Border collision bifurcations in boom and bust cycles

Boom and bust cycles are widely documented in the literature on industry
dynamics. Rigidities and delays in capacity adjustment in combination with bounded
rational behavior have been identified as central driving forces.We construct a model
that features only these two elements and we show that this is indeed sufficient to
reproduce some stylized facts of a boom and bust cycle. The bifurcation diagrams
summarizing the dynamic behavior reveal complex cycles and in particular also
abrupt changes in the nature of these cycles. We apply new insights from the mathematical
theory of piecewise smooth dynamic systems - in particular, results from
the theory of border collision bifurcations - and show that the very existence of borders
such as capacity constraints or nonnegativity constraints may lie behind abrupt
changes in the dynamic behavior of economic variables.