FRACTALS AND SELF-SIMILARITY IN ECONOMICS: THE CASE OF A STOCHASTIC TWO-SECTOR GROWTH MODEL
Keywords:fractals, iterated function system, self-similarity, Sierpinski gasket, stochastic growth
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.
How to Cite
La Torre, D., Marsiglio, S., & Privileggi, F. (2011). FRACTALS AND SELF-SIMILARITY IN ECONOMICS: THE CASE OF A STOCHASTIC TWO-SECTOR GROWTH MODEL. Image Analysis and Stereology, 30(3), 143–151. https://doi.org/10.5566/ias.v30.p143-151
Original Research Paper