Munich Personal RePEc Archive

Properties of critical points and operators in economics

Chichilnisky, Graciela and Kalman, P.J. (1977): Properties of critical points and operators in economics. Published in: Journal of Mathematical Analysis and Applications , Vol. 57, No. no. 2 (February 1977): pp. 340-349.


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The study of the local characteristics of equilibrium positions generated by the constrained maximization of some criterion functions (such as utility, profit, cost, etc.) goes back to Antonelli's paper [2] of 1886. Certain local properties have been proved to be particularly fruitful for economic theory since the early works of Slutsky, Hicks, and Samuelson [9]; they have been formulated in terms of a matrix of "compensated" terms and they concern the properties of partial derivatives of the demand function in some neighborhood of the equilibrium. We now discuss this matrix and its applications.

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