Economic Survival When Markets Are Incomplete

We consider an infinite horizon economy with incomplete markets with two agents and one good. We begin with an example in which an agent's equilibrium consumption is zero eventually with probability one even if she has correct beliefs and is marginally more patient. We then prove the following general result: if markets are effectively incomplete forever then on any equilibrium path on which some agent's consumption is bounded away from zero eventually, the other agent's consumption is zero eventually. This implies that either some agent vanishes, in that she consumes zero eventually, or the consumption of both agents is arbitrarily close to zero infinitely often. Later we show that the first possibility is a robust outcome since for a wide class of economies with incomplete markets, there are equilibria in which an agent's consumption is zero eventually with probability one even though she has correct beliefs as in the example. Our results mark a sharp contrast with the case studied by Sandroni (2000) and Blume and Easley (2004) where markets are complete.