No, this isn't right - you don't provide anything to buttress this I note.
Again, you fail to accept the fact that nobody says the total collected increases. It is simply that the breakdown of that total changes to include more paid by those who currently cheat the income tax system and less from those who are current legal participants.
In figuring a % of GDP, there is no difference between who buys for consumption. A criminal who buys bread pays tax just like a legal. THe same is not true of our current income tax system.... a criminal "submits" no tax today.
Again, the simple [and I do mean simple] result is that more tax is taken from criminals [and less from legals - resulting in the same total.]
Simply taking a % of GDP is enough to guarantee it. You see, criminals' expenditures are no different than your or my expenditures. THey both count in GDP.
That is what the hooker example precisely does. Let's assume a hooker collects $50,000 for her services.
If she filed under the income tax (she doesn't) it would look something like this:
Gross - +$50K
Minus Bus. Expenses - $10K
Minus Personal Exemptions -
Minus Standard Deductions -
Without looking up these figures, it would probably workout including her self-emplyment taxes to $10-12K that she is suppose to pay, but doesn't.
Under the fairtax:
Gross for her services - $50K
23% that she should remit but doesn't - $11.5K
Under BOTH system, the hooker illegally pockets roughly the same amount. This isn't rocket science. From the criminal perspective, there is no significant difference between the two systems. Really.