David R. Stockman () (Department of Economics,University of Delaware) Judy Kennedy () (Department of Mathematical Sciences,University of Delaware) Brian Raines () (Department of Mathematical Sciences,Baylor University)
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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.
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Paper provided by University of Delaware, Department of Economics in its series Working Papers with number
07-16.
Find related papers by JEL classification: C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Chari, V.V. & Kehoe, Patrick J., 1999.
"Optimal fiscal and monetary policy,"
Handbook of Macroeconomics,
in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 26, pages 1671-1745
Elsevier.
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