Quasi-periodic motions in a two-class economy with technology choice: an extreme case

This paper constructs a simple overlapping generations (OLG) model with the working and capitalist classes and two types of production technologies. The behavior of agents belonging to the working class is basically the same as that in the standard Diamond (Am Econ Rev 55:1126–1150, 1965) type OLG model, whereas agents belonging to the capitalist class face two available technologies, select the one with a higher return on capital, and bequeath their assets to the next generation without supplying labor. Using techniques concerning the circle map in dynamical systems theory, we show that in an extreme case in which one technology is linear and the other is of the Leontief type, the economy exhibits bounded, non-periodic but non-chaotic motions for a large set of parameter values. We provide explicit formulas for the rotation number and the absolutely continuous invariant probability measure of the model.