IDEAS home Printed from https://ideas.repec.org/a/cup/macdyn/v7y2003i03p317-332_02.html
   My bibliography  Save this article

Simple Proof Of Existence Of Equilibrium In A One-Sector Growth Model With Bounded Or Unbounded Returns From Below

Author

Listed:
  • Durán, Jorge
  • Le Van, Cuong

Abstract

We analyze a Ramsey economy in which gross investment is constrained to be nonnegative. We prove the existence of a competitive equilibrium for the case in which utility need not be bounded from below and the Inada-type conditions need not hold. The analysis is carried out by means of a direct and technically standard approach. This direct approach allows us to obtain detailed results concerning properties of competitive equilibria, and is easily adapted for the analysis of analogous models often found in macroeconomics.

Suggested Citation

  • Durán, Jorge & Le Van, Cuong, 2003. "Simple Proof Of Existence Of Equilibrium In A One-Sector Growth Model With Bounded Or Unbounded Returns From Below," Macroeconomic Dynamics, Cambridge University Press, vol. 7(3), pages 317-332, June.
    • Handle: RePEc:cup:macdyn:v:7:y:2003:i:03:p:317-332_02
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S1365100502020047/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Peleg, Bezalel & Yaari, Menahem E, 1970. "Markets with Countably Many Commodities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 11(3), pages 369-377, October.
    2. 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(4), pages 669-679, December.
    3. Amir, Rabah, 1996. "Sensitivity analysis of multisector optimal economic dynamics," Journal of Mathematical Economics, Elsevier, vol. 25(1), pages 123-141.
    4. 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.
    5. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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. Le Van, Cuong & Nguyen, Manh-Hung & Vailakis, Yiannis, 2007. "Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 287-317, April.
    2. Le Van, Cuong & Nguyen, Manh-Hung & Vailakis, Yiannis, 2007. "Equilibrium dynamics in an aggregative model of capital accumulation with heterogeneous agents and elastic labor," Journal of Mathematical Economics, Elsevier, vol. 43(3-4), pages 287-317, April.
    3. Erol, Selman & Le Van, Cuong & Saglam, Cagri, 2011. "Existence, optimality and dynamics of equilibria with endogenous time preference," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 170-179, March.
    4. 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).
    5. Robert A. Becker, 2012. "Optimal growth with heterogeneous agents and the twisted turnpike: An example," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 27-47, March.
    6. Becker, Robert A. & Mitra, Tapan, 2012. "Efficient Ramsey Equilibria," Macroeconomic Dynamics, Cambridge University Press, vol. 16(S1), pages 18-32, April.
    7. Marrero, Gustavo A., 2008. "Revisiting The Optimal Stationary Public Investment Policy In Endogenous Growth Economies," Macroeconomic Dynamics, Cambridge University Press, vol. 12(2), pages 172-194, April.
    8. 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.
    9. Sağlam Çağri & Turan Agah & Turan Hamide, 2014. "Saddle-node bifurcations in an optimal growth model with preferences for wealth habit," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(2), pages 145-156, April.
    10. Robert A. Becker, 2012. "Optimal growth with heterogeneous agents and the twisted turnpike: An example," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 27-47, March.
    11. Luis A. Alcala, 2016. "On the time consistency of collective preferences," Papers 1607.02688, arXiv.org, revised Jul 2018.

    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. Goenka, Aditya & Nguyen, Manh-Hung, 2020. "General existence of competitive equilibrium in the growth model with an endogenous labor–leisure choice," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 90-98.
    2. van der Laan, Gerard & Withagen, Cees, 2003. "Quasi-equilibrium in economies with infinite dimensional commodity spaces: a truncation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 423-444, January.
    3. Besada, M. & Vazquez, C., 1999. "The generalized marginal rate of substitution," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 553-560, May.
    4. 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.
    5. Charalambos Aliprantis & Kim Border & Owen Burkinshaw, 1996. "Market economies with many commodities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 19(1), pages 113-185, March.
    6. 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," LERNA Working Papers 09.21.297, LERNA, University of Toulouse.
    7. Kaori Hasegawa, 2000. "The Second Fundamental Theorem of Welfare Economics and the Existence of Competitive Equilibrium over an Infinite Horizon with General Consumption Sets," Econometric Society World Congress 2000 Contributed Papers 1377, Econometric Society.
    8. Florenzano, Monique, 1991. "Markets with countably many periods," Economics Letters, Elsevier, vol. 36(3), pages 233-238, July.
    9. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2001. "A Theory of Value with Non-linear Prices: Equilibrium Analysis beyond Vector Lattices," Journal of Economic Theory, Elsevier, vol. 100(1), pages 22-72, September.
    10. Abramovich, Y A & Aliprantis, C D & Zame, W R, 1995. "A Representation Theorem for Riesz Spaces and Its Applications to Economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 527-535, May.
    11. 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.
    12. Le Van, Cuong & Cagri Saglam, H., 2004. "Optimal growth models and the Lagrange multiplier," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 393-410, June.
    13. Truman Bewley, 2010. "An Integration of Equilibrium Theory and Turnpike Theory," Levine's Working Paper Archive 1381, David K. Levine.
    14. Aliprantis, Charalambos D. & Tourky, Rabee & Yannelis, Nicholas C., 2000. "Cone Conditions in General Equilibrium Theory," Journal of Economic Theory, Elsevier, vol. 92(1), pages 96-121, May.
    15. 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).
    16. Aliprantis, Charalambos D. & Border, Kim C. & Burkinshaw, Owen, 1997. "Economies with Many Commodities," Journal of Economic Theory, Elsevier, vol. 74(1), pages 62-105, May.
    17. Carlos Hervés-Beloso & V. Martins-da-Rocha & Paulo Monteiro, 2009. "Equilibrium theory with asymmetric information and infinitely many states," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 295-320, February.
    18. Gerard van der Laan & Cees Withagen, 2000. "General Equilibrium in Economies with Infinite Dimensional Commodity Spaces: A Truncation Approach," Tinbergen Institute Discussion Papers 00-023/1, Tinbergen Institute.
    19. 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.
    20. Balasko, Yves, 1997. "Equilibrium analysis of the infinite horizon model with smooth discounted utility functions," Journal of Economic Dynamics and Control, Elsevier, vol. 21(4-5), pages 783-829, May.

    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • E13 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Neoclassical

    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:cup:macdyn:v:7:y:2003:i:03:p:317-332_02. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/mdy .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.