Researches into the Mathematical Principles of the Theory of Wealth
Two rival sellers, each second-guessing the other, settle where calculus says they must — the first equilibrium in economics.
In 1838 a French mathematician did something no one had done before: he used calculus to predict what two competing sellers would charge — and out fell the first equilibrium in economics.
The idea, unpacked
Cournot asked a sharp question: if two companies sell the same thing, how much will each make, and what price results? His answer was to treat every seller as a reasoner. Each one picks how much to produce, guessing the other's output and choosing its own best reply. There is exactly one pair of choices where both guesses come true and neither seller regrets its decision.
That balance point is the prediction. And two sellers, it turns out, produce more and charge less than a single monopolist would — but not as much, or as cheaply, as a whole crowd of competitors. Two is genuinely its own case, sitting between the one and the many.
Where it came from
Antoine Augustin Cournot was a mathematician and philosopher, not a merchant, and in 1838 he wrote a slim book putting economics into equations for the first time — demand as a curve, profit as something to maximise with calculus. The book sold almost nothing. The economists of the day found the mathematics alien and looked away. Cournot, stung, spent the rest of his life rewriting the ideas in plain words, and died in 1877 still largely unread. Only afterward did the founders of modern economics — Walras, Jevons, Marshall — realise he had got there first.
Why it mattered
Two firsts live in this little book. It is the start of mathematical economics: after Cournot, you could calculate an answer, not just argue for one. And buried in chapter seven is the first equilibrium of strategy — the very idea John Nash would make famous in 1950 and win a Nobel for. Cournot had written down a special case of the Nash equilibrium 112 years early, and used it to explain why competition pushes prices down toward cost.
Two lemonade stands
Picture two lemonade stands on the same corner — the only two in town. If you make a huge batch, the street floods with lemonade and the price drops, so the more your rival makes, the less it's worth your while to make. Each of you settles on an amount that is your best answer to the other's. When you're both doing that at once, the market has found Cournot's balance point. Try being one of the stands below.
What came before and after
Cournot sits at a hinge in the story of economics. Before him, Adam Smith (1776, elsewhere in this Library) had described markets in words; Cournot gave them equations. After him, Léon Walras and Alfred Marshall built the theory of value his demand curves were missing, and — a century on — John Nash (1950, also here) generalised his equilibrium to every game, turning a footnote about mineral springs into the foundation of game theory.
Let us now imagine two proprietors and two springs of which the qualities are identical, and which, on account of their similar positions, supply the same market in competition.