Global analysis and focal points in a model with boundedly rational consumers

In this paper we present a contribution toward a dynamic theory of the consumer. Canonical economic theory assumes a perfectly rational agent that acts according to optimization principles of a utility function subject to budget constraints. Here we propose a two-dimensional discrete dynamical system that describes the choice problem of a consumer under the assumption of bounded rationality. The map representing this adaptive process is characterized by the presence of a denominator that can vanish. We use recent results on the global bifurcations of this kind of maps in order to explain the coexistence of different attractors and the structure of the corresponding basins of attraction. The stationary equilibria of the map represent the rational choices of the consumer in the static setting, i.e. solutions of the utility maximization problem under budget constraints. We use geometric and numerical methods to study the problem of coexistence of different attractors and the related problem of the basins of attraction and their global bifurcations