A Unifying Framework for Farrell Profit Efficiency Measurement

Measuring profit efficiency is a challenging task, and many different approaches have been suggested. This paper synthesizes existing approaches and develops a general Farrell-type approach of the profit efficiency measurement. Our derivations unveil new and useful relationships between existing measures and the proposed new Farrell-type measures. In addition, this helps us establish a generalized and unifying framework for studying efficiency behavior of firms, where the profit efficiency measure satisfies desirable properties and contains the conventional Farrell measures of technical efficiency and allocative efficiency as multiplicative components. A new component of the decomposition of profit efficiency, which we call the revenue-efficient allocative efficiency measure, is introduced to identify the necessary changes of input scale and input mix in addition to output changes. The proposed new approach also encompasses and is coherent with profit-maximizing behavior as a benchmark case. Funding: The authors acknowledge the financial support provided by their institutions and partial supports from the Australian Research Council [Grants ARC DP130101022 and ARC FT170100401] and the Research Committee's Matching Scheme for Inviting High Quality Sabbatical Visitors/Distinguished Scholars of Hong Kong Baptist University. Keywords: profit efficiency * Farrell-type measures * revenue-efficient allocative efficiency * invariance property of allocative efficiency measure
1. Introduction Two types of scaling, inputs and outputs, are frequently used in measuring the technical efficiency of production: (i) scaling each element of a vector by a potentially distinct [...]