Returns to scale in one-shot information processing when hours count

The decentralized information processing approach pioneered by Radner and Van Zandt endogenously determines the optimal hierarchy for decision making within an organization. The simplest information processing model is the one-shot problem (one set of information to process) which serves as the testing ground for ever richer descriptions of managers and their tasks. Meagher and Van Zandt observed that an hours-based measure should be used for calculating managerial costs rather than the fixed cost per employee used by Radner. Surprisingly they show that the set of efficient hierarchies is equivalent under the two different measures. 

In this paper we show that using the hours-based measure can give quite different results for returns to scale than were found by Radner. We find constant returns to scale over a wide range of delay costs, whereas Radner found increasing returns to scale: In other words, costs rise proportionally with the size of the firm's information problem. Constant returns to scale implies that distortions in firm size will not arise from the need for hierarchical organization per se, but rather from organizational issues from the theory of the firm, such as incentives and abilities.