Chapter 16, Problem 2E

a)

To determine

Calculation of individual’s human wealth and total wealth.

Explanation of Solution

The percentage discourage value of labor income is known as the individual human wealth. One can calculate individual human wealth as follows:

$\begin{array}{c}\text{Individual human wealth}={\text{Y}}_{\text{Today}}+\frac{{\text{Y}}_{\text{Future}}}{1+\text{R}}\\ =100,000+\frac{10,000}{1+\text{0}\text{.05}}\\ =100,000+\frac{10,000}{1.05}\\ =100,000+95,24\\ =109,524\end{array}$

Based on the calculated value, one can calculate the total wealth as follows.

$\begin{array}{c}\text{Total wealth}=\text{Human wealth}+\text{Financial wealth}\\ =109,524+50,000\\ =159,524\end{array}$

Thus, the human wealth is $ 109,524 and financial wealth is $159,524.

b)

To determine

Neo classical consumer’s consumption today and in future and the saving rate.

Explanation of Solution

One can calculate the wealth used for consumption by a neo classical consumer in today and in future as follows:

$\begin{array}{c}{\text{C}}_{\text{Today}}=\frac{1}{2}\times \overline{\text{w}}\\ =\frac{1}{2}\times \text{159,524}\\ =79,762\\ {\text{C}}_{\text{Future}}=\frac{1}{2}\times \left(1+\text{R}\right)\overline{\times \text{w}}\\ =\frac{1}{2}\times 1.05\times \text{159,524}\\ =83,750\end{array}$

The wealth used for consumption by a neo classical consumer will be $79,762 today and $83,750 in the future. Then, the saving rate can be calculated as follows:

$\begin{array}{c}{\text{S}}_{\text{Today}}=100,000-79,762\\ =20238\end{array}$

c)

To determine

Change in today’s saving rate if current labor income increased by $20,000.

Explanation of Solution

The increase of income by $20,000 will raise the total wealth by the same amount. Then, the marginal propensity to consume will become $\frac{1}{2}$ ($\frac{1}{2}\times \overline{\text{w}}$) out of total wealth. Thus, there is a $10,000 increase in the consumption today. That is $\frac{20,000}{2}=10,000$. Then, the consumption today will increased to 89, 762 and the saving rate will be $10,238 (100,000 - 89, 762).

d)

To determine

Change in today consumption if future labor income increased by $10,000.

Explanation of Solution

If there is an increase in the future income, one can calculate the changes in total wealth only based on the present value of the interest rate. Thus, the total wealth will be changed to $9,524. Then, the consumption will be raised by the half of the total wealth. That is, the current consumption will increased by $4762 $\left(\frac{9,524}{2}\right)$.

e)

To determine

Change in the total wealth and today consumption if the interest rate rises to 10.

Explanation of Solution

If the interest rate becomes 10 %, one can calculate the new human wealth as follows:

$\begin{array}{c}\text{Individual human wealth}={\text{Y}}_{\text{Today}}+\frac{{\text{Y}}_{\text{Future}}}{1+\text{R}}\\ =100,000+\frac{10,000}{1+\text{0}\text{.1}}\\ =100,000+\frac{10,000}{1.1}\\ =100,000+90,90.91\\ =109,090.91\end{array}$

Based on the calculated value, one can calculate the total wealth as follows.

$\begin{array}{c}\text{Total wealth}=\text{Human wealth}+\text{Financial wealth}\\ =109,090+50,000\\ =159,090\end{array}$

Thus the, human wealth is $ 109,090 and total wealth is $159,090. Then, he will definitely change his consumption accordance with the change in the interest rate. Hence, one can calculate the today consumption as follows:

$\begin{array}{c}{\text{C}}_{\text{Today}}=\frac{1}{2}\times \overline{\text{w}}\\ =\frac{1}{2}\times \text{159,090}\\ =79,545\end{array}$

Here, the consumption changes from $79,762 to $79,545. Thus, the savings will be $20,455 (100,000 – 79,545). The decrease in consumption leads to an increase in the saving by $217 (20,455 – 20,238).

f)

To determine

Changes in the consumption if the professor could not borrow today.

Explanation of Solution

According to the problem, initially, the student has a very low income. According to the model of neo classical consumption, she can line up her current consumption better with the future income through a borrowing of higher amount. This will not be possible if she refused to borrow. Suppose she consumes as much as she can consume today, it implies that the she will use up all her resources.