Journal of Dynamics and Games doi:10.3934/jdg.2016015 c American Institute of Mathematical Sciences Volume 3, Number 3, July 2016 pp. 279–301 EVOLUTION AND JUMP IN A WALRASIAN FRAMEWORK Elvio Accinelli Facultad de Economa de la UASLP Aveninda Pintores S/N San Luis Potosi, 78280, M´ exico Enrique Covarrubias Facultad de Economa de la UASLP Aveninda Pintores S/N San Luis Potosi, 78280, M´ exico (Communicated by Athanasios Yannacopoulos) Abstract. Lower profit rates play an importan role in the evolution of an ownership private economy. We argue that if managers look to maximize profits rates, then the decision to change, to those branches, or technologies, that offer higher rates of profits, plays an important role in the characterization of economies. If managers choose to produce according to those technologies that promise higher profit rates, then along the time, the distribution of the firms over the set of available technologies change, and therefore the economic fundamentals change. Under conditions of imperfect information, the imitation of the most successful firms plays can a decisive role in deciding how to produce. Along a path of Walrasian equilibria, regular economies can become singular and if this occurs, big changes must be expected after decisions of the firms for the next period. 1. Introduction. The search for higher profit rates by owners or managers of firms, is undoubtedly an important engine for change in productivity and economic performance. This is an issue widely considered in modern literature, but so far, at least in the knowledge of the authors, has not been considered the role that this process plays in characterizing the evolution of the economies along an equilibrium path. This analysis is of no less importance given that possible changes in regular economies arising from small perturbations in its foundations are soft, but not so in the case of so-called singular economies, precisely these economies are character- ized by the possibility of abrupt changes in response to small perturbations in its foundations. 2010 Mathematics Subject Classification. D51, D21. Key words and phrases. Equilibrium path, regular and singular economies, profit rates. The authors are grateful for useful comments and suggestions from Mario Ibarburu and par- ticipants of seminars at the Economics Department of the Social Sciences School, Uruguay. Also, the authors would like to acknowledge the careful reading and suggestions made by an anony- mous referee, which allowed a substantial improvement of this work. The author wishes to thank CONACYT for the support given to this work through the project 167004 basic science.Facultad de Econom´ ıa, Universidad Aut´onoma de San Luis Potos´ ı. M´ exico. Facultad de Econom´ ıa, Uni- versidad Aut´ onoma de San Luis Potos´ ı. M´ exico. 279