You didn't keep consumption consistent from the income tax to the NRST. You're assuming consumption will increase.
Silly me, you mean the family has a choice to save more under the NRST? Now why didn't I think of that?
I assumed you wanted to compare the worst case effective tax rate of the NRST for the particulars of your example to the family's tax burden under the current system.
We can always do the calculation assuming no change in dollars spent and provide that number. After all it becomes the family's choice to do which ever they wish, instead of one driven by government extracting it's pound of flesh limiting the family options of utilizing their resourses as they see fit.
How can you compare a tax on income to a tax on consumption if they aren't consistent?
Easy by looking at worst cases, and noting the family is still much better off under the NRST, as well as the economy from expansion of sales.
I thought a benefit of the NRST is people will save and invest more. If you want to show a reduction of prices, you will have to reduce the cost of consumption, not raise the amount of consumption.
"A" benefit yes, and one a family can choose to take advantage of to the full degree of their available resources before government can take its cut out of them.
So let the family choose to save/invest the maximum they can after holding their expenditure to the original level of $77,500.
If you hold the expenditure constant to $77,500 expenditure, and save, invest, etc. $27,146 each year instead, the family's effective tax rate of the NRST will drop to
NRSTrate = 100*((0.23*$77,500)-$4,646) / $104,626 = 12.59%
They will purchase approximately the same amount of stuff with $77,500 since prices would fall 20-25% under competition, build a nice retirement, provide capital for enhancing productivity and the creation of new industry expanding the economy, with expanding revenues to the government under the Laffer effect.
OTOH, they could choose keep paying a 35% tax burden, making out report cards on there family life to the IRS, and continue to have their retirement taxed away as well, by not supporting the NRST.
It's all a matter of the family's choice.
Save max:
NRSTrate = 100*((0.23*$77,500)-$4,646) / $104,626 = 12.59%
Spend max
NRSTrate = NRSTnet/GrossIncome = $18,794.68/$104,646 = 17.96%
Or anything inbetween max invest and minmum possible spending to max spending and no saving and investment as the individual citizen may choose.
Or limit individual liberty to make such choices, because government has already limited your options for you:
ITrate = ITnet/GrossIncome = $35,270/$100,000 = 35.27%
If you want to show a reduction of prices, you will have to reduce the cost of consumption, not raise the amount of consumption.
Prices can certainly fall as consumption & demand rises my friend. Prime example of point being computers, where high productivity and strong competition drives prices down while consumption & demand grow.
With the removal of the income/payroll tax system the economy becomes more efficient, thereby allowing reductions in price under market competition.
Even with maximum consumption dollars flowing into the economy, the indivual benefits through increasing wages earned, greater returns on investment and increases in productivity for higher corporate earnings distributed to individuals, and prices constrained as company's compete for market share in an expanding economy.
Your "save max" still assumes a consistent expenditure rate, not a consistent consumption rate. You say "They will purchase approximately the same amount of stuff with $77,500 since prices would fall 20-25% under competition." You're making an assumption that prices falling and the sales tax will be a wash. You can't do that, you have to factor in the falling prices into your equation. (As it turns out, a 20% price reduction is not a wash. Tax inclusive prices go up.)
Here it is with a theoretical 20% drop in prices:
NRSTrate = (($77,500 * 80%) * 29.87%) - $4,646 / $104,626 = 13.26%
Now looky there. I made an accurate comparison of the effects of the income tax vs. the NRST using the tax exclusive sales tax rate. How is that possible?