Optimal income taxation and the ability distribution: implications for migration equilibria

As recently argued by Diamond [1998], one of the key factors explaining the progressivity of an optimal non-linear income tax is the distribution of productivity among workers. Migration is one source of changes in the productivity distribution. How changes in the population's ability distribution affect optimal income tax schedules has received little attention. Changing the distribution generally changes both the objective function and the government budget constraint. We first consider the comparative statics of the fraction of highly-skilled workers with a Rawlsian welfare function (so that only the second effect is present) and a quasi-linear utility function. We perform the same analysis for a despotic social welfare function, and present some results for a utilitarian social welfare function. We study the interaction between mobility and redistributive taxation. We consider mobility by either the skilled or unskilled population in both Rawlsian and majority voting frameworks where governments take the population as fixed. Our main result is that equal ability distributions across jurisdictions is a stable equilibrium when the unskilled are mobile, but only under certain conditions when the skilled are mobile.