Archive

Volume 2, Number 6 / December issue 2016
Manuel Alberto M. Ferreira
A topological approach to consumer theory
Abstract

The presentation of an interesting application of mathematics in economics, more concretely of topological notions in economics: the formulation of the theory of consumer basic problem built on topology, is the main target of this work. This is made grounded on the concept of preferences relation and operationalized with optimization tools.
Keywords: Preferences relation, optimization, consumer theory, demand

Cite this article:
Manuel Alberto M. Ferreira. A topological approach to consumer theory. Acta Scientiae et Intellectus, 2(6)2016, 15-19.


REFERENCES

  1. BORCH, K. (1974), The Mathematical Theory of Insurance. Lexington, Mass.: Lexington Books, D.C. Heath and Co.
  2. BORCH; K. (1990), Economics of Insurance. Edited by Aase K. K. and Sandmo A., Amsterdam, North-Holland.
  3. CHAVAGLIA, J., FILIPE, J.A., FERREIRA, M.A.M. (2016), ”Neuroeconomics and reinforcement learning an exploratory analysis”, APLIMAT 2016-15th Conference on Applied Mathematics 2016, Proceedings 2016, Bratislava, 527-534.
  4. CYSNE, R.P., MOREIRA, H.A. (1997), Curso de Matemática para Economistas. São Paulo, Editora Atlas, S. A.
  5. DEBREU, G. (1959), Theory of value and axiomatic analysis of economic equilibrium. Monograph, 17, Cowles Foundation.
  6. FERREIRA, M.A.M. (2015), “The Hahn-Banach theorem in convex programming”, APLIMAT 2015-14th Conference on Applied Mathematics 2015, Proceedings 2015, Bratislava, 283-291.
  7. FERREIRA, M.A.M. (2015a), “The minimax theorem as Hahn-Banach theorem consequence”, Acta Scientiae et Intellectus, 1 (1), 58-65.
  8. FERREIRA, M.A.M., AMARAL, I. (2002), Cálculo Diferencial em R^(n ). Edições Sílabo-5ª Edição, Lisboa.
  9. FERREIRA, M. A. M., AMARAL, I. (2005), Integrais Múltiplos e Equações Diferenciais. Edições Sílabo-5ª Edição, Lisboa.
  10. FERREIRA, M.A.M., FILIPE, J.A. (2014), “Convex sets strict separation in Hilbert spaces”, Applied Mathematical Sciences, (61-64), 3155-3160. DOI: 10.12988/ams.2014.44257
  11. FERREIRA, M.A.M., FILIPE, J. A. (2015), “A ratio to evaluate harvest procedures management in an economic system where resources dynamics is ruled by an Ornstein-Uhlenbeck process”, Applied Mathematical Sciences, 9(25-28), 1213-1219. DOI: 10.12988/ams.2015. 410871
  12. FERREIRA, M. A. M., MATOS, M. C. (2014), “Convex sets strict separation in the minimax theorem”, Applied Mathematical Sciences, 8(33-36), 1781-1787. DOI: 10.12988/ams.2014.4271
  13. FERREIRA, M.A.M., ANDRADE, M., MATOS, M.C., FILIPE, J.A., COELHO, M. (2012), “Kuhn-Tucker’s Theorem-the Fundamental Result in Convex Programming Applied to Finance and Economic Sciences”, International Journal of Latest Trends in Finance & Economic Sciences, 2 (2), 111-116.
  14. FILIPE, J.A., FERREIRA, M.A.M. (2013), “Chaos in humanities and social sciences: An approach”, APLIMAT 2013-12th Conference on Applied Mathematics 2013, Proceedings 2013, Bratislava.
  15. NEUMÄRKER, B. (2007), “Neuroeconomics and the Economic Logic of Behavior”, Analyse & Kritik, 29, 60-85.
  16. ROBERTS, B., SCHULZE, D. L. (1973), Modern Mathematics and Economic Analysis. New York: W. W. Norton & Company, Inc.
  17. SIMONSEN, M.H. (1989), Análise convexa no R^n. Rio de Janeiro: EPGE, nº 145.