# On the Use of Elasticities of Substitution

## Abstract

In the framework of an import allocation model, we usually work with bilateral imports from more than two trade partners, the demand for which is derived using a partial aggregator function or import quantity index. The choice of such a function is decisive for the substitution possibilities between the products supplied by the different trade partners. The question is how one may describe the substitution possibilities between products supplied by any pair of trade partners. One would like to give physical notions such as “strong” or “weak” substitutes a quantitative analogue. One would pose a similar question regarding the substitution possibilities among production factors in producer theory and among consumer goods in consumer theory. As long as the aggregator function involved in all these cases contains only two elements, the question may be given a sufficient answer in the form of a uniquely defined concept of *elasticity of substitution* (E3) which may be shown to have an acceptable economic interpretation. This concept was originally defined as representing the elasticity of the ratio of two factors with respect to their marginal rate of substitution^{1)}. The concept may be applied to production theory, consumer theory, linkage models and many other fields. But when the number of factors in the aggregator function becomes greater than two, there is confusion in the different notions of ES that may be employed.

## Keywords

Production Function Price Change Hessian Matrix Price Elasticity Trade Partner## Preview

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