Our model of a multi-sector infinite horizon economy contains uncertainty about future input-output possibilities and labor supply. Future utilities are not discounted. Even under perfect certainty a competitive program which satisfies some transversality condition (e.g., a bounded price system) does not have to be optimal. We prove that if the technology satisfies some concavity condition, a necessary and sufficient condition for optimality of any competitive program is that the expected present value of the inputs (or outputs) be bounded over time.