On Lipschitz continuity of the iterated function system in a stochastic optimal growth model
This paper provides qualitative properties of the iterated function system (IFS) generated by the optimal policy function for a class of stochastic one-sector optimal growth models. We obtain, explicitly in terms of the primitives of the model (i) a compact interval (not including the zero stock) in which the support of the invariant distribution of output must lie, and (ii) a Lipschitz property of the iterated function system on this interval. As applications, we are able to present parameter configurations under which (a) the support of the invariant distribution of the IFS is a generalized Cantor set, and (b) the invariant distribution is singular.
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- Mirman, Leonard J. & Zilcha, Itzhak, 1975. "On optimal growth under uncertainty," Journal of Economic Theory, Elsevier, vol. 11(3), pages 329-339, December.
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- Montrucchio, Luigi, 1987. "Lipschitz continuous policy functions for strongly concave optimization problems," Journal of Mathematical Economics, Elsevier, vol. 16(3), pages 259-273, June.
- Mirman, Leonard J & Zilcha, Itzhak, 1976. "Unbounded Shadow Prices for Optimal Stochastic Growth Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(1), pages 121-32, February.
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