Inverse Limits and Models with Backward Dynamics

David Stockman, Judy Kennedy () and James Yorke
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Judy Kennedy: Department of Mathematics,University of Delaware
James Yorke: Institute for Physical Science and Technology, University of Maryland

No 06-12, Working Papers from University of Delaware, Department of Economics

Abstract: Some economic models like the cash-in-advance model of money have the property that the dynamical system characterizing equilibria is multi-valued going forward in time, but single-valued going backward in time, i.e., the model has backward dynamics. In this paper, we apply the theory of inverse limits to characterize topologically the set of equilibria in a dynamic economic model with this property. We show that such techniques are particularly well-suited for analyzing the dynamics going forward in time even though the dynamics are multi-valued in this direction. In particular, we analyze the inverse limit of the cash-in-advance model of money and illustrate how information about the inverse limit is useful for detecting or ruling out complicated dynamics.

Keywords: backward dynamics; chaos; inverse limits; continuum theory; cash-in advance (search for similar items in EconPapers)
JEL-codes: C6 E3 E4 (search for similar items in EconPapers)
Pages: 38 pages
Date: 2006
New Economics Papers: this item is included in nep-cba and nep-mac
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Forthcoming in Topology and Its Applications.

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