The Random Two-Sector Rss Model : On Discounted Optimal Growth Without Ramsey-Euler Conditions1

The fact that consumption and investment goods are perfect substitutes in discounted stochastic optimal growth theory, as represented by a one-sector neoclassical model, results in a smooth production-possibility-frontier (PPF) for which first-order Ramsey-Euler conditions can be fully exploited. The two-sector discrete-time deterministic (RSS) model due to Robinson-Solow-Srinivasan yields a kinked PPF, and yields a theory in which not only optimal cyclical and chaotic trajectories emerge but an “anything goes” theorem can be proved. In this paper, we show that uncertainty fully subdues the veritable plethora of the deterministic results: we show the existence and uniqueness of the steady state measure, and its asymptotic stability, and also present comparativestatic results that invoke the “supermodularity” and “increasing-differences property” of Veinott-Topkis-Milgrom-Shannon. The methodological novelty of this contribution to the theory developed by Brock-Mirman lies in the consideration of non-smooth settings where Ramsey-Euler first-order conditions cannot be invoked. (144 words) JEL Classification : C60, D90, O21