Preliminary { Incomplete { InconsistentStructure and Returns to Scale ofReal - Time Hierarchical Resource

Companion papers develop a model of real-time hierarchical computation of resource allocations by boundedly rational members of an administrative staa. The nodes of a hierarchy are ooces within which information processing may be decentralized. Decision making is decentralized across the nodes of the hierarchy. A version in which the cost functions are quadratic and the cost parameters follow rst-order autoregressive processes yields a tractable reduced form. The current paper uses that reduced form to address speciic questions about organizational structure and returns to scale. We nd that the possibility of decentralizing decision making within these hierarchical organizations allows for larger hierarchies. However, organization size is still bounded because the combined eeect of cumulative delay and administrative costs means that in large enough hierarchies, the value of the root ooce's information processing is less than the ooce's administrative costs. We also nd that as the environment changes more rapidly, optimal hierarchies become smaller and more internally decentralized.