Factor Price Equalization when the World Equilibrium is not Unique

It is shown that, whatever the multiplicity of the integrated world equilibrium, (i) factor prices are equalized if and only if the distribution of primary factors between trading countries can be represented by a point in or on the boundary of a certain convex subset of R ^m , where m is the number of primary factors, and (ii) the likelihood of factor price equalization is independent of the multiplicity of the equilibrium.