Arieh Gavious

Abstract

We introduce a simple model of a firm consisting of two interacting divisions with capacity constraints which are private information. We find a balanced mechanism which is incentive-compatible (via dominant strategies) and which yields efficient outcomes. This mechanism model the common situation where the capacity of every division is known only to the division managers. In this case, the top management can monitor only the parameters that followed by a paper work and not the accurate state of the divisions.

Introduction

The transfer pricing problem is an open question that has a significant impact on the performance of a large decentralized organization. The term `transfer price' denote the pricing of internal transactions (goods and services) between two divisions of the same firm. It is known that inappropriate transfer pricing mechanisms may lead firms to poor performance and monetary losses (see Kaplan 1982). The transfer pricing problem appears when a large organization decides to decentralize. Under decentralization, divisions considered as profit centers and their managers may choose to maximize their own profit rather than that of the organization. One aspect of the problem appears when managers manipulate the quantity that they transfer to each other in order to increase their own profit at the expense of the other divisions. In this case, it may damage the firm's total profitability. Another aspect is that an inappropriate transfer pricing mechanism may damage the incentive to reduce production cost or to apply a new technology (see for example Tisdell(1989)).

The transfer pricing problem was first formalized in economic terms by Hirshleifer (1956). Hirshleifer describes the transfer pricing problem with full information as a maximization problem, where the optimal solution is achieved when the marginal cost of the selling division equals the marginal gross profit of the buying division. In the 60's, mathematical programming techniques were used to solve the problem for the case of multiple selling and buying divisions, multiple products (see for example Hirshleifer (1957), and Hass (1968)), and for situations where there are selling expenses for the intermediate goods (for example Arrow (1959), Gould (1964)). An exhaustive review of these methods can be found in Abdul-Khalik and Lusk (1974).

At the same time, researchers recognized the need to deal with models of incomplete information since the top management of a decentralized organization often lacks information about marginal cost of production or marginal gross profit (see for example Gould (1964)). This information is known to the division managers, but they have no incentive to reveal it. Ronen and McKinney (1970) were the first to suggest an incentive- compatible transfer pricing mechanism\footnote{ This type of mechanism is known in the accountancy literature as Dual Pricing mechanism.}; their model is similar in spirit to those of Clarke (1971) and Groves and Loeb (1975). The difference between the Ronen-McKinney mechanism and the Groves-Loeb mechanism is discussed in Groves and Loeb (1976). The main problem with both mechanisms is that they are not balance in the sense that the total firm profit is not equal to the sum of the divisions' profits. Green and Laffont (1977) showed that, in general, there is no balanced mechanism that generates optimal outcomes and that is incentive-compatible via dominant strategies. Unfortunately, balancing is crucial in practice,and nonbalancing mechanisms are often abandoned (see Eccles (1983)).

Harris, Kriebel and Raviv (1982) introduced a model for resource allocation (a problem that is similar to the transfer pricing problem) with incomplete information and moral hazard. They found a revelation mechanism that is optimal in the sense that it minimizes the firm's total production cost for a given production level. Their model deals with the problem of resource capacity constraint where the quantity of resources available for allocation is fixed. We relate to the capacity constraints in a different way. In our model capacity is not an upper bound on the production level. Rather, it represents the production level achievable with the current resources - and it can be increased by using additional resources such as overtime. Banker and Datar (1992) extended Harris et al.'s model to a situation where the division managers are allowed to cooperate - and are thus able to increase their own profits at the expense of that of the firm. Their goal was to find a mechanism that induces no such collusion. They found a mechanism that satisfies this requirement and also yields an optimal solution but the division managers' performance is not measured by their division's profit. However, as we can find in the literature, one of the main uses of the transfer pricing mechanism is to measure the performance of the divisions and their managers (see for example Finnie (1978)). Thus, in the current paper, we assume that division managers are measured by the profit of their divisions. There are many papers that deal with the transfer pricing problem by applying the mechanism design approach; for an extensive summary of this approach see Brown and Weida (1992).

Another approach to the problem can be found in the accountancy literature. This approach deals with the practical questions - which mechanism to implement and when. Manes and Verrecchia (1982) suggest allocating the profit between the divisions that are involved in the production of a specific product, using the Shapley value. This approach can applied only in the case of full information. The problem of implementing a desired mechanism is dealt with in Eccles (1983) and Kaplan (1984). Adelberg (1986) studied the problem when there exists an outside market for the intermediate good. He suggested using a synthetic price when there is uncertainty about the market price for the intermediate good. The synthetic price is the sum of the variable cost, incurred by the selling division, and the opportunity cost of the firm as a whole. Lesser (1987) shows that when a transfer pricing mechanism is set incorrectly, it can give negative motivation for reducing costs. This problem arises when the transfer pricing is cost-plus-fixed- percentage. Rickwood, Coates and Stacey (1987) argued that the best way to examine the transfer pricing problem is to study real cases. Antle (1989) shows the need for a new approach to the transfer pricing problem, since the theoretical model does not fit the real world. However, he does not offer such an approach. We can see that the accountancy literature reflects the gap between the theoretical models and the real problems that the accountants and economists have to deal with every day. We apply the mechanism design approach to model a common aspect of the transfer pricing problem as we explain next.

In this paper, we will follow in the footsteps of Johnson and Kaplan's (1987). In their book "Relevance Lost", they point out that the structure of the cost function in the last few decades is different from that of the beginning of the century when the accounting tools were developed. Today, salary is considered as a fixed cost and not a variable cost as it was thirty years ago. Thus, the main variable cost in an industrial firm today is raw materials (other variable costs are energy, part of the amortization etc.). In our model `capacity' is the production level that the division can achieve by optimal use of its current resources. The resources can be labor, machinery or any other factors needed for production (except raw material, which is assumed to be unlimited). However, if the division wishes to increase its level of production above capacity, it can do so by purchasing additional resources. The cost of the current resources is considered to be a fixed cost and the raw material and any additional resources are variable costs. Usually in a large corporation's top management can monitor the cost of all components used to produce the output since the procurement and the sale afollowed by paper work that documents all the firm's expenses and income. However, the capacity level is usually unclear - and only the division managers know precisely how many units they can produce without increasing the basic resources they have. Thus, the capacity of every division is the private information of its manager. We will introduce a simple balanced mechanism that models this common situation. Our mechanism represents the actions of the top management and the division managers in a decentralized firm when they set the transfer price for the intermediate good. The mechanism induces the division managers to reveal their private information (capacity) truthfully.

In Section 2 we introduce the model. In Section 3 we introduce the mechanism and in Section 4 we show the conditions which imply individual rationality. Keywords: Transfer Pricing, Mechanism Design, Decentralization, Capacity.

Classification: C69, C79, D81, D82, L22, M11.