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Andreas Röthig, Willi Semmler and Peter Flaschel

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Ingo Barens, Peter Flaschel, Florian Hartmann and Andreas Röthig

We show that the Kaldor (1940) trade cycle mechanism can be meaningfully applied to the market for residential housing space, since the demand for houses may be positively related to the housing price in a mid-range price domain, while it is downward sloping for house prices sufficiently small as well as sufficiently large. Confronted with the current supply of houses this gives rise to multiple equilibria. Then the employed nonlinear house demand schedule is coupled with backward-looking house price expectations and a planar dynamics is obtained with the same range of model-consistent expectations equilibria as in the partial situation studied beforehand. The model however is not dependent on the backward oriented expectation scheme, but also applies to the case of myopic perfect foresight. The nonlinear demand function for houses in connection with changes in the housing stock initiates sudden reversals from booms into busts and vice versa, which from a mathematical point of view give locally rise to fold catastrophes at the bifurcation points, with the dynamics being described by relaxation oscillations from the global perspective.