My understanding is that &quot;progressive tax&quot; is more typically defined as a rising average tax rate, which <i>would</i> make &quot;BI plus flat tax&quot; represent a set of smooth progressive curves.<p>It&#x27;s very much worth noting, though, that there are plenty of progressive curves - including those currently in use by many jurisdictions - that have no close approximation in that set.  And in particular, if what you want is an increasing marginal tax rate, it does not do that.