Factor Intensity reversal and Chaos I

We derive necessary and sufficient conditions for the occurrence of ergodic oscillations and geometric sensitivity in a two-sector model of economic growth with labor augmenting externalities. We transform the Euler equation into a first order backward first order equation. Factor intensity reversal is a necessary condition for the dynamics to be chaotic, both in the sense of ergodic oscillations and geometric sensitivity when utility is linear. Under reasonable assumptions on the economic fundamentals, we show that a necessary and sufficient condition for the occurrence of ergodic oscillations and geometric sensitivity is that the representative consumer is sufficiently patient.