We attack the standard problem of optimal taxation by departing from the premise, universally adopted in the literature, that the optimal tax function does not induce bunching or gaps in the distribution of income. Formally, we do extend the set of admissible functions and allow for functional forms and resulting behavioral responses that are normally discarded at the outset in the literature. In other words, we do recast the optimal taxation problem on a richer domain and we explicitly consider tax functions that are routinely ignored in the literature. The tax functions that we consider do induce bunching and gaps. In fact, the tax functions that we focus on while being fully admissible make the standard methodology - based on the first order approach - inapplicable. Therefore, in the paper we develop a procedure - based on elementary variations - that allows us to derive conditions that identify the optimal tax function on the domain of functions that includes tax functions that allow for the possibility of bunching or gaps.
JEL Codes: H21