## March 15, 2016

### Toward the true economic axioms

Comment on Paul Davidson on ‘The gross substitution axiom’

Blog-Reference and Blog-Reference on Mar 17

Paul Davidson describes the methodology of Orthodoxy as follows: “Building their economic models, modern mainstream neoclassical economists ground their models on a set of core assumptions (CA) — describing the agents as ‘rational’ actors — and a set of auxiliary assumptions (AA).” (See intro)

Keynes saw that the set of core assumptions, a.k.a. axioms was unacceptable and consequently started his paradigm shift: “Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry. Something similar is required to-day in economics.” (1973, p. 16)

Keynes based his approach on this set of objective axioms: “Income = value of output = consumption + investment. Saving = income − consumption. Therefore saving = investment.” (1973, p. 63)

This set is free of the green cheese assumptions of maximization-and-equilibrium. This obviously goes in the right direction but Keynes’ axioms are also defective. As a result, Keynes got the relationship between the product market and the money market wrong. Both markets are coupled via saving/dissaving (2015a; 2015b).

In order to see this, Keynes’ foundational propositions have to be replaced. The most elementary economic configuration is the production-consumption economy which is given by three objective structural-systemic axioms:
(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 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 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 W is the AVERAGE wage rate if the individual wage rates are different among the employees, which is normally the case. Under the INITIAL conditions of budget balancing and market-clearing holds P=W/R.

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 productivity, and profit for the business sector as a whole is zero. All changes in the system are reflected by the market-clearing price. The elementary consumption economy is reproducible for an indefinite number of periods at any level of employment.

In the next period, the households save. The condition of budget balancing is lifted. The condition of market clearing remains in place. 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 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 as in Keynes’ formal foundations. I=S is always false.#1

The crucial result is that the business sector makes a monetary loss that 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 most elementary form of the macroeconomic Profit Law. It follows directly from the profit definition Qm≡C−Yw. It always holds Qm+Sm=0.

Now, monetary saving increases the stock of money of the household sector. Yet, the complementary monetary loss decreases the stock of money of the business sector. This effect is obviously missing in the gross substitution axiom. Neither Orthodoxy nor Keynes came to grips with profit and as a consequence with the interaction of the product and the money market. Substitution is inapplicable because saving and profit are complimentary.

Conclusion: The orthodox set of subjective-behavioral axioms is false. The Keynesian set of objective axioms is false. Ergo, BOTH versions of the so-called gross substitution axiom are false. Alone the objective-systemic set of axioms is true.

Egmont Kakarot-Handtke

References
Kakarot-Handtke, E. (2015a). Essentials of Constructive Heterodoxy: Financial Markets. SSRN Working Paper Series, 2607032: 1–33. URL
Kakarot-Handtke, E. (2015b). Essentials of Constructive Heterodoxy: Money, Credit, Interest. SSRN Working Paper Series, 2569663: 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.

#1 For details of the big picture see cross-references Refutation of I=S,

‡ The notation for consumption expenditures has later been changed from C to EC.

For more about axiomatization see AXECquery.