Location of Repository

## Consumption dynamics in general equilibrium : a characterisation when markets are incomplete\ud

### Abstract

We introduce a methodology for analysing infinite horizon economies with two agents, one good, and incomplete markets. We provide 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–so 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 (a) for most economies in which individual endowments are finite state time homogeneous Markov processes, the consumption of an agent who has a uniformly positive endowment cannot converge to zero and (b) the possibility that an agent vanishes 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. In sharp contrast to the results in the case studied by Sandroni (2000) and Blume and Easley (2006) where markets are complete, our results show that when markets are incomplete not only can the more patient agent (or the one with more accurate beliefs) be eliminated but there are situations in which neither agent is eliminated.\ud \u

Topics: HB
Publisher: University of Warwick
Year: 2009
OAI identifier: oai:wrap.warwick.ac.uk:3540

### Citations

1. (1996). An Asymptotic Theory of Bayesian Inference for Time Series,”
2. (1982). An Integration of Equilibrium Theory and Turnpike Theory,” Journ a lo fM a t h e m a t i c a lE c o n o m i c s
3. (1973). Another Note on the Borel-Cantelli Lemma and the Strong Law, with the Poisson approximation a by-product ,”
4. (1996). Asset Pricing with Heterogeneous Consumers,”
5. (1996). Debt Constraint and Equilibrium in Inﬁnite Horizon Economies with Incomplete Markets,”
6. (2000). Do Markets Favour Agents Able to Make Accurate Predictions,”
7. (2006). If You Are So Smart, Why Aren’t You Rich? Belief Selection
8. (2005). Market Selection when Markets Are Incomplete,”
9. (2004). Non-existence of Recursive Equilibria on Compact State Spaces when Markets are
10. (1980). On the Long Run Steady State in a Simple Dynamic Model of Equilibrium with Heterogeneous Households,”
11. (1969). Optimization by Vector Space Methods,”
12. (2004). Recursive Macroeconomic Theory,”
13. (1997). Stationary Ramsey Equilibria under
14. (2004). Testable Implications of Consumption-Based Asset Pricing Models with Incomplete Markets,”
15. (2008). The Dynamics of Eﬃc i e n tA s s e tT r a d i n gw i t h Heterogeneous Beliefs” mimeo
16. (1967). The Random Character of Stock Prices,”
17. (1953). Three Essays on the State of Economic Science,”
18. (1950). Uncertainty, Evolution, and Economic Theory,”
19. (1981). Utility over Time: The Homothetic Case,”

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.