A General Measure for Output‐Variable Input Demand Elasticities

In recent years the development of new production function forms has given impetus to empirical work of measuring input demand and substitution elasticities in a variety of industries. The so-called "flexible" functional forms have given us a much richer set of tools to investigate these relationships, as compared to the familiar Cobb-Douglas and constant-elasticity-of-substitution functions. The majority of researchers have reported their results in terms of input parameters estimated under the assumption of fixed output. While this is appropriate for some questions, we argue in the next section that output-variable measures often will be more useful for the problem at hand. In the third section, we derive a general expression for the output variable price elasticity of input demand, of which the well-known expression of Allen is a special case.