Local convergence properties of a cobweb model with rationally heterogeneous expectations

Abstract

This paper gives local stability conditions for convergence of the price dynamics in a cobweb model with rationally heterogeneous expectations, generalizing the example of Brock and Hommes (1997). When agents choose between rational, naive, and adaptive beliefs, the steady state may be locally asymptotically stable if the adaptive predictor places enough weight on past prices and is costless. If adaptive expectations are sufficiently more costly than naive expectations the steady state will be an unstable saddle point. Our results imply that adding a choice can stabilize a system which is unstable under the Brock and Hommes model. These results illustrate how the critical parameter that governs stability is dependent on the array of available predictors.