Factor endowment--commodity output relationships in a three-factor two-good general equilibrium trade model: Further analysis

TL;DR

This paper analyzes the relationships between factor endowments and output in a three-factor, two-good trade model, providing methods to estimate key vectors and conditions for specific economic sign patterns.

Contribution

It introduces a method to estimate the EWS-ratio vector's position and derives conditions for extreme factors to be economy-wide complements and for specific sign patterns.

Findings

EWS-ratio vector exists on the line segment

Method developed to estimate EWS-ratio vector position

Conditions for strong Rybczynski and specific Stolper-Samuelson patterns

Abstract

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.