The authors show how the transformation loci in the specific factors model (capital specificity) and the Heckscher-Ohlin-Samuelson model (capital mobility) can be rigorously derived and easily compared by using geometric techniques on the basis of Savosnick geometry. The approach shows directly that the transformation locus with capital specificity has a greater degree of curvature than with capital mobility, given the same technology, and that the latter is an envelope of the former. It can also be used to show how incentives in the short run would lead to the long-run capital reallocation implied by the assumption of capital mobility. (Contains 3 figures.)