May 18, 2016

The worst economic equation

Comment on Matias Vernengo on 'The great economic equations'


Economics abounds with logical/mathematical blunder. Keynes’ I=S is the worst error/ mistake measured by overall methodological fallout.

1. The argument
Keynes formulated the formal core of the General Theory as follows: “Income = value of output = consumption + investment. Saving = income − consumption. Therefore saving = investment.” (1973, p. 63)

This elementary syllogism is conceptually defective because Keynes never came to grips with profit (Tómasson et al., 2010, p. 12). This is fatal for an economist.

2. Rectification
The Keynesian premises have to be replaced by the correct macrofoundations. This is achieved as follows
(A0) The objectively given and most elementary configuration of the economy consists of the household and the business sector which in turn consists initially of one giant fully integrated firm.
(A1) Yw=WL wage income Yw is equal to wage rate W times working hours. L,
(A2) O=RL output O is equal to productivity R times working hours L,
(A3) C=PX consumption expenditure C is equal to price P times quantity bought/sold X.
For the graphical representation of this ABSOLUTE formal MINIMUM see Wikimedia AXEC31

(A1) to (A3) asserts: At any given level of employment L, the wage income Yw that is generated in the consolidated business sector follows by multiplication with the wage rate W. On the real side, output O follows by multiplication with the productivity R. Finally, the price P follows as the dependent variable under the conditions of (i) budget balancing, i.e. C=Yw, and (ii), market clearing, i.e. X=O.

Under the conditions (i)|(ii) the price is derived in each period as P=W/R, i.e. the market-clearing price is in the most elementary case equal to unit wage costs which vary over successive periods.

In the next period, the households save, i.e. condition (i) is now lifted. The result is shown here.

Consumption expenditures C fall below Yw and with it the market-clearing price P. The product market is cleared due to (ii) and there is no such thing as inventory investment, i.e. I=0. Monetary saving of the household sector is given by Sm≡Yw−C.

The business sector makes a monetary loss which is equal to the household sector’s saving, i.e. Qm≡−Sm. Therefore, loss is the exact counterpart of saving; by consequence, profit is the exact counterpart of dissaving. This is the most elementary form of the Profit Law. It follows directly from the profit definition Qm≡C−Ym and the definition of household sector saving. The sector balances always add up to zero, i.e. Qm+Sm=0.

Saving and investment are NEVER equal, neither ex-ante nor ex-post. Saving/dissaving is complementary to loss/profit.

The correct profit equation for the investment economy reads Qm≡Yd+I−Sm. Legend: Qm monetary profit, Yd distributed profit, Sm monetary saving, I investment expenditures.

3. Conclusion
(a) I=S is the worst economic equation. All I=S/IS-LM models from Keynes to Krugman are provably false (2014). (b) The multiplier is formally defective. (c) All microfounded profit theories are provably false. (d) The representative economist has NOT gotten (a) to (c) to this very day.

Egmont Kakarot-Handtke

Kakarot-Handtke, E. (2014). Mr. Keynes, Prof. Krugman, IS-LM, and the End of Economics as We Know It. SSRN Working Paper Series, 2392856: 1–19. URL
Keynes, J. M. (1973). The General Theory of Employment Interest and Money.  London, Basingstoke: Macmillan.
Tómasson, G., and Bezemer, D. J. (2010). What is the Source of Profit and Interest? A Classical Conundrum Reconsidered. MPRA Paper, 20557: 1–34. URL

Immediately preceding The great economic equations.

For more details see cross-references Refutation of I=S.