Unequal wages for equal utilities

When educational policy is supplemented by a redistributive income tax, and when individualsdiffer in their ability to benefit from education, the optimal policy is typically rather regressive.Resources are concentrated on the most able individuals in order to get a "cake" as big aspossible to share among individuals through income taxation. In this paper we put forwardanother reason to push for regressive education. It is not linked to heterogeneity in innate ability to benefit from education but to pervasive non-convexities that arise in the optimal income tax problem when individual productivities are endogenous. For simplicity we assume a lineareducation technology and a given total education budget. To give the equal wage outcome thebest chance to emerge, we also assume that individuals have identical learning abilities.Nevertheless, it turns out that in the first-best wage inequality is always preferable to wageequality. Even more surprisingly, this conclusion remains valid in the second-best (unless adhoc restriction on the feasible degree of a wage differentiation are imposed). This is in spite ofthe fact that wage equalization would eliminate any need for distortionary income taxation.