The Heckscher-Ohlin Theorem

The Heckscher-Ohlin theorem states that a country which is capital-abundant will export the capital-intensive good. Likewise, the country which is labor-abundant will export the labor-intensive good. Each country exports that good which it produces relatively better than the other country. In this model a country's advantage in production arises solely from its relative factor abundance.

The Heckscher-Ohlin Theorem - Graphical Depiction - Variable Proportions

The H-O model assumes that the two countries (US and France) have identical technologies, meaning they have the same production functions available to produce steel and clothing. The model also assumes that the aggregate preferences are the same across countries. The only difference that exists between the two countries in the model is a difference in resource endowments. We assume that the US has relatively more capital per worker in the aggregate than does France. This means that the US is capital-abundant compared to France. Similarly, France, by implication, has more workers per unit of capital in the aggregate and thus is labor-abundant compared to the US. We also assume that steel production is capital-intensive and clothing production is labor-intensive.

The difference in resource endowments is sufficient to generate different PPFs in the two countries such that equilibrium price ratios would differ in autarky. To see why, imagine first that the two countries are identical in every respect. This means they would have the same PPF (depicted as the brown PPF₀ in the adjoining figure), the same set of aggregate indifference curves and the same autarky equilibrium. Given the assumption about aggregate preferences, that is U = C_CC_S, the indifference curve, I, will intersect the countrys' PPFs at point A, where the absolute value of the slope of the tangent line (not drawn), (P_C/P_S), is equal to the slope of the ray from the origin through point A. The slope is given by C_S^A/C_C^A. In other words, the autarky price ratio in each country will be given by,

Next suppose that labor and capital are shifted between the two countries. Suppose labor is moved from the US to France while capital is moved from France to the US. This will have two effects. First, the US will now have more capital and less labor, France will have more labor and less capital than initially. This implies that K/L> K*/L*, or that the US is capital-abundant and France is labor-abundant. Secondly, the two countries PPFs will shift. To show how, we apply the Rybczynski theorem.

The US experiences an increase in K and a decrease in L. Both changes will cause an increase in output of the good that uses capital intensively (i.e. steel) and a decrease in output of the other good (clothing). The Rybczynski theorem is derived assuming that output prices remain constant. Thus if prices did remain constant, production would shift from point A to B in the diagram and the US PPF would shift from the brown PPF₀ to the green PPF.

Using the new PPF we can deduce what the US production point and price ratio would be in autarky given the increase in the capital stock and decline in labor stock. Consumption could not occur at point B since, 1) the slope of the PPF at B is the same as the slope at A since the Rybczynski theorem was used to identify it, and 2) homothetic preferences implies that the indifference curve passing through A must have a steeper slope since it lies along a steeper ray from the origin.

Thus, to find the autarky production point we simply find the indifference curve which is tangent to the US PPF. This occurs at point C on the new US PPF along the original indifference curve, I. (Note: the PPF was conveniently shifted so that the same indifference curve could be used. Such an outcome is not necessary but does make the graph less cluttered.) The negative of the slope of the PPF at C is given by the ratio of quantities C_S'/C_{C' .} Since C_S'/C_C' > C_S^A/C_C^A, it follows that the new US price ratio will exceed the one prevailing before the capital and labor shift, i.e., P_C/P_S > (P_C/P_S)⁰. In other words, the autarky price of clothing is higher in the US after it experiences the inflow of capital and outflow of labor.

France experiences an increase in L and a decrease in K. These changes will cause an increase in output of the labor-intensive good (i.e. clothing) and a decrease in output of the capital-intensive good (steel). If price were to remain constant, production would shift from point A to D in the diagram and the French PPF would shift from the brown PPF₀ to the red PPF^*.

Using the new PPF we can deduce the French production point and price ratio in autarky, given the increase in the capital stock and decline in labor stock. Consumption could not occur at point D since homothetic preferences implies that the indifference curve passing through D must have a flatter slope since it lies along a flatter ray from the origin. Thus to find the autarky production point we simply find the indifference curve which is tangent to the French PPF. This occurs at point E on the new French PPF along the original indifference curve, I. (As before, the PPF was conveniently shifted so that the same indifference curve could be used.) The negative of the slope of the PPF at C is given by the ratio of quantities C_S"/C_C", Since C_S'/C_C" < C_S^A/C_C^A, it follows that the new French price ratio will be less than the one prevailing before the capital and labor shift, i.e., P_C*/P_S* < (P_C/P_S)⁰. This means that the autarky price of clothing is lower in France after it experiences the inflow of labor and outflow of capital.

All of the above implies that as one country becomes labor-abundant and the other capital-abundant, it causes a deviation in their autarky price ratios. The country with relatively more labor (France) is able to supply relatively more of the labor-intensive good (clothing) which in turn reduces the price of clothing in autarky relative to the price of steel. The US with relatively more capital can now produce more of the capital-intensive good (steel) which lowers its price in autarky relative to clothing. These two effects together imply that

Any difference in autarky prices between the US and France is sufficient to induce profit-seeking firms to trade. The higher price of clothing in the US (in terms of steel) will induce firms in France to export clothing to the US to take advantage of the higher price. The higher price of steel in France (in terms of clothing) will induce US steel firms to export steel to France. Thus, the US, abundant in capital relative to France, exports steel, the capital-intensive good. France, abundant in labor relative to the US, exports clothing, the labor-intensive good. This is the Heckscher-Ohlin theorem. Each country exports the good intensive in the country's abundant factor.

International Trade Theory and Policy - Chapter 60-8: Last Updated on 7/31/06