Structure and Returns to Scale of Real-Time Hierarchical Resource Allocation

Companion papers develop a model of real-time hierarchical computation of resource allocations by boundedly rational members of an administrative staff. The nodes of a hierarchy are multi-person decision-making units offices. The current Paper uses a reduced form to address specific questions about organizational structure and returns to scale. We find that the possibility of decentralizing decision-making within these hierarchical organizations allows for larger hierarchies. Organization size is, however, still bounded because the combined effect of cumulative delay and administrative costs means that in large enough hierarchies, the value of the root office ’s information processing is less than the office ’s administrative costs. We also find that as the environment changes more rapidly, optimal hierarchies become smaller and more internally decentralized. A speed-up of managerial processing, such as through improved information technology, has the opposite effect.