## January 5, 2015

### The Profit Law

Comment on Lars Syll on 'Ditch marginal productivity theory once and for all'

Blog-Reference

The economy is a complex system. Because it is impossible to directly observe the actual economy in its totality, the first task is to create a simplified mental representation. As a matter of fact, what is needed for good methodological reasons is the simplest possible description of the monetary economy. This description cannot be other than highly abstract and it all depends on whether the abstraction succeeds. This is what J. S. Mill called the opus magnum (2006, p. 746).

The most elementary economic configuration is the production-consumption economy. It 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. Note finally that W is the average wage rate if the individual wage rates are different among the employees, which is normally the case.

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 by the market-clearing price.

We know, of course, that the firm sets a price that is different from the market-clearing price. This case has to be treated separately (2014a).

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, monetary saving which is given by Sm≡Yw−C is not equal to investment I=0.

The crucial conclusion is that the business sector makes a monetary loss which is exactly 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 elementary form of the macroeconomic Profit Law. It follows from the profit definition Qm≡C−Ym. Note well that profit for the economy as a whole has nothing at all to do with productivity and certainly nothing at all with marginal productivity.

And this is why all stories that economists tell about the functioning of the market system and the price mechanism are false (2014b).

In the next step, we have to make the economy again a bit more complex. Then we get the general relationship between monetary profit Qm, distributed profit Yd, investment I, and saving Sm as shown on Wikimedia AXEC143d

In the next but one step government and foreign trade have to be included. Each step brings the Profit Law closer to the complexity of the real world. Best of all: the Profit Law is testable with the precision of two decimal places.

There can be no reasonable doubt about the test's outcome: the marginal productivity theory of distribution is refuted once and for all. Economics can become real science.

Egmont Kakarot-Handtke

References
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
Mill, J. S. (2006). Principles of Political Economy With Some of Their Applications to Social Philosophy, Vol. 3, Books III-V of Collected Works of John Stuart Mill. Indianapolis: Liberty Fund. URL

For more about the Profit Law see AXECquery.