The almighty Wikipedia speaks!
http://en.wikipedia.org/wiki/Poverty_in_the_United_States
Poverty level on a 2 person household is $13,200. Higher then $10,000, but hardly enough to make much difference. Also, the actual average Household income is $53,100. $43,000 is the median income. Since the average household is 2.69 and not 2, we'll add .69 people per the guidelines in the above link, which is $2,346.
This will render the % GDP bound for prebates as 29.2%, a fairly significant difference.
In another stupid cockup, the difference between nontaxed government spending and total spending in GDP terms is 13.2% NOT 11.2%, where 2.8/13.2 Trillion yields 21% Govt spending, meaning that after the interest deduction, the total is 12.8%.
Fair warning, this would increase overall taxes anyway since it produces enough to satisfy the budget, ie. no deficit.
r(GDP) - ((r) * .292GDP) = (1 + r).128GDP + .078GDP
rGDP - r.292GDP = .128GDP + r.128GDP + .078GDP
(Just divide out GDP and sum the vars in one step.)
.580r = .206
r = 36% sales tax.
Let's see if the upped prebate makes any difference.
Mr. and Mrs. Poverty. We'll keep them under the extreme pressure of a $10,000 income, and state that they have $9,235 in expenses. Now, the poverty threshold for FOUR is $20,000, and they will get 36% of that as their prebate, or $7,200. Their preceding expenses go up to $12,559.60, leaving them $4,640.40 more then they had, although this has a PP of $3,412.06. That's a significant improvement for the really poor.
Mr. and Mrs. Median. Pretax income of $40,000, expenditure of all post tax expenses at $36,495.26. Their prebate is now $7,200 for a total of $47,200. Total expenses are now $49,633.55. This means they lose $2,433.55, although this is only a PP of $1,789.38. That is still 4.4% of their old income.
DL and LJ had $120,000 in income, $50,000 in expenses and $40,280.18 in disposable income. Their prebate, having no children, is only $4,752, their expenses have shot up to $68,000. They now posess a surplus of $56,752, but this has PP of $41,729.41 meaning they have gained $1,449.23 in purchasing power. This is only ~1% of income.
BH and Small boy had $120,000 with $90,280.18 in expenses. Same prebate. $124,752.00, expenses now $122,781.04, leaving a gain of $1970.96, which is $1,449.23 in PP. Identical to the more responsible couple.
Lawyer #1 $500,000 with $200,000 in spending. Old disposable income is $149,233.86. This family has 5 children, and thus their cost of living is $30,200. (See above link.) This yields a Prebate of $10,872. New income is $510,872, with the expenses trending up to $272,000. New disposable income is $238,872, $175,641.18 PP for a net gain of $26,407.32.
Lawyer #2 $500,000 with $350,000 in spending. Old disposable income is -$766.14. New income is $510,872, with the expenses trending up to $476,000. New disposable income is $34,872, $25,641.18 PP for a net gain of $26,407.32. Again, no difference.
Lastly, we'll take another look at our elderly couple. Their old pretax income was $27,909.52 leaving $26,022.52 disposable, of which $20,000 is spent. With the the prebate set $4,752, their new income is $32,661.52. $27,800 is their new expense and this means they now have a disposable income of $4,861.52, $3,574.65 PP and a $3,774.39 loss in purchasing power.
Clearly for any kind of fairness to seniors, social security needs to have a cost of living increase.but that's bad for just about everyone else. Vis-a-vis, we move about 4.5 percentage points from fixed costs over to variable costs.
r(GDP) - ((r) * .292GDP) = (1 + r).173GDP + .033GDP
rGDP - r.292GDP = .173GDP + r.173GDP + .033GDP
.535r = .206
r = 39% sales tax.
If we take Malice's advice and move the GDP cost of living percentage for the Prebate up to 50%, then things are going to get really ugly.
r(GDP) - ((r) * .5GDP) = (1 + r).173GDP + .033GDP
rGDP - r.5GDP = .173GDP + r.173GDP + .033GDP
.327r = .206
r = 63% sales tax.
The interested party can plug these rates into the numbers above, remembering to up Social Security benefits in proportion to the sales tax for the elderly couple. But I think I have enough info to describe how the FairTax Gains/Loss function works. There two graphs to worry about. The 1st is for wage earners, the second for fixed income retirees. Imagine an X/Y graph where Y is the money saved by FairTax and X is the income level.
On the wage earners graph the curve starts at X = 0 and Y = Prebate amount. It then descends towards 0, and crosses the X axis at the point where the Prebate is equal to the amount that the income tax equivalent of the sales tax rate exceeds the sum of the former income and payroll taxes. It then continues to drop until it turns back up and then hits the point where the old income and payroll tax are less then the sales tax's income equivalent by the amount of the prebate. The curve then goes up again, peaking at or about the the point where the old income and payroll tax combo peaked, perhaps 45% at best. It then starts to curve back down towards the limit of the old Alternative Minimum Tax. If the old AMT is less then the income equivalent of the sales tax, 28%, as it almost certainly is in this case, then the the line will recross the X axis and the super rich will begin paying more in direct proportion to their incomes.
The seniors have it MUCH harder. Assuming they have no Social Security or Medicare income, or personal retirement resources of any kind, the system is a godsend since it means the Prebate gives them an income. But, even if Social Security gets ratcheted up in proportion to the tax, the line will go screaming through the X axis just after the lost purchasing power exceeds whatever meagre income tax they have recouped plus the Prebate, and the curve is going to keep right on going that way until the various old federal tax receipts exceed the income equivalent of the sales tax rate. With a sales tax rate much above 40%, this will never happen.
So with the standard FairTax deployment, the destitute get some advantages, as do the upper echelons of the middle class and low to middle portion of the upper class. The super rich get hit to some extent, but the hit isn't quite as much to them as it is for the lower class and the lower portions of the middle class. The biggest losers are the retired.
As the base of the Prebate goes up, each graph is pushed somewhat to the right and the lines on the wage graph get pulled down and flattened out a bit. Eventually both do achieve a degree of progressive redistribution, by which point the lower classes and poorer seniors are getting all the benefits and the middle and upper classes are taking all the flack. But the rate will be quite huge by that point.
I think this should end any argument for the FairTax as a viable alternative, unless someone can demonstrate a serious flaw in my math.
I will post my own thoughts on tax reform later.