Imagine we have two accountants, one for the business sector, Mr. B, and one for the household sector, Mrs. H. Mr. B is supposed to make an entry every time the firm makes a wage payment and every time the firm sells its output. To make matters simple, the condition of market-clearing holds, that is, quantity sold X = output O, that is, there is no change of inventory. Mrs. H is supposed to make an entry every time one of the households receives wage income and every time a household buys the firm’s product.
At the end of the first period, they meet at the Honest Accountant Bar and compare their numbers, which are shown in the form of accounts on Wikimedia.
(a) National accounts, elementary production-consumption economy, two sectors, initial period, consumption expenditures = wage income, C=Yw.
Before they depart, they sum up loosely: The sum of all expenditures in the domestic economy has been equal to the sum of all incomes.
At the end of the second period, they meet again at the Honest Accountant Bar and compare their numbers. This time they have:
(b) National accounts, consumption expenditures greater than wage income, C>Yw.
The accountants are again pleased that their respective numbers are exactly equal but this time their accounts show balances.
Says Mr. B, I call my balance profit or loss, as the case may be, more specifically I define monetary profit as Qm≡C−Yw.
Well, says Mrs. H, I call my balance saving or dissaving, as the case may be, more specifically I define monetary saving as Sm≡Yw−C.
Then they calculate their respective balances and find out, to nobody’s surprise, that Qm≡−Sm or Qm+Sm=0. Note that NO real transactions and transaction entries correspond to the balances. To draw the balances is an ex-post exercise.
Before they depart, they sum up loosely: The sum of all expenditures in the domestic economy has been greater than the sum of all incomes and accordingly the profit of the business sector has been equal to dissaving of the household sector.
The next day, the two accountants hand their numbers = Figure (b) over to the economist. Says the economist, hmm, for my purposes I have to rearrange the accounts, after all, profit has to be treated as the income of capital analogous to wage income. I define Gross Domestic Income as GDI≡Yw+Qm. He does not realize that he puts a flow and a balance together, something no accountant worth his salt would ever do. Now the accounts look like this:
(c) National accounts, consumption expenditures greater than wage income, with profit redefined as a kind of income.
The economist now says to himself, obviously, Gross Domestic Income GDI is equal to consumption expenditures, which follows from the definitions GDI≡Yw+Qm and Qm≡C−Yw, so GDI≡C by indirect definition. Let us call the right-hand side of the business sector’s account Gross Domestic Product GDP for the general case of the sum of consumption expenditures C and investment expenditures I, i.e. GDP≡C+I. Then we have always, lo and behold, GDI≡GDP. This the fundamental macroeconomic accounting identity, after all, accounts must be always balanced. Yes? NO! The balances must always add up to zero, i.e. Qm+Sm=0.
The economist’s exercise is futile because profit is NOT the income of capital but the mirror image of dissaving, i.e. the household sector’s increase of debt. Income is a flow and profit is a balance of flows and to lump the two together is sheer accounting madness.#1
From the graphics, it is immediately obvious that Keynes’ foundational identity “Income = value of output” is false. This seemingly commonsensical identity leads to I=S which is one of the biggest methodological blunders in all of economics.
Because the profit theory is false since Adam Smith, economics became the failed science that it is today. The scientific incompetence of the representative economist is documented by the fact that he cannot tell the difference between profit and income until this very day. The concept of total income or GDI as the sum of wage income and profit is of unsurpassable mathematical idiocy.
#1 See also The Common Error of Common Sense: An Essential Rectification of the Accounting Approach.
Related 'How money emerges out of nothing ― the functional account' and 'How the intelligent non-economist can refute every economist hands down' and 'Economists: just too stupid for counting'. For details of the bigger picture see cross-references Accounting and cross-references Refutation of I=S.