IDEAS home Printed from https://ideas.repec.org/p/aim/wpaimx/1830.html
   My bibliography  Save this paper

Competitive Equilibrium Cycles for Small Discounting in Discrete-Time Two-Sector Optimal Growth Models

Author

Abstract

We study the existence of endogenous competitive equilibrium cycles under small discounting in a two-sector discrete-time optimal growth model. We provide precise concavity conditions on the indirect utility function leading to the existence of period-two cycles with a critical value for the discount factor that can be arbitrarily close to one. Contrary to the continuous-time case where the existence of periodic-cycles is obtained if the degree of concavity is close to zero, we show that in a discrete-time setting the driving condition does not require a close to zero degree of concavity but a symmetry of the indirect utility function’s concavity properties with respect to its two arguments.

Suggested Citation

  • Alain Venditti, 2018. "Competitive Equilibrium Cycles for Small Discounting in Discrete-Time Two-Sector Optimal Growth Models," AMSE Working Papers 1830, Aix-Marseille School of Economics, France.
    • Handle: RePEc:aim:wpaimx:1830
    as

    Download full text from publisher

    File URL: https://www.amse-aixmarseille.fr/sites/default/files/_dt/2012/wp_2018_-_nr_30.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. VIAL, Jean-Philippe, 1983. "Strong and weak convexity of sets and functions," LIDAM Reprints CORE 529, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Venditti, Alain, 1997. "Strong Concavity Properties of Indirect Utility Functions in Multisector Optimal Growth Models," Journal of Economic Theory, Elsevier, vol. 74(2), pages 349-367, June.
    3. Boldrin, Michele & Deneckere, Raymond J., 1990. "Sources of complex dynamics in two-sector growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 14(3-4), pages 627-653, October.
    4. Alain Venditti, 2012. "Weak concavity properties of indirect utility functions in multisector optimal growth models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 13-26, March.
    5. Becker, Robert A. & Tsyganov, Eugene N., 2002. "Ramsey Equilibrium in a Two-Sector Model with Heterogeneous Households," Journal of Economic Theory, Elsevier, vol. 105(1), pages 188-225, July.
    6. Jess Benhabib & Kazuo Nishimura, 2012. "The Hopf Bifurcation and Existence and Stability of Closed Orbits in Multisector Models of Optimal Economic Growth," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 51-73, Springer.
    7. Jess Benhabib & Kazuo Nishimura, 2012. "Competitive Equilibrium Cycles," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 75-96, Springer.
    8. Benhabib, Jess & Nishimura, Kazuo, 1981. "Stability of Equilibrium in Dynamic Models of Capital Theory," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 275-293, June.
    9. Magill, Michael J. P., 1977. "Some new results on the local stability of the process of capital accumulation," Journal of Economic Theory, Elsevier, vol. 15(1), pages 174-210, June.
    10. Montrucchio, Luigi, 1995. "A turnpike theorem for continuous-time optimal-control models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(3), pages 599-619, April.
    11. Brock, William A. & Scheinkman, JoseA., 1976. "Global asymptotic stability of optimal control systems with applications to the theory of economic growth," Journal of Economic Theory, Elsevier, vol. 12(1), pages 164-190, February.
    12. Cass, David & Shell, Karl, 1976. "The structure and stability of competitive dynamical systems," Journal of Economic Theory, Elsevier, vol. 12(1), pages 31-70, February.
    13. Montrucchio, Luigi, 1995. "A New Turnpike Theorem for Discounted Programs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 371-382, May.
    14. Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 259-273, June.
    15. Tyrrell Rockafellar, R., 1976. "Saddle points of Hamiltonian systems in convex Lagrange problems having a nonzero discount rate," Journal of Economic Theory, Elsevier, vol. 12(1), pages 71-113, February.
    16. Jean-Philippe Vial, 1983. "Strong and Weak Convexity of Sets and Functions," Mathematics of Operations Research, INFORMS, vol. 8(2), pages 231-259, May.
    17. Venditti, Alain, 1996. "Hopf bifurcation and quasi-periodic dynamics in discrete multisector optimal growth models," Ricerche Economiche, Elsevier, vol. 50(3), pages 267-291, September.
    18. Benhabib, Jess & Rustichini, Aldo, 1990. "Equilibrium cycling with small discounting," Journal of Economic Theory, Elsevier, vol. 52(2), pages 423-432, December.
    Full references (including those not matched with items on IDEAS)

    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. Alain Venditti, 2012. "Weak concavity properties of indirect utility functions in multisector optimal growth models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 13-26, March.
    2. Venditti, Alain, 1997. "Strong Concavity Properties of Indirect Utility Functions in Multisector Optimal Growth Models," Journal of Economic Theory, Elsevier, vol. 74(2), pages 349-367, June.
    3. Bosi, Stefano & Magris, Francesco & Venditti, Alain, 2005. "Competitive equilibrium cycles with endogenous labor," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 325-349, April.
    4. Montrucchio, Luigi, 1995. "A turnpike theorem for continuous-time optimal-control models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(3), pages 599-619, April.
    5. Maćkowiak, Piotr, 2009. "Adaptive Rolling Plans Are Good," MPRA Paper 42043, University Library of Munich, Germany.
    6. Pelgrin, Florian & Venditti, Alain, 2022. "On the long-run fluctuations of inheritance in two-sector OLG models," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    7. Kazuo Nishimura & Florian Pelgrin & Alain Venditti, 2022. "Medium term endogenous fluctuations in three-sector optimal growth models," Working Papers hal-03923999, HAL.
    8. Ghiglino, Christian & Venditti, Alain, 2011. "Wealth distribution and output fluctuations," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2478-2509.
    9. Frédéric Lordon, 1991. "Théorie de la croissance : quelques développements récents [Première partie : la croissance récente]," Revue de l'OFCE, Programme National Persée, vol. 36(1), pages 157-211.
    10. Mitra, Tapan & Nishimura, Kazuo, 2001. "Discounting and Long-Run Behavior: Global Bifurcation Analysis of a Family of Dynamical Systems," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 256-293, January.
    11. Willi Semmler & Malte Sieveking, 1994. "On the optimal exploitation of interacting resources," Journal of Economics, Springer, vol. 59(1), pages 23-49, February.
    12. M. Marena & L. Montrucchio, 1999. "Neighborhood Turnpike Theorem for Continuous-Time Optimization Models," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 651-676, June.
    13. Wolff, Reiner, 1997. "Saddle-point dynamics in non-autonomous models of multisector growth with variable returns to scale," Journal of Mathematical Economics, Elsevier, vol. 27(3), pages 267-282, April.
    14. Venditti, Alain, 2005. "The two sector overlapping generations model: A simple formulation," Research in Economics, Elsevier, vol. 59(2), pages 164-188, June.
    15. Martinez-Garcia, Maria Pilar, 2003. "The general instability of balanced paths in endogenous growth models: the role of transversality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 27(4), pages 599-618, February.
    16. Truman Bewley, 2010. "An Integration of Equilibrium Theory and Turnpike Theory," Levine's Working Paper Archive 1381, David K. Levine.
    17. Venditti, Alain, 1998. "Indeterminacy and endogenous fluctuations in two-sector growth models with externalities," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 521-542, January.
    18. Yacov Tsur & Amos Zemel, 2017. "Steady state properties of multi-state economic models," Canadian Journal of Economics, Canadian Economics Association, vol. 50(2), pages 506-521, May.
    19. Ghiglino, Christian & Venditti, Alain, 2007. "Wealth inequality, preference heterogeneity and macroeconomic volatility in two-sector economies," Journal of Economic Theory, Elsevier, vol. 135(1), pages 414-441, July.
    20. Brock, William & Xepapadeas, Anastasios, 2008. "Diffusion-induced instability and pattern formation in infinite horizon recursive optimal control," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2745-2787, September.

    More about this item

    Keywords

    two-sector optimal growth model; small discounting; period-two cycles; strong and weak concavity;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:aim:wpaimx:1830. 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: Gregory Cornu (email available below). General contact details of provider: https://edirc.repec.org/data/amseafr.html .

    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.