A classic puzzle in the economic theory of the firm concerns the fundamental cause of decreasing returns to scale. If a plant producing product quantityX at costC can be replicated as often as desired, then the quantityrX need never cost more thanrC. Traditionally the firm is imagined to take its identity from a fixednon-replicable input, namely a ‘top manager’; as more plants or divisions are added, the communication and computation burden imposed on the top manager (who has information not possessed by the divisions) grows more than proportionately. Decreasing returns are experienced as the top manager hires more variable inputs to cope with the rising burden. Suppose it turns out, however, that when the divisions are assembled, and are given exactly the same totally independent tasks that they fulfilled when they were autonomous, then asaving can be achieved if they adopt a joint procedure for performing those tasks rather than replicating their previous separate procedures. Then the top manager's rising burden must be shown to be particularly onerous—otherwise there may actually beincreasing returns. We show that for a certain model of the information-processing procedure used by the separate divisions and by the firm, there may indeed be such an odd unexpected saving. The saving occurs with respect to the size of the language in which members of each division, or of the firm, communicate with one another, provided that language is finite. If instead the language is a continuum then the saving cannot occur, provided that the procedures used obey suitable ‘smoothness’ conditions. We show that the saving for the finite case can be ruled out in two ways: by requiring the procedures used to obey a regularity condition that is a crude analogue of the smoothness conditions we impose on the continuum procedures, or by insisting that the procedure used be a ‘deterministic’ protocol. Such a protocol prescribes a conversation among the participants, in which a participant has only one choice, whenever that participant has to make an announcement to the others. The results suggest that a variety of information-processing models will have to be studied before the traditional explanation for decreasing returns to scale is understood in a rigorous way.