The problem: it's unlikely the 10% flat tax, as proposed, can replace the individual income tax, much less also replace the payroll taxes (which are 15.4% combined, on the first $118,000 of wage income).
I've done the math: With a simple deduction of about $36,000 per household, we would need a 21% flat tax rate on the income above that just to replace current income tax revenues.
This isn't hypothetical. I've used the IRS's own numbers, and chose $36,000 for the standard deduction because it would eliminate individual income taxes completely for the bottom 50%.
So, Cruz's 10% plan will fall short by about 50% even BEFORE the elimination of the payroll tax was instituted.
There's simply no way it can work, as proposed.
Your model assume income would be static, which it would not be. The economy would explode.
That said, I agree there would be a shortfall, at least in the short run, but the 10% number is like a used car negotiation.
You start low, and meet in the middle — say a 15% flat tax.