If the reward for creating a successful innovation is a top income, for extreme parameter values, maximizing the welfare of the middle class requires a negative top tax rate

Taxing Top Incomes in a World of Ideas. Charles I. Jones. Stanford Univ, September 2018. https://web.stanford.edu/~chadj/papers.html

Abstract: This paper considers the taxation of top incomes when the following conditions apply: (i) new ideas drive economic growth, (ii) the reward for creating a successful innovation is a top income, and (iii) innovation cannot be perfectly targeted by a separate research subsidy --- think about the business methods of Walmart, the creation of Uber, or the ``idea'' of Amazon.com. These conditions lead to a new term in the Saez (2001) formula for the optimal top tax rate: by slowing the creation of the new ideas that drive aggregate GDP, top income taxation reduces everyone's income, not just the income at the top. When the creation of ideas is the ultimate source of economic growth, this force sharply constrains both revenue-maximizing and welfare-maximizing top tax rates. For example, for extreme parameter values, maximizing the welfare of the middle class requires a {\it negative} top tax rate: the higher income that results from the subsidy to innovation more than makes up for the lost redistribution. More generally, the calibrated model suggests that incorporating ideas and economic growth cuts the optimal top marginal tax rate substantially relative to the basic Saez calculation.