Abstract: Many studies on present discounted value asset pricing model with heterogeneous agents have been developed afterwards the work of Brock and Hommes (1998). Only small part of the literature has been focused on the study of the evolution of agents’ wealth and its effect on price dynamics, by assuming Constant Relative Risk Aversion (CRRA) utility function. In particular, two classes of models in the CRRA framework are developed. The first class considers fixed proportions of agents. Differently, the second class of contributions allows agents to switch between different trading strategies. We observe that this last class of models makes the following simplified assumption: when agents switch from an old strategy to a new strategy, they agree to accept the average wealth level of agents belonging to the new group.

Following this research line, we develop a new model based upon the following more sophisticated assumption: all agents belonging to the same group agree to share their wealth whenever an agent gets in the group (or leaves it). As a consequence, the average wealth of agents belonging to each group has to be updated at each time. This leads the final system to a particular form, where at each time the average wealth of agents is defined by two different equations and, a priori, it is unknown what equation has to be used. We derive the resulting deterministic nonlinear dynamic system and analyze the model in order to investigate complicated dynamics and to consider the effects on wealth distribution among agents.