More on the Fox paradox

This paper shows that the compatibility between efficiency measures and the aggregation procedure is not enough to resolve the Fox paradox when different inputs are employed in each activity. We explicitly illustrate this point by considering the additive aggregation of cost efficiency indicators for production and advertising activities, which use different inputs. Then, the overall cost efficiency indicator is given by the weighted (rather than the simple) sum of the production and the advertising cost efficiency indicators. The reason is that the value of the directional vector used to normalize the difference between the minimum and the observed cost in each activity-based efficiency indicator will differ.