Internal Pricing and Cost Allocation in a Model of Multiproduct Competition with Finite Capacity Increments

Internal prices are used in practice to allocate central resources to a firms' profit centers. The fixed costs of capacity acquisitions are often included in these prices. We examine the interaction between capacity acquisition and competition when capacity is available in fixed increments. We find predictably that if the increments are small, unit capacity cost is a good approximation for the internal price, and if the increments are large, the internal price is zero. However, the relationship between the internal price and the capacity increment for intermediate cases is quite irregular, to the extent that it is not possible to approximate the internal price with accounting data. The analysis also suggests that full cost allocation overcharges for the opportunity cost of capacity. Furthermore, the right internal price does not act either as a way of recovering fixed costs or as a proxy for externalities such as congestion costs. The conclusions are not materially altered in the case where variable costs increase at the margin, and where these costs rather than hard capacity constraints are the reason to restrict output.