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A stylised model for wealth distribution
chapter
posted on 2023-06-09, 07:45 authored by Bertram Duering, Nicos GeorgiouNicos Georgiou, Enrico ScalasEnrico ScalasThe recent book by T. Piketty (Capital in the Twenty-First Century) promoted the important issue of wealth inequality. In the last twenty years, physicists and mathematicians developed models to derive the wealth distribution using discrete and continuous stochastic processes (random exchange models) as well as related Boltzmann-type kinetic equations. In this literature, the usual concept of equilibrium in economics is either replaced or completed by statistical equilibrium. In order to illustrate this activity with a concrete example, we present a stylised random exchange model for the distribution of wealth. We first discuss a fully discrete version (a Markov chain with finite state space). We then study its discretetime continuous-state-space version, and we prove the existence of the equilibrium distribution. Finally, we discuss the connection of these models with Boltzmannlike kinetic equations for the marginal distribution of wealth. This paper shows in practice how it is possible to start from a finitary description and connect it to continuous models following Boltzmann’s original research programme.
Funding
The flat edge in last passage percolation; G2031; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/P021409/1
Novel discretisations of higher-order nonlinear PDE; G1603; LEVERHULME TRUST; RPG-2015-069
History
Publication status
- Published
File Version
- Accepted version
Publisher
Springer SingaporePublisher URL
External DOI
Volume
9Page range
95-117Pages
23.0Book title
Economic Foundations of Social Complexity SciencePlace of publication
SingaporeISBN
9789811057045Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
- Numerical Analysis and Scientific Computing Research Group Publications
Full text available
- No
Peer reviewed?
- Yes