Risky educational investment and the dynamics of inequality

We modify the model developed by Ray, D. ( 2006), On the dynamics of inequality, Economic Theory in the sense that the technology for education is convex but involves uncertainty. More specifically, we assume that the probability of successful education is an increasing an concave function of the amount of educational investment. It is shown that equilibrium paths are characterized as the solutions of a discrete-time dynamical system, that under generic parameter constellations the steady states of this dynamical system are isolated, and that the equilibrium paths may exhibit damped oscillations around a steady state. All of these findings are in contrast to the results derived by Ray, D. (2006), On the dynamics of inequality, Economic Theory for the model with a deterministic but non-convex education technology.