We provide an axiomatic foundation for efficiency measurement in the full space, referred to as "graph efficiency" measurement by Färe, Grosskopf, and Lovell [1985]. We posit four types of axioms: indication, monotonicity, independence of units of measurement, and continuity. We analyze six...

Professor Sten Malmquist constructed the Malmquist quantity index and in doing so developed a distance function defined on a consumption space. This function is the consumer analog to the Shephard input distance function of producers and is used in ratio form to define the quantity index. This...