Structural Axioms Research Articles

Walras's Law of Markets as Special Case of the General Triangle Theorem: A Laconic Proof

From the set of the first three structural axioms follows the Period Core theorem. It asserts that the product of the key ratios, which characterize the firm, the market outcome, and the income distribution, is always equal to unity.The theorem contains only unit-free variables, is testable in principle, and involves no behavioral assumptions. The differentiated Period Core theorem applies to an arbitrary number of firms. Therefrom Walras’s Law can be derived without recourse to demand and supply functions or the notion of equilibrium. It is shown that the familiar interpretation is methodologically illegitimate.

Settling the Theory of Saving

There is no way around it: each theory rests on a tiny set of foundational propositions. Standard economics rests on behavioral axioms. After a long intellectual detour it should be clear by now that behavioral axioms are the wrong formal departure point. Being beyond repair, they have to be replaced by objective structural axioms. This paper deals with saving and its relation to investment and profit. It starts from the fact that there is no such thing as a real economy. Hence economic phenomena are only explicable as the outcome of the interaction of real and nominal variables.

Make a Bubble, Take a Free Lunch, Break a Bank

Standard economics is known to be incapable of integrating the real and the monetary sphere. The ultimate reason is that the whole theoretical edifice is built upon a set of behavioral axioms. Therefore, the formal starting point is moved to structural axioms. This makes it possible to formally track the complete process of value creation and destruction in the asset market and its consequences for the household and business sector. From the set of structural axioms emerge the well-known phenomena of a bubble from free lunches through appreciation to defaults due to a lack of potential next buyers.

Income Distribution, Profit, and Real Shares

This paper clarifies first the nature and significance of financial profit by applying the structural axiom set as consistent point of departure. As a crucial result the fundamental theorem of income distribution emerges. It states: profit is no factor income. Since the individual firm is blind to this structural fact it subjectively interprets profit as some kind of reward. As a matter of fact, firms do not ‘make’ profit, they only redistribute it among themselves. With profit consistently defined it is possible to determine the nominal and real shares of the elementary income categories wage income and distributed profit.

Primary and Secondary Markets

The analytical starting point determines the course of a theoretical investigation and, ultimately, the productiveness of an approach. The classics took production and accumulation as their point of departure; the neoclassics, exchange. Exchange implies behavioral assumptions and notions like rationality, optimization, and equilibrium. It is widely recognized that this approach has led into a cul-de-sac. To change a theory means to change its premises; or, in Keynes's words, to throw over the axioms. The present paper swaps the standard behavioral axioms for structural axioms and applies the latter to the analysis of the emergence of secondary markets from the flow part of the economy. Real and nominal residuals at first give rise to the accumulation of the stock of money and the stock of commodities. These stocks constitute the demand-and-supply side of secondary markets. The pricing in these markets is different from the pricing in the primary markets. Realized appreciation in the secondary markets is different from income or profit. To treat primary and secondary markets alike is therefore a category mistake. Vice versa, to take a set of objective propositions as the analytical starting point yields a comprehensive and consistent theory of market exchange and valuation.

Trade, Productivity, Income, and Profit: The Comparative Advantage of Structural Axiomatic Analysis

The classical case of comparative advantage is put into a new formal framework, that is, the behavioral axioms of standard economics are replaced by a set of structural axioms. This enables a comprehensive analysis that takes the effects on income and profit explicitly into account. The axioms in combination with the conditions of market clearing, budget balancing and initial zero profit determine all measurable variables objectively. It is the purpose of the present paper to formally restate the notion of comparative advantage and to ascertain whether this leads to a well-grounded new perspective on this time-honored doctrine.

The Value of Water and Diamonds: Back to Square One

Taking the water–diamond paradox as a time-honored challenge, at first the structural value theorem is derived from the set of structural axioms. This enables a reevaluation of classical and neoclassical conceptions. Ricardo realized that there are two entirely different kinds of markets but excluded the secondary markets by defining commodity in a restricted sense. Walras’s markets are secondary markets by construction. Primary markets thereby drop from sight. Since secondary markets presuppose primary markets the marginalistic approach is hanging in the air. The structural axiomatic approach demonstrates that the pricing in primary and secondary markets depends on different principles.

Matter Matters: Productivity, Profit, and Non-Marginal Factor Prices

Tastes and technology are the ultimate givens of standard economics. Their interaction is mediated by the marginal principle. This approach is unsuitable to explain the nature and magnitude of overall profit and its distribution within the business sector. The present paper therefore takes a quite different analytical route. The standard behavioral axioms are replaced by objective structural axioms and the standard production function is replaced by a sequential production function. From this new formal basis two exemplary factor prices, the product price, and the real wage are derived under the conditions of market clearing and equal profit ratios.

The Wine Maker’s Business and the Logical Origin of Interest in the Monetary Economy

Any serious alternative to the standard approach requires a distinct axiomatic foundation. The crucial point is not axiomatization per se but the real world content of axioms. The purpose of the present paper is to make the implications of the objective structural axiom set concerning the relation of profit, money, the nominal/real rate of interest, and the time structure of production explicit and to contrast them with the familiar conceptions.

When Ricardo Saw Profit, He Called it Rent: On the Vice of Parochial Realism

According to Ricardo the principal problem in Political Economy is to determine the laws which regulate the distribution of profits, rents and wages. Ricardo determined the respective shares in real terms and to this end invented an engine of analysis that became paradigmatic. The present paper applies a consistent real and monetary analysis, which is based on a set of objective structural axioms, and contrasts the results with Ricardo’s approach. The general result is that real analysis misses economic reality. The specific result is that rent is a misnomer for the distributed profit of the land owning firm.

Increasing Returns and Stability

Increasing returns are an incontrovertible fact since Adam Smith hailed them as the very originators of wealth, yet they play havoc with general equilibrium. They fit, in marked contrast, nicely into the structural axiomatic framework. This indicates that it is worthwhile to replace the behavioral axioms of standard economics by objective structural axioms. These are in the present paper applied to the question of how increasing returns affect the systemic interrelations in the pure consumption economy. To invite a reality check the logical implications of the structural employment equation are set in relation to three well-known statistical relationships.

Primary and Secondary Markets

The present paper swaps the standard behavioral axioms for structural axioms and applies the latter to the analysis of the emergence of secondary markets from the flow part of the economy. Real and nominal residuals at first give rise to the accumulation of the stock of money and the stock of commodities. This stocks constitute the demand and supply side of secondary markets. The pricing in these markets is different from the pricing in the primary markets. Winnings are different from income or profits. The emergence of secondary markets implies that the plans of households and firms are mutually incompatible.

Squaring the Investment Cycle

The present paper replaces the standard behavioral axioms by structural axioms and applies these to the analysis of the accumulation and decumulation of capital. This yields a coherent view of the interrelations of real and nominal saving–investment, of profit–loss, of money–credit, and of internal–external financing. The main result is that asymmetric growth is indispensable for the viability of the market system.

Uniform Profit Ratios

The equalization of profit rates as the outcome of free competition is one of the oldest tenets in theoretical economics. Being intuitively convincing its premises and implications, though, are not well defined. As Walras put it: ‘To state a theory is one thing; to prove it is another.’ First of all a consistent concept of profit is required. In the present paper the structural axiom set is taken as premise. Thereof the determinants of profit and the profit ratio follow. This makes it possible to definitively state the conditions for uniform profit ratios in a hierarchical market structure.

Unemployment Out of Nowhere

Unemployment is usually explained with reference to the equilibrium of supply and demand in the labour market. This approach rests on specific behavioral assumptions that are formally expressed as axioms. The standard set of axioms is replaced in the present paper by a set of structural axioms. This approach yields the objective determinants of employment. They consist of effective demand, the actual outcome of price formation, structural stress as determined by the heterogeneity within the business sector and the income distribution. Sudden changes of employment are effected by latent relative switchers that are hard to spot empirically.

Exploitation and its Unintended Outcomes: An Axiomatic View of Marx's Surplus Value

The present paper scrutinizes the logical foundation of Marx’s dialectic analysis of the evolving money economy. The minimalistic frame of reference is thereby given with the set of structural axioms. It turns out, first, that the commonplace notion of exploitation has to be replaced by crossover exploitation among capitalists and workers; second, that the concept of surplus value cannot explain the existence and magnitude of overall profits; finally, that the shares of output are determined in the spheres of income and expenditure and not, as classical, Marxian and neoclassical economists unanimously maintain, in the sphere of production.

Properties of an Economy Without Human Beings

Standard economics starts with behavioral axioms and arrives at conclusions about the equilibrium properties of the economy as a whole at point t. The present paper employs objective structural axioms and random changes in order to determine the conditions for market clearing and budget balancing in the pure consumption economy until the limit t → ∞. From the conditions of stochastic supersymmetry six simple behavioral rules are derived that guarantee the desired outcome. These rules contrast with actual behavior and this explains why the plans and expectations of economic man are many times frustrated.

The Coherency of Money, Profit, Price, and Distribution

When anything goes and nothing fits together this can be euphemized as pluralism. Lacking a common point of reference, discussions between various schools of economic thought proceed in the ‘hyperspace of assumptions’ (Mc- Closkey). The incoherency of perspectives is due to self-chosen fundamental assumptions. The present paper submits three objective structural axioms as a minimalist formal core that is neutral with regard to different assumptions about human behavior.

Schumpeter and the Essence of Profit

Schumpeter had a clear vision of the developing economy, but he did not formalize it. The quest for a germane formal basis is in the following guided by the general question: what is the minimum set of foundational propositions for a consistent reconstruction of the evolving money economy? We start with three structural axioms. The claim of generality entails that it should be possible to free Schumpeter’s approach from its irksomeWalrasian legacy and to give a consistent formal account of the elementary circular flow that served him as a backdrop for the analysis of the entrepreneur-driven market system.

The Pure Logic of Value, Profit, Interest

Standard economic models are based on axioms that epitomize the fundamental behavioral assumptions. This approach is not conductive to convincing results. The suggested change of perspective is guided by the question: what is the minimum set of propositions for the consistent reconstruction of the evolving money economy? We start with three structural axioms and determine their real world implications. The claim of generality entails that it should be possible to demonstrate that well-understood parts of theoretical economics fit consistently into the structural axiomatic framework. We focus here on the classical theory of value.