Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model
We study a stochastic, discrete-time, two-sector optimal growth model in which the production of the homogeneous consumption good uses a Cobb-Douglas technology, combining physical capital and an endogenously determined share of human capital. Education is intensive in human capital as in Lucas (1988), but the marginal returns of the share of human capital employed in education are decreasing, as suggested by Rebelo (1991). Assuming that the exogenous shocks are i.i.d. and affect both physical and human capital, we build specific configurations for the primitives of the model so that the optimal dynamics for the state variables can be converted, through an appropriate log-transformation, into an Iterated Function System converging to an invariant distribution supported on a generalized Sierpinski gasket.
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| Length: | 16 pages |
| Date of creation: | Jun 2011 |
| Date of revision: | |
| Handle: | RePEc:uca:ucapdv:157 |
| Contact details of provider: | Web page: http://polis.unipmn.it
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- Mitra, Tapan & Privileggi, Fabio, 2009. "On Lipschitz continuity of the iterated function system in a stochastic optimal growth model," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 185-198, January.
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- Davide LA TORRE & Edward R. VRSCAY & Mehran EBRAHIMI & Michael F. BARNSLEY, 2008. "Measure-valued images, associated fractal transforms and the affine self-similarity of images," Departmental Working Papers 2008-45, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
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