...Sacrifice theory and the marginal utility of money
...Sacrifice theory is perhaps the most historically prominent and persistent argument in favor of progressive taxation. Stated simply, the theory posits that the fairest tax is one that extracts from each taxpayer an equal or proportionate “sacrifice.” The theory rejects the quid-pro-quo notion that taxes are remitted in return for government benefits and instead treats taxes simply as a burden that must be shared in the most equitable way. Sacrifice theory is dependent upon the economic principle that holds there is a marginal-utility curve for money to the effect that the more money one earns, the less utility (or satisfaction) will be derived from the last dollar earned. Thus, if you plot a chart in which the vertical axis is units of marginal utility a person gets from money, and the horizontal axis is the amount of money the person earns, the curve will eventually have a downward slope. A downward slope indicates, for example, that an incremental $1,000 has greater utility to a person earning $10,000 a year than it has to someone earning $100,000.
The economic principle of marginal utility on which sacrifice theory depends is sound. However, there are several difficulties with the sacrifice theory itself that render it untenable as an argument for progression.
First, the basic premise of sacrifice theory is conceptually flawed. The notion that taxes are simply a burden that must be tolerated rather than a payment for benefits raises the question: Why would the citizens of a democracy vote to impose taxes on themselves if they did not expect benefits in return? And if the government does provide benefits (which of course it does), why would the payment of taxes be considered a sacrifice rather than a fair payment for value received?...
Second, the validity of the theory depends on more than just the existence of a downward sloping marginal-utility curve. For progression to be justified under a theory of equal sacrifice, the curve must not only decline, but decline more rapidly than income rises. In the view of British economist Arthur Pigou and others, there is no way to prove this is true:
All that the law of diminishing utility asserts is that the last ₤1 of a ₤1000 income carries less satisfaction than the last ₤1 of a ₤100 income does. From this datum it cannot be inferred that, in order to secure equal sacrifice . . . taxation must be progressive. In order to prove that the principle of equal sacrifice necessarily involves progression we should need to know that the last ₤10 of a ₤1000 income carries less satisfaction than the last ₤1 of a ₤100 income; and this the law of diminishing utility does not assert.
Seligman credits the Dutch economist A.J. Cohen-Stuart with debunking the notion that there is a universal marginal-utility curve that dictates progression. Here Seligman summarizes Cohen-Stuart: “It is perfectly possible . . . to construct tables [curves] which lead not to progression, but to proportion and even to regression.”*
Third, the sacrifice argument for progression is dependent upon the additional assumption that the marginal-utility curves of all persons are essentially the same. While it is well accepted that marginal-utility curves will eventually slope downward, it is by no means true that all curves have the same slope. In fact, in comparing the marginal-utility curves of Tom, Dick, and Harry Class, there are any number of reasons why Harry’s marginal utility curve might decline less steeply than Tom’s and Dick’s. Imagine, for example, that Harry has a learning-disabled son who needs costly special education, or that Harry’s wife has an illness that requires expensive medication not covered by insurance.... Seligman calls this the “very core objection” to sacrifice theory:
The imposition of “equal sacrifices” on all taxpayers must always remain an ideal impossible of actual realization. Sacrifice denotes something psychical; something psychological . . . Two men may have the same income, which they may value at very different rates. The one may be a bachelor, the other a man with a large family dependent upon him; the one may be well, the other ill . . . the one may earn his income, the other may receive it as a gift . . . The attempt to ascertain a
mathematical scale of progression, so as to avoid a charge of arbitrariness, is foredoomed to failure...
This inability to prove the sameness of the marginal-utility curves of different people troubled Blum and Kalven to the point that they dismissed sacrifice theory as a theory on which to base a fair tax system:
The error lies in trying to translate money, which can be measured in definite units, into corresponding units of satisfaction or well-being. In the end satisfaction in the sense of happiness defies quantification. Utility is a meaningful concept; units of utility are not. It is in the face of this difficulty that, even waiving all other objections, the whole elaborate analysis of progression in terms of sacrifice and utility doctrine finally collapses