Chapter 16, Problem 16.1P

a)

To determine

To find:

Individual’s full income, number of working hours if 75% income is devoted to leisure.

Explanation of Solution

Total number of working hours = 8000

Wage per hour = $5

Total income annually :

$\begin{array}{l}=8000\times 5\\ =\$40000\end{array}$

Amount sacrificed for leisure = $5

Amount to be spent on leisure :

$\begin{array}{l}=0.75\times 40000\\ =30000\end{array}$

Number of hours for leisure:

$\begin{array}{l}=\frac{30000}{\$5}\\ =6000hours\end{array}$

Number of working hours= Total hours − Leisure Time

$\begin{array}{l}\text{=}\text{}\text{8000}\text{-}\text{6000}\text{hours}\\ \text{=}\text{2000}\text{hours}\end{array}$

Total working hours is 2000.

Economics Concept Introduction

Introduction: Envelop theorem states that changes in exogeneous variables must be considered for profit maximizing equations, ignoring the change in endogeneous variable.

b)

To determine

To know:

Number of working hours if 75% income is devoted to leisure when rich uncle dies

Explanation of Solution

An annual income, which is left by a rich uncle = $4000

Labor income:

Total number of working hours = 8000

Wage per hour = $5

Labor income annually :

$\begin{array}{l}=8000\times 5\\ =\$40000\end{array}$

Total income :

$\begin{array}{l}=\$40000+\$4000\\ =\text{}\$44000\end{array}$

Amount spent on leisure:

$\begin{array}{l}=8000-5900\\ =2100hours\end{array}$

Therefore, number of leisure hours :

$\begin{array}{l}=\frac{29000}{5}\\ =5800hours\end{array}$

So, Work = Total time − Leisure time

$\begin{array}{l}=8000hours-5800hours\\ =2200hours\end{array}$

Economics Concept Introduction

Introduction: Envelop theorem states that changes in exogeneous variables must be considered for profit maximizing equations, ignoring the change in endogeneous variable.

c)

To determine

To ascertain:

Number of working hours if 75% income is devoted to leisure when hourly wage is $10.

Explanation of Solution

New wage rate = $10

Non labor income = $4000

Total annual earned income:

$\begin{array}{l}=8000\times 10\\ =\$80000\end{array}$

Total income:

$\begin{array}{l}=\text{}80000+4000\\ =\text{}\$84000\end{array}$

Amount spent on leisure:

$\begin{array}{l}=(0.75\times \$84000)\\ =\text{}\$63000\end{array}$

Therefore, time spent on leisure:

$\begin{array}{l}=\frac{\$59000}{10}\\ =\text{}5900\text{}hours\end{array}$

So, work = Total time − Leisure time

$\begin{array}{l}=8000-5900\\ =2100hours\end{array}$

Economics Concept Introduction

Introduction: Envelop theorem states that changes in exogeneous variables must be considered for profit maximizing equations, ignoring the change in endogeneous variable.

d)

To determine

To Plot:

Graphical representation of supply labor curve..

Explanation of Solution

The supply curve is shown below in the graph:

When the wage rate is $5 per hour, number of working hours is S1500

When the wage rate is $10 per hour, number of working hours is 1650.

Economics Concept Introduction

Introduction: Envelop theorem states that changes in exogeneous variables must be considered for profit maximizing equations, ignoring the change in endogeneous variable.