The I=S discussion is the widely visible monument of a lack of genuine scientific instinct of both orthodox and heterodox economists. In order to make this perfectly clear it is necessary not to accept the familiar premises but to dig deeper. As Keynes already recognized: “For if orthodox economics is at fault, the error is to be found not in the superstructure, which has been erected with great care for logical consistency, but in a lack of clearness and of generality in the premises.” (1973, p. xxi)
That an error/mistake is almost always located in the premises is well-known from methodology: “In fact, the history of every science, including that of economics, teaches us that the elementary is the hotbed of the errors that count most.” (Georgescu-Roegen, 1970, p. 9)
So, what has, first of all, to be replaced is this formal description of the economy: “In the most simple model of a closed economy without government, income (Y) = consumption (C) + saving (S), but also expenditure (Y) = consumption (C) + investment (I). So S=I by definition. But here investment includes what is called ‘stockbuilding’ or ‘inventory accumulation’, which includes goods that firms wanted to sell but could not.” (quote from intro)
Instead: The most elementary economic configuration, i.e. the production-consumption economy, is defined by (i) Yw=WL wage income Yw is equal to wage rate W times working hours L, (ii) O=RL output O is equal to productivity R times working hours L, (iii) C=PX consumption expenditure C is equal to price P times quantity bought/sold X.
This is the formal minimum and there is no way to reduce it further. For the graphical representation see Wikimedia AXEC31
At any given level of employment L, the wage income that is generated in the consolidated business sector follows by multiplication with the wage rate. On the real side, output follows by multiplication with the productivity. Finally, the price follows as the dependent variable under the conditions of budget balancing, i.e. C=Yw, and market clearing, i.e. X=O. Note that the ray in the southeastern quadrant is not a linear production function; the ray tracks any underlying production function.
If the wage rate W is lowered, the market-clearing price P falls. If the number of working hours L is increased the price remains constant, provided productivity R does not change. If productivity decreases the price rises. In any case, labor gets the whole product, the real wage is invariably equal to the productivity, and profit for the business sector as a whole is zero. All changes in the system are reflected in the market-clearing price.
In the next period, the households save. The result is shown on Wikimedia AXEC33.
Of course, we could also consider the case where the price is sticky, and part of the output O is not sold, i.e. O−X>0 (see 2014a). This, however, would not alter the crucial conclusion.
The crucial conclusion is indeed that the business sector makes a monetary loss which is exactly equal to the household sector's saving, i.e. Qm≡−Sm. Therefore, loss (and not investment) is the exact counterpart of saving; by consequence, profit is the exact counterpart of dissaving.
And this is why almost everything that conventional professors tell their students is false. Household sector saving has never been equal and will never be equal to business sector investment.
The general relationship between monetary profit, distributed profit, investment, and monetary saving is given on Wikimedia AXEC09.
As a matter of fact, Keynes' conceptual problems started with profit: “His Collected Writings show that he wrestled to solve the Profit Puzzle up till the semi-final versions of his GT but in the end he gave up and discarded the draft chapter dealing with it.” (Tómasson et al., 2010, p. 12)
This kicks off the chain reaction of errors/mistakes: When profit is not correctly defined, income is not correctly defined, and then saving is not correctly defined. It is with profit where the confusion about saving “equals” investment starts. The conceptual mess has been verbally papered over with capital investment/inventory investment or ex-ante/ ex-post and the representative economist has swallowed all this hook, line, and sinker. For the formally correct solution see (2014b).
Because neither the Post-Neo-New Keynesians nor the Post-Neo-New Classicals have solved the profit puzzle and with it the saving-investment puzzle, they are collectively out of science (2013).
Georgescu-Roegen, N. (1970). The Economics of Production. American Economic Review, Papers and Proceedings, 60(2): 1–9. URL
Kakarot-Handtke, E. (2013). Why Post Keynesianism is Not Yet a Science. Economic Analysis and Policy, 43(1): 97–106. URL
Kakarot-Handtke, E. (2014a). Economics for Economists. SSRN Working Paper Series, 2517242: 1–29. URL
Kakarot-Handtke, E. (2014b). The Three Fatal Mistakes of Yesterday Economics: Profit, I=S, Employment. SSRN Working Paper Series, 2489792: 1–13. URL
Keynes, J. M. (1973). The General Theory of Employment Interest and Money. The Collected Writings of John Maynard Keynes Vol. VII. 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