Kinetic Models of Need-Based Transfers

Kinetic exchange models of markets utilize microscopic binary descriptions of wealth transfers to derive a Boltzmann-like equation describing the evolution of the corresponding wealth distribution. We develop such a model to describe a binary form of welfare called need-based transfer (NBT), inspired by the gift-giving of cattle practiced among the Maasai of East Africa. Variants of such welfare schemes can be attributed to other human and animal communities. Specifically, we consider NBTs relative to a given welfare threshold such that individuals with surplus give to individuals with need in order to preserve the recipient’s continued viable participation in the economy. Our NBT kinetic model considers redistribution rules parameterized to vary between regressive and progressive redistribution.