Different orders of one-sided scale elasticities in multi-output production

In this paper we explore properties of different orders of one-sided scale elasticities in multi-input multi-output production using the theoretical framework developed by Hadjicostas and Soteriou (Eur J Oper Res 168:425–449, 2006), Krivonozhko et al. (J Oper Res Soc 55:1049–1058, 2004), and others. That framework includes as a special case the well-known operations research method of data envelopment analysis (DEA). A special case of the theory in this paper is the Banker-Morey (Oper Res 34:513–521, 1986a) DEA model for data that include both discretionary and non-discretionary inputs and outputs. Several inequalities among different orders of one-sided scale elasticities are presented. An example is used to illustrate many of the results and ideas of the paper. Finally, we show how the theory and results of this paper can be used to shed some light on implicit Hicks input technical change.