Question

Economists in Funlandia, which has a closed economy, have collected the following information about the economy for a particular year:

Y$\mathit{Y}$	= $\mathit{ }=\mathit{ }$	12,500$\mathrm{12,500}$
C$\mathit{C}$	= $\mathit{ }=\mathit{ }$	9,000$\mathrm{9,000}$
T$\mathit{T}$	= $\mathit{ }=\mathit{ }$	2,100$\mathrm{2,100}$
G$\mathit{G}$	= $\mathit{ }=\mathit{ }$	2,200$\mathrm{2,200}$

The economists also estimate that the investment function is:

I$\mathit{I}$

= $\mathit{ }=\mathit{ }$

2,000−100r$\mathrm{2,000}-100\mathit{r}$

where r$\mathit{r}$ is the country’s real interest rate, expressed as a percentage.

Complete the following table by calculating private saving, public saving, national saving, investment, and the equilibrium real interest rate.

Component	Amount
Private Saving	1,400
Public Saving	-100
National Saving	1,300
Investment	1,300
Equilibrium Real Interest Rate	7%

Answer 1

Private saving is the amount of income that households have left after paying their taxes (T$\mathit{T}$) and paying for their consumption (C$\mathit{C}$):

SPrivate${\mathit{S}}_{\mathrm{Private}}$	= $\mathit{ }=\mathit{ }$	Y−T−C$\mathit{Y}-\mathit{T}-\mathit{C}$
	= $\mathit{ }=\mathit{ }$	12,500−2,100−9,000$\mathrm{12,500}-\mathrm{2,100}-\mathrm{9,000}$
	= $\mathit{ }=\mathit{ }$	1,400$\mathrm{1,400}$

Public saving is the amount of tax revenue that the government has left after paying for its spending (G$\mathit{G}$):

SPublic${\mathit{S}}_{\mathrm{Public}}$	= $\mathit{ }=\mathit{ }$	T−G$\mathit{T}-\mathit{G}$
	= $\mathit{ }=\mathit{ }$	2,100−2,200$\mathrm{2,100}-\mathrm{2,200}$
	= $\mathit{ }=\mathit{ }$	−100$\mathrm{-100}$

National saving is the sum of private and public saving:

National Saving$\mathit{National Saving}$	= $\mathit{ }=\mathit{ }$	SPrivate+SPublic${\mathit{S}}_{\mathrm{Private}}+{\mathit{S}}_{\mathrm{Public}}$
	= $\mathit{ }=\mathit{ }$	1,400+(−100)$\mathrm{1,400}+\left(\mathrm{-100}\right)$
	= $\mathit{ }=\mathit{ }$	1,300$\mathrm{1,300}$

Because investment must equal national saving in a closed economy, investment is also $1,300.

You can find the equilibrium interest rate by setting investment equal to 1,300 and solving for r$\mathit{r}$:

I$\mathit{I}$	= $\mathit{ }=\mathit{ }$	2,000−100r$\mathrm{2,000}-100\mathit{r}$
1,300$\mathrm{1,300}$	= $\mathit{ }=\mathit{ }$	2,000−100r$\mathrm{2,000}-100\mathit{r}$
100r$100\mathit{r}$	= $\mathit{ }=\mathit{ }$	2,000−1,300$\mathrm{2,000}-\mathrm{1,300}$
100r$100\mathit{r}$	= $\mathit{ }=\mathit{ }$	700$700$
r$\mathit{r}$	= $\mathit{ }=\mathit{ }$	7%$7\mathrm{\%}$

Answer 2

SOLUTION :

Y = 12500 . C = 9000, T = 2100, G = 2300 and I = 2000 - 100r 

Private saving 

= Total income - consumption - taxes 

= Y - C - T

= 12500 - 9000 - 2100

= 1400

Public saving 

= Govt. revenue - Govt. expenses

= T - G 

= 2100 = 2200

= - 100 

National saving 

= Private saving + Public saving

= 1400 + (-100)

= 1300 

Investment = 2000 - 100r

=>  National saving = 2000 - 100r

= > 1300 = 2000 - 100r

So,

 r = interest rate 

= (2000 - 1300) / 100 

= 7%

Hence, the table will be as under :

Details                          Value

Private saving               1400

Public saving                 - 100

National saving             1300

Interest rate                     7%