Relative Shares and Elasticities Simplified: Reply
We are gratified that mention of our paper on Relative Shares has been made in the preceding note by Paul Samuelson. Consistent with his past contributions, Samuelson has provided a simplified treatment of the various concepts of elasticity of substitution. We would like to take this occasion to make some further observations. With regard to Samuelson's statement about the usefulness of the elasticity concepts, first, it is hard to imagine that Samuelson would go so far as to belittle the theoretical contributions of all the studies done in such areas as growth, production functions, and technical progress which have greatly benefited by the use of the elasticity of substitution concept. In these studies the elasticity of substitution concept was not used in a trivial manner. Secondly, and this is more relevant to the type of problems we address, there is the matter of substitutes and complements which is an integral aspect of the multifactor analysis. In problems dealing with multifactor production, dual partial elasticity concepts developed by Allen, Hicks, Sato-Koizumi, etc.1 serve several useful functions. Besides providing a taxonomy of effects that need to be measured, these various concepts provide us with alternative frameworks of conceiving of substantive problems. Although it can be shown that the partial concepts are related to some of the other elasticitv concepts and hence need not be glorified bv fancy names, there do exist particular problems where it is crucial to understand how the total effect is divided into its component effects. For example, in the case where we are dealing with derived demand with some factors (subsitutes or complements) limited in supply, it is important to know exactly how the existence of substitutability or coomplementarity among factors works for or against a particular factor share.
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