A marginal sales tax is not a tax based on the fraction of your income/wealth that you spend, it is simply based on the nominal amount of spend.
Obviously this whole idea is politically impossible as it would result in huge wealth redistribution, but it is funny that with all the technological innovations, a simple exponential function for determining taxes is considered to not be feasible.
Yes — the nominal amount spent is a different fraction of their income for different income brackets, leading to a regressive tax.
Your final point is a non-sequitur:
The objection to an exponential function isn’t the technical complexity, but the behavior of exponential functions. You’re just dressing up “seize the wealthy’s money” in fancy math.
Though, you’re also understating the complexity of having such a variable tax and the second order impacts you’re likely to cause.
Edit — replying here as I hit my posting cap:
We care because our goal is a prosperous society for our citizens, for which we need a robust and active middle class.
We don’t exempt those goods from taxes (as we do with the essentials). My point has been that your vision for taxes creates a bi-modal distribution between rich and poor by laying a heavy tax burden on the middle class, until they wither — essentially creating feudalism.
A healthy society (with progressive taxes) creates opportunities for the poor to advance their well-being out of poverty by not over-encumbering the path to a middle class life. Regressive taxes are antithetical to that.
> Yes — the nominal amount spent is a different fraction of their income for different income brackets, leading to a regressive tax.
I am not understanding this. Why would we care what the percentage of tax paid is as a proportion of income? Poorer people have already been helped by reducing sales tax rates for the amount of spend needed to ascertain a certain quality of life. If they choose to spend more, and a higher income person chooses to spend less, why would society care that the lower income person pays more as a percentage of their income?
A lot of these schemes to “help the poor” in fact “cement feudalism” by destroying the middle class to the benefit of elites.