Chapter 11, Problem 7P

(a)

To determine

Determine the values of national saving, capital inflows, domestic investment, and the real interest rate.

Explanation of Solution

Since the savings is the sum total of national savings and the capital inflow, the saving–investment equality can be represented as follows:

$\begin{array}{c}\text{Savings (S)}+\text{Capital inflow (KI)}=\text{Investment (I)}\\ \left(1,500+2,000\text{r}\right)+\left(-100+6,000\text{r}\right)=2,000-4,000\text{r}\end{array}$  

Rearrange the equation to get the value of the real interest rate (r) as follows:

$\begin{array}{c}\left(1,500+2,000\text{r}\right)+\left(-100+6,000\text{r}\right)=2,000-4,000\text{r}\\ 12,000\text{r}=600\\ \text{r}=\frac{600}{12,000}\\ =0.05\end{array}$

Thus, the real interest rate is 0.05 or 5%.

Substitute the value of ‘r’ in the given functional form of domestic supply of saving:

$\begin{array}{c}\text{S}=1,500+\left(2,000\times 0.05\right)\\ =1,600\end{array}$

Thus, the domestic saving is 1,600.

Substitute the value of ‘r’ in the given functional form of investment:

$\begin{array}{c}\text{I}=2,000-\left(4,000\times 0.05\right)\\ =1,800\end{array}$

Thus, the investment is 1,800.

Substitute the value of ‘r’ in the given functional form of capital inflow:

$\begin{array}{c}\text{KI}=-100+\left(6,000\times 0.05\right)\\ =200\end{array}$

Thus, the capital inflow is 200.

(b)

To determine

Determine the values of national saving, capital inflows, domestic investment, and the real interest rate.

Explanation of Solution

If the desired national savings declined by 120, then the new functional form of domestic savings can be represented as follows:

$\begin{array}{c}\text{S}=\left(1,500-120\right)+2,000\text{r}\\ \text{S}=1,380+2,000\text{r}\end{array}$

Since the savings is the sum total of national savings and the capital inflow, the new saving–investment equality can be represented as follows:

$\begin{array}{c}\text{Savings (S)}+\text{Capital inflow (KI)}=\text{Investment (I)}\\ \left(1,380+2,000\text{r}\right)+\left(-100+6,000\text{r}\right)=2,000-4,000\text{r}\end{array}$  

Rearrange the equation to get the value of the real interest rate (r):

$\begin{array}{c}\left(1,380+2,000\text{r}\right)+\left(-100+6,000\text{r}\right)=2,000-4,000\text{r}\\ 12,000\text{r}=720\\ \text{r}=\frac{720}{12,000}\\ =0.06\end{array}$

Thus, the real interest rate is 0.06 or 6%. This means that the real interest rate increases from 5% to 6%

Substitute the value of ‘r’ in the new functional form of domestic supply of saving:

$\begin{array}{c}\text{S}=1,380+\left(2,000\times 0.06\right)\\ =1,500\end{array}$

Thus, the domestic saving is 1,500. This means that the domestic savings decrease from 1,600 to 1,500.

Substitute the value of ‘r’ in the given functional form of investment:

$\begin{array}{c}\text{I}=2,000-\left(4,000\times 0.06\right)\\ =1,760\end{array}$

Thus, the investment is 1,760. Therefore, the investments decrease from 1,800 to 1,760.

Substitute the value of ‘r’ in the given functional form of capital inflow:

$\begin{array}{c}\text{KI}=-100+\left(6,000\times 0.06\right)\\ =260\end{array}$

Thus, the capital inflow is 260. This means that the capital inflow increased from 200 to 260. Here, the increase in capital inflow will be offset by the decline in domestic savings. 

(c)

To determine

Determine the values of national saving, capital inflows, domestic investment, and the real interest rate.

Explanation of Solution

Since the savings is the sum total of national savings and the capital inflow, the new saving–investment equality after the fall in capital inflow can be represented as follows:

$\begin{array}{c}\text{Savings (S)}+\text{Capital inflow (KI)}=\text{Investment (I)}\\ \left(1,500+2,000\text{r}\right)+\left(-700+6,000\text{r}\right)=2,000-4,000\text{r}\end{array}$  

Rearrange the equation to get the value of the real interest rate (r):

$\begin{array}{c}\left(1,500+2,000\text{r}\right)+\left(-700+6,000\text{r}\right)=2,000-4,000\text{r}\\ 12,000\text{r}=1,200\\ \text{r}=\frac{1,200}{12,000}\\ =0.10\end{array}$

Thus, the real interest rate is 0.10 or 10%. That means that the real interest rate increases from 5% to 10%

Substitute the value of ‘r’ in the given functional form of domestic supply of saving:

$\begin{array}{c}\text{S}=1,500+\left(2,000\times 0.10\right)\\ =1,700\end{array}$

Thus, the domestic saving is 1,700. This means that the domestic savings increase from 1,600 to 1,700.

Substitute the value of ‘r’ in the given functional form of investment:

$\begin{array}{c}\text{I}=2,000-\left(4,000\times 0.10\right)\\ =1,600\end{array}$

Thus, the investment is 1,600. Therefore, the investments decrease from 1,800 to 1,600.

Substitute the value of ‘r’ in the given functional form of capital inflow:

$\begin{array}{c}\text{KI}=-700+\left(6,000\times 0.10\right)\\ =-100\end{array}$

Thus, the capital inflow is -100. This means that the capital inflow decreases from 200 to -100. Here, the decrease in the capital inflow will be offset by the increase in domestic savings.