> We can't put a precise worth on it for different people, sure. But I think it's indisputable that there's a curve, we know it's rough shape, and that it's a reflection of marginal utility.

There is indeed a curve, and we do know its rough shape (it's nonincreasing). But that curve is for one individual. Utility is not an objective measure. Every individual has their own "unit" of utility and there is no conversion factor which would allow utility to be summed or compared across multiple individuals.

This is heresy to utilitarians, to be sure. How are you supposed to implement policies which ensure the greatest benefit for the greatest number if you can't calculate a collective utility score? That doesn't bother me, though, since I'm not a utilitarian. So far as I'm concerned the utilitarians are just implementing policies based on their own preferences and ignoring what anyone else actually wants.

> Diminishing marginal utility of income (DMUI) means that the greater a taxpayer's income, the less an additional dollar of income is worth to him.

This is a fairly standard description of the concept of marginal utility, aside from the fact that it's confusing income and wealth. (The greater one's wealth the less each additional dollar is worth. Income is irrelevant except as a poor proxy for wealth.)

Note that it only talks about one person. As I acquire more wealth I'm less and less willing to put in the same effort / pay the same cost to acquire each additional dollar. No issues there, this is not particularly controversial.

> If DMUI holds, the government exacts a lesser sacrifice from a higher-income taxpayer, with each dollar taxed, than from a lower-income taxpayer.

And here they make an extraordinary leap from talking about one individual's marginal utility to comparing the "sacrifice" (lost utility) of multiple individuals. They're making the assumption that all individuals have exactly the same utility scale, which is manifestly false. Everyone has their own utility scale, which varies over time and is in general unknowable, even to them, except as it is partially revealed through their actions. It can readily be observed, however, that a dollar of additional income does not have the same utility to two different people with the same wealth: For any given level of wealth, some pursue higher-paying work while others don't consider it worth the effort. Taking some amount of money from the first group represents a larger sacrifice than taking the same amount from the second group, even though their wealth is the same. Since you can't even say that equal wealth results in equal marginal utility, how can you claim that lower or higher wealth (much less income) necessarily implies higher or lower marginal utility? There is absolutely no reason why one person with $1M cannot get the same marginal utility out of an additional dollar—by whatever objective measure you care to name—as someone else with a net worth of $10k.

> … well, sure the tax code is necessarily imperfect.

I'm not asking for perfection. I'm just asking that the law, which is supposed to be just, not discriminate against people based on irrelevant factors such as annual income. The fact that a progressive tax system based on annual income imposes different levels of taxation on two people with the same earnings merely because one received their pay in a lump sum while the other received it in installments is a strong hint that the system is based on unsound principles.