# How to calculate National Savings, Public savings and Private Savings

National savings, Public Savings and Private savings are all national aggregates which measure the level of savings of all private individuals within an economy; the level of savings held by government and the previous two combined.

Public savings equations

The public savings equation tells us how much the government is saving. It is defined as the difference between how much money the government collects in tax revenue (T) minus its spending (G):

Public Savings = T - G

Government savings can be either positive, negative or equal to zero.

When the government has higher Taxation (T) than Government Spending (G) they are said to be running a Budget Surplus. In this case, Government savings is positive.

When the Government Spending (G) is spending more than they are collecting in Tax (T) they are said to be running a Budget Deficit. In this case, Government savings is negative.

When the government spends (G) exactly what they collect in Tax (T) they are said to be running a Balanced Budget. In this case, government savings is zero.

Private savings equation

The private savings equation tells us how much all the people who reside within an economy are saving. Private savings is defined as the total income (Y)  (might be referred to as GDP or National income or just Income) minus the tax that they pay (T) and how much of their expenditure is used on consumption (C) :

Private savings = Y - T - C

In essence, private savings is how much income all private citizens have “left over” after they pay their taxes and purchase all the goods they desire.

National Savings equation

National savings (S) is the combination of both private savings and public savings:

National Savings = Public savings + Private savings

S= T - G + Y - T - C

S = Y - C - G

It tells us the total level of savings in an economy. It can also be shown that (S=I).

Example

Suppose that GDP is 10,000, Tax is 1,500, Government spending is 4,000 and consumption is 4,000. Calculate Public Savings, Private savings and National Savings.

Using the public savings equation

Public Savings = T - G

Public Savings = 1,500 - 4,000

Public Savings = -2500

This suggests that the government is running  a budget deficit.

Using the Private savings equation

Private savings = Y - T - C

Private savings = 10,000 - 1,500 - 4,000

Private savings = 4,500

Now using the National savings equation

National Savings = Public Savings + Private Savings

National Savings = -2500 + 4,500

National Savings = 2,000

References:

Central Intelligence Agency. (2016). Budget. In The world factbook. Retrieved from https://www.cia.gov/library/publications/the-world-factbook/fields/2056.html

##### 28 Responses
1. thank you 🙂

2. Why is Government Spending 2000 under Public Savings in the problem. I thought in the question it stated that it was 4000? Is there a step that I'm missing?

1. My mistake, it has been corrected! Thanks!

3. In the question, consumption is stated as 5000

Private savings = Y - T - C
Private savings = 10,000 - 1,500 - 4,000(???? it should be 5000)

so Private savings = 3500
and total savings = 1000

1. You are correct, the question has been amended.

4. So helpful you are a life saver

1. Y = GDP and is given in the question as 10,000.

5. i'm confused...
what if there's government transfer (TR) comes in ?
will Private Saving= (Y + TR - T) - C ?

1. Assuming I understand the question correctly: Government transfers should not come into the equation since they are just transfers from one economic to another, so the aggregate effect would be zero.

6. where does C come from and how did you solve for it?
i can understand it in text but not in the equation.

1. C is consumption and for this example we are just assuming that we have been told what level it is.

7. How can I calculate Taxation here?
Closed economy of a city is is described by the following equations GDP (Y) = $10 trillions, G =$2 trillions, Consumption (C) = $6.5 trillions. Budget deficit =$300 billions.

1. Firstly, recall that Savings equals investment in a closed economy. Therefore, using Y = C + I + G we get 10 = 2 + 6.5 + I which implies that investment equals 1.5 trillion. If we add public and private savings our total savings becomes

S = (Y - T - C) + (G - T) where the first bracket is private savings and the second bracket is public savings.

We are told that the budget deficit is 300 billion or .3 trillion which means G - T = -0.3. We can now substitute all the other parts we know into the above savings formula:

1.5 = 10 - T - 6.5 -0.3 and just re-arrange this equation.
T = 1.7 trillion dollars.

Hope that helped.

1. Hi,

I just wondering why the 'S' = 1.5 ? Does investment equal to saving? As the value of 1.5 is the figure of investment based on your calculation previously.

"Y = C + I + G we get 10 = 2 + 6.5 + I, which implies that investment equals 1.5 trillion."

1. Yes, savings equals investment in a closed economy. So investment would equal 1.5 using those figures.

8. So please how will you account for Retained Earnings in National Savings?

9. assume GDP = 65000, disposable income 5600, government deficit 700, consumption 4300 trade deficit 600. how large z saving? what is the size of the investment? and how is government spending?

1. The private savings in this question is:

S = Y - T - C

The first thing to note is that disposable income aka "after tax income" is defined as Y - T, thus:

Y - T = 5,600

and we were told that consumption is $4,300, therefore: Private savings =$5,600 - $4,300 Private savings =$1,300

we are told the level of public savings as we are told that there is a government deficit, thus:

Public savings = -$700 This question relates to an open economy since it includes the trade deficit, so the formula you need is: Y = C + I + G + NX We know that total savings are defined as: S = Y - C - G So if we re-arrange the above equation we get: Y - C - G = I + NX S = I + NX We are also told that there is a trade deficit (which means that net exports are negative) so we get: S = I -$600

We can also figure out total savings from above:

S = $1300 -$700

S = $600 Plugging this into our previous equation:$600 = I - $600 I =$1,200

C=250+0.75(y-t)
I=1000-50r
T=total tax from income =1000
R=rate of interest in percentage

(a),if in equilibrium, Y=5000,compute the equilibrium level of private saving, public saving, and the interest rate in the given economy.

11. Sorry sir I have forgotten,
In this question government expenditure was given By= 1000