Department of Economics Working Papers,
Vienna University of Economics and Business, Department of Economics

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, which 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.

Keywords: capacity constraint, depreciation constraint, nonnegativity constraint, piecewise smooth system, border collision bifurcation, centre bifurcation

JEL-codes: C61; C63 August 2018

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