Plate iii in print

The Increment

Gossen; the two laws beneath it all — that each added unit yields less satisfaction than the last, and that means are spent best by equalizing the satisfaction of the last unit of each.

Each added unit of a good brings less pleasure than the one before, until the want is sated; and a man spends his limited means best when he so apportions them that the last coin laid out on each good yields him the same small increment of satisfaction — two laws, set down a generation too early and ignored, on which the whole logic of rational choice would later be built.

— the argument of this plate, after Hermann Heinrich Gossen, 1854

Jevons resolved the paradox of value by looking to the last unit, but the laws governing that last unit had been set down, in obscurity and a generation too early, by a man almost no one read. Hermann Heinrich Gossen published in 1854 a book stating, with a completeness that would not be matched for decades, the two laws on which the marginal theory of value rests: that the satisfaction from each additional unit of a good diminishes as one consumes more, and that a person with limited means spends them best by equalizing, across all his wants, the satisfaction won from the last unit of each. The book failed utterly; its author, embittered, withdrew it and died unknown. But the two laws were the foundation, and when the marginalists arrived a generation later they were, without knowing it, building on Gossen.

The story is among the most poignant in the history of the subject. Gossen, a retired Prussian official, believed he had accomplished for the science of human exchange what Copernicus had accomplished for astronomy, and he may not have been altogether wrong; but his Laws of Human Relations, published in 1854 in a forbidding style heavy with a mathematics his contemporaries were unprepared for, sold almost nothing. Disappointed past bearing, he had the unsold copies withdrawn, and he died a few years later in complete obscurity. Only after Jevons, Menger, and Walras had independently rediscovered the marginal principle did anyone think to look back; and Jevons, learning of his forgotten predecessor, acknowledged in the preface to his own second edition, with great generosity, that Gossen had completely anticipated him in the general theory. The priority was restored too late for its author ever to know it.1

1. Gossen, a retired Prussian official, thought he had done for exchange what Copernicus did for astronomy. His Laws of Human Relations (1854), forbidding and heavily mathematical, sold almost nothing; embittered, he withdrew the unsold copies and died obscure a few years on. Only after Jevons, Menger, and Walras independently rediscovered the marginal principle did anyone look back — and Jevons, in his second edition, generously acknowledged that Gossen had wholly anticipated him. The priority was restored too late for its author to know.

The first of the two laws describes how satisfaction behaves as consumption grows. The pleasure a person draws from each successive unit of a good, Gossen observed, is smaller than the pleasure from the unit before, and continues to fall as consumption proceeds, until the want is wholly sated and a further unit yields nothing, or worse. The first cup of water to the thirsty, the first slice of bread to the hungry, is worth a great deal; the tenth, much less; the twentieth, nothing. This is the law of diminishing marginal utility, and it is the reason the marginal unit of an abundant good is worth so little — the reason, in the previous plate, that water is cheap. It is a law about the margin: it concerns not the total satisfaction a good affords, which may be immense, but the rate at which satisfaction grows as the last unit is added, which steadily declines toward zero.2

2. Gossen's first law: the pleasure from each successive unit of a good is less than from the one before, falling as consumption proceeds until the want is sated and a further unit yields nothing. The first cup to the thirsty is worth much; the tenth less; the twentieth nothing. This is diminishing marginal utility — why the last unit of an abundant good is worth so little, why water is cheap. It is a law about the margin: not the total satisfaction (which may be immense) but the declining rate at which satisfaction grows as the last unit is added.
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The second law is the deeper, for it tells a person with limited means how to spend them. Suppose one's money divided among several goods. If the last penny spent on bread brings more satisfaction than the last penny spent on wine, then one is misallocating: a penny shifted from wine to bread would gain more than it loses, raising total satisfaction. One should keep shifting until no such gain remains — until the last penny spent on each good yields exactly the same increment of satisfaction. At that point, and only there, is total satisfaction as great as the budget allows. This is Gossen's second law, the equimarginal principle: the optimum is reached when the marginal utility of the last unit of money is equal across every use to which money is put. It is the precise logic of the consumer's best choice, and the first exact statement of what it means to allocate a scarce resource well.3

3. Gossen's second law tells how to spend limited means. If the last penny on bread brings more satisfaction than the last on wine, shift a penny from wine to bread — it gains more than it loses. Keep shifting until the last penny on each good yields the same increment; only there is total satisfaction maximal. This is the equimarginal principle: the optimum is where the marginal utility of the last unit of money is equal across all uses. It is the exact logic of the consumer's best choice — the first precise account of allocating a scarce resource well.

The equimarginal principle proved to reach far beyond the shopper balancing bread against wine, for it is the general logic of any scarce resource divided among competing uses. A firm with a fixed budget for inputs allocates it best when the last dollar spent on labor adds as much to output as the last dollar spent on machinery or on materials; a government with a fixed budget does best when the last dollar of every program yields the same marginal benefit; a person with only so many hours allots them best when the last hour given to each pursuit returns the same marginal reward. In every case the rule is the same: shift the resource from uses where its marginal return is low to uses where it is high, until the marginal returns are equal everywhere, for only then can no further reshuffling improve the whole. This is the marginal theory of allocation in its most general form, and it is why the marginalists could claim to have found not merely a theory of value but the logic of economizing itself — the rational disposition of scarce means among competing ends.4

4. The principle reaches far past the shopper. A firm allocates a fixed input budget best when the last dollar on labor adds as much as the last on machines or materials; a government, when the last dollar of every program yields equal marginal benefit; a person, when the last hour on each pursuit returns equal reward. Always: shift from low-marginal-return uses to high until returns equalize, for only then can no reshuffling improve the whole. This is allocation in its general form — the logic of economizing itself, the rational disposition of scarce means among competing ends.

Gossen's two laws are the floor beneath the marginal revolution. The first, diminishing marginal utility, explains why the last unit of a good is worth less than the units before, and so why abundant goods are cheap; the second, the equimarginal principle, explains how a rational agent disposes of scarce means, equalizing marginal returns across all uses. Together they convert the bare insight that value is marginal into a working theory of choice and allocation. But Gossen, like Jevons, framed his laws in the language of pleasure and pain, of measurable utility added and subtracted, as though satisfaction were a substance one could weigh on a scale. The Austrian founders of the marginal school would carry the subjective insight further, dispensing with the measurable hedonic quantity and grounding value instead in the ordered wants of the valuing mind. The next plate turns to their source. The next plate is the subjective.5

5. The two laws are the floor beneath the revolution: the first (diminishing marginal utility) explains why the last unit is worth less and abundant goods are cheap; the second (the equimarginal principle) explains how the rational agent allocates, equalizing marginal returns. Together they turn the bare insight that value is marginal into a working theory of choice. But Gossen, like Jevons, weighed pleasure as if a measurable substance. The Austrians would ground value instead in ranked wants, dispensing with the hedonic quantity. Next: the subjective.

Beneath the marginalists' theory of value lie the two laws Hermann Heinrich Gossen set down in 1854, a generation too early to be heard. His first law, diminishing marginal utility, holds that each added unit of a good yields less satisfaction than the last, until the want is sated — which is why the marginal unit of an abundant good is worth so little. His second law, the equimarginal principle, holds that a person spends limited means best by equalizing the satisfaction won from the last unit of money across every use, and it is the exact logic of rational allocation, reaching from the shopper's basket to the firm's budget to the disposition of a nation's resources. Ignored in his lifetime and rediscovered only after the marginalists had independently arrived at the same ground, Gossen supplied the floor on which they built. The next plate is the subjective.