On the equilibrium in a discrete-time Lucas Model

In this paper I study a discrete-time version of the Lucas model with the endogenous leisure but without physical capital. Under standard conditions I prove that the optimal human capital sequence is increasing. If the instantaneous utility function and the production function are Cobb-Douglas, I prove that the human capital sequence grow at a constant rate. I finish by studying the existence and the unicity of the equilibrium in the sense of Lucas or Romer.