We present a continuous 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 then appears : a non zero NRU is compatible with Pareto-optimality and conversely, full employment is compatible with sub-optimality. Nevertheless, contrary to the usual wisdom of job searching models, we show that a non-zero NRU is not necessary in order to get convergence towards an efficient rest-point. Indeed, each trade-and-production path of our price-quantity dynamics converges to some infinitesimal Pareto optimal point provided there are no unsold inventories at the limit.