IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this article

Solution to nonlinear MHDS arising from optimal growth problems

  • Ruiz-Tamarit, J.R.
  • Ventura-Marco, M.

In this paper we propose a method for solving in closed form a general class of nonlinear modified Hamiltonian dynamic systems (MHDS). This method is used to analyze the intertemporal optimization problem from endogenous growth theory, especially the cases with two controls and one state variable. We use the exact solutions to study both uniqueness and indeterminacy of the optimal path when the dynamic system has not a well-defined isolated steady state. With this approach we avoid the linearization process, as well as the reduction of dimension technique usually applied when the dynamic system offers a continuum of steady states or no steady state at all.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/pii/S0165-4896(11)00002-3
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 61 (2011)
Issue (Month): 2 (March)
Pages: 86-96

as
in new window

Handle: RePEc:eee:matsoc:v:61:y:2011:i:2:p:86-96
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Guerrini, Luca, 2010. "The Ramsey model with a bounded population growth rate," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 872-878, September.
  2. José Ramón Ruiz-Tamarit, . "The Closed-Form Solution for a Family of Four-Dimension Non-Linear MHDS," Working Papers 2002-18, FEDEA.
  3. Guerrini, Luca, 2010. "The Ramsey model with AK technology and a bounded population growth rate," Journal of Macroeconomics, Elsevier, vol. 32(4), pages 1178-1183, December.
  4. Bovenberg, A.L. & Smulders, J.A., 1995. "Environmental quality and pollution-augmenting technological change in a two-sector endogenous growth model," Other publications TiSEM 6784bb12-71fb-45a5-bf7e-8, Tilburg University, School of Economics and Management.
  5. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711.
  6. Raouf Boucekkine & Blanca Martínez & José Ramón Ruiz-Tamarit, 2008. "Note on global dynamics and imbalance effects in the Lucas-Uzawa model," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(4), pages 503-518.
  7. Sergio Rebelo, 1999. "Long Run Policy Analysis and Long Run Growth," Levine's Working Paper Archive 2114, David K. Levine.
  8. J. Aznar-Marquez & J.R. Ruiz-Tamarit, 2001. "Endogenous Growth, Capital Utilization and Depreciation," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2001037, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
  9. M. Kurz, 1968. "The General Instability of a Class of Competitive Growth Processes," Review of Economic Studies, Oxford University Press, vol. 35(2), pages 155-174.
  10. Hassan Benchekroun & Cees Withagen, 2008. "Global Dynamics In A Growth Model With An Exhaustible Resource," Departmental Working Papers 2008-01, McGill University, Department of Economics.
  11. Brunner, Martin & Strulik, Holger, 2002. "Solution of perfect foresight saddlepoint problems: a simple method and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 737-753, May.
  12. BENCHEKROUN, Hassan & WITHAGEN, Cees, 2010. "The Optimal Depletion of Exhaustible Resources : A Complete Characterization," Cahiers de recherche 04-2010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  13. Casey B. Mulligan & Xavier Sala-i-Martin, 1993. "Transitional Dynamics in Two-Sector Models of Endogenous Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 108(3), pages 739-773.
  14. Hiraguchi, Ryoji, 2009. "A note on the closed-form solution to the Lucas-Uzawa model with externality," Journal of Economic Dynamics and Control, Elsevier, vol. 33(10), pages 1757-1760, October.
  15. Boucekkine, Raouf, 1995. "An alternative methodology for solving nonlinear forward-looking models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 711-734, May.
  16. Smith William T, 2007. "Inspecting the Mechanism Exactly: A Closed-form Solution to a Stochastic Growth Model," The B.E. Journal of Macroeconomics, De Gruyter, vol. 7(1), pages 1-33, August.
  17. Russell, Thomas & Zecevic, Aleksandar, 2000. "Indeterminate growth paths and stability," Journal of Economic Dynamics and Control, Elsevier, vol. 24(1), pages 39-62, January.
  18. Guerrini, Luca, 2010. "A closed-form solution to the Ramsey model with logistic population growth," Economic Modelling, Elsevier, vol. 27(5), pages 1178-1182, September.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:matsoc:v:61:y:2011:i:2:p:86-96. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.