Later On

A blog written for those whose interests more or less match mine.

Why progressive taxation is fair: Marginal utility theory of value as foundation for progressive taxation

with 10 comments

Progressive taxation is taxing increasing increments of net income at increasingly higher rates. “Net income” is a bit of a misnomer, since true “net income” the income you have remaining after paying all your expenses, including taxes. I’m discussing how to tax the income that remains after deducting allowable expenses (business expenses, medical expenses above a certain amount, and so on) and other deductions (for dependents, blindness, and so on): the income called on tax forms “adjusted gross income.” For example, look at the current (progressive) tax rates for a single person:

Marginal Tax Rate                Single

10%                                  $0 – $8,700
15%                           $8,701 – $35,350
25%                         $35,351 – $85,650
28%                        $85,651 – $178,650
33%                       $178,651 – $388,350
35%                       $388,351+

The first $8,700 of adjusted gross income (income left after all deductions) is taxed at 10%, and the next $26,650 of AGI is taxed at a higher rate, 15%. The next $50,300 is taxed at a higher rate still (25%), and so on: progressively bigger percentage bites of the higher increments.

The marginal utility of a (fungible) good is based on the observation that the value of an incremental quantity of such a good declines as you get more: the first pound of salt you buy has a value, the second pound a lesser value, and ultimately the value pretty much goes negative: you’d take more only if they paid you.

This applies to fungible goods because with unique goods it’s somewhat different: even if you own many paintings you might still place a high value on a particular additional painting. But with fungible goods the idea does seem to work—with things like salt, sugar, tea (to a degree—not all teas are alike), coffee (same caution), and—a very fungible good—money (any dollar is like any other dollar).

You, for example, place a much higher value on $10,000 than would (say) Bill Gates. One reason the prices for luxury goods seem so high to ordinary consumers is that the price amount holds much greater value for them than it does for (say) a multi-millionaire. The price may well reflect the cost of exquisite materials and superior workmanship and so on, but here I’m talking only about the price amount (in dollars): the value of a given amount of dollars is relative to how many dollars someone already has. A poor person is willing to take more risks for $10,000 than would a wealthy person. This is now well known, thanks in large part to the work of Amos Tversky and Daniel Kahneman (q.v.).

Thus those higher margins of adjusted income—the income that one gets above and beyond (say) $388,350—is of less value per dollar to the individual than the per-dollar value of income below that level: indeed, according to marginal utility, the per-dollar value drops steadily as you get more dollars. So in terms of taxes, the value of the tax paid, to be constant, must be an increasing percentage of the incremental dollars.

In this way, the value to the taxpayer of the taxes paid is held constant by increasing appropriately the percentage paid at the higher margins. Progressive taxation is thus fair: every increment is taxed at (roughly) the same value to the individual taxpayer. QED.

Written by LeisureGuy

16 November 2012 at 10:04 am

Posted in Daily life

10 Responses

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  1. I think this makes sense. It would appear to come closer than the current system to finding a way to generate revenue without placing undue burden on any segment of the population.
    If properly implemented, this might be a way for states such as Maine to get away from our excise tax system, which places a huge burden on those with lower income. Especially in the case of automobiles- here you must pay an excise tax each year before you can register your vehicle- and the excise tax is based on the original purchase price of the vehicle, not it’s current value. So, as an example, a 20 year old Mercedes with 300 thousand miles on it that might be a hand me down to a young mother requires the payment of more excise tax than a 3 year old base model Toyota that the same young mother could not afford to purchase.

    Jeff Beyea

    16 November 2012 at 3:33 pm

  2. I like taxing income since it more or less guarantees the taxpayer has money—taxing property can hit people hard: they may have paid for their home but have little income, for example: cash poor. Same with the excise tax, as you point out. And sales taxes are terribly regressive. Income tax is, I think, the way to go, with progressive taxation of it. The trick then is to find appropriate increments and tax them so the value to the taxpayer is as equal as you can make it.


    16 November 2012 at 5:34 pm

  3. Isn’t the argument more simple: (1) given the fact a minimum of earning is required to live and moving above the minimum permits increasing levels of discretionary income; (2) as a society our culture is to share the burden of government costs as we can afford it; and (3) those with more wealth have more to gain and protect.
    BTW, can’t the “hand me down” person can sell the Mercedes, and give the proceeds to the young mother to buy the less valuable car.


    17 November 2012 at 12:21 pm

  4. That’s the argument I formerly made, but I was delighted to see that, in fact, increasing the proportion taxed reflects the declining value to the individual of incremental wealth. In other words, it doesn’t call for generosity in supporting government, it calls for simply providing tax amounts of equal value. This morning, in fact, I suddenly remembered a story that illustrates this idea—that the value of an amount of money depends heavily on how much money the individual has, so that a smaller amount from a person with little money has the same value (to the person) as a much larger amount from a wealthy person (and thus paying in taxes amounts of equal value necessitates a progressive tax rate). Here’s the story:

    Then he [Jesus] sat down opposite the offering box, and watched the crowd putting coins into it. Many rich people were throwing in large amounts. And a poor widow came and put in two small copper coins, worth less than a penny. He called his disciples and said to them, “I tell you the truth, this poor widow has put more into the offering box than all the others. For they all gave out of their wealth. But she, out of her poverty, put in what she had to live on, everything she had.”


    17 November 2012 at 12:43 pm

  5. maybe over a lifetime, but not in a given year


    30 May 2017 at 10:00 am

  6. Could you say a bit more. I don’t understand what you’re talking about.


    30 May 2017 at 10:10 am

  7. Outside of the argument that rich people can afford to pay more in taxes, most calls for taxing the rich seem to be based in an entitlement mentality. Why should someone be entitled to the fruits of the labor of another person?


    20 March 2019 at 3:44 pm

  8. I’ve seen that, and in general it’s a common argument against capitalism: the immense wealth the rich have gained (that portion not inherited, which gives them a big head start and advantage over those lacking that) is (of course) due to the labor and creativity of the employees (all who work for the company/capitalist). Thus the capitalist rakes in all this money from the employees (the money they earned by their work) because the capitalist feels entitled to it. Just as slaveowners felt entitled to be slaveowners. Just as businesses like Walmart that pay their employees so little that the taxpayers must help them (through food stamps and the like)—in effect, Walmart in its greed (and, as you say, sense of entitlement) saddled the government with covering part of normal payroll expense.

    And that’s why they cover a larger proportion of the costs of having a good country, well-defended and productive, with investments in infrastructure, education, healthcare, firefighters, law enforcement (better training is desperately needed), and all the other government services that benefit us: libraries, FDA, FTC, EPA, OSHA, and so on.


    20 March 2019 at 4:19 pm

  9. You do make valid points. The problem is that the fair vs unfair argument on the tax issue is ultimately self-defeating.


    24 March 2019 at 11:35 am

  10. How is that? Can you explain? It certainly doesn’t seem self-defeating to me, and apparently you agree with the points I made.

    You really need to expand on your argument—indeed, right now it’s not an argument, but only a statement with no supporting evidence or reasons. I do try to explain my position, not simply state it. I ask that you do the same.


    24 March 2019 at 11:40 am

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