IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v61y2011i2p86-96.html
   My bibliography  Save this article

Solution to nonlinear MHDS arising from optimal growth problems

Author

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

Abstract

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.

Suggested Citation

  • Ruiz-Tamarit, J.R. & Ventura-Marco, M., 2011. "Solution to nonlinear MHDS arising from optimal growth problems," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 86-96, March.
  • Handle: RePEc:eee:matsoc:v:61:y:2011:i:2:p:86-96
    as

    Download full text from publisher

    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 below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Russell, Thomas & Zecevic, Aleksandar, 2000. "Indeterminate growth paths and stability," Journal of Economic Dynamics and Control, Elsevier, vol. 24(1), pages 39-62, January.
    3. Benchekroun, Hassan & Withagen, Cees, 2011. "The optimal depletion of exhaustible resources: A complete characterization," Resource and Energy Economics, Elsevier, vol. 33(3), pages 612-636, September.
    4. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, September.
    5. 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.
    6. 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.
    7. 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.
    8. J. Aznar-Márquez & J. R. Ruiz-Tamarit, "undated". "Endogenous Growth, Capital Utilization and Depreciation," Working Papers 2004-21, FEDEA.
    9. Guerrini, Luca, 2010. "The Ramsey model with a bounded population growth rate," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 872-878, September.
    10. Lans Bovenberg, A. & Smulders, Sjak, 1995. "Environmental quality and pollution-augmenting technological change in a two-sector endogenous growth model," Journal of Public Economics, Elsevier, vol. 57(3), pages 369-391, July.
    11. Rebelo, Sergio, 1991. "Long-Run Policy Analysis and Long-Run Growth," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 500-521, June.
    12. 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, December.
    13. 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.
    14. 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.
    15. Ruiz-Tamarit, José Ramón, 2008. "The closed-form solution for a family of four-dimension nonlinear MHDS," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 1000-1014, March.
    16. 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.
    17. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. J.Aznar-Márquez & J.R. Ruiz-Tamarit, 2004. "Non-Catastrophic Endogenous Growth with Pollution and Abatement," Economic Working Papers at Centro de Estudios Andaluces E2004/80, Centro de Estudios Andaluces.
    2. J. Aznar-Márquez & J. R. Ruiz-Tamarit, "undated". "Non-Catastrophic Endogenous Growth and the Environmental Kuznets Curve," Working Papers 2004-15, FEDEA.
    3. Ruiz-Tamarit, José Ramón, 2008. "The closed-form solution for a family of four-dimension nonlinear MHDS," Journal of Economic Dynamics and Control, Elsevier, vol. 32(3), pages 1000-1014, March.
    4. J., AZNAR-MARQUEZ & Jose-Ramon, RUIZ-TAMARIT, 2005. "Demographic Transition Environmental Concern and the Kuznets Curve," Discussion Papers (ECON - Département des Sciences Economiques) 2005001, Université catholique de Louvain, Département des Sciences Economiques.
    5. Juana AZNAR-MARQUEZ & Jose-Ramon RUIZ-TAMARIT, 2012. "Sufficient and Necessary Conditions for Non-Catastrophic Growth," LIDAM Discussion Papers IRES 2012027, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    6. J. Aznar-Márquez & J. R. Ruiz-Tamarit, "undated". "Endogenous Growth, Capital Utilization and Depreciation," Working Papers 2004-21, FEDEA.
    7. Aznar-Márquez, J. & Ruiz-Tamarit, J.R., 2016. "Environmental pollution, sustained growth, and sufficient conditions for sustainable development," Economic Modelling, Elsevier, vol. 54(C), pages 439-449.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wei Jin & ZhongXiang Zhang, 2018. "Capital Accumulation, Green Paradox, and Stranded Assets: An Endogenous Growth Perspective," Working Papers 2018.33, Fondazione Eni Enrico Mattei.
    2. Antony, Jürgen & Klarl, Torben, 2019. "Resource depletion in a Ramsey economy with subsistence consumption, exogenous technical change and capital depreciation: A full characterization," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203640, Verein für Socialpolitik / German Economic Association.
    3. De, Supriyo, 2014. "Intangible capital and growth in the ‘new economy’: Implications of a multi-sector endogenous growth model," Structural Change and Economic Dynamics, Elsevier, vol. 28(C), pages 25-42.
    4. Hettich, Frank, 1997. "Growth effects of a revenue neutral environmental tax reform," Discussion Papers, Series II 351, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    5. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    6. Iulia PARA & Ioana VIASU, 2018. "On the Solutions to the Ramsey Model with Logistic Population Growth via the Partial Hamiltonian Approach," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 142-150, December.
    7. Constantin Chilarescu & Ioana Viasu, 2016. "A Closed-form Solution of a Two-sector Endogenous Growth Model with Habit Formation," Australian Economic Papers, Wiley Blackwell, vol. 55(2), pages 112-127, June.
    8. Boucekkine, R. & Martínez, B. & Ruiz-Tamarit, J.R., 2013. "Growth vs. level effect of population change on economic development: An inspection into human-capital-related mechanisms," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 312-334.
    9. Barro, Robert J & Mankiw, N Gregory & Sala-i-Martin, Xavier, 1995. "Capital Mobility in Neoclassical Models of Growth," American Economic Review, American Economic Association, vol. 85(1), pages 103-115, March.
    10. Tramontana, Fabio & Sushko, Iryna & Avrutin, Viktor, 2015. "Period adding structure in a 2D discontinuous model of economic growth," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 262-273.
    11. Brito, Paulo & Venditti, Alain, 2010. "Local and global indeterminacy in two-sector models of endogenous growth," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 893-911, September.
    12. Fabio Tramontana & Viktor Avrutin, 2014. "Complex endogenous dynamics in a one-sector growth model with differential savings," DEM Working Papers Series 078, University of Pavia, Department of Economics and Management.
    13. Sjak Smulders, 1995. "Entropy, environment, and endogenous economic growth," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 2(2), pages 319-340, August.
    14. C. Chilarescu & I. Viasu, 2019. "Uniqueness and Multiple Trajectories for the Case of Lucas Model," Computational Economics, Springer;Society for Computational Economics, vol. 54(3), pages 1157-1177, October.
    15. Iacopetta, Maurizio, 2010. "Phases of economic development and the transitional dynamics of an innovation-education growth model," European Economic Review, Elsevier, vol. 54(2), pages 317-330, February.
    16. 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.
    17. Trimborn, Timo, 2018. "On the analysis of endogenous growth models with a balanced growth path," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 40-50.
    18. Posch, Olaf, 2009. "Structural estimation of jump-diffusion processes in macroeconomics," Journal of Econometrics, Elsevier, vol. 153(2), pages 196-210, December.
    19. Smulders, Sjak & Gradus, Raymond, 1996. "Pollution abatement and long-term growth," European Journal of Political Economy, Elsevier, vol. 12(3), pages 505-532, November.
    20. Bretschger, Lucas & Lechthaler, Filippo & Rausch, Sebastian & Zhang, Lin, 2017. "Knowledge diffusion, endogenous growth, and the costs of global climate policy," European Economic Review, Elsevier, vol. 93(C), pages 47-72.

    More about this item

    Keywords

    Nonlinearity Hamiltonian Closed form Growth Transitional dynamics;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. 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: (Nithya Sathishkumar). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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 CitEc recognized a reference but did not link an item in RePEc 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 RePEc Author Service 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.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.