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The following is a quote of The Triumph of Injustice by Saez and Zucman.

According to the Constitution, direct taxes had to be apportioned among the states according to the population of each state. For example, if 10% of the US population lived in the state of New York, 10% of tax revenue had to come from there—even if a third of national income was earned in that state (which was roughly the case at the end of the nineteenth century), and even if most taxable individuals (those earning more than $4,000) lived there. Neither the 1894 income tax nor the one of 1862 were apportioned among the states, because apportioning them would have been nonsensical: it would have forced the government to tax the rich very little in the states where they were over-represented (such as New York), defeating the whole purpose of progressive income taxation.

I don't understand how this apportioning would be implemented, if the original tax would be a percentage on the upper tiers of incomes. Maybe I'm just not understanding the English here...

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    I think that's the point. It's not allowed to be a percentage on the upper tiers of incomes.
    – user253751
    Jan 15 at 14:41
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    This might actually be better fit for law stack exchange because it seems to be more about exactly how the US constitution works. This could be possibly interpreted as that New York just has to supply 10% of tax revenue from direct taxes - but not that necessarily all individuals have to pay the same 10% rate and it could be collected by taxing better-off individuals at higher rate - that would in my opinion satisfy the economic meaning of the phrase but again this is better question for lawyers that specialize in US constitution rather than economists
    – 1muflon1
    Jan 15 at 15:11
  • @1muflon1 well, if you would be so kind as to migrate the question, I wouldn't oppose. ;)
    – An old man in the sea.
    Jan 16 at 11:23
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No one else figured out a good way to apportion an income tax either, which is why there was a constitutional amendment, the sixteenth, that permits an income tax withotu apportionment.

The original apportionment clause seems to have been intended for a head tax ($X from every person) or perhaps a property tax, which would have had to have different rates in different states to make the apportionment work.

A direct federal tax must be apportioned. That is, if a state has 10% of the total population according to the most recent census, 10% of the tax must co0me from that state. Suppose there was a federal property tax, a tax rate of 0.1% on all property up to $10,000, and 0.25% on property over that amount. That would be a direct tax, and would have to be apportioned. If New York State had 10% of the population, but 25% of the property value, its tax rates would have to be factored down so that only 10% of the tax collected from the nation as a whole came from NY. The awkwardness of this provision has discouraged its use.

The Federalist suggests that this is a safeguard against a temptation to inflate population figures in the census in order to get more seats in Congress, as this would also result in an increase in the tax burden on the state.

In practice, because of the problems that apportionment would cause, the US Federal Government has avoided direct taxes. Some method of applying a tax that does not require apportionment has generally been found -- in fact I don't know of any tax by the Federal government which has required apportionment, although there may have been one.

The Supreme Court decision saying that an income tax was a direct tact that was subject to apportionment simply ended the tax until the 16thy amendment was passed -- no one tried to create a method to apportion it.

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