Fractals and Self-Similarity in Economics: the Case of a Stochastic Two-Sector Growth Model
AbstractWe 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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Bibliographic InfoPaper provided by Institute of Public Policy and Public Choice - POLIS in its series POLIS Working Papers with number 157.
Length: 16 pages
Date of creation: Jun 2011
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fractals; iterated function system; self-similarity; Sierpinski gasket; stochastic growth;
Find related papers by JEL classification:
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-06-18 (All new papers)
- NEP-DGE-2011-06-18 (Dynamic General Equilibrium)
- NEP-FDG-2011-06-18 (Financial Development & Growth)
- NEP-ORE-2011-06-18 (Operations Research)
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