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Optimal growth models and the Lagrange multiplier

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  • LE VAN, Cuong
  • SAGLAM, Cagri

Abstract

We provide sufficient conditions on the objective functional and the constraint functions under which the Lagrangean can be represented by a L exp.1 sequence of multipliers in infinite horizon discrete time optimal growth models.

Suggested Citation

  • LE VAN, Cuong & SAGLAM, Cagri, 2003. "Optimal growth models and the Lagrange multiplier," CORE Discussion Papers 2003083, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2003083
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    References listed on IDEAS

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    1. Rustichini, A., 1998. "Lagrange multipliers in incentive-constrained problems," Journal of Mathematical Economics, Elsevier, vol. 29(4), pages 365-380, May.
    2. Jorge DurÂn, 2000. "On dynamic programming with unbounded returns," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(2), pages 339-352.
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    4. Dechert, W. Davis & Nishimura, Kazuo, 1983. "A complete characterization of optimal growth paths in an aggregated model with a non-concave production function," Journal of Economic Theory, Elsevier, vol. 31(2), pages 332-354, December.
    5. Le Van, Cuong & Morhaim, Lisa, 2002. "Optimal Growth Models with Bounded or Unbounded Returns: A Unifying Approach," Journal of Economic Theory, Elsevier, vol. 105(1), pages 158-187, July.
    6. repec:dau:papers:123456789/416 is not listed on IDEAS
    7. Dana, Rose-Anne & Van, Cuong Le, 1991. "Optimal growth and Pareto optimality," Journal of Mathematical Economics, Elsevier, vol. 20(2), pages 155-180.
    8. Alvarez, Fernando & Stokey, Nancy L., 1998. "Dynamic Programming with Homogeneous Functions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 167-189, September.
    9. Aliprantis, Charalambos D. & Border, Kim C. & Burkinshaw, Owen, 1997. "New Proof Of The Existence Of Equilibrium In A Single-Sector Growth Model," Macroeconomic Dynamics, Cambridge University Press, vol. 1(04), pages 669-679, December.
    10. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
    11. Majumdar, Mukul, 1972. "Some general theorems on efficiency prices with an infinite-dimensional commodity space," Journal of Economic Theory, Elsevier, vol. 5(1), pages 1-13, August.
    12. Dechert, W. D., 1982. "Lagrange multipliers in infinite horizon discrete time optimal control models," Journal of Mathematical Economics, Elsevier, vol. 9(3), pages 285-302, March.
    13. Martin L. Weitzman, 1973. "Duality Theory for Infinite Horizon Convex Models," Management Science, INFORMS, vol. 19(7), pages 783-789, March.
    14. McKenzie, Lionel W., 2005. "Optimal economic growth, turnpike theorems and comparative dynamics," Handbook of Mathematical Economics,in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 2, volume 3, chapter 26, pages 1281-1355 Elsevier.
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    Citations

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    Cited by:

    1. Mohamed Ben Ridha Mabrouk, 2011. "Translation invariance when utility streams are infinite and unbounded," International Journal of Economic Theory, The International Society for Economic Theory, vol. 7(4), pages 317-329, December.
    2. Hiraguchi, Ryoji, 2011. "A two sector endogenous growth model with habit formation," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 430-441, April.
    3. Goenka, Aditya & Nguyen, Manh-Hung, 2009. "Existence of Competitive Equilibrium in an Optimal Growth Model with Elastic Labor Supply and Smoothness of the Policy Function," TSE Working Papers 09-064, Toulouse School of Economics (TSE).
    4. Marrero, Gustavo A., 2008. "Revisiting The Optimal Stationary Public Investment Policy In Endogenous Growth Economies," Macroeconomic Dynamics, Cambridge University Press, vol. 12(02), pages 172-194, April.
    5. Jean-Michel Grandmont, 2013. "Tribute to Cuong Le Van," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(1), pages 5-10, March.
    6. Cuong Le Van & Yiannis Vailakis, 2004. "Existence of competitive equilibrium in a single-sector growth model with elastic labour," Cahiers de la Maison des Sciences Economiques b04123, Université Panthéon-Sorbonne (Paris 1).
    7. Aditya Goenka & Cuong Le Van & Manh-Hung Nguyen, 2011. "A study of the dynamic of influence through differential equations," Documents de travail du Centre d'Economie de la Sorbonne 11023, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    8. Nguyen Manh Hung & San Nguyen Van, 2005. "The Lagrange multipliers and existence of competitive equilibrium in an intertemporal model with endogenous leisure," Cahiers de la Maison des Sciences Economiques b05041, Université Panthéon-Sorbonne (Paris 1).
    9. Goenka, Aditya & Le Van, Cuong & Nguyen, Manh-Hung, 2012. "Existence Of Competitive Equilibrium In An Optimal Growth Model With Heterogeneous Agents And Endogenous Leisure," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S1), pages 33-51, April.
    10. Goenka, Aditya & Nguyen, Manh-Hung, 2011. "Equilibrium in the growth model with an endogenous labor-leisure choice," LERNA Working Papers 11.06.340, LERNA, University of Toulouse.
    11. repec:eee:macchp:v2-725 is not listed on IDEAS
    12. Mohamed Mabrouk, 2005. "Intergenerational anonymity as an alternative to the discounted- sum criterion in the calculus of optimal growth II: Pareto optimality and some economic interpretations," GE, Growth, Math methods 0511007, EconWPA.
    13. Mohamed Mabrouk, 2005. "Intergenerational anonymity as an alternative to the discounted- sum criterion in the calculus of optimal growth I: Consensual optimality," GE, Growth, Math methods 0510013, EconWPA.
    14. Golosov, M. & Tsyvinski, A. & Werquin, N., 2016. "Recursive Contracts and Endogenously Incomplete Markets," Handbook of Macroeconomics, Elsevier.
    15. Cuong Le Van & Manh-Hung Nguyen, 2005. "Existence of competitive equilibrium in a single-sector growth model with heterogeneous agents and endogenous leisure," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00197533, HAL.

    More about this item

    Keywords

    optimal growth; Lagrange multipliers;

    JEL classification:

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

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