Generalization of the Heckscher-Ohlin Model

Question

The Heckscher-Ohlin Model is normally presented for the case of 2 countries, 2 factors of production and 2 traded goods, leading to statements that, subject to free trade and various other assumptions:

1. A country with a relative abundance of a factor will specialize in and export the good whose production makes relatively intensive use of that factor (the Heckscher-Ohlin Theorem).

2. The return to a factor will be equalized between the countries (the Factor Price Equalization or Heckscher-Ohlin-Samuelson Theorem).

Do these results generalize, subject to the same assumptions, to cases with more than 2 countries, factors or traded goods, and what are good sources that treat this topic? Of particular interest are cases with 3 factors: labour, man-made capital and natural capital.

I appreciate that the predictions of the Heckscher-Ohlin Model often differ from empirical findings (eg the Leontief Paradox), but this question is about the model itself.

Answer 1

The HO model has been generalised. Vanek does a good job of it.

Instead of only two countries, there is an index of countries.

• There are many industries.

• Identical technology

• Identical, homothetic tastes.

The HOV theorem states that if a country is abundant in a factor, its factor content of trade in that factor should be positive, and negative otherwise.

Empirically, this model is not that successful. Here is a good paper discussing the applications and results.

See below for that extension: Vanek, Jaroslav, The Factor Proportions Theory: The N-Factor Case,” Kyklos, October 1968, 21, 749-755.