Herman Heinrich Gossen and the Theory of Marginal Utility

How a Failed Prussian Civil Servant Upended the Classical Theory of Value

TL;DR: Herman Heinrich Gossen’s radical insight (versus the prevailing views in his mid-19^th century times) was that “value,” and thus price, was a function of the subjective utility that a buyer and seller awarded to a good. His proofs, using differential calculus, gave rise to “Gossen’s Laws,” which are still taught to economics students today.

Source: AI-enhanced portrait of Herman Heinrich Gossen from WikiCommons

A Mathematical Maverick

Herman Heinrich Gossen’s overbearing father finally died in 1847.  To Gossen, this came with a sense of relief. His father had been a Napoleonic era tax inspector.  After Gossen finished his university studies, his father forced his son, much against his will, into the Prussian civil service. Gossen failed at it miserably. So too did he fail as an insurance salesman, of policies to protect against hailstorms and cattle death. 

With his father dead, Gossen felt finally free to live the intellectual life he had always secretly craved, and to become the maverick mathematician he always imagined himself to be. A lifelong bachelor, he put himself into the care of his affectionate sisters and toiled for four years on his intellectual labor of love.  

In 1854, he finally published it under the clumsy title Die Entwickelung der Gesetze des menschlichen Verkehrs, und der daraus fließenden Regeln für menschliches Handeln; roughly translatable as The Development of the Laws of Human Relations and the Rules of Human Action Derived Therefrom.

Gossen certainly thought highly of Die Entwickelung; its preface suggests he imagined it would make him “the Copernicus of the social universe.”  The book, however, like the other vocational ventures of his short life, was an utter flop.  It received almost no notice. Just before he died in 1858 at 47 years old, from pulmonary tuberculosis, he had the few remaining copies of his book pulled from circulation.

Saved from Obscurity

Gossen thus might well have remained in eternal oblivion, but for the fortuitous hand of synchronicity. Two decades after his death, an unwitting Scottish researcher spotted a reference to Gossen’s work in an obscure Hungarian treatise on economic history, and made William Stanley Jevons aware of it. 

Soon after, in the stacks of  the library of the British Museum, Jevons stumbled upon what was likely the only copy of Die Entwickelung existing in Britain.  He immediately recognized the book’s importance, and quickly brought it to the attention of Léon Walras, whose assessment of Die Entwickelung was the same as Jevons’s.  (We’ll hear more about Jevons and Walras in our next post).

Thus it came to be that these two standard bearers of the marginalist revolution – as the nineteenth century moment in economic history which undid classical theories of value came to be called -- in a profound act of academic honesty and generosity, both promptly took measures to make the world aware of Herman Heinrich Gossen.

Jevons did so by citing Gossen in the preface to the second edition of his Theory of Political Economy.

Walras did so by writing an extensive biographical essay.

Value as a Function of Subjective “Utility”

Gossen’s path-breaking contribution to economic theory was that where price is concerned, “absolute value” simply does not exist.  He posited that value is instead dependent on the subjective “utility” awarded to a good or service by a buyer and a seller, each of whose goals is to obtain maximum pleasure. 

This ran completely contrary to the classical labor theory of value, advocated by Adam Smith, David Ricardo, and even Karl Marx, which stated that prices were an objective function of the amount of labor it took to produce a good.

Two ideas in particular emerged from the densely written pages  of Gossen’s Die Entwickelung which, relative to the conventional thinking of his time, were so radical that posterity has elevated them to the status of “Gossen’s Laws;” these two “laws” still form the basis today of the neoclassical theory of consumer behavior, and are taught to economic students to this day.

Gossen’s First Law: Diminishing Marginal Utility

In non-technical language, Gossen’s first law states that the amount of pleasure we obtain from consuming another unit of the same good decreases to the point where our desire to consume the good is completely satiated.  

This is, of course, pure common sense.  If I crave a chocolate bar, I may be willing to pay a price to buy one.  If my craving is not satisfied, I may be willing to pay a price to buy a second, or marginal, chocolate bar.  This will continue as long as I assign a positive “utility” to the consumption of an additional, marginal, chocolate bar. 

This concept became known as “diminishing marginal utility.” It is a linchpin of the neoclassical paradigm, and is still taught in introductory micro economic courses worldwide today.  Gossen’s contribution was the realization that this common-sense idea, because it dealt with rates of change, lent itself to differential calculus, which he applied to his analysis in great detail. Because the focus was on “marginal” and not absolute levels of consumption, it also lent its name to the thought transformation we are discussing here, the “marginalist” revolution.

The exact wording of Gossen’s First Law is:

“The magnitude of a given pleasure decreases continuously if we continue to satisfy this pleasure without interruption until satiety is ultimately reached.”

Gossen’s Second Law

Gossen’s second law states that in the theoretical world of his first law, an economic agent will allocate resources until the marginal utilities of all activities are exactly equal. By extension, the optimal allocation of all resources implies that each of their “marginal utilities” is exactly equal. Put a slightly different way, at the point of optimal allocation, a person will be completely indifferent between consuming one good or another, as each have the same marginal utility.

The exact wording of the Gossen’s Second Law is:

“The magnitude of each single pleasure at the moment when its enjoyment is broken off shall be the same for all pleasure.”

Walras, Jevons and Menger

While Gossen may have been the first to quantitatively conceptualize utility in this way, history ultimately crowned William Stanley Jevons, Carl Menger, and Léon Walras as the founding fathers of marginalism. All three were brilliant minds who came to wrestle with economic theory mostly by sheer force of imagination.

Like Smith, Bentham and Mills, posterity has been kind to this threesome, albeit in a much more narrow-gauge, technical sense. Because they helped accelerate the transformation of economics into a mathematically based science, the audience for their celebrity is mostly limited to economists.

We shall introduce these three pioneering thinkers in our next post. We’ll also come to show how concurrently with the development of their new mathematical approach, Jevons, Walras, and Menger also helped erode even further the relevance of ethical thinking to economics.

Further Reading:

For those who want to dig deeper, the books and readings that inspired this post are available at The Grove.