Top Down Axiomatic Modeling of Metatechnologies and Evaluating Directional Economic Efficiency

We contrast two distinct axiomatic approaches to model metatechnologies. The traditional bottom up approach revolves around axioms characterizing group technologies. In contrast, our innovative top down approach introduces a new set of axioms that directly identify the metatechnology itself. These new axioms lead to discover new algebraic statements of two metatechnologies: in particular, one metatachnology maintaining a new within-group convexity axiom, and another one without it that is essentially nonconvex. Through these metatechnology specific axioms, we derive novel minimum extrapolation results for these two metatechnologies. We adopt a directional economic inefficiency concept as a general measurement framework and its additive decomposition into technical and allocative components. We develop single-stage linear programs for the measurement of directional economic and technical inefficiencies within these two metatechnologies. Our key results are illustrated using a numerical illustration. We manage to establish links between this new top down approach and some key findings from the existing bottom up metatechnology literature.