Strategic intergenerational bequests with stochastic convex production

This note reconsiders the well-known model of strategic bequest* altruistic growth, but with stochastic production satisfying a strong convexity condition: The probability that the next stock exceeds any given level is concave in investment. Existence of a Markov-stationary equilibrium 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.