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A stylised model for wealth distribution

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posted on 2023-06-09, 07:45 authored by Bertram Duering, Nicos GeorgiouNicos Georgiou, Enrico Scalas
The 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 Singapore

Volume

9

Page range

95-117

Pages

23.0

Book title

Economic Foundations of Social Complexity Science

Place of publication

Singapore

ISBN

9789811057045

Department 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

Editors

Yuji Akura, Alan Kirman

Legacy Posted Date

2017-09-01

First Compliant Deposit (FCD) Date

2017-09-01

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