title: Master equation for a kinetic model of a trading market and its analytic solution.
abstract: We analyze an ideal-gas-like model of a trading market with quenched random saving factors for its agents and show that the steady state income (m) distribution P(m) in the model has a power law tail with Pareto index nu exactly equal to unity, confirming the earlier numerical studies on this model. The analysis starts with the development of a master equation for the time development of P(m) . Precise solutions are then obtained in some special cases.
authors.affiliation: Theoretical Condensed Matter Physics Division and Centre for Applied Mathematics and Computational Science, Saha Institute of Nuclear Physics, Block-AF, Sector-I Bidhannagar, Kolkata-700064, India. arnab.chatterjee@saha.ac.in
authors.forename: Arnab
authors.initials: A
authors.lastname: Chatterjee
authors.forename: Bikas K
authors.initials: BK
authors.lastname: Chakrabarti
authors.forename: Robin B
authors.initials: RB
authors.lastname: Stinchcombe