Economy, geometry and dynamics
Abstract
The present work tries to show how the differential geometry and the dynamic systems allow to understand, explain and advance in the study of relevant economic problems. We try to convince the reader that a formally developed theory may not be very far from the most immediate practice and that, on the other hand, the problems that everyday reality poses to us can be an excellent pretext to devote ourselves to the most abstract theory. The article is intended for a wide audience, particularly those interested in Economic Theory and particularly in Mathematical Economics. However, we hope that mathematicians and economists from different areas will find in it an incentive for future studies on the subject. We hope that the declared objective is not far from the results achieved.
Keywords
Walarasian equilibria, dynamics of the auctioneer, equilibrium manifold
References
- Arrow, J. y F. Hahn (1971). General competitive analysis San Francisen, Holden-Day.
- Balasko, Y. (2009). The equilibrium manifold: postmodern developments in the theory of general economic equilibrium. Arne Ryde Memorial Lectures, MIT Press.
- Balasko, Y. (1988). Foundations of the Theory of General Equilibrium. Mit Pres.
- Debreu G. (1959). Theory of Value: An Axiomatic Analysis of Economic Equilibrium. Cowles Foundation Monographs Series.
- Debreu G. (1970), "Economies with a Finite Set of Equilibria", Econometrica, 38/3 pp. 387-392.
- Hicks, J. (1939). "The Foundations of Welfare Economics" Economic Journal, vol. 49/196, pp. 696-712.
- Mantel, Rolf (1974), "On the characterization of aggregate excess demand", Journal of Economic Theory, núm., 7, pp. 348-353.
- Samuelson, P. A. (1947), Foundations of Economic Analysis. Harvard University Press, enlarged ed. 1983.
- Samuelson, P. A. (1944). "The relation between Hicksian stability and true dynamic stability", Econometrica 12.
- Smith, A. Teora de los sentimientos morales (1759), ed, conmemorativa 70 Aniversario, México, 2004. ISBN 968-16-7339-5.
- Varian, H. R. (1992). "Microeconomic Analysis". W. W. Norton & Co Inc (Np), ed. 3a.
- Walras, L. (1874). Eléments d'Aconomie politique pure, ou théorie de la richesse sociale. Traducción de Julio Segura. Madrid. Alianza Editorial, 1987.