Expected Utility in Models with Chaos

David R. Stockman (), Judy Kennedy () and Brian Raines ()
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Judy Kennedy: Department of Mathematical Sciences,University of Delaware
Brian Raines: Department of Mathematical Sciences,Baylor University

No 07-16, Working Papers from University of Delaware, Department of Economics

Abstract: In this paper, we provide a framework for calculating expected utility in 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 : X ! X where X is a compact metric space and f is continuous. The map f could represent the forward dynamics xt+1 = f(xt) or the backward dynamics xt = f(xt+1). If f represents the forward/backward dynamics, the set of equilibria forms a direct/inverse limit space. We use a natural f-invariant measure on X to induce a measure on the direct/inverse limit space and show that this induced measure is a natural ¾-invariant measure where ¾ is the shift operator. 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.

Keywords: chaos; inverse limits; direct limits; natural invariant measure; cash-in-advance (search for similar items in EconPapers)
JEL-codes: C6 E3 E4 (search for similar items in EconPapers)
Date: 2007-10
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