This paper deals with empirical computation of Aumann–Shapley cost shares for joint production. We show that if one uses a mathematical programing approach with its non-parametric estimation of the cost function there may be observations in the data set for which we have multiple Aumann–Shapley prices. We suggest to overcome such problems by using lexicographic goal programing techniques. Moreover, cost allocation based on the cost function is unable to account for differences between efficient and actual cost. We suggest to employ the notion of rational inefficiency in order to supply a set of assumptions concerning firm behavior. These assumptions enable us to connect inefficient with efficient production and thereby provide consistent ways of allocating the costs arising from inefficiency.