Diagonality of Cost Allocation Prices

The problem of allocating the production cost of a finite bundle of divisible consumption goods (or services) by means of per unit costs or prices is a basic problem in economics. Recently an axiomatic approach has been proposed (Billera and Heath [Billera, L. J., D. C. Heath. 1981. Allocation of shared costs: a set of Axioms yielding a unique procedure. Math. Oper. Res.7 32–39.] and Mirman and Tauman [Mirman, L. J., Y. Tauman. 1981. Demand compatible equitable cost sharing prices. Math. Oper. Res.7 40–56.]) in which one considers a class of cost problems and studies the mappings from that class of cost problems to prices by means of the properties these prices satisfy. We look for a list of properties on the class of cost problems and the price mechanism that imply the “diagonality” of the price mechanism.