.5\times \$0\right)\\ =\$2,000\end{array}$

Thus, the expected income of L is $2,000.

Economics Concept Introduction

Expected income: Expected income is the money value that of what a person expects to own at a given point of time.

 (b)

To determine

Identify the expected utility.

Explanation of Solution

The given graph shows that when the income is $4,000, the corresponding utility is 100; when the income is $0, then the corresponding utility is also 0. Now the expected utility can be calculated as follows:

$\begin{array}{c}\text{Expected utility}=\left({\text{Probaility}}_1\times {\text{Utility}}_1\right)+\left({\text{Probaility}}_2\times {\text{Utility}}_2\right)\\ =\left(0.5\times \$100\right)+\left(0.5\times \$0\right)\\ =50\end{array}$

Thus, the expected utility of L is 50.

Economics Concept Introduction

Expected income: Expected income is the money value of what a person expects to own at a given point in time.

 (c)

To determine

Identify the amount that is offered by another firm with certainty to persuade L not to take the risky sales job.

Explanation of Solution

The given graph shows that the expected utility of L is 50. The corresponding wealth in the graph along the x-axis is $1,250. Hence, L would have to be offered about $1,250 a month with certainty to persuade L not to take the risky sales job.

Economics Concept Introduction

Expected income: Expected income is the money value of what a person expects to own at a given point in time.

Expected income: Expected income is the money value of what a person expects to own at a given point in time.

 (d)

To determine

Identify the cost of risk.

Explanation of Solution

The cost of risk is the difference between the expected income and the certain income offered by the other firms to persuade L not to take the risky sales job. Thus, the cost of risk can be calculated as follows;

$\begin{array}{c}\text{Cost of income}=\text{Expected income}-\text{Certain income}\\ =\$2,000-\$1,250\\ =\$750\end{array}$

The amount of the cost of risk is $750.

Economics Concept Introduction

Cost of risk: The cost of risk is found by comparing the expected wealth in a given risky situation with the wealth that gives the same utility with no risk.