  The position of the EWS (economy-wide substitution)-ratio vector determines
the Rybczynski sign pattern, which expresses the factor endowment--commodity
output relationships, and the Stolper-Samuelson sign pattern, which expresses
the commodity price--factor price relationships in a three-factor two-good
general equilibrium trade model (see Nakada (2016a)). In this article, we show
that the EWS-ratio vector exists on the line segment. Using this relationship,
we develop a method to estimate the position of the EWS-ratio vector. We derive
a sufficient condition for extreme factors to be economy-wide complements,
which implies "a strong Rybczynski result." Additionally, we derive a
sufficient condition for a specific Stolper-Samuelson sign pattern to hold. We
assume factor-intensity ranking is constant. This article provides a basis for
further applications.
