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Multiple Solutions in Systems of Functional Differential Equations

  • d'Albis, Hippolyte
  • Augeraud-Véron, Emmanuelle
  • Hupkes, Herman Jan

This paper proposes conditions for the existence and uniqueness of solutions to systems of linear differential or algebraic equations with delays or advances, in which some variables may be non-predetermined. These conditions represent the counterpart to the Blanchard and Kahn conditions for the functional equations under consideration. To illustrate the mathematical results, applications to an overlapping generations model and a time-to-build model are developed.

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File URL: http://mpra.ub.uni-muenchen.de/54777/1/MPRA_paper_54777.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 54777.

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Date of creation: 25 Mar 2014
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Handle: RePEc:pra:mprapa:54777
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  1. BOUCEKKINE, RAOUF & de la CROIX, David & LICANDRO, Omar, 2004. "Modelling vintage structures with DDEs : principles and applications," CORE Discussion Papers 2004047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Boucekkine, R. & Fabbri, G. & Gozzi, F., 2010. "Maintenance and investment: Complements or substitutes? A reappraisal," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2420-2439, December.
  3. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Venditti, Alain, 2010. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," LERNA Working Papers 10.13.319, LERNA, University of Toulouse.
  4. repec:hal:journl:halshs-00717198 is not listed on IDEAS
  5. Boucekkine, Raouf & de la Croix, David & Licandro, Omar, 2000. "Vintage Human Capital, Demographic Trends and Endogenous Growth," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2000007, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  6. Buiter, W, 1982. "Saddlepoint Problems in Continuous Time Rational Expectations Models : A General Method and Some Macroeconomic Examples," The Warwick Economics Research Paper Series (TWERPS) 200, University of Warwick, Department of Economics.
  7. Patrick Asea & Paul J. Zak, 1997. "Time-to-Build and Cycles," UCLA Economics Working Papers 767, UCLA Department of Economics.
  8. 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.
  9. Bambi, Mauro & Gozzi, Fausto & Licandro, Omar, 2014. "Endogenous growth and wave-like business fluctuations," Journal of Economic Theory, Elsevier, vol. 154(C), pages 68-111.
  10. Fabbri, Giorgio & Gozzi, Fausto, 2008. "Solving optimal growth models with vintage capital: The dynamic programming approach," Journal of Economic Theory, Elsevier, vol. 143(1), pages 331-373, November.
  11. M. Bambi & G. Fabbri & F. Gozzi, 2012. "Optimal policy and consumption smoothing effects in the time-to-build AK model," Economic Theory, Springer, vol. 50(3), pages 635-669, August.
  12. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
  13. Hippolyte d'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2012. "Discontinuous Initial Value Problems for Functional Differential-Algebraic Equations of Mixed Type," Documents de travail du Centre d'Economie de la Sorbonne 12043, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  14. El-Hodiri, Mohamed A & Loehman, Edna & Whinston, Andrew B, 1972. "An Optimal Growth Model with Time Lags," Econometrica, Econometric Society, vol. 40(6), pages 1137-46, November.
  15. 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.
  16. Gray, Malcolm R & Turnovsky, Stephen J, 1979. "Expectational Consistency, Informational Lags, and the Formulation of Expectations in Continuous Time Models," Econometrica, Econometric Society, vol. 47(6), pages 1457-74, November.
  17. Jovanovic, Boyan & Yatsenko, Yuri, 2012. "Investment in vintage capital," Journal of Economic Theory, Elsevier, vol. 147(2), pages 551-569.
  18. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.
  19. Hippolyte D'Albis & Emmanuelle Augeraud-Véron & Alain Venditti, 2012. "Business cycle fluctuations and learning-by-doing externalities in a one-sector model," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00717198, HAL.
  20. Raouf Boucekkine & Omar Licandro & Christopher Paul, . "Differential-Difference Equations in Economics: On the Numerical Solution of Vintage Capital Growth Models," Computing in Economics and Finance 1996 _036, Society for Computational Economics.
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