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Cantor Type Attractors in Stochastic Growth Models

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Author Info
Mitra, Tapan ()
Privileggi, Fabio ()

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Abstract

We study a one-sector stochastic optimal growth model where production is affected by a shock taking one of two values. Such exogenous shock may enter multiplicatively or additively. A result is presented which provides sufficient conditions to ensure that the attractor of the iterated function system (IFS) representing the optimal policy, is a generalized topological Cantor set. To indicate the role of the strict monotonicity condition on the IFS in this result, examples of attractors, which are not of the Cantor type, are constructed with iterated function systems, whose maps are contractions and satisfy a no overlap property.

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Paper provided by Department of Public Policy and Public Choice - POLIS in its series P.O.L.I.S. department's Working Papers with number 43.

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Length: 23 pages
Date of creation: Feb 2005
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Handle: RePEc:uca:ucapdv:43

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Tapan Mitra & Luigi Montrucchio & Fabio Privileggi, 2003. "The nature of the steady state in models of optimal growth under uncertainty," Economic Theory, Springer, vol. 23(1), pages 39-71, December. [Downloadable!] (restricted)
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  2. Ferruccio Ponzano, 2001. "Efficiency wages and endogenous supervision technology," P.O.L.I.S. department's Working Papers 23, Department of Public Policy and Public Choice - POLIS. [Downloadable!]
  3. Mitra, Tapan & Privileggi, Fabio, 2003. "Cantor Type Invariant Distributions in the Theory of Optimal Growth under Uncertainty," Working Papers 03-09, Cornell University, Center for Analytic Economics. [Downloadable!]
  4. Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December. [Downloadable!] (restricted)
  5. Marchese, Carla & Privileggi, Fabio, 2001. "Who participates in tax amnesties? Self-selection of risk-averse taxpayers," P.O.L.I.S. department's Working Papers 21, Department of Public Policy and Public Choice - POLIS. [Downloadable!]
  6. Brock, William A. & Mirman, Leonard J., 1972. "Optimal economic growth and uncertainty: The discounted case," Journal of Economic Theory, Elsevier, vol. 4(3), pages 479-513, June. [Downloadable!] (restricted)
  7. Ponzano, Ferruccio, 2004. "The allocation of the income tax among different levels of government: a theoretical solution," P.O.L.I.S. department's Working Papers 40, Department of Public Policy and Public Choice - POLIS. [Downloadable!]
  8. Montrucchio, Luigi & Privileggi, Fabio, 1999. "On Fragility of Bubbles in Equilibrium Asset Pricing Models of Lucas-Type," P.O.L.I.S. department's Working Papers 5, Department of Public Policy and Public Choice - POLIS. [Downloadable!]
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  9. Ottone, Stefania, 2004. "Transfers and Altruistic Punishments in Third Party Punishment Game Experiments," P.O.L.I.S. department's Working Papers 41, Department of Public Policy and Public Choice - POLIS. [Downloadable!]
  10. Marchese, Carla & Privileggi, Fabio, 1999. "Taxpayers Attitudes Toward Risk and Amnesty Participation: Economic Analysis and Evidence for the Italian Case," P.O.L.I.S. department's Working Papers 6, Department of Public Policy and Public Choice - POLIS. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Guido Cozzi & Fabio Privileggi, 2009. "The fractal nature of inequality in a fast growing world: new version," Working Papers 2009_30, Department of Economics, University of Glasgow. [Downloadable!]
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