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/
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.:
- Michener, Ronald & Ravikumar, B., 1998. "Chaotic dynamics in a cash-in-advance economy," Journal of Economic Dynamics and Control, Elsevier, vol. 22(7), pages 1117-1137, May.
- 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
- Robert E. Lucas Jr. & Nancy L. Stokey, 1984.
"Money and Interest in Cash-In-Advance Economy,"
628, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- David Stockman & Judy Kennedy & James Yorke, 2006. "Inverse Limits and Models with Backward Dynamics," Working Papers 06-12, University of Delaware, Department of Economics.
- Kennedy, Judy A. & Stockman, David R., 2008. "Chaotic equilibria in models with backward dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 939-955, March.
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