re: If the US enacted a true flat rate tax, what would be the ideal tax rate?

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That's why a national sales tax passed as being the only tax allowable and the % rate would need to be passed as a Constitutional Amendment. Any other way and whatever tax and whatever rates will be political footballs eventually.

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Then you'd be looking at exemptions on the sales tax.

Would you tax the sale of stocks, bonds, real estate all the same? Would this tax be piled up on existing sales taxes?