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. 340349.

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Abstract
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.
Item Type:  MPRA Paper 

Original Title:  Properties of critical points and operators in economics 
Language:  English 
Keywords:  Antononelli; Slutsky; Hicks; Samuelson; equilibrium; contstrained maximization; maximization; matrix; compensated; economic theory; SlutskyHicksSamuelson equation; utility analysis; demand; optimization; topological; topology 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C68  Computable General Equilibrium Models B  History of Economic Thought, Methodology, and Heterodox Approaches > B1  History of Economic Thought through 1925 C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61  Optimization Techniques ; Programming Models ; Dynamic Analysis 
Item ID:  7976 
Depositing User:  Graciela Chichilnisky 
Date Deposited:  29. Mar 2008 07:02 
Last Modified:  25. Feb 2015 03:08 
References:  R. Abraham and J. Robbin, "Transversal Mappings and Flows," Benjamin, New York, 1967. G. B. Antonelli, Silla teoria matematica della economics politica Pisa, 1886. Reprinted in Giorn, Economista e Economica,, Nuova Ser. 10 (1951). K. J. Arrow and F. H. Hahn, "General Competitive Analysis," HoldernDay, San Francisco, 1971. G. Chichilnisky and P. J. Kalman, Comparative statics of less neoclassical agents, International Economic Review, 1978. G. Debreu, Economics with a finite set of equilibria, Econometrics 38 (1970). P. J. Kalman, R. Dusansky, and B. A. Wicksthom, On the major Slutsky properties when money is the sole medium of exchange, International Economics Review (1974). P. J. Kalman and M. Intriligator, Generalized comparative statics with applications to consumer theory and producer theory, International Economics Review 14 (1973). M. Peixoro, On an approximation theorem of Kupka and Smale, J. Differential Equations 3 (1966). P. A. Samuelson, "The Foundations of Economic Analysis," Harvard University Press, Cambridge, Mass., 1947. S. Smale, Global analysis and economics, IIA, J. Math. Econ. 1 (1974). 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/7976 