This paper considers the question: How should a firm allocate a resource among divisions when the productivity of the resource in each division is known only to the division manager? Obviously if the divisions (as represented by their managers) are indifferent among various allocations of the resource, the headquarters can simply request the division managers to reveal their private information on productivity knowing that the managers have no incentive to lie. The resource allocation problem can then be solved under complete (or at least symmetric) information. This aspect is a flaw in much of the recent literature on this topic, i.e., there is nothing in the models considered which makes divisions prefer one allocation over another. Thus, although in some cases elaborate allocation schemes are proposed and analyzed, they are really unnecessary. In the model we develop, a division can produce the same output with less managerial effort if it is allocated more resources, and effort is costly to the manager. We further assume that this effort is unobservable by the headquarters, so that it cannot infer divisional productivity from data on divisional output and managerial effort. Given these assumptions, we seek an optimal resource allocation process. Our results show that certain types of transfer pricing schemes are optimal. In particular, if there are no potentially binding capacity constraints on production of the resource, then an optimal process is for each division to choose a transfer price from a schedule announced by the headquarters. Division managers receive a fixed compensation minus the cost of the resource allocated to them at the chosen transfer price. Resources are allocated on the basis of the chosen transfer prices. If there is a potentially binding constraint on resource production, a somewhat more complicated, but similar, scheme is required.
Harris et al. (Tue,) studied this question.