FairTax would still be federal. States could do their state taxation however they choose. However, given that states with an income tax currently piggy-back on the federal income tax filings...it might be more work for them.
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<br>The tricky thing would be all the programs currently receiving federal funding that would "all of a sudden" have to rely on state funding. What I would expect is for states to increase their rate of taxation in order to allow them to replace the federal funds with state funds. Liberal-leaning states, at least. More conservative-leaning states might just try to go it without the federal funds, which would essentially give their residents a massive tax break relative to the rest of the country.
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<br>Those benefiting from social programs would leave those states when their programs would ceased to exist. Those looking to avoid high state taxes would move in instead. Eventually some sort of equilibrium (between states) would be reached.