Optimal Disbursement of a Sunk Resource and Decentralised Cost Allocation

Abstract

We consider whether the allocation of the sunk cost of a central resource to operating divisions can be consistent with economically optimal resource consumption decisions. When it is recognised that the central resource is scarce, one may, in principle, defend the allocation of sunk cost, if it measures the opportunity cost of usage. However, typically it has been proposed that such allocations are, at best, a proxy for opportunity cost. Applying classical control theory techniques in a wide range of operating environments, we are able to identify cost allocations that exactly equal opportunity cost. Hence, for our model environment, we provide a rationale for sunk cost allocation in terms of guiding optimal decisions, in contrast to the traditional defence in terms of providing a proxy for opportunity cost. We demonstrate clearly how cost allocations are related to opportunity costs, and identify the circumstances under which the allocation of full costs or alternatively a fixed proportion (related to acquisition conditions) of costs, results in the implementation of economically optimal resource consumption decisions.