We explore the relationship between Shephard's input distance function and Luenberger's benefit function. We point out that the latter can be recognized in a production context 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 then extended to the directional input distance function. Working Paper 95-09 Scientific Article No. , Contribution No. from the Maryland Agricultural Experiment Station.

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We study the wavefronts (i.e. the surfaces of constant phase) of the wave discussed by Aharonov and Bohm, representing a beam of particles with charge q scattered by an impenetrable cylinder of radius R containing magnetic flux @. Defining the quantum flux parameter by a = q@/h, we show that for the case