Stolper-Samuelson theorem

Stolper-Samuelson theorem

Ask a question about 'Stolper-Samuelson theorem'
Start a new discussion about 'Stolper-Samuelson theorem'
Answer questions from other users
Full Discussion Forum
The Stolper–Samuelson theorem is a basic theorem in Heckscher–Ohlin type trade
Trade is the transfer of ownership of goods and services from one person or entity to another. Trade is sometimes loosely called commerce or financial transaction or barter. A network that allows trade is called a market. The original form of trade was barter, the direct exchange of goods and...

 theory. It describes a relation between the relative prices of output goods and relative factor rewards, specifically, real wage
Real wage
The term real wages refers to wages that have been adjusted for inflation. This term is used in contrast to nominal wages or unadjusted wages. Real wages provide a clearer representation of an individual's wages....

s and real returns to capital.

The theorem states that—under some economic assumptions (constant returns, perfect competition, equality of the number of factors to the number of products)—a rise in the relative price of a good will lead to a rise in the return to that factor which is used most intensively in the production of the good, and conversely, to a fall in the return to the other factor.

History of the theorem

It was derived in 1941 from within the framework of the Heckscher–Ohlin model by Wolfgang Stolper
Wolfgang Stolper
Wolfgang Friedrich Stolper was an American economist.-Life:Wolfgang Stolper was born in Vienna, the eldest son of liberal economist Gustav Stolper. In 1925 the family moved to Berlin and emigrated in 1933 to the USA. In 1938 Stolper completed his economics studies at Harvard University...

 and Paul Samuelson
Paul Samuelson
Paul Anthony Samuelson was an American economist, and the first American to win the Nobel Memorial Prize in Economic Sciences. The Swedish Royal Academies stated, when awarding the prize, that he "has done more than any other contemporary economist to raise the level of scientific analysis in...

, but has subsequently been derived in less restricted models. As a term, it is applied to all cases where the effect is seen. Ronald W. Jones
Ronald W. Jones
Ronald Winthrop "Ron" Jones is an influential international trade economist and Xerox Professor of Economics at the University of Rochester. His recent highly acclaimed book Globalization and the Theory of Input Trade summarizes much of his past work and also discusses the recent market trend...

 and José Scheinkman
José Scheinkman
José Alexandre Scheinkman is a Brazilian-American mathematical economist, currently the Theodore A Wells '29 Professor of Economics at Princeton University. He spent the bulk of his career at the University of Chicago, where he served as department chair immediately prior to his departure for...

 (1977) show that under very general conditions the factor returns change with output prices as predicted by the theorem. If considering the change in real returns under increased international trade
International trade
International trade is the exchange of capital, goods, and services across international borders or territories. In most countries, such trade represents a significant share of gross domestic product...

 a robust finding of the theorem is that returns to the scarce factor will go down, ceteris paribus
Ceteris paribus
or is a Latin phrase, literally translated as "with other things the same," or "all other things being equal or held constant." It is an example of an ablative absolute and is commonly rendered in English as "all other things being equal." A prediction, or a statement about causal or logical...

. A further robust corollary of the theorem is that a compensation
A payment is the transfer of wealth from one party to another. A payment is usually made in exchange for the provision of goods, services or both, or to fulfill a legal obligation....

 to the scarce-factor exists which will overcome this effect and make increased trade Pareto optimal.

The original Heckscher–Ohlin model was a two factor model with a labour market specified by a single number. Therefore, the early versions of the theorem could make no predictions about the effect on the unskilled labour force in a high income country under trade liberalization. However, more sophisticated models with multiple classes of worker productivity have been shown to produce the Stolper–Samuelson effect within each class of labour: Unskilled workers producing traded goods in a high-skill country will be worse off as international trade increases, because, relative to the world market in the good they produce, an unskilled first world
First World
The concept of the First World first originated during the Cold War, where it was used to describe countries that were aligned with the United States. These countries were democratic and capitalistic. After the fall of the Soviet Union and the end of the Cold War, the term "First World" took on a...

 production-line worker is a less abundant factor of production than capital.

The Stolper–Samuelson theorem is closely linked to the factor price equalization theorem, which states that, regardless of international factor mobility, factor prices will tend to equalize across countries that do not differ in technology.


Considering a two-good economy that produces only wheat and cloth, with labour and land being the only factors of production, wheat a land-intensive industry and cloth a labour-intensive one, and assuming that the price of each product equals its marginal cost, the theorem can be derived.

The price of cloth should be:

with P(C) standing for the price of cloth, r standing for rent paid to landowners, w for wage levels and a and b respectively standing for the amount of land and labour used.

Similarly, the price of wheat would be:

with P(W) standing for the price of wheat, r and w for rent and wages, and c and d for the respective amount of land and labour used.

If, then, cloth experiences a rise in its price, at least one of its factors must also become more expensive, for equation 1 to hold true, since the relative amounts of labour and land are not affected by changing prices. It can be assumed that it would be labour, the intensively used factor in the production of cloth, that would rise.

When wages rise, rent must fall, in order for equation 2 to hold true. But a fall in rent also affects equation 1. For it to still hold true, then, the rise in wages must be more than proportional to the rise in cloth prices.

A rise in the price of a product, then, will more than proportionally raise the return to the most intensively used factor, and a fall on the return to the less intensively used factor.

Criticism of the theorem

The validity of the Heckscher–Ohlin model has been questioned since the classical Leontief paradox
Leontief paradox
Leontief's paradox in economics is that the country with the world's highest capital-per worker has a lower capital/labor ratio in exports than in imports....

. An advanced course textbook writer estimated that "the Heckscher–Ohlin model is hopelessly inadequate as an explanation for historical and modern trade patterns." As for the Stolper–Samuelson theorem itself, Davis and Mishra (2006) pointed recently that "[i]t is time to declare Stolper–Samuelson dead." They argue that the Stolper-Samuelson theorem is "dead" because following trade liberalization in some developing countries (particularly in Latin America), wage inequality rose and, under the assumption that these countries are labor abundant, the SS theorem predicts, they argue, that wage inequality should have fallen. Aside from the declining trend in wage inequality in Latin America that has followed trade liberalization in the longer run (see Lopez-Calva and Lustig (2010)), an alternative view would be to recognize that technically the SS theorem predicts a relationship between output prices and relative wages. Interestingly, papers that actually compare output prices with changes in relative wages find moderate to strong support for the Stolper-Samuelson theorem, such as Beyer et al. (1999) for Chile, Robertson (2004) for Mexico, and Gonzaga et al. (2006) for Brazil.

External links

  • J. Peter Neary
    J. Peter Neary
    J. Peter Neary FBA is an economist specialising in international trade. He is Professor of Economics at Oxford University, and a Professorial Fellow of Merton College, Oxford as well as Associate Member of Nuffield College, Oxford. He was previously Professor of Political Economy at University...

    , History of the theorem (2004, J Peter Neary, CEPR)