Returns to scale and scale elasticity in data envelopment analysis

The purpose of this paper is to provide mathematical characterizations of the data envelopment analysis based scale elasticity that is computable for both frontier and nonfrontier units. In order to accomplish this, we first review existing frontier results, extend them formally to the nonfrontier case and then analyze how the scale elasticity behaves. We also study how shadow pricing can be done, as an application of the scale elasticity, and show how upper and lower scale elasticity bounds can be obtained. Finally, we provide an illustrative example for the clarification and verification of our results.