Chapter 4 Elasticities of Substitution

This draft chapter, prepared for inclusion in the (prospective) Handbook of Production Economics, Vol. 1 (Theory), edited by Subash Ray, Robert Chambers, and Subal Kumbhakar, lays out the theoretical foundation of the measurement of the degree of substitutability among inputs utilized in a production process. It proceeds from the well-settled (Hicksian) notion of this measure for two inputs (typically labor and capital) to the more challenging conceptualization for technologies with more than two inputs (most notably, Allen-Uzawa and Morishima elasticities). Dual elasticities of substitution (also called elasticities of complementary) and gross elasticities of substitution (measuring substitutability for non-homothetic technologies taking account of output changes) are also covered. Also analyzed are functional representations of two-input technologies with constant elasticity of substitution (CES) and of n-input technologies with constant and identical elasticities for all pairs of inputs. Finally, the chapter explores the relationship between elasticity values and the comparative statics of factor income shares and the relationships between certain elasticity identities and separability conditions rationalizing consistent aggregation of subsets of inputs.