Efficient Cost Allocation

Firms routinely allocate the costs of common corporate resources down to divisions. We seek to understand whether cost allocation rules can induce efficient consumption of corporate resources in an incomplete contracting framework. We propose a new allocation rule (the polynomial rule), which achieves efficiency and approximate budget balance. We also examine conditions under which simple allocation rules induce efficiency. Finally, we show that welfare losses due to linear allocation rules increase with firm size. Thus polynomial allocation rules should be preferred to linear rules for larger firms. The multiple divisions within a firm often share a variety of common resources, such as information technology, legal services, human resource management, executive time, etc. Managerial accounting textbooks (Horngren et al. (2005), Zimmerman (2006)) and surveys of company practice (Fremgen and Liao (1981), Atkinson (1987), Ramadan (1989), Dean et al. (1991)) document the widespread practice of common cost allocation to induce appropriate consumption of corporate resources. For example, if divisions were not allocated any corporate costs, they may have adverse incentives to overconsume such common resources. The objective of this paper is to examine cost allocation rules in an incomplete contracting framework that solve this free-rider problem, i.e. induce efficient resource use by divisions acting simultaneously and independently. Our main result proposes a new allocation rule (the polynomial rule) that achieves efficiency and approximately balances the budget. ∗All correspondence should be directed to Korok Ray. We would like to thank Madhav Rajan, Stefan Reichelstein, and participants of the Chicago Accounting brown bag for helpful comments and suggestions. Alex Frankel provided outstanding research assistance. Our second assumption is that the asymmetry of information in the firm evolves over time. In particular, the divisions have private information on the production functions at the time of contracting. At the initial stage, the firm does not know the type of the divisional manager and therefore the firm cannot implement the first-best resource choice through a forcing contract. After nature reveals this uncertainty, the private information is no longer private but now public within the firm: all division managers in the firm as well as all division managers know each others’ types. However, because the nature of the uncertainty is too complex to be embedded in contracts, the firm cannot redraw its contracts ex-post once the uncertainty is known, nor can it write contracts that are contingent on the division’s types at the ex-ante stage. This fits a scenario of a multidivisional firm which must write cost allocation rules in the beginning of the year but cannot seamlessly change those contracts once production uncertainty resolves through the course of the year. For example, think of the oil division of a large energy company that must hire workers to drill in an oil well. Two inputs into that decision are the market wage for labor and the rental price of capital, both which fluctuate daily. If the energy company seeks to allocate the cost of executive time to the oil division, that cost allocation rule cannot realistically vary with all possible realizations of market prices for capital and labor. Thus, this paper effectively seeks to obtain conditions of efficient cost allocation of common resources in an incomplete contracting framework. We demonstrate that the main feature of any efficient allocation is that it must reflect the firm’s underlying costs. While this point may seem obvious, the linear rules used in practice make allocations without regard to the shape of the firm’s cost function, and this keeps such rules from achieving efficiency. The reason for this failure is straightforward: charging for each unit of common resource used at the same constant rate (whether an actual average cost or a budgeted per-unit overhead rate) ignores the fact that the actual marginal cost of each unit of resource used may depend on the total amount of resources used (for example, if the firm’s cost function is highly convex, it is much more costly for the firm to acquire an additional unit of the resource if it already has a hundred than if it only had one). Consequently, under such cost allocation schemes, the price that a division pays for an additional unit of resource (the private cost to the division) differs from the actual marginal cost to the firm, which causes inefficient resource consumption decisions by the division. The analysis here operates in environments that more closely resemble real-world settings, with the aim of recommending cost allocations that will be practically useful to managers. First, we depart from formal mechanism design theory (such as Green and Laffont (1979)) in that we assume that the private information of the divisional managers is too complex to be embedded within the firm’s contracts. Therefore, the firm cannot perfectly obtain the manager’s entire private information through a complex reporting game and through contracts that de-