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The LeChatelier principle, in the form introduced into economics by Paul A. Samuelson, asserts that, at a point of long-run equilibrium, the derivative of long-run compensated demand with respect to own price is larger in magnitude than the derivative of short-run compensated demand. The authors introduce an extended LeChatelier principle that applies also to large price changes and to uncompensated demand as well as to a wide range of concave and nonconcave maximization problems outside the scope of demand theory. This extension also clarifies the intuitive basis of the principle. Copyright 1996 by American Economic Association.