Stolper-Samuelson Theorem Research Paper

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In 1941 Wolfgang Stolper (1912-2002) and Paul Samuelson (b. 1915) put forward a proposition relating changes in the real incomes of workers and of capitalists to changes in the level of protection from import competition. They showed that lowering protection lowered the real income of the scarce factor used intensively in the import-competing sector and raised the real income of the other factor. Previously, international economists believed that opening an economy to international trade would, by increasing the aggregate supply of goods available, enable all income earners to be better off.

Stolper and Samuelson constructed a model of an economy in which only two factors, capital and labor, are used to produce two goods. Households either own capital or supply labor. The home economy cannot change world prices, but it can change the relative price of the two goods by changing the taxes levied on the imported good. In a neoclassical economy in which prices adjust smoothly and all factors are fully employed, a change in goods prices induces a change in the real income of the households owning the factors that produce the goods so that one group of factor owners is better off and the other is worse off.

The crux of the theorem is the link between the changes in the relative price of the goods and the changes in the prices of factors thereby induced. Since 1941 other international economists have stressed that this link has nothing to do with factor scarcity or the cause of the change in goods prices, but rather that it applies generally whenever relative prices change. The importance of the theorem derives from its fundamental message that changes in goods prices necessarily create conflict between households owning different factors. A vast literature developed in response to Stolper and Samuelson seeking to generalize the theorem to a world in which there are many goods and many factors. However, unless very strong restrictions were imposed on the technology of the producers, generating general propositions linking factor income changes to goods price changes proved difficult.

A later model that uses a criterion of real income change corresponding to the change in the utility of the income earner has obtained general propositions. Subject to a weak restriction that there is some diversity among households in their preferences and/or their ownership of factors, a change in any goods price will make some households better off and some worse off. Conversely, for any household there is some goods price change that will make it better off and some that will make it worse off. This generalizes the essential message of the original theorem. It shows that there are universal incentives for households to lobby government to change policies to yield benefits for them, and for other households to oppose them.

As an example, take the original Stolper-Samuelson model in which two factors produce two goods. Suppose the shares of capital and labor in the costs of producing a unit of good 1 (clothing) are 6/10 and 4/10 respectively and that the corresponding shares in producing a unit of good 2 (machinery) are 3/10 and 7/10. Thus, clothing is the good that uses a relatively labor-intensive technique of production. Then, if the price of clothing is raised by 1 percent, the wage rate of workers goes up by 2.3 percent, and the rate of return on capital goes down by 1 percent. Conversely, if the price of a unit of machinery goes up by 1 percent, the wage rate of workers goes down by 1.3 per cent, and the rate of return on capital goes up by 2 percent. As predicted by the theory, both workers or capital-owners will benefit if the price of the good which uses their factor intensively rises because of some government intervention in markets.

The theorem has applications to changes in goods prices that originate because of changes in any government taxes or policies or supply shocks. In particular, the theorem is the foundation of models of political economy that seek to explain patterns of government taxes and expenditures. It has been applied empirically to models that explain the structure of national tariffs, other taxes, subsidies, and transfers to households.


  1. Deardorff, Alan V., and Robert M. Stern, eds. 1994. The Stolper-Samuelson Theorem: A Golden Jubilee. Ann Arbor: University of Michigan Press.
  2. Lloyd, Peter J. 2000. Generalizing the Stolper-Samuelson Theorem: A Tale of Two Matrices. Review of International Economics 8 (4): 597–613.
  3. Stolper, Wolfgang F., and Paul A Samuelson. 1941. Protection and Real Wages. Review of Economic Studies 9 (1): 58–73.

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