Stolper-Samuelson theorem

The Stolper-Samuelson theorem is a doctrine of foreign trade theory . It says that when the price of a commodity rises, the reward for that factor of production rises which is used more intensively in the production of the commodity in question.

Development of the theorem

The theorem was first proven in 1941 by the American economists Wolfgang F. Stolper and Paul Anthony Samuelson , who met at Harvard University in Cambridge. Stolper completed his economics studies there in 1938 and Samuelson received his doctorate in 1941. In addition to the Rybczynski theorem , the Heckscher-Ohlin theorem and the factor balancing theorem , the developed theorem is part of the Heckscher-Ohlin model and is therefore part of the traditional factor proportion models. The original version is based on five limiting ideal-typical assumptions:

1. There are perfect markets that are not characterized by personal, factual, temporal or spatial preferences and where there is complete market transparency. The goods offered on the market are homogeneous and the market adjustment processes happen immediately.
2. There are constant economies of scale , so that if the input factors change, the output increases in the same ratio (proportionally).
3. Only two different goods are produced.
4. Only two production factors are used in production, which are available to a limited extent.
5. The factors are completely mobile between production sites.

The reasons for the change in the price of goods were seen in trade policy measures (introduction of tariffs) and only the production factors labor and capital were considered.

Statement of the theorem

The following two effects can be derived from the theorem:

Distribution effect

Under the given assumptions, an increase in the relative price of a good (e.g. as a result of the establishment of trade relations) leads to an increase in the real reward for the factor that is intensively used in production. The reward for the other factor goes down.

Magnification effect

This effect says that the relative price increase in goods prices has a disproportionate effect on the factor price, which is used intensively to produce the goods.

Furthermore, when the relative goods prices are adjusted , the mobile production factors also lead to the adjustment of the relative factor prices for the production factors labor and capital.

Derivation

Mathematical approach

Suppose an economy only produces two goods, textiles and steel, with labor and capital being the only factors of production. In the following, textile production is shown as a labor-intensive and steel production as a capital-intensive branch of the economy. Labor-intensive production means that the importance of the production factor labor is assigned a higher priority than other production factors (capital). A production is considered capital-intensive if the cost structure is characterized by a high share of capital costs compared to other types of cost (labor). The price of a good is formed from the marginal costs . Under these conditions the theorem can be derived as follows:

The prices of textiles and steel are made up of:

${\displaystyle {\begin{aligned}(I)\ P(T)=a_{T}\cdot r+b_{T}\cdot w\\(II)\ P(S)=a_{S}\cdot r+b_{S}\cdot w\\\end{aligned}}}$

where:

${\displaystyle {\begin{aligned}P(T)&:\ {\text{Preis für Textilien}}\\P(S)&:\ {\text{Preis für Stahl}}\\r\ {\text{(rate)}}&:\ {\text{Zinssatz}}\\w\ {\text{(wage)}}&:\ {\text{Lohn}}\\a&:\ {\text{eingesetzte Mengen von Kapital}}\\b&:\ {\text{eingesetzte Mengen von Arbeit}}\\\end{aligned}}}$

• Postulates

1. If the price of the textiles produced increases, at least one of its factors also becomes more expensive. Due to the fact that textile production is a labor-intensive industry, it can be assumed that the costs of the production factor labor (wages) will increase. ${\displaystyle P(T)}$
2. If wages rise, then interest must fall for equation (II) to continue to hold. However, a decrease in interest rates also affects equation (I). For this to remain valid, the rise in wages must be disproportionate to the rise in the price of textiles.
3. An increase in the price of a good causes a disproportionate increase in the remuneration of the most intensively used factor, whereas the remuneration of the other factor (ceteris paribus) falls in absolute terms.

Graphic access

General graphic example

Point E represents the equilibrium of wages (w1) and interest rate (r1) when the prices of P (S) and P (T) are equal to the marginal cost.

Assuming the price of steel P (S) rises (for example through the imposition of tariffs or if a country develops from self-sufficiency to free trade), then the blue line shifts upwards and a new equilibrium at point F is established. This shift causes an increase in the interest rate from r1 to r2 and a decrease in equilibrium wages from w1 to w2. So when the price of steel rises, the reward for the most intensely used factor in production also rises, while the reward for labor goes down.

example

This graphic illustrates the example on the left.

I: II: ${\displaystyle P(S)=a_{S}\cdot r+b_{S}\cdot w}$
${\displaystyle P(T)=a_{T}\cdot r+b_{T}\cdot w}$

In the following example, the following variables are used for the set of the production factors labor and capital:
${\displaystyle {\begin{aligned}a_{S}=2\\b_{S}=1\\a_{T}=1\\b_{T}=2\end{aligned}}}$

For the prices of the respective goods textiles and steel , the following values are assumed: , ${\displaystyle T}$ ${\displaystyle S}$
${\displaystyle P(S)=4}$ ${\displaystyle P(T)=5}$

This results in the following two formulas:
I: II: ${\displaystyle 4=2\cdot r+1\cdot w}$
${\displaystyle 5=1\cdot r+2\cdot w}$

If one equates these formulas and after interest and wage surrounded, the following values result: , ${\displaystyle r}$ ${\displaystyle w}$
${\displaystyle r=1}$ ${\displaystyle w=2}$

Assuming a price increase for steel from 4 to 5, the following formula results: I: II: ${\displaystyle P(S)}$
${\displaystyle 5=2\cdot r+1\cdot w}$
${\displaystyle 5=1\cdot r+2\cdot w}$

By the price increase resulting for wages and interest following values: ,
${\displaystyle r={\tfrac {5}{3}}}$ ${\displaystyle w={\tfrac {5}{3}}}$

The example can be used to visualize two effects:

Distribution effect
in the example is reduced from on (price reduction of 17%) and increases from on (price increase of 66%). ${\displaystyle w}$ ${\displaystyle 2}$ ${\displaystyle {\tfrac {5}{3}}}$ ${\displaystyle r}$ ${\displaystyle 1}$ ${\displaystyle {\tfrac {5}{3}}}$

This is shown in the graphic by the black arrow between and . ${\displaystyle w_{1}}$ ${\displaystyle w_{2}}$

Magnification Effect
in the example increases disproportionately (price increase of 66% compared to price increase of 25%). ${\displaystyle r}$ ${\displaystyle r}$ ${\displaystyle P(S)}$

This is illustrated by the black arrow between and in the graphic opposite . ${\displaystyle r_{1}}$ ${\displaystyle r_{2}}$

It can be observed that the price level is increasing overall. This is made clear in the example graphic by the blue arrow.

application

Further empirical studies (e.g. by José Scheinkman, Ronald W. Jones) have shown that fundamental elements of the theorem can be generalized and also used for more global considerations. This explains the effects of increasing globalization on income distribution in developed countries and the resulting long-term trade alliances between these countries. Using the theorem, general statements can be made about the relationship between goods prices and real factor income. The causes which lead to these changes are irrelevant for the theorem.

criticism

A prerequisite of the Stolper-Samuelson theorem are the linear-homogeneous production functions, i.e. the constant returns to scale that only take into account the relative factor input, but not the absolute production quantities. Increasing economies of scale, for example, provide an incentive to increase production volumes. In this case, remuneration would be based on the marginal revenue product, contrary to Samuelson and Stolper.

Publications comparing producer prices with relative wage changes recognize moderate to strong confirmation of the Stolper-Samuelson theorem, such as Beyer et al. (1999) for Chile, Robertson (2004) for Mexico and Gonzaga et al. (2006) for Brazil.

literature

• Wilfried J. Ethier: Modern foreign trade theory. Oldenbourg, Munich 1997, ISBN 3-486-23980-5 .
• WF Stolper, PA Samuelson: Protection and Real Wages. In: Review of Economic Studies. 9, 1941, pp. 58-73. doi: 10.2307 / 2967638
• Rolf Peffekoven: Customs and wages. Duncker & Humblot, 1966, DNB 457781475
• Klaus Rose, Karlhans Sauernheimer: Theory of foreign trade. Vahlen, Munich 2006, ISBN 3-8006-3287-X .
• J. Peter Neary: History of the Theorem. (Center for Economic Policy Research: London, 2004).

Web links

• Steven M. Suranovic: The Stolper-Samuelson Theorem (engl.)
• J.Peter Neary: The Stolper-Samuelson Theorem Encyclopedia of the World Economy since 1450 (English; PDF file; 14 kB)

Individual evidence

1. ^ J. Peter Neary: The Stolper-Samuelson Theorem. In: John J. McCusker et al. (Ed.): History of World Trade Since 1450. Thomson Gale, Detroit / Munich et al. 2006, ISBN 0-02-865840-X .
2. ^ WF Stolper, PA Samuelson: Protection and Real Wages. In: Review of Economic Studies. 9, 1941, p. 70.
3. ↑ Springer Gabler Verlag (editor), Gabler Wirtschaftslexikon, keyword: work-intensive, online on the Internet: http://wirtschaftslexikon.gabler.de/Archiv/72890/arbeitsintensiv-v6.html
4. ↑ Springer Gabler Verlag (editor), Gabler Wirtschaftslexikon, keyword: capital-intensive, online on the Internet: http://wirtschaftslexikon.gabler.de/Archiv/72892/kapitalintensiv-v4.html
5. ^ J. Peter Neary, "History of the Theorem", (Center for Economic Policy Research: London, 2004).
6. ^ Rolf Peffekoven: Customs and wages . 1966, p. 100f.
7. ↑ Beyer, H., P. Rojas, and R. Vergara (1999), “Trade Liberalization and Wage Inequality”, Journal of Development Economics, Vol. 59, pp. 103-123.
8. ^ Robertson, Raymond (2004) “Relative Prices and Wage Inequality: Evidence from Mexico”, Journal of International Economics Vol 64, no. 2 (December), pp. 387-409.
9. ↑ Gonzaga, Gustavo, Naércio Menezes Filho and Christina Terra, "Trade Liberalization and the Evolution of Skill Earnings Differentials in Brazil", Journal of International Economics 68, no. 2 (March 2006): 345-367.