Markets work best when many companies vie for customers’ favour. They work badly when a few firms dominate, carving up sales between them. Economists therefore need a measure of whether markets are competitive or concentrated.

The most famous measure was invented by Albert Hirschman in 1945. It starts by summing the squares of each supplier’s market share. That makes it sensitive both to the number of suppliers and inequalities between them. A staple of antitrust investigations, his index, with minor modifications, crops up in courtrooms and classrooms. Almost every economics student comes across it.

Few will know that Hirschman invented the index to measure something else: the economic power wielded not by firms but by countries. It appeared in a book examining trade as a source of “political pressure and leverage”. Hitler’s Germany had exerted its influence over its neighbours in the 1930s not only through “diabolical cunning” but also the gravitational pull of its economy.

Hirschman rejected the naive belief that because trade is voluntary and mutually beneficial, it is geopolitically innocuous. Benefits can be mutual without being symmetrical. And if one country depends less on a relationship than its partner, it can extract concessions by threatening to walk away.

The German economist would not have been surprised by President Donald Trump’s tariffs or indeed China’s own attempts at economic coercion, which include export restrictions on vital inputs, such as rare earths. It is, therefore, a good time to revive the spirit of his inquiries, according to Christopher Clayton of Yale School of Management, Matteo Maggiori of Stanford University and Jesse Schreger of Columbia Business School. They are seeking to apply the modern toolkit of economics to geopolitics. The result is something they call “geoeconomics” (borrowing a term coined by Edward Luttwak, a historian and military strategist, in 1990). Whatever the subject is called, it is inescapable. Three years ago people asked the authors what geoeconomics was. Now they are asked not to go on about Mr Trump too much.

In their models, big economies—hegemons—can make demands of smaller ones by subjecting them to economic sticks and carrots. The losses a country suffers if it rejects such demands are a measure of the power the hegemon wields. Smaller countries can try to protect themselves in advance by decoupling and diversifying their economies. They might, however, overdo it, according to the authors’ models. Economic networks, be they banking systems, industrial ecosystems, or global trade itself, increase in value the more people take part in them. If one country withdraws to protect itself, it makes that network less attractive to others. That might shift their calculus in favour of decoupling, too.

To dissuade countries from insulating themselves, a hegemon might promise not to exploit its power too much. It might say, “Do business with me. I’m not going to bully you like crazy later. I’m only going to bully you a little bit,” as Mr Maggiori has put it. The hegemon might, for example, submit to international trade rules that put a ceiling on its tariffs. If the rules are credible, they can benefit the hegemon as well as everyone else. In these models, trade rules emerge not as the result of “globalist” planning, but as an act of enlightened self-interest on the part of a hegemon. The models make the nationalist case for multilateralism.

Their theory also aids measurement. In the spirit of Hirschman, they calculate their own indices of power, based on market shares and the ease with which imported inputs can be replaced. Their calculations bring out a vital implication of their theory: power does not grow in a straight line. It tends to shoot up as a hegemon’s market share nears 100%. There is an enormous difference between claiming most of a market and claiming almost all of it. The same is true of hard-to-replace inputs. There is a big difference between having few substitutes and none or nearly none.

This result makes intuitive sense. If a hostile America provides 80% of a country’s foreign financial services, the country’s other providers would have to expand their sales by 400% to replace it (an increase from 20 to 100 equals growth of 400%). If America instead provides 90%, the alternative providers would have to expand by 900%. An increase in market share of ten percentage points makes a 500 percentage-point difference.

All this has practical implications. America and its allies have a large share of the world’s financial services. Adding a country like Singapore to the coalition might not seem like much of a prize. But it would make a big difference; a small increase in a large market share yields disproportionate gains in power.

The same is true in reverse. Even small efforts to decouple from an abrasive hegemon can diminish its power by a surprising degree. America’s rivals are, for example, experimenting with alternatives to the dollar in international finance. These alternatives do not have to match the dollar in order to erode America’s financial clout. If they can capture even 10% of the market in small and medium-size countries, they can make a big difference, according to the authors. Going from 1% of the market to 10% can reduce American financial power as much as going from 10% to 50%, they argue. According to this logic, currencies like China’s yuan can defang the dollar even if they never dethrone it.

Hirschman’s book, in which he outlined his index, was largely forgotten by the economics profession until recently. Political scientists and other scholars now account for most of its citations, according to Messrs Clayton, Maggiori and Schreger. The three authors hope to revive interest in Hirschman’s work among their fellow economists. The inventor of the best known index of concentration warrants a broader, more diversified readership. ■

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