“There can be no doubt whatsoever that a problem which has not yet been solved in all its aspects under its simplest conditions will be still more difficult to tackle if other, ‘more realistic’ assumptions are being made.” (Morgenstern, 1941, p. 373)
It all depends on whether the abstraction succeeds. Keynes bore the challenge and dealt with the very first task of macroeconomics. He gave the following elementary formal description of the economy: Income = value of output = consumption + investment. Saving = income − consumption. Therefore saving = investment. (Keynes, 1973, p. 63)
Since theories have an architectonic structure it is clear that if there is a fault in the formal foundations the whole superstructure of the theory is vulnerable. Actually, the fault in Keynes' two-liner is in the premise income = value of output. This equality holds — see the formal proof in (2011) — only in the limiting case of zero profit in both the consumption and investment good industry.
Profit does not appear in Keynes' elementary formalism. That is, he in effect talks about capitalism without profit. Note well that Walras' economy was also a zero profit economy. Obviously, neither approach provides an acceptable description of the market economy.
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 and Bezemer, 2010, p. 12)
This failure kicked off the chain reaction of errors/mistakes because when profit is not correctly defined, income is not correctly defined, and then saving is not correctly defined. By consequence, all I=S models, including the long-lived workhorse IS-LM, are logically defective (2014). Since the days when Keynes wrote down his faulty syllogism, the representative economist realized nothing.
Keynes' economy is still not simple enough. First of all, the two sectors have to be reduced to the elementary production-consumption economy. This alters the foundational formalism. The most elementary economic configuration, i.e. the elementary production-consumption economy, is defined by
(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 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, the output follows by multiplication with 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. Note also that it is methodologically inadmissible to take the assumption of decreasing returns into the premises. This dilettantism is known since antiquity as petitio principii.
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. If productivity increases the price falls. 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.
Consumption expenditure C falls below Yw and with it the market-clearing price P. With perfect price flexibility, there are NO unsold quantities and NO change of inventory. The product market is always cleared and there is no such thing as an inventory investment. So we have household sector saving but no business sector investment, that is, saving which is given by S≡Yw−C is NOT equal to investment I=0.
The crucial conclusion is that the business sector makes a loss which is exactly equal to the household sector's monetary saving, i.e. Sm≡−Qm. Therefore, loss (and NOT investment) is the exact counterpart of saving; by consequence, profit is the exact counterpart of dissaving.
And this is why all stories that economists tell about the functioning of the market system and the price mechanism are 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 saving is given by this equation on Wikimedia AXEC09c
How could economists get the basics so badly wrong? This is the question for future historians of economic thought.
The fact of the matter is: Neither Classicals, nor Walrasians, nor Marshallians, nor Marxians, nor Keynesians, nor Institutionalists, nor Monetary Economists, nor Austrians, nor Sraffaians, nor Evolutionists, nor Game theorists, nor EconoPhysicists, nor RBCers, nor New Keynesians, nor New Classicals ever came to grips with profit (cf. Desai, 2008). Hence, 'they fail to capture the essence of a capitalist market economy' (Obrinsky, 1981, p. 495).
Because he cannot tell the difference between profit and income the representative economist has a distorted understanding of economic reality. Economics is a science without scientists.
Desai, M. (2008). Profit and Profit Theory. In S. N. Durlauf, and L. E. Blume (Eds.), The New Palgrave Dictionary of Economics Online, 1–11. Palgrave Macmillan, 2nd edition. URL
Kakarot-Handtke, E. (2011). Keynes’s Missing Axioms. SSRN Working Paper Series, 1841408: 1–33. URL
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. The Collected Writings of John Maynard Keynes Vol. VII. London, Basingstoke: Macmillan.
Morgenstern, O. (1941). Professor Hicks on Value and Capital. Journal of Political Economy, 49(3): 361–393. URL
Obrinsky, M. (1981). The Profit Prophets. Journal of Post Keynesian Economics, 3(4): 491–502. URL
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