Paper Accepted at Economics Letters

My paper Derivation of the Hicks, or Direct, Elasticity of Substitution from the Input Distance Function has been accepted for publication at Economics Letters. As I've mentioned before, the elasticity of substitution measures the difficulty of replacing one input to production such as energy with another such as capital, usually under the assumption that the level of output must be kept constant. This parameter is very important in the study of long-run economic growth and sustainability, the costs of climate policy, among many other areas. The traditional elasticity of substitution measured the percent change in the ratio of input quantities for a given percentage change in the ratio of their prices (or marginal products) holding output constant. The formula was derived using the production function. My paper derives the elasticity from the more general input distance function, which can have multiple outputs and can accommodate possibly inefficient production. I also show that "distance" or technical efficiency must be held constant when calculating the elasticity. This is an additional condition which was classically implicitly assumed to be the case rather than explicitly stated. This new derivation helps complete the classification of many different related elasticities.