National Economy: Accounting Algebra

The basic income-expenditure model in macroeconomics can be viewed in (at least) two ways: (a) from the perspective of the sources of spending; and (b) from the perspective of the uses of the income produced. Bringing these two perspectives (of the same thing) together generates the sectoral balances.

From the sources perspective we write:

GDP = C + I + G + (X – M)

which says that total national income (GDP) is the sum of total final consumption spending (C), total private investment (I), total government spending (G) and net exports (X – M).

From the uses perspective, national income (GDP) can be used for:

GDP = C + S + T

which says that GDP (income) ultimately comes back to households who consume (C), save (S) or pay taxes (T) with it once all the distributions are made.

Equating these two perspectives we get:

C + S + T = GDP = C + I + G + (X – M)

So after rearranging this equation we get the sectoral balances view of the national accounts:

(I – S) + (G – T) + (X – M) = 0

That is the three balances have to sum to zero. The sectoral balances derived are:

  • The private domestic balance (I – S) – positive if in deficit, negative if in surplus.
  • The Budget Deficit (G – T) – negative if in surplus, positive if in deficit.
  • The Current Account balance (X – M) – positive if in surplus, negative if in deficit.

These balances are usually expressed as a per cent of GDP but that doesn’t alter the accounting rules that they sum to zero, it just means the balance to GDP ratios sum to zero.

A simplification is to add (I – S) + (X – M) and call it the non-government sector. Then you get the basic result that the government balance equals exactly $-for-$ (absolutely or as a per cent of GDP) the non-government balance (the sum of the private domestic and external balances).

This is a basic rule derived from the national accounts and has to apply at all times.

REF: Paj Holden

Whilst most of this was provided by Bill Mitchell we think it would be more appropriate for you to comment on this blog here at Modern Money.

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9 Responses to National Economy: Accounting Algebra

  1. Magpie says:

    Mr. Senexx, sir,

    Very clear and understandable.

    As usual, I have questions:

    (1) Another way to express GDP is as the sum of the incomes by factors of production (i.e. labour, capital, land). That’s why GDP is also considered GD income.

    Is there a clear, straightforward relationship between income by productive factors and C, S, I?

    I myself don’t see any obvious answer (maybe that’s a long-shot kind of question) , but maybe you have an answer.

    (2) How about value added? Is there one such relationship detailing C, S, I in terms of value added?

    The same caveat applies here.


  2. Ray Phenicie says:

    I am recommending this site to everyone who wants to understand MMT.


  3. This theory is not true MMT, it has been used well before the loss of the gold standard was even considered. What bothers me is that in fact this equation is for the flow of money into the producer’s accounting. What about the other 5 sectors of the total economy (see my diagram for the total system, on Google Images: DiagFuncMacroSyst.pdf. In this fully comprehesive system equilibrium is established by the input and outpur money flows of 6 entities which are Government, Landlord, Producer, Householder, Capitalist and Finance Institution (Bank).

    Without modelling the system properly before building the algebraic equations, it is impossible to properly represent what is really going on and the difference between MMT (which is intended to deal with all of the money-circulation) and warmed up Keynesian Theory is not apparent!

    In other words some of your (our) MMT experts are still living in the previous world of Keynes where a free-lunch was still thought to be possible by “Pump-Priming” etc. This is not MMT as it logically follows from the initial assumptions and claims.


  4. Tom Hickey says:

    1. MMT differs from Old Keynesian in rejecting “pump-priming.”

    2. Your model (Government, Landlord, Producer, Householder, Capitalist and Finance Institution (Bank)) is missing the external sector.


  5. tradepar says:

    Can someone please explain GDP formula from the sources and uses perspective in still more simpler layman terms?


  6. Pingback: National accounting: easy as pie – gramme of soma

  7. Armando Fernandez says:

    Can you explain how C+S+T can equal GDP when the economy consists of more than households? Also, how can C be both a source and a use? Thank you.


    • Yaser Alali says:

      Ill try my best to explain the consumption part, consumption exist in both as a source and use from a simple concept “one person’s spending (consumption) is another person’s income” so the income is new spending (consumption) amount.


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