Multi-criteria production theory: convexity propositions and reasonable axioms

Multi-criteria production theory is a generalization of traditional production theories that can be utilized to expand knowledge on the theory and practice of non-financial performance analysis. Based on decision theory, its main idea is the capability of strictly distinguishing technologically determined inputs and outputs of a production system’s activity from its desired or undesired impacts on artificial or natural environments in the form of generalized benefits and costs. For the special cases of linear and of monotonic multiple cost and benefit functions, a recent paper in this journal proves first main propositions and applies them to some topics often discussed in the literature. This paper extends these results. General theorems for convex production possibility sets, convex cost functions, and concave benefit functions are proven, and it is shown that some technological assumptions, which are usual in economics and data envelopment analysis, particularly those on strong disposability, are unessential for efficiency measurement or even unrealistic, whereas a newly introduced axiom of value disposability may be reasonable.