Decreased production levels also result in decreased income and therefore decreased tax revenues, making taxation less attractive even to the taxing authority. Paradoxically, for this reason, a reduction in tax rates may often generate an increase in revenues. Particularly at higher marginal tax rates, the income tax affects the productivity of taxpaying workers in much the same manner as slavery affects the productivity of the slave (cf. pp. 4.11:81-2): in each case, the worker receives a relatively low marginal return on his or her efforts and consequently provides less revenue to the slaveholder or tax collector.

The type of tax structure most favored by income-tax proponents is the so-called "progressive" graduated income tax, under which the percentage of income paid in taxes increases as income increases. Here the term "progressive" refers to a mathematical relationship: if income i and tax paid t are regarded as variables, then the tax rate t / i "progresses" with i—that is, it varies in the same direction. Unfortunately, the term "progressive" suggests to the mathematically uninformed that such a tax is socially "progressive," that it represents an advance toward the future or somehow ameliorates the conditions of the masses. (In reality, the opposite would be closer to the truth.) In order to avoid this misleading connotation, we shall denote such tax structures here by the neutral term convex, referring to the characteristic shape of the generated curve when variables i and t are plotted on a graph. An example will be provided shortly.