by Costis Maglaras and Joern Meissner
Consider a monopolist firm that owns a fixed capacity of a resource that is consumed in the production of multiple products. There is a finite horizon over which the resource must be used, and the firm's problem is to choose a dynamic pricing strategy for each product in order to maximize its total expected revenues. This paper shows that this problem is equivalent to one where the firm controls the aggregate rate at which all products jointly consume resource capacity, rather than the multi-dimensional product pricing strategies. Given the desired aggregate capacity consumption rate, the product prices are chosen so as to maximize the instantaneous revenue rate subject to the constraint that all products jointly use up capacity at the specified rate. This defines an efficient frontier for multi-product pricing problems. Other applications of this idea are pursued in settings where the firm uses capacity rather than pricing controls and in network revenue management problems. Overall, the reduction in the control dimension leads to algorithmic simplifications and highlights the essential features of good pricing / allocation policies.