Sacrifice and efficiency of the income tax schedule

We investigate the efficiency of equal sacrifice tax schedules in an economy which primitives are exactly those in Mirrlees (1971): a continuum of individuals with identical preferences defined over consumption and leisure who differ with respect to their labor market productivity. Using a separable specification for preferences we derive the minimum equal sacrifice allocation and recover the tax schedule that implements it. The separable specification allows us to use the methodology developed by Werning (2007b) to check whether the schedule is efficient, that is, whether there is no alternative tax schedule that raises more revenue while delivering less utility to no one. We find that inefficiency does not arise for most parametrizations we use to approximate the US economy. For the few cases for which inefficiency does arise, it does so only for very high levels of income and marginal tax rates.