Rybczynski theorem

Classical representation of the Rybczynski theorem.

The Rybczynski theorem was published in 1955 by the Polish economist Tadeusz Rybczynski (1923-1998) in his article Factor Endowments and Relative Commodity Prices and is based on the assumptions of the Heckscher-Ohlin theorem (after Eli Heckscher and Bertil Ohlin ).

It says that if only one production factor increases at a constant international price level , the production of that good that uses this factor relatively intensively increases disproportionately. The production of the other good, however, is reduced in absolute terms. It thus describes the unequal effects of changes in resources on production in different sectors.

Derivation in the Heckscher-Ohlin model

In the context of the Heckscher-Ohlin model and its assumptions, the effect can be derived if

there is a one-sided expansion of resources in a box diagram with two factors (that is, a production factor increases due to, for example, immigration and capital imports)
and the relative factor prices remain constant.

Since only one production factor is expanded, but the relative factor prices remain constant, one can see a one-sided increase in the output quantity of the good that uses this production factor relatively intensively. Due to this increase in the total factor endowment, however, the production possibilities of the other sector also increase. However, the increase in production in the sector that makes greater demands on the expanded production factor is higher relative to the other sector that uses this factor less intensively. As a result, the transformation curve of the resource allocation shifts disproportionately strongly in the direction of the sector that uses the resources the most. The production of that good thus increases disproportionately. This effect, the so-called Rybczynski effect, is seen as a possible explanation for foreign trade.

Assumptions of the Rybczynski theorem

First of all, the assumptions of the Heckscher-Ohlin model apply with regard to production factors, labor and capital flexibility, production technology and functions, economies of scale, specialization, goods prices and international competition.

In addition, constant costs for production factors and goods are assumed for the Rybczynski theorem, as well as a one-sided expansion of resources in both countries: while the production factor labor expands in the labor-rich country, there is an expansion of the production factor capital in the capital-rich country.

Graphical derivation

The graphic derivation of the Rybczinsky effect becomes clear in the context of the so-called Edgeworth box . This is created by two coordinate systems. First, the coordinate system of the steel is created, which shows the input of production factors on the two axes, in this case capital on the abscissa (x-axis) and work on the ordinate (y-axis). In this example, steel is considered to be relatively capital-intensive. The graph therefore runs steeply along the ordinate. The second graph, which shows the production factor input of textiles, is rotated by 180 ° and placed so that the origin is diagonally opposite to the first origin , thus creating a box. Textiles are relatively labor-intensive and the graph runs relatively steeply along the abscissa. The graphs are drawn according to the capital-labor ratio. ${\ displaystyle O_ {T}}$ ${\ displaystyle O_ {S}}$

The intersection of the two graphs shows the necessary use of the production factors that has to be applied in each case to achieve the current output. The width of the box shows the total amount of work available and the height of the box shows the total amount of capital in the economy. In order to recognize the Rybczinsky effect, the theorem is based on the assumption that the amount of one production factor increases while the other remains constant at the same time. This example assumes that the amount of work in the economy is increasing. As a result, the box has to be larger in width, so that the amount of work increases while the amount of capital remains constant. A new origin is emerging for the graphene of textiles. From this point of view, the new graph must be set up parallel to the original graph, since the capital-labor ratio remains constant in production. Consequently, a new point of intersection of the two graphs is created. ${\ displaystyle P_ {1}}$ ${\ displaystyle O_ {T '}}$ ${\ displaystyle P_ {2}}$

The result and the effect can now be read from the associated axes. With regard to the capital-intensive good steel, it can be seen that both the use of capital and the use of labor are falling, which results in a lower output volume. As a result, an increase in labor input and also in capital input can be seen in the labor-intensive commodity textiles. The output of textiles is increasing in absolute terms. The effect is thus confirmed by the Edgeworth box, since if a production factor is expanded, the output of the good that uses the production factor relatively more increases. At the same time, the output of the other good decreases.

Graphic example

Graphic example of the Rybczynski theorem

The Rybczynski effect describes the consequences of changing one production factor while the other remains constant. The production of that good increases disproportionately if it uses the unilaterally increased production factor relatively more intensively. This is illustrated in the following example.

The figure shows textiles, on the one hand, which are labor-intensive and, on the other hand, steel, which is capital-intensive. The graph of describes the normal case, whereby the output quantities are balanced or equal. At the point where the straight line of the price ratio intersects the graph , the associated production point appears . ${\ displaystyle T_ {0}}$ ${\ displaystyle T_ {0}}$ ${\ displaystyle H_ {0}}$

As the production factor labor increases, the graph shifts from to . The capital base remains constant. This shift increases the production possibilities for textiles, while the production of steel tends to decline. With a constant price ratio, this results in a new production point at . ${\ displaystyle T_ {0}}$ ${\ displaystyle T_ {1}}$ ${\ displaystyle H_ {1}}$

The graph describes the opposite case. The capital stock is increased while the production factor labor remains constant. With this assumption, the graph shifts from to . With a constant production ratio, the new production point is set at . This results in an increase in the production possibilities of steel and at the same time a reduction in the production possibilities of textiles. ${\ displaystyle T_ {2}}$ ${\ displaystyle T_ {0}}$ ${\ displaystyle T_ {2}}$ ${\ displaystyle H_ {2}}$

Statements about foreign trade

Within the framework of the Heckscher-Ohlin model, with the help of the Rybczynski theorem, statements can be made about the foreign trade of an economy and its growth (the one-sided factor increase actually represents economic growth).

In the following, a country is used as an example, which in its initial state is relatively rich in the labor factor. The Heckscher-Ohlin model predicts that this country will export labor-intensive goods and import capital-intensive goods. With a one-sided exogenous expansion of the labor factor, according to Rybczynski theorem, the production and thus also the export of labor-intensive goods (textiles) will increase, while the production of capital-intensive goods will decrease. As a result, this country has to import more and more capital-intensive goods (steel). There is thus a strongly positive trading effect. If, on the other hand, the capital stock is increased exogenously, the production of the labor-intensive good (export product) falls and the production of the capital-intensive good (import good) increases. The result is a strongly negative trade effect.

literature

Tadeusz M. Rybczynski: Factor Endowments and Relative Commodity Prices . In: Economica 22 (1955), pp. 336-341
Paul R. Krugman, Maurice Obstfeld: International Economy. Theory and Politics of Foreign Trade . Pearson Studium, Munich 2004, ISBN 3-8273-7081-7 (especially chapter 4).
Dixit, Avinash / Norman, Victor; Foreign trade theory ; 4th edition; 1993
Krugman, Paul R./Obstfeld, Maurice; International Economy - Theory and Politics of Foreign Trade ; 9th edition; 2012
Maening, Wolfgang; Foreign trade - theory and politics ; 2nd Edition; 2013
Rose, Klaus / Sauernheimer, Karlhans; Theory of foreign trade ; 14th edition; 2006
Van Marrewijk, Charles; International Economics: theory, application, and policy ; 2nd Edition; 2012

Web links

Rybczynski theorem - definition in the Gabler Wirtschaftslexikon