Wealth distribution under Yard-Sale exchange with proportional taxes

Recent analysis of a Yard Sale (YS) exchange model supplemented with redistributive proportional taxation suggested an asymptotic behavior P(w) similar to 1/w(mu) for the wealth distribution, with a parameter-dependent exponent mu. Revisiting this problem, it is here shown analytically, and confirmed by extensive numerical simulation, that the asymptotic behavior of P(omega) is not power-law but rather a Gaussian. When taxation is weak, we furthermore show that a restricted -range power-law behavior appears for wealths around the mean value. The corresponding power-law exponent equals 3/2 when the return distribution has zero mean.