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

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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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File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2012/12043.pdf
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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne in its series Documents de travail du Centre d'Economie de la Sorbonne with number 12043.

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Length: 57 pages
Date of creation: Jun 2012
Date of revision:
Handle: RePEc:mse:cesdoc:12043

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

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References

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  1. Benhabib, Jess, 2004. "Interest Rate Policy in Continuous Time with Discrete Delays," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 36(1), pages 1-15, February.
  2. Grandmont, Jean-Michel & Pintus, Patrick & de Vilder, Robin, 1998. "Capital-Labor Substitution and Competitive Nonlinear Endogenous Business Cycles," Journal of Economic Theory, Elsevier, vol. 80(1), pages 14-59, May.
  3. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, Elsevier, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
  4. Lloyd-Braga, Teresa & Nourry, Carine & Venditti, Alain, 2005. "Indeterminacy in Dynamic Models: When Diamond Meets Ramsey," CEPR Discussion Papers 5255, C.E.P.R. Discussion Papers.
  5. Nourry, C. & Vendetti, A., 1998. "Determinacy of Equilibrium in an Overlapping Generations Model with Heterogenous Agents," G.R.E.Q.A.M., Universite Aix-Marseille III 98a02, Universite Aix-Marseille III.
  6. Benhabib, Jess & Schmitt-Grohe, Stephanie & Uribe, Martin, 2001. "The Perils of Taylor Rules," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 40-69, January.
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Cited by:
  1. repec:hal:journl:halshs-00786419 is not listed on IDEAS
  2. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Herman Jan, 2014. "Stability and Determinacy Conditions for Mixed-type Functional Differential Equations," MPRA Paper 56600, University Library of Munich, Germany.
  3. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2013. "Bounded Interest Rate Feedback Rules in Continuous-Time," MPRA Paper 45424, University Library of Munich, Germany.
  4. Emmanuelle Augeraud-Veron & Mauro Bambi, 2012. "Does habit formation always increase the agents' desire to smooth consumption?," Discussion Papers 12/12, Department of Economics, University of York.
  5. d’Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Multiple solutions in systems of functional differential equations," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 50-56.
  6. Hippolyte D'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Backward- versus Forward-Looking Feedback Interest Rate Rules," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00721289, HAL.
  7. repec:hal:journl:halshs-00721289 is not listed on IDEAS
  8. Emmanuelle AUGERAUD-VERON & Marc LEANDRI, 2013. "Optimal pollution control with distributed delays," Cahiers du GREThA, Groupe de Recherche en Economie Théorique et Appliquée 2013-03, Groupe de Recherche en Economie Théorique et Appliquée.

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