The Transfer Pricing (TP) problem was first formalized in economic terms by Hirshleifer (1956). Hirshleifer describes the TP 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 Hass (1968)) and for situations where there are selling expenses for the intermediate goods (see, for example, Arrow (1959), Gould (1964)). An exhaustive review of these methods can be found in Abdul-Khalik and Lusk (1974). For an extensive review of the TP problem, see Grabski (1985), who reviewed 81 papers from 1974 to 1983. Kanodia (1979) considered the same model as Hirshleifer, but he included uncertainty about the market price. He introduced a transfer pricing scheme that shares the risk between the selling and the buying divisions by randomizing the transfer prices. Furthermore, Kanodia's scheme maximizes the expected firm profit.
The literature from the 70's presents three main approaches to the TP problem: the strategic approach, the accounting approach and the behavioristic approach.
1. The strategic approach: This approach emerges when there is asymmetry of information. Equating marginal cost with marginal gross profit is impossible when central management does not know the exact cost functions of the divisions. Division managers are likely to have the information (or at least partial information) about these costs, but they do not always have an incentive to reveal it to central management. Central management seeks to interact with division managers to achieve an optimal outcome. The revelation principle (Gibbard (1973)) asserts that it is sufficient for the interaction to employ ``simple'' mechanisms that are direct and incentive compatible. A direct mechanism is one in which every division manager reports his type (i.e., his private information). Central management then dictates an outcome and every division manager is compensated an amount (positive or negative) that depends on the reports of all the division managers. The mechanism is incentive compatible if reporting of true information by every division manager generates a Nash equilibrium. Ronen and McKinney (1970) suggest that every division manager be compensated an amount that depends on the reports of the other managers only. The division managers (and not central management) determine their production levels. Central management chooses the compensation levels so as to induce the division managers to truthfully reveal their private information. This method achieves an optimal outcome in one Nash equilibrium, but the other equilibrium outcomes may not be optimal. Another difficulty is that the mechanism is not balanced. That is, the divisions' profits may not add up to the firm's profit. Ronen (1992) has shown that in a model of incomplete information about the divisions' cost functions, the probability that the division managers will agree on an ex-post nonoptimal quantity, is ``relatively'' small. A stronger concept was introduced by Groves (1976) and Groves and Loeb (1979). The difference between the Ronen-McKinney mechanism and the Groves-Loeb mechanism is discussed in Groves and Loeb (1976), who suggested a solution that achieves optimal outcome not only via Nash equilibrium but also via dominant strategies. However, like the Ronen-McKinney mechanism it is not balanced. In the Groves-Loeb mechanism, central management dictates both the compensation level and the production quantity of every division manager, whereas in the Ronen-McKinney mechanism, production levels are determined by the division managers. Green and Laffont (1977) showed that, in general, there is no balanced mechanism that generates efficient outcomes and that is incentive compatible via dominant strategy. Harris, Kriebel and Raviv (1982) dealt with the problem of resource allocation (which is a problem similar to the TP problem), where in addition to the asymmetry of information, there are moral hazard problems. The goal is to minimize production cost. They consider one division supplying resources to $n$ divisions, each producing a different product. The production function of each division is a linear function of both the manager's effort (which is unobservable by the planner) and of the resources that they received from the supplying division. Furthermore, the production function depends on a specific productivity parameter which is the private information of the division manager. The utility of a division manager is his salary net of his effort cost. The mechanism of Harris, Kriebel and Raviv induces truthtelling by the division managers and minimizes the production cost for each level of output. Production cost is the sum of the costs of the resources and the compensation of the division managers. This mechanism induces the managers to exert effort, which is optimal for the firm. Ronen and Balachandran (1988) assumed utility functions with risk aversion, uncertainty about the production cost and moral hazard. In their model there are two divisions and the planner is the buying division, which delegates the production decision to the selling division manager, the reason being that communication of private information from the selling to the buying division is ``blocked'' (that is, it is too costly). Their mechanism achieves an optimal solution.
Darrough and Stoughton (1989) study the TP problem in a two-firm model. The two firms cooperate to produce a final product, acting as a monopoly in the market for the final good. Furthermore, the production cost of each firm is linear and each firm knows only its own parameter in this cost function. The authors introduce a revelation mechanism which guarantees an ex-ante second-best optimal solution. This outcome is the same as the one that Myerson (1982) obtained in his bargaining model with asymmetric information. Amershi and Cheng (1990) considered a situation where every division has private information about its cost function, which is not necessarily linear. Furthermore, the buying division has an effort parameter which is a decision variable of its manager. In this environment, Amershi and Cheng found a mechanism that is incentive compatible via domonant strategies, efficient and balanced too (notice that there is no contradiction between their mechanism and the Green-Laffont theorem since they deal with a restricted environment). Besanko and Sibley (1991) studed the problem where the planner is the buying division and dictates the mechanism to be used. In this model, the production function of the selling division is quite general and it includes one unknown parameter, which is the private information of the selling division. In addition, the model considers a moral hazard aspect. Here too a revelation mechanism is introduced that is optimal for the buying division but is not optimal for the firm.
Brown and Weida (1991) suggested a new approach to the TP problem whereby central management decides which division (buying or selling) will be the planner. It takes the decision of who is to be the leader after comparing the expected profit obtained when the buying division is the leader to that when the selling division is the leader. The practical motivation for this approach is that central management, being well aware of the inferiority of its information, prefers to leave all the decisions to the divisions themselves through negotiation. (A few industrial surveys support this motivation. For example, see Frederick and Douglas (1979).) This mechanism is balanced, but it is not necessarily optimal for the firm.
Banker and Datar (1992) extended Harris, Kriebel and Raviv's model to a situation where the division managers are allowed to cooperate in a way that enables them to increase their profits at the expense of that of the firm. Their goal was to find a mechanism that prevents such collusion. The mechanism they found also yields an optimal solution but is not balanced. Vaysman (1992) suggests a cost-plus mechanism in a model of asymmetry of information with limited communication between the division managers and the planner. The managers in this model cannot report their private information precisely. Vaysman found that a cost-based transfer pricing mechanism where the division managers taking the operating decisions strictly dominates a centralized mechanism where the planner makes the operating decision.
In the last 15 years, a vast number of papers have been published on the TP problem in multinational organizations, Stoughton and Talmor (1989), Prusa (1990), Donnenfeld and Prusa (1992) among others. These authors use similar methods to those mentioned above, though, the multinational TP is much more complex because of legal and tax considerations.
2. The accounting approach: Accountants suggest various ad hoc methods, each of which is best suited to the particular situation arising in a given large firm. A comprehensive review of practical methods can be found in Kaplan (1982). Manes and Verrechia (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 be applied only in the case of full information. The problem of implementing a desired mechanism is dealt with in 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, generated by the selling division, and the opportunity cost of the firm as a whole. Rickwood, Coates and Stacey (1987) argued that the best way to examine the TP problem is to study real cases. Lesser (1987) shows that when a TP mechanism is set incorrectly, it can give negative motivation for reducing costs. This problem arises when the transfer pricing is cost plus fixed percentage. This method gives negative compensation to the division managers when they reduce the cost of production. Cassel and McCormack (1987) studied the problem of a firm selling an entire project. They suggest a dual-pricing solution where the price that the buying division pays is not equal to the price that the selling division obtains (see also the previous section on the dual-pricing method). Antle (1988) argued the need for a new approach to the TP problem, since the theoretical model does not fit to the real world, though he himself does not offer such an approach. Cats-Baril, Gatti and Grinnell (1988) outlined the TP problem as a dynamic situation where the solution changes over time. They suggest changing the transfer pricing scheme over time according to the stage in the life cycle of the final product. Tisdell (1989) relates to the inconsistency between the assumptions in the models and reality.
Kovac and Troy (1989) showed that a TP problem may arise when an inappropriate cost allocation method is used. Galway (1990) discussed the problem of the cost-plus method when an intermediate good is transferred through many divisions until it reaches the last division in the chain. In this situation the last division, which sells the finished good in the market, has to pay a transfer price to its predecessor which includes the cumulative mark up. Obviously, this damages its ability to compete in the market if it has to cover its cost.
3. The behavioristic approach: Let us mention three important papers in this area. Eccles (1983) carried out an extensive study of the practical use of TP methods in industry. In this paper he linked the TP method used by a firm to the firm's strategy. Furthermore, he argued that in reality the personal relationship between the division managers may lead to noncooperative behaviour and hence to nonoptimal outcomes. Dejong et al' (1989), performed a laboratory experiment to compare three TP mechanisms: the classic Hirshleifer mechanism, the bargaining mechanism (Negotiated Price) and the dual-price mechanism of Ronen and McKinney. They found that the Ronen-McKinney mechanism elicits the best performance, with the Hirshleifer mechanism coming in second. Chalos and Haka (1990) performed a laboratory experiment to examine the effect of the manager's compensation method on the firm's profits. They compared the outcome when managers are compensated according to their division's profit with the case where the compensation depends on both the division's profit and the firm's profit. There is no strong evidence that mixed compensation increases the manager's willingness to cooperate.