How optimal nonlinear income taxes change when the distribution of the population changes

a r t i c l e i n f o The impacts of changing the number of individuals of a particular skill level on the solutions to two versions of the finite population optimal nonlinear income tax problem are investigated. In one version, preferences are quasilinear in leisure. For this version, it is shown that it is possible to sign the directions of change in everyone's optimal consumptions and optimal marginal tax rates. In the other version, preferences are quasilinear in consumption. For this version, it is shown that it is possible to sign the directions of change in everyone's optimal before-tax incomes and optimal marginal tax rates. Moreover, the directions of change in the optimal marginal tax rates are the same for the two specifications of preferences. Following the work of Mirrlees (1971), the theory of optimal nonlinear income taxation has investigated the properties of optimal income tax schedules when a government's limited information about taxpayers prevents the use of non-distorting lump-sum taxes. Comparative static analyses of optimal nonlinear income taxes attempt to gauge how changes in the underlying structure of the economy affect optimal taxes and their associated distortions. In this article, we derive new comparative static results that show how optimal nonlinear income taxes and the associated allocations change when the distribution of skills changes. Changes in the demographic structure of the population may arise for a number of reasons. For example, the skill distribution may change due to mobility between jurisdictions, as in Hamilton and Pestieau (2005); it may change over time due to the augmentation of skills through education, as in Brett and Weymark (2003); or it may differ between identifiable subgroups of the population who, because of this tagging, may face different tax schedules, as in Boadway and Pestieau (2007). We focus our attention on models with a discrete skill distribution and an arbitrary finite number of skill types. As noted by Brett and Weymark (2008a), it is possible to perturb discrete skill distributions in two ways. One can change the support of the distribution, say by increasing the skill level of individuals of a particular type. Comparative static analyses of this sort have been carried out by Brett and Weymark (2008a) and Simula (2010). Alternatively, one can keep the set of possible skill levels fixed and change the number of individuals with some skill level. This second kind of comparative static analysis …