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Capital-Labor Substitution and Competitive Nonlinear Endogenous Business Cycles

  • Grandmont, Jean-Michel
  • Pintus, Patrick
  • de Vilder, Robin

We develop in this paper simple geometrical methods to study local indeterminacy, bifurcations and stochastic (sunspot) equilibria near a steady state, in nonlinear two dimensional economic models. We present stochastic sunspot equilibria, which allows a constructive description of local bifurcations. The latter analysis is relevant when some eigenvalues of the linearized dynamics, near the steady state, have a modulus close to one (“unit root(s)”), as taking into account small nonlinearities generates linear local approximation. These methods are applied to a simple aggregative model (Woodford (JET, 1986)), to study in particular the influence of capital-labor substitution and of the aggregate labor supply wage elasticiy, on the occurrence of competitive endogenous deterministic or stochastic fluctuations.

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Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 80 (1998)
Issue (Month): 1 (May)
Pages: 14-59

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Handle: RePEc:eee:jetheo:v:80:y:1998:i:1:p:14-59
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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  1. Grandmont, Jean-Michel, 2008. "Nonlinear difference equations, bifurcations and chaos: An introduction," Research in Economics, Elsevier, vol. 62(3), pages 122-177, September.
  2. Pintus, Patrick & Sands, Ducan & De Vilder, Robin, 1996. "On the transition from local regular to global irregular fluctuations," CEPREMAP Working Papers (Couverture Orange) 9617, CEPREMAP.
  3. David Cass & Menahem E. Yaari, 1965. "A Re-Examination of the Pure Consumption Loans Model," Cowles Foundation Discussion Papers 195, Cowles Foundation for Research in Economics, Yale University.
  4. Benhabib, Jess & Farmer, Roger E.A., 1991. "Indeterminacy and Increasing Returns," Working Papers 91-59, C.V. Starr Center for Applied Economics, New York University.
  5. Kiminori Matsuyama, 1990. "Increasing Returns, Industrialization and Indeterminacy of Equilibrium," Discussion Papers 878, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Chiappori, P.A. & Guesnerie, R., 1990. "Sunspot Equilibria in Sequential Markets Models," DELTA Working Papers 90-05, DELTA (Ecole normale supérieure).
  7. Michele Boldrin & Michael Woodford, 1988. "Equilibruim Models Displaying Endogenous Fluctuations and Chaos: A Survey," UCLA Economics Working Papers 530, UCLA Department of Economics.
  8. Grandmont Jean-michel, 1985. "Stabilizing competitive business cycles," CEPREMAP Working Papers (Couverture Orange) 8518, CEPREMAP.
  9. Roger Guesnerie & Costas Azariadis, 1982. "Prophéties créatrices et persistance des théories," Revue Économique, Programme National Persée, vol. 33(5), pages 787-806.
  10. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
  11. Benhabib Jess & Rustichini Aldo, 1994. "Introduction to the Symposium on Growth, Fluctuations, and Sunspots: Confronting the Data," Journal of Economic Theory, Elsevier, vol. 63(1), pages 1-18, June.
  12. Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, vol. 40(1), pages 89-102, October.
  13. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
  14. Benhabib, Jess & Laroque, Guy, 1986. "On Competitive Cycles in Productive Economies," Working Papers 86-19, C.V. Starr Center for Applied Economics, New York University.
  15. Woodford, Michael, 1986. "Stationary sunspot equilibria in a finance constrained economy," Journal of Economic Theory, Elsevier, vol. 40(1), pages 128-137, October.
  16. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 725-737.
  17. Brock, William A. & Dechert, W. Davis, 1991. "Non-linear dynamical systems: Instability and chaos in economics," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 40, pages 2209-2235 Elsevier.
  18. de Vilder, Robin, 1996. "Complicated Endogenous Business Cycles under Gross Substitutability," Journal of Economic Theory, Elsevier, vol. 71(2), pages 416-442, November.
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