Judy Kennedy*
University of Delaware, Newark, DE, and Lamar University, Beaumont, TX, USA
The problem of backward dynamics in economics and inverse limits
We provide a framework for calculating expected utility in economic
models with chaotic equilibria and consequently a framework for ranking
chaos. Suppose that a dynamic economic model's equilibria correspond
to orbits generated by a chaotic dynamical system f from a compact metric
space X to itself, where f is continuous. The map could represent the forward dynamics or the backward dynamics. If f represents the forward/backward dynamics, the set of equilibria forms forms a direct/inverse limit space. We use an f-invariant measure on X to induce a measure on the direct/inverse limit space and show that this induced measure is invariant relative to the shift operator. Moreover, we show that if the f-invariant measure is a natural invariant measure, then the induced measure on the direct/inverse limit space will also be a natural invariant measure. We utilize this framework in the cash-in-advance model of money where f is the backward map to calculate expected utility when equilibria are chaotic.
* This is a joint work with Brian Raines, David R. Stockman, James A. Yorke.
