Concave and convex serial cost sharing

A finite set of agents jointly own a production technology for one or more but a finite set of output goods, and to which they have equal access rights. The production technology is fully described by a cost function that assigns to each level of output the minimal necessary units of (monetary) input. Each of the agents has a certain level of demand for the good; then given the profile of individual demands the aggregate demand is produced and the corresponding costs have to be allocated. This situation is known as the cooperative production problem. For instance, sharing the overhead cost in a multi-divisional firm is modeled through a cooperative production problem by Shubik (1962). Furthermore, the same model is used by Sharkey (1982) and Baumol et al. (1982) in addressing the problem of natural monopoly. Israelsen (1980) discusses a dual problem, i.e., where each of the agents contributes a certain amount of inputs, and correspondingly the maximal output that can thus be generated is shared by the collective of agents. In this chapter I consider cost sharing rules as possible solutions to cooperative production problems, i.e. devices that assign to each instance of a cooperative production problem a unique distribution of costs. In particular the focus will be on variations of the serial rule of Moulin and Shenker (1992), the cost sharing rule that caught the most attention during the last decade

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