Stolper–Samuelson, Rybczynski and factor price equalisation

In Ricardo’s model there is one factor, so if the country gains, everyone in it gains. With two factors, trade changes the price of each good, and that changes what each factor earns. The chain is:

1. Trade raises the price of the export good and lowers the price of the import good.
2. The export good uses the abundant factor intensively (Lesson 4).
3. So the abundant factor’s reward rises and the scarce factor’s falls.

In India, labour gains from trade and capital loses; in Germany, the reverse. The country as a whole still gains, as in Lesson 3: the winners gain more than the losers lose, so they could in principle compensate them.

Wolfgang Stolper and Paul Samuelson proved the second step precisely in Protection and Real Wages (1941):

“Real” is the important word. The wage doesn’t just rise; it rises by a bigger percentage than the price of either good, so workers can buy more of everything. This is the magnification effect (Ronald Jones, 1965). If the price of X rises 10% and Y’s stays the same:

% change in w > % change in P_X > % change in P_Y > % change in r

Try it in the lab. In the model here, a 10% rise in the price of the labour-intensive good raises the wage about 18% and cuts the rental about 7%.

A tariff raises the domestic price of the import good. The import good uses the scarce factor intensively. So a tariff helps the scarce factor and hurts the abundant one, the reverse of what free trade does. That was Stolper and Samuelson’s original question: could protection raise American wages? In a labour-scarce country, yes.

JNU 2014 asked it in one line: a tariff on capital-intensive imports raises the real reward of capital. The options with nominal changes are traps. One caveat for a large country: if the foreign offer curve is inelastic enough, a tariff can improve the terms of trade so much that the domestic price of imports falls. This is the Metzler paradox, and then the effects run the other way.

Follow the chain in both countries at once. Trade raises the wage in the labour-abundant country and lowers it in the capital-abundant one, and does the opposite to the rental. The wage gap narrows from both sides. Paul Samuelson showed in 1948 that under the model’s assumptions it closes completely:

Why? With free trade, goods prices are the same everywhere. With the same technology and both goods made in both countries, zero profit in each industry pins down one wage and one rental for those prices. So both countries end up with the same w and r. Trade in goods is a substitute for moving the factors themselves.

The conditions, each of which JNU has asked:

• the same technology, constant returns, and perfect competition in goods and factor markets (JNU 2016: all three);
• incomplete specialisation: both countries keep making both goods (JNU 2011). Set very different endowments in the Lesson 4 lab and one country specialises; then its factor prices stop following the other’s;
• endowments in the same cone of diversification, which is the same condition stated geometrically (JNU 2015);
• no transport costs or tariffs, and no factor-intensity reversal.

Note what is not assumed: factors are immobile between countries. CUET 2023 gave “because factors are perfectly mobile internationally” as the reason: the assertion is true and the reason false.

Stolper–Samuelson changes a price and holds endowments fixed. T. M. Rybczynski did the reverse in 1955: hold goods prices fixed and change an endowment.

Switch the lab to Rybczynski. With prices fixed, factor prices are fixed, so each industry keeps the same capital per worker. The only way to employ more workers is to make more of the labour-intensive good; and since it also needs some capital, the capital has to come out of the other industry. Output of X rises by more than labour did, and output of Y falls: the magnification effect again.

JNU asked this three times (2014, 2019, 2021), always with the conditions spelt out: different, non-reversible factor intensities and constant returns. The answer is always an absolute increase in the good intensive in the growing factor and an absolute decrease in the other. CUET 2022 matched Rybczynski with “effects of factor endowment changes on trade”. Lesson 7 uses the theorem for growth and Dutch disease.

Heckscher–Ohlin is a long-run model: capital can move from textiles to chemicals. In the short run it can’t. A loom is a loom. The specific-factors model, set out by Paul Samuelson and Ronald Jones in 1971 (UGC NET 2025), has labour mobile between industries and a factor specific to each one: capital in manufacturing, say, and land in agriculture.

When trade raises the price of the export good:

• the factor specific to the export sector gains, since its industry expands and it can’t be used anywhere else;
• the factor specific to the import-competing sector loses;
• the mobile factor, labour, may gain or lose. Its wage rises, but by less than the price of the export good. Workers gain if they spend mostly on the import good, and lose if they spend mostly on the export good.

So all four of UGC NET 2023’s statements are true: export-specific factors gain, import-specific factors lose, and the mobile factor may gain or may lose. This is also why the losers from trade in Lesson 1 were workers and owners in import-competing industries.

A memory aid: Stolper–Samuelson takes a price and gives Salaries; Rybczynski takes Resources and gives output. Each moves one variable and magnifies the effect on the other side.