Abstract
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.
Funder
Oesterreichische Nationalbank
Publisher
Springer Science and Business Media LLC
Subject
Economics and Econometrics,Business and International Management
Reference56 articles.
1. Agliari A, Commendatore P, Foroni I, Kubin I (2011) Border collision bifurcations in a footloose capital model with first nature firms. Comput Econ 38:349–366
2. Aramburo SA, Castaneda Acevedo JA, Moralesa YA (2012) Laboratory experiments in the system dynamics field. Syst Dyn Rev 28:94–106
3. Barnett WA, Serletis A, Serletis D (2015) Nonlinear and complex dynamics in economics. Macroecon Dyn 19:1749–1779
4. Bischi G, Lamantia F (2012) Routes to complexity induced by constraints in Cournot oligopoly games with linear reaction functions. Stud Nonlinear Dyn Econom 16:1–30
5. Bischi G, Lamantia F, Sushko I (2012) Border Collisopn Bifurcation in a simple oligopoly model with constraints. Int J Appl Math Stat 26:121–135