Comment on John Legge on ‘Maths of competitive equilibrium’
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Standard economics is built upon this set of hardcore propositions, a.k.a. axioms: “HC1 economic agents have preferences over outcomes; HC2 agents individually optimize subject to constraints; HC3 agent choice is manifest in interrelated markets; HC4 agents have full relevant knowledge; HC5 observable outcomes are coordinated, and must be discussed with reference to equilibrium states.” (Weintraub 1985)
Marginalism follows logically from the green cheese behavioral assumption of constrained optimization HC2. From this follows ultimately the biggest ever idea of economics: supply-demand-equilibrium.
What can be said with certainty is that the whole set of Walrasian axioms is methodologically inadmissible. From this follows that supply-demand-equilibrium is proto-scientific garbage. Hence, the proof that the competitive equilibrium is unstable is for the birds because, to begin with, equilibrium is a NONENTITY.
What has to be done is to fully replace HC1/HC5, that is, one has to switch from microfoundations to macrofoundations. The paradigm shift is achieved as follows.
(A0) The objectively given and most elementary configuration of the (world-) 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.
These premises are certain, true, and primary, and therefore satisfy ALL methodological requirements. The macro axiom set contains NO NONENTITIES like utility, maximization, and equilibrium. For the graphical representation of the absolute formal minimum set, see link #1.
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. Note that the ray in the southeastern quadrant is NOT a linear production function; the ray tracks ANY underlying production function.
Under the conditions of (i) market-clearing and (ii) budget-balancing in each period the price is derived as P=W/R (1), i.e. the market-clearing price is in the most elementary case equal to unit wage costs. This is the elementary form of the Law of Supply and Demand.
The first thing to notice is that the real wage W/P is invariably equal to the productivity R according to (1). So, for the economy as a WHOLE, the marginal principle does NOT hold. The real wage is NOT equal to marginal productivity. This explodes the welfare theorems.
The fatal blunder of standard economics does NOT reside in the instability of equilibrium but in taking equilibrium into the axioms (see also #2). This is a petitio principii.
Egmont Kakarot-Handtke
#1 Wikimedia The pure consumption economy with market clearing and budget balancing
#2 Mathiness is NOT the problem — scientific incompetence is.
