Local and global analysis of speculative housing market with production lag

We extend the model of Dieci and Westerhoff (2012) where the authors analyse a speculative housing market populated by heterogenous interacting agents described by a two dimensional nonlinear discrete time dynamical system. They show the emergence of complicated dynamics trough the occurrence of bifurcations for particular parameter combinations. We enlarge their model in several ways. To one hand, we introduce time lag in the supply side and we consider two new scenarios characterised by agents expectations formation. First, naive expectations instead of perfect foresight are considered, while in the second scenario we study a mix between the model of Dieci and Westerhoff (2012) and the one we propose. As a consequence, we, analytically and numerically, explain the appearance of instability in the housing market providing conditions on the parameters that lead to a bifurcation. To the other hand, thanks to further numerical simulations, we conduct a global analysis providing the structure of the basin of attractions of the map showing coexistence of attractors.