Chapter 18, Problem 5P

Sub part (a):

To determine

Accounting and economic profit before and after the tax.

Answer to Problem 5P

Total explicit cost is $220,000: Accounting profit with low income is -$20,000 and with high profit is $180,000.

Explanation of Solution

Current earning per worker is $60,000. She would prefer to become an entrepreneur unless she  earns an accounting profit of at least $60,000. As an entrepreneur, she is planning to open a small grocery store. She has an annual cost of $150,000 for labor, $40,000 for rent and $30,000 for equipments.

There is a one-half probability that the revenue equals to $200,000 (low revenue) and one-half probability that revenue equals to $400,000.

Total explicit cost can be calculated as follows.

$\begin{array}{c}\text{Total explicit cost}=\left(\text{Labor cost}\right)+\left(\text{Rent}\right)+\left(\text{Equipment cost}\right)\\ =(150,000+40,000+30,000)\\ =220,000\end{array}$

Total explicit cost is $220,000.

Accounting profit with low revenue can be calculated as follows.

$\begin{array}{c}\text{Accounting profit}=\text{Low revenue}-\text{Cost}\\ =200,000-220,000\\ =-20,000\end{array}$

Accounting profit with low income is -$20.000.

Accounting profit with low revenue can be calculated as follows.

$\begin{array}{c}\text{Accounting profit}=\text{High revenue}-\text{Cost}\\ =400,000-220,000\\ =180,000\end{array}$

Accounting profit with high income is $180.000.

Economics Concept Introduction

Concept introduction:

Accounting profit: Accounting profit refers to the excess revenue after subtracting the total cost from the total revenue.

Economic profit: Economic profit refers to the additional profit after subtracting the opportunity cost from the accounting profit.

Sub part (b):

To determine

Expected average revenue, Accounting profit and economic profit.

Answer to Problem 5P

Expected average revenue is $300,000: Accounting profit is $80,000 and Economic profit is $20,000.

Explanation of Solution

Expected average revenue can be calculated as follows

$\begin{array}{c}\text{Expected revenue}=\left(\begin{array}{l}\left({\text{Probability}}_{\text{High income}}\times \text{High income}\right)\\ +\left({\text{Probability}}_{\text{Low income}}\times \text{Low income}\right)\end{array}\right)\\ =\left(\text{0}\text{.5}\times \text{400,000}\right)+\left(\text{0}\text{.5}\times \text{200,000}\right)\\ =200,000+100,000\\ =300,000\end{array}$

Expected average revenue is $300,000.

Expected accounting profit can be calculated as follows.

$\begin{array}{c}\text{Expected accounting profit}=\text{Expected revenue}-\text{Explicit cost}\\ =300,000-220,000\\ =80,000\end{array}$

Expected accounting profit is $80,000.

Expected economic profit can be calculated as follows.

$\begin{array}{c}\text{Expected accounting profit}=\text{Expected revenue}-\text{Explicit cost}-\text{Wage}\\ =300,000-220,000-60,000\\ =20,000\end{array}$

Expected economic profit is $20,000. The person would quit the job since there is a positive economic profit.

Sub part (c):

To determine

Accounting profit after tax, and expected profit.

Answer to Problem 5P

Accounting profit after tax is $135,000: Expected profit is $57,500 and  -$2,500.

Explanation of Solution

There is an accounting loss with the low income. Thus, the accounting profit with the low income does not change.

Accounting profit with high income after tax can be calculated as follows.

$\begin{array}{c}\text{Accounting profit after tax}={\text{Accountign profit}}_{\text{High income}}\left(1-\text{Tax rate}\right)\\ =\text{180,000}\left(1-0.25\right)\\ =180,000\left(0.75\right)\\ =135,000\end{array}$

Accounting profit after tax is $135,000.

Expected accounting profit after tax can be calculated as follows.

$\begin{array}{c}\text{Expected accounting profit}=\left(\begin{array}{l}\left({\text{Probability}}_{\text{Low income}}\times {\text{Expected profit}}_{\text{Low income}}\right)\\ +\left({\text{Probability}}_{\text{High income}}\times {\text{Expected profit}}_{\text{High income}}\right)\end{array}\right)\\ =\left(0.5\left(-20,000\right)+0.5\left(135,000\right)\right)\\ =-10,000+67,500\\ =57,500\end{array}$

Expected accounting profit is $57,500.

Expected economic profit after tax can be calculated as follows.

$\begin{array}{c}\text{Expected economic profit}=\text{Expected accounting profit}-\text{Wage}\\ =57,500-60,000\\ =-2,500\end{array}$

Expected economic profit is -$2,500. Since the expected economic profit is negative, the person would not quit the job.

Sub part (d):

To determine

Whether the individual is indifferent or not between Accounting profit after tax and current earnings.

Explanation of Solution

The accounting profit after tax in case of average revenue is $60,000, which is equal to the current earnings. Therefore, she is indifferent about her decision to quit the job or not. So, some people would prefer to go for entrepreneurship and other will stay as workers.