Young Researchers Workshop: Kinetic models in biology and social sciences

Kinetic models of binary welfare

Kirk Kayser

Arizona State University

Kinetic exchange models of markets have been used to recover and analyze characteristics of wealth distributions using tools from econophysics. The standard treatment is to consider microscopic binary interactions where the fractional amounts of individuals’ wealths that are transferred in a trade are determined by random variables; a corresponding Boltzmann-like equation then describes the evolution of the macroscopic wealth distribution. We develop a kinetic model of wealth redistribution that deterministically aims to bring individuals with wealth below a fixed welfare threshold up to it. This model uses need-based transfers (NBTs) where welfare occurs via binary gifts from individuals above threshold to individuals below, matched according to various policies. We characterize the impact of NBTs on the wealth distribution, consider the impact of regressive to progressive policies on inequality and efficiency in providing aid, and develop a centralized redistribution model for comparison.