Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model

Davide La Torre, Simone Marsiglio and Fabio Privileggi

POLIS Working Papers from Institute of Public Policy and Public Choice - POLIS

Abstract: 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.

Keywords: fractals; iterated function system; self-similarity; Sierpinski gasket; stochastic growth (search for similar items in EconPapers)
JEL-codes: C61 O41 (search for similar items in EconPapers)
Pages: 16 pages
Date: 2011-06
New Economics Papers: this item is included in nep-dge, nep-fdg and nep-ore
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:uca:ucapdv:157

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