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Ineconomics, a country'snational saving is the sum ofprivate andpublic saving.^[1]: 187 It equals a nation's income minus consumption and the government spending.^[1]: 174

In this simple economic model with aclosed economy there are three uses forGDP (the goods and services it produces in a year). If Y is national income (GDP), then the three uses of Cconsumption, Iinvestment, and Ggovernment purchases can be expressed as:

• ${\displaystyle Y=C+I+G}$

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

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

National saving can be split into private saving and public saving. Denoting T for taxes paid by consumers that go directly to the government and TR for 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 saving. Public saving, also known as thebudget surplus, is the term (T − G − TR), which is government revenue through taxes, minus government expenditures on goods and services, minus transfers. Thus we have that private plus public saving equals investment.

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

• ${\displaystyle S(r)=I(r)}$

where the interest rate r affects saving positively and affects physical investment negatively.

In anopen economic modelinternational trade is introduced. Therefore thecurrent account is split intoexports andimports:

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

The net exports is the part of GDP which is not consumed by domestic demand:

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

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.

• ${\displaystyle Y-C-G=S=I+NX}$

Therefore the difference between the national saving and the investment is equal to the net exports:

• ${\displaystyle S-I=NX}$

Thegovernment budget can be directly introduced into the model. We consider now an open economic model with public deficits or surpluses. Therefore the budget is split into revenues, which are the taxes (T), and the spendings, which are transfers (TR) and government spendings (G). Revenue minus spending results in the public (governmental) saving:

• ${\displaystyle S_G=T-G-TR}$

Thedisposable income of the households is the income Y minus the taxes net of transfers:

• ${\displaystyle Y_d=Y-T+TR}$

Disposable income can only be used for saving or for consumption:

• ${\displaystyle Y_d=C+S_P}$

where the subscript P denotes the private sector. Therefore private saving in this model equals the disposable income of the households minus consumption:

• ${\displaystyle S_P=Y_d-C}$

By this equation the private saving 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 obtain

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

By one transformation we get the determination of net exports and investment by private and public saving:

• ${\displaystyle S_P+S_G=I+(X-M)}$

By another transformation we get thesectoral balances of the economy as developed byWynne Godley. This corresponds approximately toBalances Mechanics developed byWolfgang Stützel:

• ${\displaystyle (S_P-I)+S_G=(X-M)}$

• Balances Mechanics
• Government debt
• Inflation
• IS/LM model
• Sectoral balances

• Macroeconomic aggregates
• Investment

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