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Capital-Labor Substitution and Competitive Nonlinear Endogenous Business Cycles

  • Jean-Michel Grandmont

    (Crest)

  • P, A, Pintus

    (Crest)

  • R, De Vilder

    (Crest)

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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Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 97-28.

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Date of creation: 1997
Handle: RePEc:crs:wpaper:97-28
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  1. Patrick Pintus & Ducan Sands & Robin De Vilder, 1998. "On the Transition from Local Regular to Global Irregular Fluctuations," Working Papers 98-54, Centre de Recherche en Economie et Statistique.
  2. 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.
  3. Benhabib Jess & Farmer Roger E. A., 1994. "Indeterminacy and Increasing Returns," Journal of Economic Theory, Elsevier, vol. 63(1), pages 19-41, June.
  4. Boldrin, Michele & Woodford, Michael, 1990. "Equilibrium models displaying endogenous fluctuations and chaos : A survey," Journal of Monetary Economics, Elsevier, vol. 25(2), pages 189-222, March.
  5. Cass, David & Shell, Karl, 1983. "Do Sunspots Matter?," Journal of Political Economy, University of Chicago Press, vol. 91(2), pages 193-227, April.
  6. Kiminori Matsuyama, 1990. "Increasing Returns, Industrialization and Indeterminacy of Equilibrium," Discussion Papers 878, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. de Vilder, Robin, 1996. "Complicated Endogenous Business Cycles under Gross Substitutability," Journal of Economic Theory, Elsevier, vol. 71(2), pages 416-442, November.
  8. 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.
  9. Woodford, Michael, 1986. "Stationary sunspot equilibria in a finance constrained economy," Journal of Economic Theory, Elsevier, vol. 40(1), pages 128-137, October.
  10. 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.
  11. Grandmont, Jean-Michel, 2008. "Nonlinear difference equations, bifurcations and chaos: An introduction," Research in Economics, Elsevier, vol. 62(3), pages 122-177, September.
  12. Roger Guesnerie & Costas Azariadis, 1982. "Prophéties créatrices et persistance des théories," Revue Économique, Programme National Persée, vol. 33(5), pages 787-806.
  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. Chiappori, Pierre Andre & Guesnerie, Roger, 1991. "Sunspot equilibria in sequential markets models," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 32, pages 1683-1762 Elsevier.
  15. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
  16. 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.
  17. Grandmont, Jean-Michel, 1986. "Stabilizing competitive business cycles," Journal of Economic Theory, Elsevier, vol. 40(1), pages 57-76, October.
  18. Costas Azariadis & Roger Guesnerie, 1986. "Sunspots and Cycles," Review of Economic Studies, Oxford University Press, vol. 53(5), pages 725-737.
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