Strategic Transfer Pricing and Social Welfare under Product Differentiation

Abstract

In this paper, we investigate the social impacts of strategic transfer pricing by oligopoly firms, aiming to derive regulatory implications for transfer prices. A notable finding from our model is that the negative effects on social welfare of transfer prices being set above marginal cost are pronounced when either (1) the number of competing firms is large and the product is relatively highly differentiated or (2) the number of firms is small and the product is not very differentiated. This result indicates that even when the number of firms in the industry is significant and the market is thus apparently competitive, the authorities should not overlook the possibility that setting transfer prices above marginal cost might seriously damage social welfare if the product is highly differentiated.

Acknowledgement

I gratefully acknowledge insightful comments from two anonymous reviewers. I would also like to thank Salvador Carmona (Editor) and John Christensen (Associate Editor) for valuable feedback. An earlier version of this paper was presented at the Annual Meeting of American Accounting Association, New York, August 2009. I thank discussant Naomi Rothenberg and participants in the concurrent session of the meeting for their helpful comments. Financial support of Grant-in Aid for Scientific Research (A) (20243026) from the Japan Society for the Promotion of Science is greatly appreciated. Of course, the author is solely responsible for any remaining errors.

Notes

Regulators in advanced economies other than Europe also present such guidelines for utility industries. In the USA, Public Utility Commission of Texas (1998) notes that: ‘[T]here is a strong likelihood that a utility will favor its affiliates where these affiliates are providing services in competition with other, non-affiliated entities … there is a strong incentive for regulated utilities or their holding companies to subsidize their competitive activity with revenues or intangible benefits derived from their regulated monopoly businesses.’ Moreover, in Asian economies, Central Asia Regional Economic Cooperation (2005, p. 17) refers to regulations on electricity sectors as: ‘Countries vary with respect to the sequencing of sector reforms. However, the elements of these reform packages either already include or are likely to include the following: … (ii) vertical unbundling, which includes measures to make the performance of each company transparent and to publish transfer prices among generation, transmission, and distribution …’

Several microeconomic studies present the analytical structure of this utility formulation (e.g. Singh and Vives, 1984; Hackner, 2000).

More specifically, net utility for the consumer is described as:

Maximization of this equation with respect to {q ₁, q ₂, …, q _n } yields the inverse demand function represented by equation (2).

This problem is equivalent to one in which all firms are decentralized and each firm is forced to transfer products from the upstream division to the downstream division at a unit price equal to marginal (average) cost, c.

No asymmetric equilibrium between firms with respect to the organizational regime arises. For example, there exists no equilibrium such that some firms choose centralization while others prefer decentralization. Recall that a centralized firm is equivalent to a decentralized firm that must transfer products to the downstream division at the marginal cost, c. Therefore, firms opt weakly for decentralization because they can control the internal transfer price as a strategic variable in addition to the retail price.

Although Figure 3 shows a curve with the values of n varying between 2 and 10, one may confirm the negative correlation between n and θ by drawing a similar three-dimensional graph with n varying from 2 to a finite integer based on ΔSS in Proposition 3.

Although we do not give formal proof that θ _r moves leftward according to n, one may confirm this tendency by drawing a graph like Figure 4 with a fixed integer of n based on in Proposition 2.

Although we do not provide formal proof that θ _p moves leftward as n increases, one may confirm this tendency by drawing a graph like Figure 5 with a fixed integer of n based on , and p ^COL in Lemma 1 and Propositions 1 and 2.

Gal-Or (1990) proves that coexistence of asymmetric organization regimes, for instance, centralization and decentralization, never emerges as long as firms' strategic variable is price and neither a manufacturer nor a retailer incurs fixed costs to handle the product.

This can be confirmed by using a mathematical software package.