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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. 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.
  2. Mauro BAMBI & Giorgio FABBRI & Fausto GOZZI, 2010. "Optimal policy and consumption smoothing effects in the time-to-build AK model," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2010029, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  3. Willem H. Buiter, 1984. "Saddlepoint Problems in Contifuous Time Rational Expectations Models: A General Method and Some Macroeconomic Ehamples," NBER Technical Working Papers 0020, National Bureau of Economic Research, Inc.
  4. 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.
  5. 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.
  6. 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.
  7. Raouf Boucekkine & David de la Croix & Omar Licandro, . "vintage human capital, demographic trends and endogenous growth," Working Papers 2000-02, FEDEA.
  8. Mauro Bambi & Omar Licandro, 2011. "Endogenous Growth and Wave-Like Business Fluctuation," Working Papers 533, Barcelona Graduate School of Economics.
  9. Asea, Patrick K. & Zak, Paul J., 1999. "Time-to-build and cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 23(8), pages 1155-1175, August.
  10. Raouf, BOUCEKKINE & David de la Croix & Omar Lidandro, 2004. "Modelling vintage structures with DDEs : principles and applications," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2004004, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  11. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.
  12. 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.
  13. 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.
  14. d'Albis, Hippolyte & Augeraud-Véron, Emmanuelle & Hupkes, Hermen Jan, 2014. "Bounded interest rate feedback rules in continuous-time," Journal of Economic Dynamics and Control, Elsevier, vol. 39(C), pages 227-236.
  15. repec:hal:journl:halshs-00717198 is not listed on IDEAS
  16. 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.
  17. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
  18. 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.
  19. 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.
  20. Jovanovic, Boyan & Yatsenko, Yuri, 2012. "Investment in vintage capital," Journal of Economic Theory, Elsevier, vol. 147(2), pages 551-569.
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