Bifurcation Structure in a Model of Monetary Dynamics with Two Kink Points

In the present paper we consider the discrete version of the Sargent & Wallace (Econometrica 41:1043–8, 1973) model with perfect foresight. We assume a piecewise linear money demand function, decreasing over a ‘normal’ range (−aR,aL) and constant when the expected inflation rate is beyond these bounds. In this way we obtain that the monetary dynamics are described by a one-dimensional map having two kink points. We show that when the slope of the money demand function (μ) is sufficiently large in absolute value and the speed of adjustment of the price to the market disequilibrium (α) is smaller than 1 either cycles of any period or chaotic dynamics may be generated by the model. The description of the bifurcation structure of the (α,μ) parameter plane is given.