PLAYING WITH WATER AND DIAMONDS

VIENNA, BETWEEN 1870 AND 1928

"This book is a masterpiece!"

Karl Menger positively shines with joy when he hears these words. He was expecting praise, but to have it lavished upon him like this by his teacher Hans Hahn is still a pleasant surprise.

No pupil, with the exception of Kurt Gödel, a curious, maverick character at the Institute, was rated as highly by Hahn as young Menger. People always had to say "young Menger" when referring to him, since his father, "old Menger," had been a professor at the University of Vienna some years before, enjoying fame as the founder of the Austrian School of Economics. If that wasn't enough, father and son both had what sounded like the same name, the only difference being the first letter — the archaic C for the father, and the modern K for the son.

In actual fact, old Menger had hoped that his son would follow in his footsteps. He himself came from the furthest reaches of the Habsburg Empire — Neu-Sandez in Galicia, a town known for its Chassidic community and Rabbi Chaim Halberstam, who taught there until his death in 1876. The son of a well-to-do family of civil servants — his father, Anton, was a lawyer and his mother, Caroline, was the daughter of a prosperous Bohemian merchant — Carl Menger came into the world in 1840. It was a small and placid world. Since Empress Maria Theresia had unwillingly received Galicia in 1772 in exchange for wealthy and much-coveted Silesia — "She wept, but she accepted," as her victorious archrival, the Prussian King Frederick, mockingly put it — the Habsburgs had been posting doctors, lawyers, teachers, and civil servants to this dreamy land. This was what they did with all of their provinces, a custom that, while not exactly giving the regions freedom, let alone independence, did bestow on them a certain prosperity, security, and progress.

For young Carl Menger, this world was much too circumscribed. He studied law in Prague and the imperial capital Vienna, where he then settled down as a journalist. He wrote feature articles, first for the Lemberger Zeitung — Lemberg (now known as Lviv) was the Galician capital — and later for the Wiener Zeitung. He was fond of writing novels and comedies for serialization, occasional works that he produced while following his true interest, the study of law and political economics. He enjoyed the acquaintance of Count Richard von Belcredi, the minister of state at the time, who familiarized him with economic issues. This enabled Carl Menger to enrich the Wiener Zeitung with his market analysis — the start of his deep interest in the laws of economics.

There was one paradox of economic theory that occupied the young lawyer and economic journalist in the months after gaining his doctorate: the paradox of value, also known as the diamond-water paradox. Nobody can survive without water. This makes it a highly valuable commodity. Very few people truly need diamonds. This makes them intrinsically almost worthless. And yet people pay horrendous sums of money for diamonds and almost nothing for water.

Adam Smith, the eighteenth-century founder of political economics, thought he could solve this paradox by differentiating between "value in use" and "value in exchange." The value in use of water is very high, since everybody needs it. Its value in exchange, on the other hand, is very low. In contrast, the value in exchange of diamonds is very high, hence the high prices paid, although their value in use is low. This rudimentary explanation is not particularly satisfactory, however, since it sheds no light on why there is a difference in the value in exchange.

Even before Adam Smith, the Scottish banker John Law had stated, "Water is of great use, yet of little value; because the quantity of water is much greater than the demand for it. Diamonds are of little use, yet of great value, because the demand for diamonds is much greater than the quantity of them." With this statement, he may well have found the pivotal point that might help to solve the paradox.

By way of explaining the diamond-water paradox, Carl Menger comes up with the idea of a farmer who owns five sacks of wheat. The farmer considers the first sack of wheat as indispensable for life, since he uses it to bake his bread, and so he will not die of hunger. With the wheat in the second sack, which is still valuable for him, he bakes even more bread. This gives him and his family strength. With the wheat in the third sack, which is not particularly valuable, he can feed the animals in his stable. He puts aside the wheat in the fourth sack for sowing the following year. The farmer doesn't actually need the wheat in the fifth sack; he uses it to distil grain schnapps.

If one of the farmer's five sacks were to be stolen, what would he do? If his use of the wheat were always the same, he would divide the wheat in the remaining four sacks into five equal heaps and use each heap for the same purpose as with the original sacks: the first heap for the bread necessary for survival, the second heap for the bread to give him strength, the third heap to feed the animals, the fourth heap for seed, and the fifth for making schnapps. But no farmer would do such a thing — farmers are clever souls, as we know. Rather, he would use the remaining four sacks as described before, omitting only the unnecessary distilling of schnapps.

Indeed, farmers are much too clever to let people steal from them. But the farmer could sell the fifth sack, instead of using it to make schnapps that he and his family might never drink. And what would the farmer consider to be the right price? Carl Menger has the answer: it is the price that the farmer would pay to buy...