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An Extension of the Lechatelier Principle

Paul A. Samuelson

Abstract

The vague and often teleological LeChatelier principle of thermodynamics can be formulated as an unambiguous mathematical theorem concerned with elements of the definite matrices associated with maximizing problems. It thus has found many applications in economic theory: e.g., in the study of how the constraints imposed by rationing diminish the price elasticity of a maximizing demander. The present paper shows that the LeChatelier principle can also be extended to Leontief-Metzler-Mosak systems by virtue of the special properties of their off-diagonal elements, and even though they do not have the symmetric and definite matrices characteristic of a maximum problem. Hence, the principle may be applicable to analysis of input-output, multisectoral Keynesian multiplier systems, and general demand analysis involving gross substitutes.