This paper explores the relationship between Shephard's input distance function and Luenberger's benefit function. It shows that the benefit function can be recognized as a directional input distance function, which can exhaustively characterize production technologies under appropriate assumptions on input disposability. McFadden's composition rules for input sets and input distance functions are extended to the directional input distance function. The benefit function is defined as the supremum of β such that x - βg is in X and u(x - βg) ≥ u. This function generalizes Shephard's input distance function, which is defined as the infimum of λ such that x/λ is in X and u(x/λ) ≥ u. Both functions are useful alternative representations of preferences, with the benefit function being useful in developing group welfare relations. The paper discusses the properties of the directional input distance function, including its concavity with respect to x, its homogeneity of degree +1 in inputs, and its ability to represent the technology completely. It also shows that the directional distance function can be obtained from the input distance function and that by choosing an appropriate direction vector g, the input distance function can be recovered from the directional distance function. The paper also introduces the affine distance function, which is defined as the inverse of the infimum of λ such that x^0 + λx is in L(y). It shows that the affine distance function is related to the directional distance function and that under certain assumptions, the directional distance function is a complete representation of the technology. The paper concludes by discussing dualities and shadow prices for the two functions.This paper explores the relationship between Shephard's input distance function and Luenberger's benefit function. It shows that the benefit function can be recognized as a directional input distance function, which can exhaustively characterize production technologies under appropriate assumptions on input disposability. McFadden's composition rules for input sets and input distance functions are extended to the directional input distance function. The benefit function is defined as the supremum of β such that x - βg is in X and u(x - βg) ≥ u. This function generalizes Shephard's input distance function, which is defined as the infimum of λ such that x/λ is in X and u(x/λ) ≥ u. Both functions are useful alternative representations of preferences, with the benefit function being useful in developing group welfare relations. The paper discusses the properties of the directional input distance function, including its concavity with respect to x, its homogeneity of degree +1 in inputs, and its ability to represent the technology completely. It also shows that the directional distance function can be obtained from the input distance function and that by choosing an appropriate direction vector g, the input distance function can be recovered from the directional distance function. The paper also introduces the affine distance function, which is defined as the inverse of the infimum of λ such that x^0 + λx is in L(y). It shows that the affine distance function is related to the directional distance function and that under certain assumptions, the directional distance function is a complete representation of the technology. The paper concludes by discussing dualities and shadow prices for the two functions.