On the significance of borders: the emergence of endogenous dynamics

Abstract

We propose a prototype model of market dynamics in which all functional relationships are linear. We take into account three borders, defined by linear functions, that are intrinsic to the economic reasoning: non-negativity of prices; downward rigidity of capacity (depreciation); and a capacity constraint for the production decision. Given the linear specification, the borders are the only source for the emerging of cyclical and more complex dynamics. In particular, we discuss centre bifurcations, border collision bifurcations and degenerate flip bifurcations—dynamic phenomena the occurrence of which are intimately related to the existence of borders.