Linking Armington and CET Elasticities of Substitution and Transformation to Price Elasticities of Import Demand and Export Supply: A Note for CGE Practitioners

Armington and constant-elasticity-of-transformation (CET) functions are routinely used in computable general equilibrium (CGE) Models to model foreign trade. The CET function is applied to producer decisions about whether to export and or sell at home. Decisions by domestic demanders whether to purchase imports or domestic output are covered by the Armington function. The Armington function is a constant-elasticity-of-substitution (CES) function. This note is concerned with the links between (a) price elasticities of import demand and constant elasticities of substitution between demand for imports and domestic output; and (b) price elasticities of export supply and constant elasticities of transformation between supply to exports and domestic market. These links are important since researchers often may wish to compare estimates of price elasticities to the price elasticities implied by elasticities of substitution and transformation. In this note, price elasticities related to each function are derived from their representation in many CGE models – the function itself and a first-order optimality condition. In an appendix, these representations are derived from cost minimization and revenue maximization given prices and the “technology” embodied by the Armington and CET functions.