What Is the Economic Meaning of FDH?

The central feature of the FDH model is the lack of convexity for its production possibility set, TF. Starting with n observed (distinct) decision making units DMUk , each defined by an input-output vector pk = [yk -xk], domination is defined by ordinary vector inequalities. DMUk is said to dominate DMUj if pk ≥ pj, pk ≠ pj. The FDH production possibility set TF consists of the observed DMUj together with all input-output vectors p=[yk,−xk] with y ≥ 0, x ≥ 0, y ≠ 0, x ≠ 0 which are dominated by at least one of the observed DMUj. DMUk is defined as “FDH efficient” if no DMUj dominates it. In the BCC (or variable return to scale) DEA model the production possibility set TB consists of the observed DMUk together with all input-output vectors dominated by any convex combination of them and DMUk is DEA efficient if it is not dominated by any p in TB. In the DEA model, economic meaning is established by the introduction of (non negative) multiplier (price) vectors w = [u,v]. If DMUk is undominated (in TB) then there exists a positive multiplier vector w for which (a) wTpk = uTyk − vTxk ≥ wTp for every p ∈ TB. In everyday language, the net return (or profit) for DMUk relative to the given multiplier vector w is at least as great as that for any production possibility p. On the other hand, if DMUk is FDH but not DEA efficient then it is proved that there exists no positive multiplier vector >w for which (a) holds, i.e. for any positive w there exists at least one DMUj for which wTpj > wTpk. Since, therefore, FDH efficiency does not guarantee price efficiency what is its economic significance? Without economic significance, how can FDH be considered as being more than a mathematical system however logically soundly it may be conceived?