This week “The Economist explains” is given over to economics. For each of six days until Saturday this blog will publish a short explainer on a seminal idea.

DOES trade hurt wages? Or, more precisely, do imports from low-wage economies hurt workers in high-wage ones? Many people assume so. Economists take a bit more convincing. Back in the 1930s, one trade economist, Gottfried Haberler, argued that “the working class as a whole has nothing to fear from international trade”—at least in the long run. This confidence rested on three observations. Labour, unlike other many other productive resources, is required in all sectors. It will thus remain in demand however much globalisation shakes up a country’s industrial mix. Over time, labour is also versatile. Workers can move and retrain; new entrants can gravitate towards sunrise sectors rather than industries in decline. Finally, workers are also consumers, who often buy the foreign goods in local shops. Even if competition from cheap imports drives down their (nominal) wages, they will come out ahead if prices fall by even more. Haberler’s confidence was not universally shared, however. Wolfgang Stolper, a Harvard economist, suspected that competition from labour-abundant countries might hurt workers elsewhere. In 1941, he teamed up with Paul Samuelson, his Harvard colleague, to prove it.

Their Stolper-Samuelson theorem concluded that removing a tariff on labour-intensive goods would depress wages by more than prices, hurting workers as a class, even if the economy as a whole gained. The theorem’s logic rests on the interaction between industries with different degrees of labour-intensity. It is perhaps best explained with an example. Suppose a high-wage economy were divided into two industries: wheat-growing (which is land-intensive) and watchmaking, which makes heavy use of labour and shelters behind a 10% tariff. If this protection were removed, watch prices would fall by 10%. That would force the industry to contract, laying off labour and vacating land. That in turn would put downward pressure on wages and rents. In response, wheat growers would expand, taking advantage of the newly available land and labour. This dance would continue until watchmaking’s costs had fallen by 10%, allowing the industry to compete with tariff-free imports.

Stolper and Samuelson paid close attention to the combination of rents and wages that would achieve this cost reduction. One might assume that both would fall by 10%. But that would be wrong. Since watchmaking is labour-intensive, its contraction releases more labour than land, putting greater downward pressure on wages than on rents. Conversely, the expansion of wheat growers would put more upward pressure on rents than on wages. The end result is that wages would have to fall by more than 10% because rents would fall by less. Rents would paradoxically rise. The combination of much cheaper labour and slightly pricier land would restore the modus vivendi between the two sectors. It would halt the contraction of the watchmakers (because cheaper labour helps them more than pricier land hurts them). It would also check the expansion of the wheat growers (because pricier land hurts them more than cheap labour helps them).

Trade liberalisation, in this example, depresses wages by more than prices, hurting labour in real terms. This gloomy conclusion has proved remarkably influential. It appears even 75 years later in debates about the Trans-Pacific Partnership between America and 11 other countries, many of them low-wage economies. Some economists regret this influence, arguing that the theorem’s crisp conclusion does not hold outside of the stylised settings in which it was first conceived. Even the theorem’s co-author, Paul Samuelson, was ambivalent about the result. “Although admitting this as a slight theoretical possibility,” he later wrote, “most economists are still inclined to think that its grain of truth is outweighed by other, more realistic considerations.”

Previously in this series