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FACTOR PRICE EQUALITY AND THE ECONOMIES OF THE UNITED STATES: Multiple cone equilibriumIn the figure, the production of Apparel and Textiles requires only physical capital and labor, while the manufacture of Machinery requires capital, labor and human capital (H). Note as well that approaching a corner of the endowment simplex along a ray emanating from that corner represents an increase in the use (for an industry input vector) or abundance (for an endowment vector) of that factor, holding the concentration of other factors constant. Thus, Textiles use more physical capital than Apparel, and both use the same ratio of human capital to labor, which is zero. Since factors become relatively more abundant as regions move closer to a given vertex, the associated factor rewards decline as regions move through cones. Thus, in the second panel, which describes a multiple cone equilibrium containing eight cones, the return to labor declines as one moves through the cones at the bottom of the endowment simplex from right to left.

In the two dimensional Lerner diagrams above, the existence of three or more cones is enough to guarantee that at least two are not neighbors. In higher dimensions, however, there is no guarantee that non-neighboring cones exist.3 Intuition for this claim is provided by panel two of figure 5: in that endowment simplex, six of the eight cones produce the machinery sector.
The complex neighborliness of cones in higher dimensions means that regions with quite disparate endowments can produce sectors in common. In the figure, for example, regions 1, 2 and 3 all produce machinery even region 1 has almost no human capital to labor, region 3 has extremely high human capital to labor, and region 2 is in between. This complication limits the use of product mix as a means of empirically discerning single from multiple cone equilibria. For example, though all regions producing the same mix of goods is evidence of a single cone equilibrium, specialization does not imply a multiple cone equilibrium.