This paper, after establishing the relations between hyperbolic graph measure of technical efficiency and the radial measures of technical efficiency, shows that the dual, cost and revenue interpretation of the hyperbolic efficiency measure is related to Georgescu-Roegen's notion of "return to the dollar" [N. Georgescu-Roegen, in: Koopmans, T. (Ed.), Activity Analysis of Production and Allocation, Wiley, New York, 1951, pp. 98-115]. Once this relation is established, it leads to a derivation of an allocative efficiency index, which measures the price distortions using data on observed costs and revenues without requiring information on prices. © 2002 Elsevier Science B.V. All rights reserved.