Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 908451, 9 pages
Research Article

Endogenous Reactivity in a Dynamic Model of Consumer’s Choice

1Department of Economics, University of Milano-Bicocca, Piazza dell'Ateneo Nuovo 1, 20126 Milano, Italy
2Department of Economics and Quantitative Methods, University of Pavia, Via S. Felice 5, 27100 Pavia, Italy

Received 16 June 2011; Revised 10 December 2011; Accepted 12 December 2011

Academic Editor: Vimal Singh

Copyright © 2012 Ahmad K. Naimzada and Fabio Tramontana. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We move from a boundedly rational consumer model (Naimzada and Tramontana, 2008, 2010) characterized by a gradient-like decisional process in which, under particular parameters conditions, the asymptotical convergence to the optimal choice does not happen but it does under a least squared learning mechanism. In the present paper, we prove that even a less sophisticated learning mechanism leads to convergence to the rational choice and also prove that convergence is ensured when both learning mechanisms are available. The stability results that we obtain give more strength to the rational behavior assumption of the original model; in fact, the less demanding is the learning mechanism ensuring convergence to the rational behavior, the higher is the probability that even quite naive consumers will learn the composition of their optimum consumption bundles.