Quasi-Periodic Motions in a Polarized Overlapping Generations Model with Technology Choice

This paper was previously circulated under the title “Polarization and Permanent Fluctuations: Quasi-Periodic Motions in a Two-Class OLG Model.”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 (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 with- out 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 our model