Profit-shifting in Two-sided Markets

We investigate how multinational two-sided platform firms set their prices on intra firm transactions. Two-sided platform firms derive income from two customer groups that are connected through at least one positive network externality from one group to the other. A main finding is that even in the absence of taxation transfer prices deviate from marginal cost of production. A second result of the paper is that it is inherently difficult to establish arm's length prices in two-sided markets. Finally, we find that differences in national tax rates may be welfare enhancing despite the use of such prices as a profit shifting device.


Introduction
Two-sided platform …rms derive income from two customer groups that are connected through at least one positive network externality from one group to the other. A platform …rm's pricing to each customer group re ‡ects these externalities and therefore does not follow standard rules of pricing where marginal revenue equals marginal costs. Two-sided platform …rms operate in some of the most economically signi…cant industries such as the …nancial sector (card holders and merchants), the computer business (software developers and end users), and the media business (viewers/readers and advertisers). They are also internationally oriented. In the media business, for example, some of the most successful newspapers and TV channels have US, Asian and European versions of their products with independent entities located abroad providing the needed tailoring. 1 In this paper we investigate how multinational two-sided platform …rms set their prices on intra …rm transactions. In the absence of taxes, we …nd that network externalities between two customer groups lead to a transfer price that di¤ers from the marginal cost of production. International tax rate di¤erentials may lead the transfer price to deviate even further from cost of production considerations. We also show that the transfer price may di¤er across importing countries depending on the strength and direction of network externalities making it in general very di¢ cult to establish what the arm's length price is in two-sided markets. We show these results in a model where we let a¢ liates of a multinational …rm be monopolists in order to purely focus on the tax e¤ects at play. We model two-sidedness by allowing one network externality between the two groups of customers in order to bring forward the basic mechanism at play.
Our analysis is related to a growing literature in Industrial Organization that analyzes the price-setting behavior of …rms in two-sided markets. In this literature a key result is that the pricing decisions in two-sided platform …rms do not follow conventional pricing rules. 2 For example, an increase in marginal costs on one side of the market does not necessarily imply a higher price on that side of the market relative to the price on the other side. This is in contrast to conventional markets (one-sided) where marginal cost equal to marginal revenue pricing is well established as a guidance. In one-sided markets the e¤ects of taxation are also well known both under perfect and imperfect competition. To the best of our knowledge there does, however, not exist any paper on two-sidedness and transfer pricing.
Our paper also relates to the literature on transfer pricing in one-sided markets. This literature …nds substantial evidence for tax-motivated transfer pricing and that transfer pricing depends on di¤erences in statutory tax rates. 3 Grubert and Mutti (1991) and Hines and Rice (1994) analyze the aggregate reported pro…tabilities of U.S. a¢ liates in di¤erent foreign locations in 1982. Both studies …nd strong indirect evidence for transfer pricing in that high taxes reduce the reported pro…tability of local operations. Collins, Kemsley and Lang (1998) study a pooled sample of U.S. multinationals and …nd that 'normalized'reported foreign pro…tability exceeds U.S. pro…tability among …rms facing foreign tax rates below the U.S. rates. In Europe, Weichenrieder (1996) presents evidence that German …rms have taken advantage of the low Irish tax rate in the manufacturing sector by shifting the returns to …nancial assets ("passive income") to its subsidiaries in Ireland. Subsequent German tax legislation that restricted the ratio of passive to active income that could be earned in a foreign country led to a shift from …nancial to real investment in Ireland, in order to relax the new constraint. Langli and Saudagaran (2004) study small and medium sized foreign controlled corporations in manufacturing, wholesale and retail industries in Norway in the period 1993-96 using simple regression techniques. They …nd that these …rms report consistently lower taxable income than domestically controlled corporations.
In presenting our model, Section 2 sets out the basic model while section 3 investigates transfer pricing incentives. Section 4 concludes.

The Model
We consider a multinational (parent) platform …rm (MNC) that is headquartered in country i and owns subsidiaries in j = 1; :::; n countries. The parent …rm produces two goods, good a is sold worldwide by the parent …rm whilst good x is sold to each a¢ liate j at transfer price q j . Each a¢ liate determines how much of good x it purchases by maximizing its own pro…t. How much each a¢ liate buys from the parent is then a function of the transfer price and local market conditions. We shall assume that both the parent …rm and the a¢ liates are monopolists in their respective markets, and that production costs are zero. Both assumptions are widely used in the literature and are known to bring forward the tax incentives of transfer pricing without a¤ecting the results qualitatively. 4 A¢ liate j sells good x j , where the (inverse) demand function is p j = p(x j ), and pays a transfer price q j (per unit sold) to the parent …rm. Good x and good a are linked by a positive externality from consumption in the following manner: @p A (x 1 ;:::;xn;a) @x j > 0 8j. This means that the willingness to pay for good a is rising in the sale of good x. The parent …rm derives revenue from the sale of good a and good x, but incur convex concealment costs C(q j ), if the transfer price deviates from the true cost of production (i.e., if q j 6 = 0). The cost function has the standard properties of C(0) = 0 and C 0 (q j ) > 0 if q j 6 = 0.
Corporate tax rates di¤er across countries (t i 6 = t j ) and we assume that the exemption method is in place. This is a reasonable assumption since it is widely used in most OECD countries and it implies that repatriated pro…t income is exempt from taxation. Pro…ts by the parent …rm after corporate taxes are ; ( 1) whereas the after tax pro…ts of an a¢ liate j are Optimal Quantities Each a¢ liate determines how much it sells in its local market by maximizing and the …rst order condition to this maximization problem is which can be written on elasticity form as where j x;p = @x j @p j p j x j is the price elasticity of demand for good x j . Comparative statics on equation (4) yield where the denominator is negative from the second order condition of the maximization problem.
The parent …rm determines the optimal quantity of good a by maximizing and associated …rst order condition is @p A @a a + p A (x 1 ; :::; x n ; a) = 0 ) a = a(x 1 (q 1 ); :::; x n (q n )):

Transfer Pricing
The optimal transfer price q j in country j follows from maximizing MNC's world-wide pro…ts after taxation , that is Inserting for the pro…t function values we maximize The …rst order conditions are given by In order to determine a benchmark result we shall assume the absence of any network externalities and that taxes are equal (t i = t j ). In this case the …rst order conditions above reduce to q j @x j @q j C 0 (q j ) = 0 ) q j = 0 8j: With su¢ ciently convex concealment costs it is straightforward to show that equation (11) can only be satis…ed if q j = 0. Thus, in the absence of any externality or tax motive for transfer pricing the …rm sets a price equal to marginal cost of production. This is in fact the transfer price that would have been chosen between independent parties in a competitive economy.
In the presence of the network externality, but with equal taxes, the …rst order conditions become from which it is seen that q j < 0 as long as @x j @q j < 0, because C 0 (q j ) 0. The transfer price is now below the marginal cost of production since each a¢ liate neglects the positive externality that the sale of good x j has on the sale of good a. In order to remedy this failure the parent …rm sets a subsidy that internalizes the externality between the two customer groups.
This result extends and strengthens an argument made by Hirshleifer (1956), who examines optimal transfer pricing rules in various settings, but in absence of taxation. The optimal transfer price normally equals marginal costs of the intermediate product, as long as demand independence prevails. However, in case of "technological dependence" (i.e., the output levels of related products a¤ecting each others'production costs), he states that internalizing this kind of interactions calls for "subsidies" or "taxes" on the transfer price causing a deviation from (pure) marginal costs. However, he neither formally shows this nor rigorously proofs it. With respect to transferpricing, two-sidedness and its externalities on the willingness to pay, running from one customer group to the other, can be seen as analog to technological dependence. Our analysis shows formally, how these externalities should be incorporated in the optimal transfer-price and thereby con…rms the conjecture in Hirshleifer (1956, section F).
Note that in our set-up the transfer price chosen in the absence of taxes as given by equation (12) is (potentially) welfare-enhancing because it increases the quantities sold of good a and of good x j : 5 Transfer pricing is normally considered to be harmful or at best neutral (if there is no tax motive), but as demonstrated here the cost of tax evasion should be weighed against the bene…t of lower prices and a larger quantity sold. Examining the tax motive and the externality motive together, the (implicit) formula for the optimal transfer price is In line with most of the literature and without consequence for our qualitative results let the concealment costs be quadratic in the transfer price and linear in the quantity sold, that is C(q j ) = q 2 j 2 x j . Using this in equation (13) , we obtain where x j q j = q j x j @x j @q j represents the transfer price elasticity of good x j and @x j can be interpreted as the elasticity of complementarity between willingness to pay for good a and sales of good x j .
As can be seen from equation (14) the transfer price will in general di¤er from marginal cost even when taxes are equal. In particular, the higher the transfer price elasticity ( x j q j ), the more negative is the transfer price. The size of the transfer price also depends positively on the network externality ( p A x j ). A large network externality means a large distortion on the transfer price relative to the marginal cost of production. As seen from (14), the tax saving motive may go in the opposite direction of the network externality e¤ect bringing the price closer to marginal cost.
In general, our analysis shows that a positive externality will lead to a downward pressure on the transfer price relative to its "true" price. Similarly, it is straightforward to show that a negative externality would have the opposite e¤ect. In some two-sided markets, several externalities could be present at the same time, and it is then the combined interactive e¤ect of these that determines the in ‡uence on the transfer price.
The OECD model double tax convention states that the arm's length price is the price that would have been chosen between independent trading parties. In the presence of network externalities, this approach causes at least three problems. First, two-sided platform …rms exist because they internalize externalities between two customer groups. Such …rms do not in general trade with each other due to the nature of the business they are in. This makes it hard to determine a market price. Second, in such markets it is unlikely to observe …rms that only serve one customer group, since the very fact that two-sided platform …rms exist in a market is an indication of that this is a superior mode of business. Third, examining the price of transactions between two customer groups in di¤erent platform …rms is also an odd basis for establishing the market price since our analysis shows that such prices are …rm speci…c and depend on the size and direction of the externalities in question.
Another interesting result that follows from equation (14) is that despite the presence of pro…t-shifting, a tax-distorted transfer price may have a positive e¤ect on welfare. Kind et al (2008) show that a two-sided monopoly platform …rm may produce too much of both goods compared to the social optimum when there are positive intergroup externalities. In the model by Kind et al (2008) there is no pro…t shifting motive at play. As our analysis has shown, introducing transfer pricing will increase the possibility of oversupply if the tax rate di¤erential has the same sign as the network externality, since this would lower the transfer price even further. However, if international di¤erences in tax rates (and thus the motive of pro…t shifting) work against the network externality, pro…t-shifting will ceteris paribus increase the transfer price and, consequently, mitigate the oversupply problem.
It is straightforward to show the e¤ect of changes in either tax rate on the transfer price. In particular, we obtain because the denominator in both expressions is negative from the second order condition for an optimal transfer price q j .
Recall that the parent …rm produces two goods, where good a is sold worldwide by the parent …rm whilst good x is sold to each a¢ liate j at transfer price q j . The parent …rm faces the tax rate t i so an increase in tax rates facing the a¢ liates (t j ) means that it becomes more pro…table to shift pro…t to the parent …rm, which is done by overinvoicing the transaction. Similarly, a higher t i means that it has become more attractive to shift pro…t to the a¢ liates by underinvoicing.
Finally, we can de…ne j = @p A @x j a as the magnitude of the externality and interpret an increase in j either as a shift in preferences for good a or as an increase in the network externality between goods a and x j . The e¤ect on the transfer price of a change in j is where the negative sign follows from @x j @q j < 0, equation (10), and the negativity of the second order condition. The intuition is that if the marginal willingness to pay for good a is rising in the amount sold of good x j , then it pays for the multinational …rm to let the parent …rm subsidize the sale of good x j by selling at an even lower transfer price q j .
Note that the magnitude of the externality and the elasticity of complementarity p A x j will vary between countries, making the …rm set di¤erent transfer prices across countries. These international di¤erences need not re- ‡ect di¤erences in international tax rates but may be entirely due to the di¤erences in demand across countries. This goes to show that it is not easy to establish what the correct transfer price is even in the absence of taxation.

Concluding Remarks
This paper has demonstrated that multinational two-sided platform …rms set transfer prices that deviate from the marginal cost of production even in the absence of taxation. We also show that the transfer price may be welfare enhancing even if di¤erences in national tax rates give rise to pro…t-shifting. If the tax rate di¤erential mitigates the externality e¤ect, the total e¤ect on welfare is ambiguous. Nevertheless, it may be that reducing (potential) oversupply overcompensates losses from tax-evasion. Out of our analysis also comes the insight that in the absence of taxation the transfer price on the same transaction will di¤er across countries depending on the strength of demand speci…c network externalities between customer groups. According to the OECD double tax convention: ". . . the correct transfer price is the price that would have been chosen if the transaction had occurred between independent agents in the market place . . . (i.e., the arm's length price)". 6 Our analysis points to that in two-sided markets arm's length prices may be di¢ cult or even impossible to establish. There are several reasons for this. First, two-sided platform …rms may …nd it profitable to charge prices that are below marginal cost or even negative for one product (customer group). Second, in such markets where the transfer price serves to internalize the externality between customer groups, there may not exist market parallels that can be used, and if they did exist, they could be from …rms serving only one customer group (i.e., a one-sided market …rm). Such …rms face very di¤erent pricing incentives and cannot be used for price comparisons.