# National savings

In economics, a country's national savings is the sum of private and public savings. It is generally equal to a nation's income minus consumption and government purchases.

## Economic model

### Closed economy with public deficit or surplus possible

In this simple economic model with a closed economy there are three uses for GDP (the goods and services it produces in a year). If Y is national income (GDP), then the three uses of C consumption, I investment, and government purchases can be expressed as:

• ${\displaystyle Y=C+I+G}$

National savings can be thought of as the amount of remaining money that is not consumed, or spent by government. In a simple model of a closed economy, anything that is not spent is assumed to be invested:

• ${\displaystyle {\text{National Savings}}=Y-C-G=I}$

National savings should be split into private savings and public savings. The new terms, T is taxes paid by consumers that goes directly to the government and TR is transfers paid by the government to the consumers as shown here:

• ${\displaystyle (Y-T+TR-C)+(T-G-TR)=I}$

(Y − T + TR) is disposable income whereas (Y − T + TR − C) is private savings. Public savings, also known as the budget surplus is the term (T − G − TR), which is government revenue through taxes, minus government expenditures, minus transfers.

The interest rate plays the important role of creating an equilibrium between saving and investment in neoclassical economics.

• ${\displaystyle S(r)=I(r)}$

In Keynesian models the identity between savings and investments is generated by the investment who determines income and by this the savings in the economy.

### Open economy with balanced public spendings

In an open economic model international trade is introduced into the model. Therefore the current account is split into export and import:

• ${\displaystyle {\text{Net eXports}}=NX={\text{eXports}}-{\text{iMports}}=X-M}$

The net exports is the part of GDP which is not consumed by domestic demand respectively the domestic demand which is not covered by the domestic production (GDP).

• ${\displaystyle NX=Y-(C+I+G)=Y-{\text{Domestic demand}}}$

If we transform the identity for net exports by subtracting consumption, investment and government spending we get the national accounts identity:

• ${\displaystyle Y=C+I+G+NX}$

The national saving is the part of the GDP which is not consumed or spent by the government respectively the invested or net exported.

• ${\displaystyle Y-C-G=S=I+NX}$

It is important to note that S is here only private saving. Because of the balanced public spendings condition public savings equals zero

Therefore the difference between the national savings and the investments is equal to the net exports:

• ${\displaystyle S-I=NX}$

### Open economy with public deficit or surplus

In addition to the model above the government budget is directly introduced into the model. We consider now an open economic model with public deficits or surpluses. Therefore the budget is split into revenues these are the taxes (T) and the spendings there are transfers (TR) and government spendings (G). Revenues minus spendings results in the public savings:

• ${\displaystyle S(G)=T-G-TR}$

The disposable income of the households is the income Y minus the taxes plus the transfers of the state.

• ${\displaystyle Yd=Y-T+TR}$

Respectively the disposable income can only be used for saving or for consumption.

• ${\displaystyle Yd=C+S(P)}$

Therefore the private savings in this model equal the disposable income of the households minus consumption.

• ${\displaystyle S(P)=Yd-C}$

By this equation the private savings can be written as:

• ${\displaystyle S(P)=Y-T+TR-C}$

And the national accounts as:

• ${\displaystyle Y=S(P)+C+T-TR}$

Once this equation is used in Y=C+I+G+X-M we get:

• ${\displaystyle C+I+G+(X-M)=S(P)+C+T-TR}$

In one transformation we get the determination of net exports and investments by private and public savings

• ${\displaystyle S(P)+S(G)=I+(X-M)}$

In another transformation we get the sectoral balances of the economy as developed by Wynne Godley. This corresponds approximately to Balances Mechanics developed by Wolfgang Stützel.

• ${\displaystyle (S(P)-I)+S(G)=(X-M)}$