Will the Real Elasticity of Substitution Please Stand Up? (A Comparison of the Allen/Uzawa and Morishima Elasticities)

Although the Allen-Uzawa elasticity of substitution (AES) has been a standard statistic reported in empirical studies of production and consumption, no intuition was provided to convince one that it is a natural generalization of Hick's 2-variable elasticity of substitution. It is shown that, while the AES reduces to the original Hicksian concept in the 2-dimensional case, in general, it preserves none of the salient properties of the Hicksian idea. In particular, the AES: 1. is not a measure of the ease of substitution, or curvature of the isoquant, 2. provides no information about relative factor shares, and 3. cannot be interpreted as a logarithmic derivative of a quantity ratio with respect to a price ratio or the marginal rate of substitution. It is also shown that an alternative concept, originally formulated by Morishima (1967), preserves these salient features of the original Hicksian concept.