STRATEGIC INTERGENERATIONAL BEQUESTS WITH STOCHASTIC CONVEX PRODUCTION

This note reconsiders the well-known model of strategic bequest/altrui stic growth, but with stochastic production satisfying a strong convex ity condition: The probability that the next stock exceeds any given l evel is concave in investment. Existence of a Markov-stationary equili brium consumption schedule, which is continuous and with all slopes in [0, 1], is established. Under smooth data and interiority assumptions , this schedule is differentiable, and marginal consumption is in (0, 1). This property allows for a rigorous and straightforward treatment of the equilibrium characterization problem.