Modelling the distribution of salaries

In this paper, we study analytically a simple model of salary distributions where two individuals, (employees) who both work for the same organisation, compare salaries. The higher paid individual does nothing but the lower paid individual leaves the organisation and is replaced by another, whose salary is picked from a power law distribution. We find that the resulting distribution is also power law, but with a different exponent. We also introduce variations to this simple model and find that the resulting distribution is dependent on the distribution from which the new individuals salary is chosen from and also find that the exponent of the resulting distribution is dependent on the total number of individuals comparing salaries. Finally we compare the mean field version and a finite dimension 1-d version of the model by carrying out numerical simulations.