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Global Characterization of the Weak Le Chatelier-Samuelson Principles and Its Applications to Economic Behavior, Preferences, and Utility-- "Embedding" Theorems

Sho-Ichiro Kusumoto

Abstract

Formal analogies between (dynamic) systems and economics have been pointed out by Paul A. Samuelson. The Le Chatelier-Samuelson principle, as a common property of extremum equilibrium (optimal) systems in respect to exogenous conditions, is such an analogy with theory of rational behavior and preference. The weak principle classifies a generalized weak principle. We shall argue that this generalized principle is "the economic integrability condition" itself in a broader sense and, going beyond that, asserts the existence of a maximal system so as for any affiliated systems, such as the equilibrium system, to be imbeddable therein. In consumer theory, this principle, with its identity with a maximal ordinal utility representation (without any regularity conditions), is implied by, or becomes equivalent for a non-satiable individual to, the (modified) strong axiom of revealed preference. The present characterization of the weak principles, making use of the mathematical results of R. Tyrrell Rockafellar [36, 37], completes Samuelson's general principle of economic method [40, pp. 22].