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Assume that the point dividing the world endowments between the two countries lies within the FPE set. The factor content of production for each country is its endowment Vc. With identical homothetic preferences, common goods prices, and production with the integrated equilibrium techniques, the factor content of absorption is sc VW. Together these yield the standard HOV prediction for the net factor content of trade: Vc – S VW. However we also know that with more goods than factors, the pattern of goods production, so also the pattern of goods trade, is not determinate.

In order to make the trade and production patterns determinate, we resort to an artifice originally introduced by Samuelson (1954) and considered within the continuum framework by Xu (1993). Imagine that all goods have iceberg transport costs, so that if j > 1 units are shipped, only one unit arrives. We will think of these trade costs as being strictly positive but arbitrarily small. Goods prices will be arbitrarily close to those of the integrated equilibrium, as will absorption and so the net factor content of trade. However, as Samuelson suggested, trade will be arranged so as to minimize trade costs. Since all goods are assumed to have the same proportional costs, this is equivalent to minimizing the volume of trade subject to achieving (approximately) the HOV-required net factor content.

This problem has a very simple solution: insofar as possible, the capital abundant country will concentrate its exports among the very most capital intensive goods (call them the X-goods), the labor abundant country will concentrate its exports among the most labor-intensive goods (call them the 7-goods). Goods of intermediate factor intensity (N-goods) will not be traded. Thus the real equilibrium features a pattern of perfect specialization in the goods that are (in equilibrium) traded. The capital abundant home country produces only X (its export) and N, while the labor abundant country produces only 7 (its export) and N.

Of course, one will find such extreme production specialization nowhere in real data. So we must discuss how the empirical industries in our data sets match up with the real equilibrium described above. It is well-known that the industrial classification system was not designed with the concerns of Heckscher-Ohlin researchers in mind. Hence actual industrial classification, in contrast to our theoretical industries, includes goods of very heterogeneous capital to labor ratios.

Consider two industries, 1 and 2. Assume that on average industry 1 has a tendency to include the more capital intensive goods, but that it actually includes goods from 7, N, and X. Similarly, assume industry 2 tends to include more goods in the labor intensive sectors, but also includes goods from 7, N, and X. For simplicity, assume the densities for sectors 1 and 2 are uniform over each of the intervals 7, N, and X (taken separately). A schematic representation appears in Figure 2. cheapest payday loans