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Endogenous Business Cycles and Dynamic Inefficiency


  • Guido Cazzavillan

    () (Department of Economics, University Of Venice Ca� Foscari)

  • Patrick Pintus

    (Universit� de la M�diterran�e and GREQAM-IDEP, France)


This paper explores how the occurrence of local indeterminacy and endogenous business cycles relates to dynamic inefficiency, as defined by Malinvaud (1953), Phelps (1965) and Cass (1972). We follow Reichlin (1986) and Grandmont (1993) by considering a two-period OLG model of capital accumulation with labor-leisure choice into the first-period of agents� life and consumption in both periods. We first show that local indeterminacy and Hopf bifurcation are necessarily associated with a capital-labor ratio that is, at steady state, larger than the Golden Rule level. Consequently, paths converging asymptotically towards the steady state are shown to be dynamically inefficient, as there always exists another trajectory that starts with the same initial conditions and produces more aggregate consumption at all future dates. More surprising, however, is our main result showing that stable orbits, generated around a dynamically inefficient steady state through a supercritical Hopf bifurcation, may, in contrast, be dynamically efficient.

Suggested Citation

  • Guido Cazzavillan & Patrick Pintus, 2006. "Endogenous Business Cycles and Dynamic Inefficiency," Working Papers 2006_37, Department of Economics, University of Venice "Ca' Foscari".
  • Handle: RePEc:ven:wpaper:2006_37

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    References listed on IDEAS

    1. Cass, David, 1972. "On capital overaccumulation in the aggregative, neoclassical model of economic growth: A complete characterization," Journal of Economic Theory, Elsevier, vol. 4(2), pages 200-223, April.
    2. de Vilder, Robin, 1996. "Complicated Endogenous Business Cycles under Gross Substitutability," Journal of Economic Theory, Elsevier, vol. 71(2), pages 416-442, November.
    3. J. D. Geanakoplos & H. M. Polemarchakis, 1986. "Walrasian Indeterminacy and Keynesian Macroeconomics," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 755-779.
    4. Lloyd-Braga, Teresa & Nourry, Carine & Venditti, Alain, 2007. "Indeterminacy in dynamic models: When Diamond meets Ramsey," Journal of Economic Theory, Elsevier, vol. 134(1), pages 513-536, May.
    5. Grandmont, Jean-Michel, 1985. "On Endogenous Competitive Business Cycles," Econometrica, Econometric Society, vol. 53(5), pages 995-1045, September.
    6. Benhabib, Jess & Laroque, Guy, 1988. "On competitive cycles in productive economies," Journal of Economic Theory, Elsevier, vol. 45(1), pages 145-170, June.
    7. Chattopadhyay, Subir & Gottardi, Piero, 1999. "Stochastic OLG Models, Market Structure, and Optimality," Journal of Economic Theory, Elsevier, vol. 89(1), pages 21-67, November.
    8. Samuelson, Larry, 1980. "The Golden Rule with Endogenous Labor Participation Rate," American Economic Review, American Economic Association, vol. 70(4), pages 752-755, September.
    9. Tito Pietra, 2004. "Sunspots, indeterminacy and Pareto inefficiency in economies with incomplete markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(3), pages 687-699, October.
    10. Cazzavillan, Guido & Pintus, Patrick A., 2006. "Capital externalities in OLG economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(7), pages 1215-1231, July.
    11. Benveniste, Lawrence M., 1976. "A complete characterization of efficiency for a general capital accumulation model," Journal of Economic Theory, Elsevier, vol. 12(2), pages 325-337, April.
    12. Luigi Montrucchio, 2004. "Cass transversality condition and sequential asset bubbles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(3), pages 645-663, October.
    13. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
    14. Cazzavillan, Guido, 2001. "Indeterminacy and Endogenous Fluctuations with Arbitrarily Small Externalities," Journal of Economic Theory, Elsevier, vol. 101(1), pages 133-157, November.
    15. Guido Cazzavillan & Patrick A. Pintus, 2004. "Robustness of Multiple Equilibria in OLG Economies," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(2), pages 456-475, April.
    16. Grandmont, Jean-Michel & Pintus, Patrick & de Vilder, Robin, 1998. "Capital-Labor Substitution and Competitive Nonlinear Endogenous Business Cycles," Journal of Economic Theory, Elsevier, vol. 80(1), pages 14-59, May.
    17. David Cass & Menahem E. Yaari, 1966. "A Re-examination of the Pure Consumption Loans Model," Journal of Political Economy, University of Chicago Press, vol. 74, pages 353-353.
    18. Dixon,Huw David & Rankin,Neil, 1995. "The New Macroeconomics," Cambridge Books, Cambridge University Press, number 9780521479479, March.
    19. d ASPREMONT, Claude, & DOS SANTOS FERREIRA , Rodolphe & GERARD-VARET , Louis-André, 1994. "Market Power, Coordination Failures and Endogenous Fluctuations," CORE Discussion Papers 1994068, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Drugeon, Jean-Pierre & Nourry, Carine & Venditti, Alain, 2010. "On efficiency and local uniqueness in two-sector OLG economies," Mathematical Social Sciences, Elsevier, vol. 59(1), pages 120-144, January.
    2. Cazzavillan, Guido & Pintus, Patrick, 2007. "Dynamic inefficiency in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 137(1), pages 754-759, November.
    3. Nourry, Carine & Venditti, Alain, 2011. "Local indeterminacy under dynamic efficiency in a two-sector overlapping generations economy," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 164-169, March.
    4. repec:hal:wpaper:halshs-00439241 is not listed on IDEAS

    More about this item


    Overlapping generations; endogenous labor supply; multiple equilibria; endogenous fluctuations; dynamic inefficiency;

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles


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