A Three-Region New Economic Geography Model in Discrete Time: Preliminary Results on Global Dynamics

In this paper, we deal with a three-region new economic geography model. The dynamic law which governs the migration of the mobile factor – in our context, “footloose” entrepreneurs (Commendatore et al. (Spat Econ Anal 3(1):115–141, 2008); Forslid and Ottaviano (J Econ Geogr 3:229–240, 2003)) – across three identical regions is formulated in discrete time. The resulting dynamical model belongs to the class of two-dimensional noninvertible maps (Mira et al. (1996) Chaotic dynamics in two-dimensional noninverible maps. World Scientific, Singapore). We present the local stability analysis of the map’s fixed points, corresponding to long term stationary equilibria of the economic system, and a preliminary study of its global stability properties. Our results show that the presence of a third region matters and that there are crucial differences with respect to the symmetric two-region footloose entrepreneurs model: firstly, when the manufacturing sector is absent in one of the three regions, stable asymmetric equilibria may emerge; secondly, we detect complex/strange two-dimensional attractors that cannot exist in two-region new economic geography models, which are typically one-dimensional; finally, we highlight the complex self-similar structure of the basins of attraction of some of the two-dimensional attractors.