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Discontinuous Initial Value Problems for Funtional Differential-Algebraic Equations of Mixed Type

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  • Hippolyte D'Albis

    ()
    (EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris, CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Emmanuelle Augeraud-Véron

    ()
    (MIA - Mathématiques, Image et Applications - Université de La Rochelle : EA3165)

  • Hermen Jan Hupkes

    ()
    (University of Missouri - Columbia - Mathematics Department)

Abstract

We study the well-posedness of initial value problems for nonlinear functional differential-algebraic equations of mixed type. We are interested in solutions to such problems that admit a single jump discontinuity at time zero. We focus specially on the question whether unstable equilibria can be stabilized by appropriately choosing the size of the jump discontinuity. We illustrate our techniques by analytically studying an economic model for the interplay between inflation and interest rates. In particular, we investigate under which circumstances the central bank can prevent runaway inflation by appropriately hiking the interest rate.

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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00717412.

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Date of creation: Jun 2012
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Handle: RePEc:hal:cesptp:halshs-00717412

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00717412
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Related research

Keywords: Functional differential equations; advanced and retarded arguments; interest rates; inflation rates; initial value problems; indeterminacy; impulsive equations.;

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  1. Nourry, C. & Vendetti, A., 1998. "Determinacy of Equilibrium in an Overlapping Generations Model with Heterogenous Agents," G.R.E.Q.A.M. 98a02, Universite Aix-Marseille III.
  2. Jess Benhabib & Stephanie Schmitt-Grohe & Martin Uribe, 1998. "The perils of Taylor Rules," Departmental Working Papers 199831, Rutgers University, Department of Economics.
  3. GRANDMONT, Jean-Michel & PINTUS, Patrick & de VILDER, Robin, 1997. "Capital-labor substitution and competitive nonlinear endogenous business cycles," CORE Discussion Papers 1997087, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Benhabib, Jess, 2004. "Interest Rate Policy in Continuous Time with Discrete Delays," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(1), pages 1-15, February.
  5. Lloyd-Braga, Teresa & Nourry, Carine & Venditti, Alain, 2007. "Indeterminacy in dynamic models: When Diamond meets Ramsey," Journal of Economic Theory, Elsevier, vol. 134(1), pages 513-536, May.
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