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Expected Utility in Models with Chaos

  • 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)

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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File URL: http://graduate.lerner.udel.edu/sites/default/files/ECON/PDFs/RePEc/dlw/WorkingPapers/2007/UDWP2007-16.pdf
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Paper provided by University of Delaware, Department of Economics in its series Working Papers with number 07-16.

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Length: 29 pages
Date of creation: Oct 2007
Date of revision:
Handle: RePEc:dlw:wpaper:07-16.
Contact details of provider: Postal: Purnell Hall, Newark, Delaware 19716
Phone: (302) 831-2565
Fax: (302) 831-6968
Web page: http://www.lerner.udel.edu/departments/economics/department-economics/

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  1. 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.
  2. V. V. Chari & Patrick J. Kehoe, 1998. "Optimal fiscal and monetary policy," Staff Report 251, Federal Reserve Bank of Minneapolis.
  3. Robert E. Lucas Jr. & Nancy L. Stokey, 1984. "Money and Interest in Cash-In-Advance Economy," Discussion Papers 628, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. 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.
  5. A. Meltzer & Peter Ordeshook & Thomas Romer, 1982. "Introduction," Public Choice, Springer, vol. 39(1), pages 1-3, January.
  6. 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.
  7. David Stockman & Judy Kennedy & James Yorke, 2006. "Inverse Limits and Models with Backward Dynamics," Working Papers 06-12, University of Delaware, Department of Economics.
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