Flat taxes are neutral under log utility

Abstract

If welfare grows with log income, then a flat 50% tax actually has no impact on the incentive to work, as the income effect exactly offsets the substitution effect. If returns diminish faster than logarithmically, then a flat tax actually increases the incentives for rich people to work. In reality, someone with no income still has some level of consumption, so a model like welfare = log(income + C) is more plausible than welfare = log(income). For the US federal taxes, the largest gap between average and marginal rates occurs at $200k, when someone pays a 35% marginal rate but only a 22% average tax rate. At this point, their incentive to work is about 83% as large as it would otherwise have been. That means that the income effect offsets about half of the disincentive from higher tax rates, which eliminates around 75% of the social cost. If the tax code was designed so that, according to this model, everyone’s incentive to work is 90% as large as it would naturally be, then the tax rate would grow continuously, and the resulting rates would look surprisingly similar to the current rate schedule, but without stopping at the current top rate. This schedule raises significantly more money than the status quo but only leads to a max disincentive of 10% (vs. 17%), because it varies continuously rather than jumping at brackets. – AI-generated abstract.