Recently an online interlocutor made the point to me that a "flat" tax is regressive rather than fair because minimum living expenses are largely fixed, thus creating a "proportionally" higher tax rate on those of lower income.

In the course of countering his attempted argument, I realized that the definition of "flat" and "progressive" have been shifted one echelon over, creating a distortion of terms in favor of the preferred Marxist/Progressive position.

A *truly* flat tax resembles a fee. If the government spends $2B on a new aircraft carrier and there are 400 million taxpayers, then a "flat" tax-- a uniform distribution of tax burden-- would simply divide that $2B among the 400M taxpayers and we'd each get a $50 bill to pay from Uncle Sam.

The ingenuity in the verbal gymnastics is in describing the *rate* as "flat." But the rate is not the tax. It is the first derivative, the rate of change.

A brief physics analogy illustrates this point. If you are traveling at a "flat" rate of speed, then your position is still changing, perhaps at a rate of 55 miles per hour. Likewise, if you are accelerating at a "flat" rate of 200 miles per hour per hour, your speed is changing and you will likely crash or get a ticket if you sustain that.

The key point here is this: tax BURDEN is the tax, not the tax RATE. The obvious corollary follows immediately behind: *any taxation scheme in which some pay more than others is in fact progressive*.

It may be progressive with respect to income-- those who earn more pay more. It might be progressive with respect to wealth-- like a property tax-- in that those with more taxable wealth pay more tax. Regardless of the basis for the progressivity, it is still "progressive" in taxation.

A proportional tax of a fixed 15% or 20% then isn't "flat" in *tax*, only in *rate*. As a *tax*, it is progressive. Returning to our car example, the flat rate of speed was still producing a change in position (predictable over time).

When we add a progressive rate, then the system becomes doubly progressive, like the way a change in position is affected by a "fixed" rate of acceleration. It's like taxing your income squared or income cubed by some fixed rate. The resulting distribution follows an exponential function and is *progressively progressive*.

This is why a so-called "flat" income tax is progressive, not regressive.

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