time traveler

four theorems of H-O model

Posted on: February 5, 2009

The Heckscher-Ohlin theorem is one of the four critical theorems of the Heckscher-Ohlin model. It states: "A capital-abundant country will export the capital-intensive good, while the labor-abundant country will export the labor-intensive good."
The critical assumption of the Heckscher-Ohlin model is that the two countries are identical, except for the difference in resource endowments. This also implies that the aggregate preferences are the same. The relative abundance in capital will cause the capital-abundant country to produce the capital-intensive good cheaper than the labor-abundant country and vice versa.
Initially, when the countries are not trading:
the price of capital-intensive good in capital-abundant country will be bid down relative to the price of the good in the other country,
the price of labor-intensive good in labor-abundant country will be bid down relative to the price of the good in the other country
.
Once trade is allowed, profit-seeking firms will move their products to the markets that have (temporary) higher price. As a result:
the capital-abundant country will export the capital-intensive good,
the labor-abundant country will export the labor-intensive good.
The Leontief paradox, presented by Wassily Leontief in 1954, found that the U.S. (the most capital-abundant country in the world by any criteria) exported labor-intensive commodities and imported capital-intensive commodities, in apparent contradiction with Heckscher-Ohlin theorem.
The Rybczynski theorem was developed in 1955 by the Polish-born English economist Tadeusz Rybczynski (1923-1998). The theorem states: At constant relative goods prices, a rise in the endowment of one factor will lead to a more than proportional expansion of the output in the sector which uses that factor intensively, and an absolute decline of the output of the other good.
In the context of the Heckscher-Ohlin model of international trade, open trade between regions means changes in relative factor supplies between regions can lead to an adjustment in quantities and types of outputs between regions that would return the system toward equality of production input prices like wages across countries (the state of factor price equalization).
The Rybczynski theorem displays how changes in an endowment affects the outputs of the goods when full employment is sustained. The theorem is useful in analyzing the effects of capital investment, immigration and emigration within the context of a Heckscher-Ohlin model. Consider the diagram below, depicting a labour constraint in red and a capital constraint in blue. Suppose production occurs initially on the production possibility frontier (PPF) at point A.
Suppose there is an increase in the labour endowment. This will cause an outward shift in the labour constraint. The PPF and thus production will shift to point B. Production of clothing, the labour intensive good, will rise from C1 to C2. Production of cars, the capital-intensive good, will fall from S1 to S2.
If the endowment of capital rose the capital constraint would shift out causing an increase in car production and a decrease in clothing production. Since the labour constraint is steeper than the capital constraint, cars are capital-intensive and clothing is labor-intensive.
In general, an increase in a country’s endowment of a factor will cause an increase in output of the good which uses that factor intensively, and a decrease in the output of the other good.
The Stolper-Samuelson theorem is a basic theorem in trade theory. It describes a relation between the relative prices of output goods and relative factor rewards, specifically, real wages and real returns to capital.
The theorem states that — under some economic assumptions (constant returns, perfect competition) — 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.
It was derived in 1941 from within the framework of the Heckscher-Ohlin model by Paul Samuelson and Wolfgang Stolper, but has subsequently been derived in less restricted models. As a term, it is applied to all cases where the effect is seen. Jones & Scheinkman (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 a robust finding of the theorem is that returns to the scarce factor will go down, ceteris paribus. A further robust corollary of the theorem is that a compensation 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 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:
(1) P(C) = ar + bw,
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 uses.
Similarly, the price of wheat would be:
(2) P(W) = cr + dw
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.
Factor price equalization is an economic theory, which states that the relative prices for two identical factors of production in the same market will eventually equal each other because of competition. The price for each single factor need not become equal, but relative factors will. Whichever factor receives the lowest price before two countries integrate economically and effectively become one market will therefore tend to become more expensive relative to other factors in the economy, while those with the highest price will tend to become cheaper.
An often-cited example of factor price equalization is wages. When two countries enter a free trade agreement, wages for identical jobs in both countries tend to approach each other. After the North American Free Trade Agreement (NAFTA) was signed, for instance, unskilled labor wages gradually fell in the United States, at the same time as they gradually rose in Mexico. The same force has applied more recently to the various countries of the European Union.
The result was first proven mathematically as an outcome of the Heckscher-Ohlin model assumptions.
Simply stated the theorem says that when the prices of the output goods are equalized between countries as they move to free trade, then the prices of the factors (capital and labor) will also be equalized between countries.
This implies that free trade will equalize the wages of workers and the profits earned on capital throughout the world.
The theorem derives from the assumptions of the model, the most critical of which is the assumption that the two countries share the same production technology and that markets are perfectly competitive.
In a perfectly competitive market the return to a factor of production depends upon the value of its marginal productivity. The marginal productivity of a factor, like labor, in turn depends upon the amount of labor being used as well as the amount of capital. As the amount of labor rises in an industry, labor’s marginal productivity falls. As the amount of capital rises, labor’s marginal productivity rises. Finally the value of productivity depends upon the output price commanded by the good in the market.
In autarky, the two countries face different prices for the output goods. The difference in prices alone is sufficient to cause a deviation in wages and rents between countries, because it affects the marginal productivity. However, in addition, in a variable proportions model the difference in wages and rents also affects the capital-labor ratios in each industry, which in turn affects the marginal products. All of this means that for various reasons the wage and rental rates will differ between countries in autarky.
Once free trade is allowed in outputs, output prices will become equal in the two countries. Since the two countries share the same marginal productivity relationships it follows that only one set of wage and rental rates can satisfy these relationships for a given set of output prices. Thus free trade will equalize goods prices and wage and rental rates.
Since the two countries face the same wage and rental rates they will also produce each good using the same capital-labor ratio. However, because the countries continue to have different quantities of factor endowments, they will produce different quantities of the two goods.
 
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