Fractals and self-similarity in economics: the case of a two-sector growth model

La Torre, Davide, Marsiglio, Simone, and Privileggi, Fabio (2011) Fractals and self-similarity in economics: the case of a two-sector growth model. Image Analysis and Stereology, 30 (3). pp. 143-151.

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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.

Item ID: 24837
Item Type: Article (Research - C1)
ISSN: 1580-3139
Keywords: fractals; iterated function system; self-similarity; sierpinski gasket; stochastic growth
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Date Deposited: 06 Feb 2013 02:39
FoR Codes: 14 ECONOMICS > 1401 Economic Theory > 140102 Macroeconomic Theory @ 30%
14 ECONOMICS > 1401 Economic Theory > 140103 Mathematical Economics @ 40%
14 ECONOMICS > 1402 Applied Economics > 140202 Economic Development and Growth @ 30%
SEO Codes: 91 ECONOMIC FRAMEWORK > 9101 Macroeconomics > 910103 Economic Growth @ 80%
97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 20%
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