Stability of Pareto-Zipf Law in Non-Stationary Economies

Generalized Lotka-Volterra (GLV) models extending the (70 year old) logistic equation to stochastic systems consisting of a multitude of competing auto-catalytic components lead to power distribution laws of the (100 year old) Pareto-Zipf type. In particular, when applied to economic systems, GLV leads to power laws in the relative individual wealth distribution and in the market returns. These power laws and their exponent a are invariant to arbitrary variations in the total wealth of the system and to other endogenous and exogenous factors. The measured value of the exponent a = 1.4 is related to built-in human social and biological constraints.