Declining marginal utility, progressive taxes, and fairness
He argued, however, that fairness required greater progressivity. Asked to explain and defend the basis for that belief, he offered the usual argument for declining marginal utility of income, claimed that fairness required equal utility burdens on rich and poor, and concluded that the tax system ought to be highly graduated.
As some of you may realize, he was making a mathematical mistake. His argument, if true, implies that richer people should pay more dollars in taxes than poorer people. But it does not tell us whether they should pay a larger or smaller proportion of their income.
To see that, consider two taxpayers, one with an income of $40,000/year, one with an income of $80,000. Consistent with declining marginal utility of income, assume that the former has a marginal utility of income of two utiles/dollar, the latter of one utile/dollar. Assume a flat tax which collects $4,000 from the poorer taxpayer, $8,000 from the richer. The utility cost of the tax is then 8000 utiles for each--"fair" by the standard of equal utility burden. The utility cost to the richer person of each dollar he pays is half as much--but he is paying twice as many dollars.
Generalizing this example, we can see that if marginal utility of income declines with increasing income less than proportionally--if, say, MU(I)=AI^(-.9)--then equal utility shares imply a regressive tax, while if it declines more than proportionally to income, the same rule implies a progressive tax.
The next interesting question is whether the rule itself makes any sense. I do not see that it does. I can see a philosophical argument for the claim that everyone should end up with the same income, although I am not convinced by it. I can see a utilitarian argument for redistribution designed to transfer income from those with low MUI to those with high MUI, although I can also see utilitarian problems with such a policy.
But a rule of equal utility cost faces two obvious problems. The first is that taxpayers do not all get the same utility benefit from the state, the second that the state does not get the same benefit from all taxpayers.
Consider a program such as social security which collects money and pays out money. Dollars collected from the richer taxpayer probably cost him less utility than dollars collected from the poorer taxpayer cost him. But dollars paid to the richer taxpayers also provide less utility than dollars paid to the poorer. So a rule of equal utility burden means that the poor are getting, in utility terms, a much better deal than the rich.
Next note that if rich and poor are bearing equal utility burdens, the state is getting a much larger benefit from rich than from poor. If one is going to imagine taxation as some sort of exchange between taxpayer and state, shouldn't costs and benefits to both sides count?
Consider the same standard in a private transaction. I offer to mow your lawn. You are much richer than I am, so--as I kindly point out--in order for the payment to cost you as much utility as the mowing costs me, you will have to pay me a hundred dollars an hour.
Assume, I think reasonably, that an hour of work costs each of us the same amount of utility--say ten utiles. You are saving me ten utiles of lawn mowing at a cost to you of ten utiles of lawn mowing. I am paying you (say) ninety utiles of money--money having a high MUI to you--at a cost to me of nine utiles of money. On net I am giving up nine utiles to get ten, you are giving up ten utiles to get ninety. That does not look like a fair transaction.
I should probably add that it is not clear to me that there is such a thing as a fair tax, even if we are willing to separate questions of fairness from questions of justice. But since many people do believe that there is such a thing and that they know about what it would be I find it interesting to try to make sense of the idea. It's a harder project than they may suppose.