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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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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
Date of revision:
Handle: RePEc:pra:mprapa:54777
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  1. M. Bambi & G. Fabbri & F. Gozzi, 2012. "Optimal policy and consumption smoothing effects in the time-to-build AK model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(3), pages 635-669, August.
  2. Boucekkine, Raouf & Licandro, Omar & Puch, Luis A. & del Rio, Fernando, 2005. "Vintage capital and the dynamics of the AK model," Journal of Economic Theory, Elsevier, vol. 120(1), pages 39-72, January.
  3. 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.
  4. Mauro Bambi, 2006. "Endogenous growth and time to build: the AK case," Computing in Economics and Finance 2006 77, Society for Computational Economics.
  5. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
  6. BOUCEKKINE, Raouf & FABBRI, Giorgio & GOZZI, Fausto, . "Maintenance and investment: complements or substitutes? A reappraisal," CORE Discussion Papers RP 2333, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. 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) hal-00759198, HAL.
  8. Raouf Boucekkine & David de la Croix & Omar Licandro, . "Modelling vintage structures with DDEs: Principles and applications," Working Papers 2004-07, FEDEA.
  9. 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).
  10. Paul, Christopher & Licandro, Omar & Boucekkine, Raouf, 1995. "Differential-difference equations in economics: on the numerical solution of vintage capital growth models," UC3M Working papers. Economics 3951, Universidad Carlos III de Madrid. Departamento de Economía.
  11. Patrick K. Asea & Paul J. Zak, 1997. "Time-to-Build and Cycles," NBER Technical Working Papers 0211, National Bureau of Economic Research, Inc.
  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. Buiter, Willem H, 1984. "Saddlepoint Problems in Continuous Time Rational Expectations Models: A General Method and Some Macroeconomic Examples," Econometrica, Econometric Society, vol. 52(3), pages 665-80, May.
  14. 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.
  15. 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.
  16. 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.
  17. Hippolyte D'Albis & Emmanuelle Augeraud-Véron & Hermen Jan Hupkes, 2014. "Bounded interest rate feedback rules in continuous-time," PSE - Labex "OSE-Ouvrir la Science Economique" hal-01015388, HAL.
  18. 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.
  19. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
  20. repec:hal:journl:halshs-00717198 is not listed on IDEAS
  21. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
  22. repec:hal:journl:halshs-00717412 is not listed on IDEAS
  23. Jovanovic, Boyan & Yatsenko, Yuri, 2012. "Investment in vintage capital," Journal of Economic Theory, Elsevier, vol. 147(2), pages 551-569.
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