Benefit and distance functions

We explore the relationship between R. W. Shephard's input distance function (''Cost and Production Functions,'' Princeton Univ. Press, Princeton, 1953) and D. G. Luenberger's benefit function (J. Math. Econ. 21 (1992a), 461-481). We point out that the latter can be recognized in a production context as a directional input distance function which can exhaustively characterize technologies in both price and input space. D. McFadden's (Cost, revenue, and profit functions, in ''Production Economics: A Dual Approach to Theory and Applications, ''North-Holland/Elsevier, New York, 1978) composition rules for input sets and input distance functions are then extended to the directional input distance function. (C) 1996 Academic Press, Inc.