Three Dimensional Fractal Attractors in a Green Transition Economic Growth Model

We analyze a two-sector stochastic economic growth model of green transition with pollution externalities and foreign capital. The final good is produced by combining dirty and clean inputs, with different implications on pollution accumulation. Pollution negatively affects production capabilities and can be reduced by switching to the clean input. The clean input is produced by using the dirty input and the foreign capital received (in the form of dirty input). Random shocks make the effective economy's ability to transition to green activities highly uncertain, eventually undermining its economic development. Such a setting gives rise to a dynamic system represented by a three dimensional affine iterated function system. We show that the economy's steady state is represented by an invariant measure supported on a compact set, characterizing its fractal nature and showing that its attractor may be a distorted Sierpiński tetrahedron.