Scale Efficiency: Equivalence of Primal and Dual Measures

In this paper we address an issue of equivalence of primal and dual measures of scale efficiency in general production theory framework. We find that particular types of homotheticity, which we refer to as scale homotheticity, provide necessary and sufficient condition for such equivalence. Specifically, we show that the input scale homotheticity of technology is necessary and sufficient condition for equivalence of primal and dual scale efficiency measures in the input/cost oriented case. Similarly, the output scale homotheticity of technology is necessary and sufficient condition for equivalence of primal and dual scale efficiency measures in the output/revenue oriented case. We also discuss the case when technology is both input scale homothetic and output scale homothetic, as well as indicate about some relationships of scale homotheticity with the homotheticity notions that have already been used in economic theory.