Learning objectives
To provide to the students some specific tools in order to properly investigate current research topics in the frame of kinetic equations for socio-economic sciences.
Course unit content
Introduction to kinetic equations for a simple market economy.
Investigation (from a modelling and an analytical point of view) of several interaction models for wealth exchange:
- basic deterministic model;
- model with random variables;
- model with taxation and redistribution.
Full programme
Wealth distribution function and macroscopic fields of an economic model.
Boltzmann-type evolution equation and its major properties.
Investigation of several interaction models for indiviuals exchanging money:
- basic deterministic model;
- model with random variables taking into account possible non-deterministic effects in the market;
- model with taxation and redistribution of the collected wealth.
We will study existence and properties of a steady state for these models, with particular reference to suitable asymptotic regimes ("continuous trading limit").
We will discuss about the possible formation of distributions with Pareto tails, in agreement with experimental data.
Bibliography
Books or extended reviews:
- B. During, D. Matthes, G. Toscani, "A Boltzmann-type approach to the formation of wealth distribution curves", Riv. Mat. Univ. Parma 1 (2009) 199–261.
- L. Pareschi, G. Toscani, "Interacting multiagent systems. Kinetic equations and Monte Carlo methods", Oxford University Press (2013).
Research papers:
- A. Chakraborti, B.K. Chakrabarti, "Statistical mechanics of money: how saving propensity affects its distributions", Eur. Phys. J. B. 17 (2000), 167-170.
- S. Cordier, L. Pareschi, G. Toscani, "On a kinetic model for a simple market economy", J. Stat. Phys 120 (2005) 253–277.
- D. Matthes, G. Toscani, "On steady distributions of kinetic models of conservative economies", J. Stat. Phys. 130 (2008), 1087-1117.
- M. Bisi, G. Spiga, G. Toscani, "Kinetic models of conservative economies with wealth redistribution", Comm. Math. Sci. 7 (2009) 901–916.
