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Cantor Type Invariant Distributions in the Theory of Optimal Growth under Uncertainty

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  • Mitra, Tapan

    (Cornell U)

  • Privileggi, Fabio

    (Universita degli Studi del Piemonte Orientale)

Abstract

We study a one-sector stochastic optimal growth model, where the utility function is iso-elastic and the production function is of the Cobb-Douglas form. Production is affected by a multiplicative shock taking one of two values. We provide sufficient conditions on the parameters of the model under which the invariant distribution of the stochastic process of optimal output levels is of the Cantor type.

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Bibliographic Info

Paper provided by Cornell University, Center for Analytic Economics in its series Working Papers with number 03-09.

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Date of creation: Aug 2003
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Handle: RePEc:ecl:corcae:03-09

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  1. Tapan Mitra & Luigi Montrucchio & Fabio Privileggi, 2003. "The nature of the steady state in models of optimal growth under uncertainty," Economic Theory, Springer, Springer, vol. 23(1), pages 39-71, December.
  2. Manuel S. Santos & Jesus Vigo-Aguiar, 1998. "Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models," Econometrica, Econometric Society, Econometric Society, vol. 66(2), pages 409-426, March.
  3. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, Elsevier, vol. 4(3), pages 479-513, June.
  4. Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 259-273, June.
  5. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, Elsevier, vol. 11(3), pages 329-339, December.
  6. Araujo, A, 1991. "The Once but Not Twice Differentiability of the Policy Function," Econometrica, Econometric Society, Econometric Society, vol. 59(5), pages 1383-93, September.
  7. Blume, Lawrence & Easley, David & O'Hara, Maureen, 1982. "Characterization of optimal plans for stochastic dynamic programs," Journal of Economic Theory, Elsevier, Elsevier, vol. 28(2), pages 221-234, December.
  8. Santos, Manuel S, 1991. "Smoothness of the Policy Function in Discrete Time Economic Models," Econometrica, Econometric Society, Econometric Society, vol. 59(5), pages 1365-82, September.
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Citations

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Cited by:
  1. Guido Cozzi & Fabio Privileggi, 2009. "The fractal nature of inequality in a fast growing world: new version," Working Papers, Business School - Economics, University of Glasgow 2009_30, Business School - Economics, University of Glasgow.
  2. Guido Cozzi & Fabio Privileggi, 2007. "The Fractal Nature of Inequality in a Fast Growing World," Working Papers, Business School - Economics, University of Glasgow 2007_45, Business School - Economics, University of Glasgow.
  3. La Torre, Davide & Marsiglio, Simone & Privileggi, Fabio, 2011. "Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model," POLIS Working Papers, Institute of Public Policy and Public Choice - POLIS 157, Institute of Public Policy and Public Choice - POLIS.
  4. Mitra, Tapan & Privileggi, Fabio, 2005. "Cantor Type Attractors in Stochastic Growth Models," POLIS Working Papers, Institute of Public Policy and Public Choice - POLIS 43, Institute of Public Policy and Public Choice - POLIS.
  5. Olson, Lars J. & Roy, Santanu, 2005. "Theory of Stochastic Optimal Economic Growth," Working Papers, University of Maryland, Department of Agricultural and Resource Economics 28601, University of Maryland, Department of Agricultural and Resource Economics.

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