Expected Utility in Models with Chaos
AbstractIn 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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Bibliographic InfoPaper provided by University of Delaware, Department of Economics in its series Working Papers with number 07-16.
Length: 29 pages
Date of creation: Oct 2007
Date of revision:
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Web page: http://www.lerner.udel.edu/departments/economics/department-economics/
More information through EDIRC
chaos; inverse limits; direct limits; natural invariant measure; cash-in-advance;
Find related papers by JEL classification:
- C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
- E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
- E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
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.:
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- Medio, Alfredo & Raines, Brian, 2007. "Backward dynamics in economics. The inverse limit approach," Journal of Economic Dynamics and Control, Elsevier, vol. 31(5), pages 1633-1671, May.
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