Natural rate of unemployment and efficiency: A dynamic analysis with flexible prices and increasing returns

We present a continous time non tatonnement process for frictionless and perfectly competitive markets with (possibly non convex) production, where the natural rate of unemployment (NRU) emerges as the asymptotic value of unemployment.  Consumers and producers are myopic and repeatedly participate in Mertens' (2003) limit-price mechanism.  We show that underemployment and unsold inventories can survive along the solution paths of our dynamics - the hallmark of the failure of Say's law.  The following paradox appears: A nonzero NRU is compatible with Pareto optimality; conversely, full employment is compatible with sub optimality.  Nevertheless, each trade and production path of our price quantity dynamics converges to some infinitesimal Pareto optimal point as long as there are no unsold inventories at the limit.