Deardorff (1994) provides a condition that is necessary for factor price equalization across countries. That condition is a generalization of "country endowments contained in the diversification cone" from the standard 2x2x2 Hecksher-Ohlin model to the case of many goods, countries and factors....

The authors give a simple, constructive proof that the lens condition implies the factor price equalization condition when there are only two factors. Taking stock of the conditions under which the lens condition is equivalent to the factor price equalization condition, there are the conditions...