Pure traded intermediate products and trade pattern predictions

It is well-known, and sometimes lamented, that in the standard two-country, two-factor trade model with pure traded intermediate products, even dropping the non-specialization assumption does not rehabilitate the HeckscherOhlin (H-O) theorem with respect to final goods. This is noted, for example, in Batra [Studies in the Pure Theory of International Trade, St. Martins, 1973] or Schweinberger ["Pure Traded Intermediate Products and the Heckscher-Ohlin Theorem," American Economic Review, 65 September 1975, pp. 634-43]. In particular, suppose that the intermediate product holds an extreme factor intensity in production. Then, both countries producing the middle capital intensity final good is destructive to the predictive power of the H-O theorem in that either the relatively capital abundant or labor abundant country may export this final good in equilibrium. There is, however, another class of pure intermediate goods preparatory to consumption but particular only to traded commodities with respect to which the H-O theorem is more resilient. Since it is undoubtedly the most important example, we will refer to such an intermediate good as the service of international shipping. That is, the H-O theorem is not substantially weakened in the presence of a resource using shipping industry. This is because the ambiguity with respect to trade in final products depends crucially on the derived nature of the demand for the intermediate product. The demand for the intermediate good in the usual analysis derives from both the ultimate domestic and foreign demand for final products. Thus, it is conceivable that a country might export only final goods and import only the intermediate product. When the intermediate product is the service of shipping goods, however, this simply cannot happen. This is because the demand for shipping is derived exclusively from the demand for foreign final goods. Clearly, in balanced trade, one country cannot exchange a final good for shipping alone because the derived demand for shipping in that country would then be zero. We conclude that both countries must export at least a final product in equilibrium. It is now easy to show that if tastes across countries are identical and homothetic, then the relatively capital abundant country exports the relatively capital intensive final product and imports the relatively labor intensive final product regardless of the capital intensity in shipping production. Furthermore, it is a trivial corollary of the Jones ["Factor Proportions and the Heckscher-Ohlin Theorem," Review of Economic Studies, 25, 1956, pp. 1-10] theorem that if shipping is capital (labor) intensive relative to the final goods, then only the capital (labor) abundant country will provide all the shipping. (The validity of Jones' "chain of comparative advantage" theorem in the variable proportions model with transport costs has been noted by Bhagwati ["The Heckscher-Ohlin Theorem in the Multi-Commodity Case," Journal of Political Economy, 80, September 1972, pp. 1052-5], for example.) Thus, when the pure intermediate product is in the nature of transportation, the H-O theQrem emerges unscathed with respect to trade in all three products or final goods only.