Chapter 17, Problem 1.2P

To determine

How high must be the new salary for the person to switch the job.

Explanation of Solution

The current salary of the individual is $115,600 per year, which gives a utility of 340. Since the main concerns of the individual is the utility from the income, the individual must be offered an income that provides a utility of over 340 utils. The probability of the company's success can be calculated by setting the probability equal to 'p' as follows:

Let the probability of success be 'p'. Then the salary from the new job would be equal to the fixed salary and the probable profit that the individual can make. This can be calculated as follows:

$\begin{array}{c}\text{Salary from new job}=\left(1-\text{p}\right)\left(\sqrt{75,000}\right)+\text{p}\left(\sqrt{350,000}\right)\\ \text{Setting this equal to 340 we get,}\\ \text{340}=\left(1-\text{p}\right)\left(273.86\right)+\text{p}\left(591.61\right)\\ 317.75\text{p}=340-273.86\\ \text{p}=\frac{66.14}{317.75}\\ =0.21\end{array}$

Thus, P must be equal to 0.21. Thus, substituting the value in the equation gives the expected value of the salary that the individual must receive in order to switch the job. This can be calculated as follows:

$\begin{array}{c}\text{New salary}=\left(1-0.21\right)\left(75,000\right)+0.21\left(350,000\right)\\ =0.79\left(75,000\right)+0.21\left(350,000\right)\\ =59,250+73,500\\ =132,750\end{array}$

Thus, the new salary must be equal to $132,750 per year, which means that the new salary must be higher than the existing salary by $17,150 in order to to switch the job.

Economics Concept Introduction

Opportunity cost: The opportunity cost is the next best alternative that one forgoes while making the decisions from the range of choices provided.