Transfer Pricing and Taxation with Heterogeneous ...

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Transfer Pricing and Taxation with Heterogeneous Firms∗ Yoshimasa Komoriya† Hitotsubashi University June, 2007

Abstract We consider transfer prices under the oligopoly with heterogeneous multinational enterprises (MNEs). Although transfer prices and decentralized MNEs have been examined in the literature, competitions among decentralized MNEs have not been considered so much. Moreover, we tackle an investigation on the effects of firm heterogeneity on transfer prices. The cost difference among MNEs arises from upstream production, downstream production, or both. For any given rate of the domestic corporate tax, transfer prices of two MNEs may be strategic complements if the rate of the foreign corporate tax is sufficiently high and may be strategic substitutes otherwise. When the cost difference is only in the upstream, the headquarter of the more efficient MNE offers lower transfer price. This price difference also occurs when the cost difference is only in the downstream as long as the foreign tax rate is not relatively high to the domestic tax rate. It is also found that the difference of margins depends on the total unit costs of MNEs. The more efficient MNE has larger margin than the less efficient MNE if the foreign tax rate is sufficiently high and the more efficient MNE has smaller margin otherwise. Keywords : decentralized firm; heterogeneous firms; oligopoly; transfer pricing JEL Classification : H25, F23

∗I

am very grateful to Jota Ishikawa. I also thank Taiji Furusawa, Kaz Miyagiwa and Hiroshi Mukunoki. School of Economics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan; E-mail: [email protected] † Graduate

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Introduction

In the trade and public finance literature, a lot of researchers have examined transfer prices and decentralized multinational enterprises (MNEs). However, the competition among decentralized MNEs has not been considered so much. Moreover, to the best of my knowledge, the effects of firm heterogeneity on transfer prices are not considered. In this paper, we consider a competition among heterogeneous decentralized MNEs. Each MNE is composed of a upstream firm, a downstream firm, and a headquarter. The downstream firms produce the final good in the foreign (host) country and compete in the foreign market. The upstream firms produce the intermediate good in the domestic (home) country and sell the intermediate good exclusively to their own downstream firm. In the case of decentralized MNEs, the level of the final good output is chosen by the downstream firm while the price of the intermediate good (that is to say, transfer price) is set by the headquarter. How are the transfer prices of two MNEs set by the headquarters in the competition? This paper addresses this question. We also analyze how the firm heterogeneity affects the transfer pricing. The cost difference among MNEs may arise from upstream production, downstream production, or both. Taking the source of the firm heterogeneity into account, we tackle to the question which MNE sets higher transfer price, a more efficient MNE or a less efficient one. When the difference in corporate tax between home and host country is small, the headquarters of MNEs do not have strong incentive to set high transfer price for tax avoidance. And they tend to help their downstream firm by offering low transfer prices. The role of this low transfer prices is similar to the role of export subsidies in Brander and Spencer (1985).

In the literature of export-subsidy competition, de

Meza (1986) found that the government of the country with the low cost firm offers higher subsidy rate than that of the country with the high cost firm. We investigate which MNE supports its own downstream firm more powerfully in the competition between decentralized MNEs. The competition between MNEs is examined in the paper. Thus, we can investigate the relationship in transfer price between MNEs and explain that the transfer prices of two MNEs are strategic complements or strategic substitutes. For any given rate of the domestic corporate tax, the transfer prices of two MNEs would be strategic complements at high foreign corporate tax rate. When the foreign tax rate is not high, the transfer prices would be strategic substitutes.

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While an increase in marginal cost of a upstream firm always raises its transfer price, the effect of an increase in marginal cost of a downstream firm depends on the tax rates. Given the domestic tax rate, an increase in marginal cost of downstream firm lowers transfer price if the foreign tax rate is high and raises it otherwise. In this paper, we take the firm heterogeneity into account. Then, we find as follows. When the cost difference is only in the upstream, the headquarter with the low cost upstream firm offers higher transfer price. This price difference also occurs when the cost difference is only in the downstream as long as the foreign corporate tax rate is relatively high to the domestic corporate tax. We examine the difference between transfer price and marginal cost in the downstream, which denoted by “margin.” It is found that the difference in margin between MNEs depends on the total unit costs of MNEs. The more efficient MNE have larger margin than the less efficient MNE when the foreign tax rate is relatively high to the domestic one. The rest of the paper is organized as follows. Section 2 gives a brief introduction our basic model and examines the competition between two downstream firms in the final goods market. Section 3 investigates the transfer-price setting stage. The relationship between transfer prices of two MNEs are considered. Section 4 analyzes the effects of the cost asymmetry on the transfer prices. We investigate the difference in transfer price and margins between two MNEs. Section 5 is devoted to confirm the robustness of our results. We take into account increasing marginal cost and transfer pricing cost. Finally, Section 6 states the conclusions.

2

Basic Model and Final-Good Market

There are two countries (domestic and foreign) and two decentralized MNEs (MNEs 1 and 2). The domestic country is the home country of these MNEs. The MNEs produce a homogenous good and engage in Cournot competition in the foreign market. Each one of the decentralized MNEs has one upstream firm in the domestic country and one downstream firm in the foreign country. The upstream firm of MNE i (i = 1, 2), upstream firm i, produces the intermediate good and sells it to downstream firm i. The downstream firm of MNE i, downstream firm i, produces the final good. One unit of the intermediate good is needed for the production of one unit of the final good. The headquarters of the MNEs simultaneously set the prices of the intermediate good. These intermediate prices are called transfer prices. Given the transfer prices set by the

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headquarters, the downstream firms simultaneously choose their output levels and compete in the final good market. Both countries impose corporate taxes: t is the rate of corporate tax in the domestic country and t∗ the rate of corporate tax in the foreign country (0 ≤ t ≤ 1 and 0 ≤ t∗ ≤ 1). The inverse demand is given by the following linear function: P (X) = α − βX,

where P and X are, respectively, the price and the demand of the final good. In equilibrium, X = x1 + x2 , where xi is the output of MNE i (i = 1, 2). The (gross) profits of upstream firm i and downstream firm i (i = 1, 2) are

Πui

= (mi − γ i ) xi ,

Πdi

= (P (X) − mi − wi ) xi ,

where γ i and wi are, respectively, marginal costs of upstream firm i and downstream firm i and where mi is the transfer price of MNE i. The first-order condition for profit-maximization of downstream firm i (i = 1, 2) is ∂Πdi = P (X) + P 0 xi − mi − wi = α − 2βxi − βxj − mi − wi = 0, ∂xi

i = 1, 2, i 6= j.

(1)

Using the first-order condition, we can derive the reaction function Ri (xj ) and the slope of it as follows. α − mi − wi − βxj , 2β 1 = − 0. ∂mj ∂wj 3β

4

(2)

Using Eq. (1) or Eq. (2), we can show the difference in output between two MNEs as follows.

x1 − x2 =

3

m2 + w2 − m1 − w1 β

(3)

Transfer Pricing

The headquarters of the MNEs set their transfer prices to maximize the total (net) profit of the MNEs. In this paper, we assume that the foreign government taxes the profit of downstream firm i and that the domestic government taxes the total profit of MNE i. And it is assumed that the MNEs can receive foreign tax credit (FTC) to prevent double taxation. Thus, we consider only the case where t ≤ t∗ ≤ 1.1 The net profit of MNE i (i = 1, 2) in the upstream is (1 − t) Πui and the net profit of MNE i in the downstream (1 − t∗ ) Πdi . Thus, the total net profit of MNE i is the sum of these net profits. Πui = (1 − t) (mi − γ i ) xi + (1 − t∗ ) (P (X) − mi − wi ) xi

The first-order condition for profit-maximization of MNE i (i = 1, 2) is ∂π ti ∂mi

= =

∂xi ∂xj + (1 − t∗ ) P 0 xi ∂mi ∂mi (−1 − 3t + 4t∗ ) (α − 2mi − 2wi + mj + wj ) − 6 (1 − t) (mi − γ i ) = 0. 9β

(t∗ − t) xi + (1 − t) (mi − γ i )

Using the first-order condition, we can derive the reaction function Rit (mj ) and the slope of it as follows.

Rit (mj )

=

dmi dmj

=

Ω (α − 2wi + mj + wj ) + 6 (1 − t) γ i , 4Γ Ω , 4Γ

1 When t∗ < t, the MNEs are taxed at the rate of t. The profits of downstream firms are taxed by the foreign government at the rate of t∗ and also taxed by the domestic government at the rate of t − t∗ . The domestic government taxes the profits of upstream firms at the rate of t. See Hines (2004).

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where



≡ −1 − 3t + 4t∗ ,

Γ

≡ 1 − 3t + 2t∗ > 0.

We can easily show that Γ is positive in the case of t∗ ≥ t. Thus, we have the following condition. dmi ≥0⇔Ω≥0 dmj For any given rate of t ∈ [0, 1], Ω ≥ 0 holds if and only if t∗ ≥ (1 + 3t) /4. For example, when t = 0, Ω ≥ 0 if and only if t∗ ≥ 1/4. And when t = 1, Ω = 0 if and only if t∗ = 1. Thus, we obtain the proposition as follows. Proposition 1 For any given rate of t ∈ [0, 1], the transfer prices of two MNEs are strategic complements if t∗ is sufficiently high (Ω > 0) and strategic substitutes otherwise (Ω < 0). To obtain economic intuition, we consider two extreme cases where t∗ = 1 and t∗ = t. When t∗ = 1 (Ω = 3 (1 − t) > 0), the profit of downstream firm i is fully taxed away and the headquarter of MNE i, headquarter i, maximizes the profit of upstream firm i, Πui . In this case, we can regard this price-setting stage as the game where two headquarters engage in Bertrand competition taking Eq. (2) as demand functions. Thus, the transfer prices of two MNEs are strategic complements and the slope of the reaction function of MNE i is 1/4. When the transfer price of the rival MNE, MNE j, increases, MNE i can raise its own transfer price since the profit of downstream firm i is not considered. When t∗ = t (Ω = − (1 − t) < 0), headquarter i maximizes Πui + Πdi . In this case, headquarter i does not have any incentive to raise its transfer price for tax avoidance and offers low (or negative) transfer price to help downstream firm i. The role of this low transfer prices is similar to the role of export subsidies in Brander and Spencer (1985). Thus, the transfer prices of two MNEs are strategic substitutes and the slope of the reaction function of MNE i is −1/4. At t∗ = (1 + 3t) /4 (Ω = 0), these effects balance. The transfer price of MNE i (i = 1, 2) is

mi =

4ΩΓ (α − 2wi + wj ) + Ω2 (α − 2wj + wi ) + 24Γ (1 − t) γ i + 6Ω (1 − t) γ j , (Ω + 4Γ) (−Ω + 4Γ)

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(4)

where Ω + 4Γ = 3 (1 − 5t + 4t∗ ) > 0 and −Ω + 4Γ = 5 − 9t + 4t∗ > 0. When Ω = 0, we have mi = γ i (i = 1, 2) from Eq. (4). However, this result could be obtained in the case where one MNE and one local firm compete in the final market.2 Supposing m1 = m2 = m and γ 1 = γ 2 = γ, we consider the symmetric case. Then, we obtain

mi

=

dmi dt∗

=

Ω (α − w) + 6 (1 − t) γ , (−Ω + 4Γ) 24 (1 − t) (α − w − γ) > 0. 2 (−Ω + 4Γ)

This implies that the transfer price of MNE i is less than γ i and may be negative when Ω < 0. It also implies that the transfer prices monotonically increase in t∗ . As t∗ increases, that is, Ω increases, it becomes easy for the headquarters to raise their transfer prices for reducing tax payments in the foreign country since the profits in the downstream gradually become less important. In the case where the cost heterogeneity exists, the effect of an increase in t∗ on the transfer prices is

dmi = dt∗

n ¡ ¢o 2 24 (1 − t) α (Ω + 4Γ) − 6Φ (wi + γ i ) − 3Ψ wj + γ j 2

2

(Ω + 4Γ) (−Ω + 4Γ)

,

where

Φ

≡ 16t∗ − 30t − 48tt∗ + 16t∗2 + 39t2 + 7,

Ψ ≡

−8t∗ + 30t − 24tt∗ + 16t∗2 − 3t2 − 11.

If the market size is small, the transfer price of the less efficient MNE may not monotonically increase in t∗ For example, this occurs at α = 10, w1 + γ 1 = 3, w2 + γ 2 = 5, t∗ = t. We can find the effects of changes in marginal costs on the transfer price of MNE i (i = 1, 2) as follows. ∂mi ∂wi ∂mi ∂wj

2 In

= =

Ω (Ω − 8Γ) ∂mi 24Γ (1 − t) , = > 0, (Ω + 4Γ) (−Ω + 4Γ) ∂γ i (Ω + 4Γ) (−Ω + 4Γ) ∂mi 6Ω (1 − t) = , ∂γ j (Ω + 4Γ) (−Ω + 4Γ)

the monopoly case, the headquarter of monopolist MNE set m = γ at t∗ = t.

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where Ω − 8Γ = −3 (3 − 7t + 4t∗ ) < 0. It is found that of

∂mi ∂wj

∂mi ∂wi

=

and

∂mi ∂γ j

∂mi ∂wj

=

∂mi ∂wi

is opposite in sign to Ω and the sign

are the same as the sign of Ω. When Ω = 0, Γ = 3 (1 − t) /2. Then,

∂mi ∂γ j

∂mi ∂γ i

= 1 and

= 0.

Proposition 2 An increase in marginal cost of upstream firm i raises the transfer price of MNE i independently of Ω. When Ω > 0, a decrease in marginal cost of downstream firm i and an increase in marginal costs of the rival MNE raise the transfer price of MNE i. When Ω > 0, the effects reverse. These results are similar to the results in the case where one MNE and one local firm compete in the final market. Next, we mention that the output of downstream firm i (i = 1, 2) is © ¡ ¢ª 2 (1 − t) (Ω + 4Γ) α + (Ω − 8Γ) (wi + γ i ) + 6 (1 − t) wj + γ j xi = . β (Ω + 4Γ) (−Ω + 4Γ)

(5)

When Ω = 0, that is, t = (1 + 3t) /4 for any given rate of t ∈ [0, 1], the output of MNE i is ¡ ¢ α − 2 (wi + γ i ) + wj + γ j xi = . 3β

(6)

This output is the same output as the case of standard Cournot duopoly. When marginal costs of firm i and firm j are, respectively, wi + γ i and wj + γ j , the Cournot output of firm i is equal to Eq. (6). Supposing m1 = m2 = m and γ 1 = γ 2 = γ, we consider the symmetric case again. Then, we obtain

xi dxi dt∗

2 (1 − t) (α − w − γ) , β (−Ω + 4Γ) 8 (1 − t) (α − w − γ) = − < 0. 2 β (−Ω + 4Γ)

=

This implies that the output levels of MNEs monotonically decrease in t∗ . In the case where the cost heterogeneity exists, the effect of an increase in t∗ on the output is n o 2 8 (1 − t) α (Ω + 4Γ) − 9Ξ (w1 + γ 1 ) − 12 (1 − t) (Ω − 8Γ) (w2 + γ 2 ) dxi , =− 2 2 dt∗ β (Ω + 4Γ) (−Ω + 4Γ)

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where Ξ ≡ 24T − 50t − 56T t + 16T 2 + 53t2 + 13. We note that the output of the less efficient MNE may not monotonically decrease in t∗ . For example, this also occurs at α = 10, w1 + γ 1 = 3, w2 + γ 2 = 5, t∗ = t. However, we should note that interior solutions may not occur in the case of small market. Suppose MNE 1 is the more efficient MNE and MNE 2 is the less efficient MNE, w1 + γ 1 < w2 + γ 2 . From Eq. (5), we find the sufficient condition under which the output levels of two MNE (downstream firm) are positive at any t∗ ≥ t as follows.

α + 2 (w + γ 1 ) − 3 (w2 + γ 2 ) > 0 The set of parameters mentioned above fulfills this condition. Finally, we show the profits as follows. The gross profits of upstream firm i and downstream firm i are Πui =

βΩ x2 , 2 (1 − t) i

Πdi = βx2i ,

where Ω = −1 − 3t + 4t∗ . The net profit of MNE i (i = 1, 2) is π ti =

βΓ 2 x , 2 i

where Γ = 1 − 3t + 2t∗ > 0.

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Transfer Pricing and Firm Heterogeneity

In this section, we investigate the relationship between transfer pricing and cost heterogeneity. We assume that marginal cost of upstream firm 1 is not higher than that of upstream firm 2, that is, γ 2 ≥ γ 1 . If w2 > w1 , marginal cost of downstream firm 1 is lower than that of downstream firm 2. In this case, MNE 1 may have cost advantages in both production stages. If w2 < w1 , marginal cost of downstream firm 1 is higher than that of downstream firm 2. In this case, MNE 1 has the cost advantage in the upstream production and MNE 2 do in the downstream production. We call wi + γ i total unit cost of MNE i (i = 1, 2). If wi + γ i < wj + γ j (i = 1, 2 i 6= j), MNE i is the more efficient MNE and MNE j the less efficient MNE. 9

4.1

Transfer Prices

We compare m1 and m2 . Using Eq. (4), the difference in transfer price between two MNEs is m1 − m2 =

3 {Ω (w2 − w1 ) − 2 (1 − t) (γ 2 − γ 1 )} , (Ω + 4Γ)

(7)

where Ω + 4Γ > 0. First, we suppose γ 1 = γ 2 . From Eq. (7), m1 − m2 =

3Ω (w2 − w1 ) . (Ω + 4Γ)

When Ω > 0, the transfer price of MNE 1 is higher than that of MNE 2 if w2 > w1 . When Ω < 0, the transfer price of MNE 1 is lower than that of MNE 2 if w2 > w1 . We obtain the intuition as follows. When Ω > 0, it seems that the headquarters engage in Bertrand competition. w2 > w1 implies that the demand for MNE 1 is larger than that for MNE 2. Thus, headquarter 1 offers higher transfer price than headquarter 2. When Ω < 0, it seems that the headquarters engage in subsidy competition. In the case of export-subsidy competition, de Meza (1986) found that the government of the country with the low cost firm offers higher subsidy rate than that of the country with the high cost firm. In this model, the MNE with low cost downstream firm has lower transfer price than that with high cost downstream firm. Next, we suppose w1 = w2 . From Eq. (7), m1 − m2 =

−6 (1 − t) (γ 2 − γ 1 ) . (Ω + 4Γ)

This mentions that the MNE with the cost advantage in the upstream has the lower transfer price regardless of Ω. Finally, we consider the general case supposing γ 2 > γ 1 . This condition implies that MNE 1 has lower transfer price that MNE 2. Then, we obtain the following condition.

m1 ≥ m2 ⇔ Ω

(w2 − w1 ) ≥ 2 (1 − t) . (γ 2 − γ 1 )

(8)

When Ω > 0, that is, the transfer prices of two MNEs are strategic complements, the condition under which m1 ≥ m2 is (w2 − w1 ) 2 (1 − t) ≥ . (γ 2 − γ 1 ) Ω This condition may hold when w2 is sufficiently larger than w1 . When Ω = 0, we have mi = γ i (i = 1, 2) from Eq. (4). Thus, m2 > m1 . When Ω < 0, that is, the transfer prices of two MNEs 10

are strategic substitutes, the condition under which m1 ≥ m2 is (w2 − w1 ) 2 (1 − t) ≤ , (γ 2 − γ 1 ) Ω where 2 (1 − t) /Ω < 0. In this case, m1 < m2 holds if w2 ≥ w1 and m1 ≥ m2 may hold if w1 is sufficiently larger than w2 . The intuition for the general results is obtained by considering the special cases: γ 1 = γ 2 and w1 = w2 . Finally, we mention the difference in output between two firms. From Eq. (7), the difference between the total costs of two downstream firms is

(m1 + w1 ) − (m2 + w2 ) =

6 (1 − t) (w1 + γ 1 − w2 − γ 2 ) . (Ω + 4Γ)

This difference depends not on the source of heterogeneity but on total unit cost of MNEs. Using Eq. (3), the difference in output between two firms can be found as follows.

x1 − x2 =

6 (1 − t) (w2 + γ 2 − w1 − γ 1 ) β (Ω + 4Γ)

(9)

The difference in output does not depend on the source of heterogeneity. We can find that the MNE with the low total unit cost produces more.

4.2

Margins

We investigated the relationship between two transfer prices in the previous subsection. Next, we consider mi − γ i (i = 1, 2) and compare m1 − γ 1 and m2 − γ 2 . We call mi − γ i “margin.” Using Eq. (4), the margin of upstream firm i is

mi − γ i =

4ΩΓ (α − 2wi + wj ) + Ω2 (α − 2wj + wi ) + Ω (Ω − 8Γ) γ i + 6Ω (1 − t) γ j (Ω + 4Γ) (−Ω + 4Γ)

and the difference in margin between two MNEs is

(m1 − γ 1 ) − (m2 − γ 2 ) =

3Ω (w2 + γ 2 − w1 − γ 1 ) . (Ω + 4Γ)

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(10)

Thus, we can obtain the following condition.

m1 − γ 1 ≥ m2 − γ 2 ⇔

3Ω (w2 + γ 2 − w1 − γ 1 ) ≥ 0. (Ω + 4Γ)

(11)

These conditions imply as follows. When Ω = 0, two MNEs have the same margin since their margin must be zero as shown in the previous subsection. When Ω > 0, the margin of the more efficient MNE is larger than that of the less efficient MNE. When Ω < 0, the margin of the more efficient MNE is smaller than that of the less efficient MNE. Rearranging Eq. (11), we have

γ 2 − m2 ≥ γ 1 − m1 ⇔

3Ω (w2 + γ 2 − w1 − γ 1 ) ≥ 0. (Ω + 4Γ)

When MNE i is the more efficient MNE, γ 1 − m1 > γ 2 − m2 holds when Ω < 0. This implies the headquarter of the more efficient MNE supports its own downstream firm powerfully. We should note that the difference in margins between the MNEs depends not on the source of cost heterogeneity but on the difference in total unit cost between the MNEs. Proposition 3 The margin of the more efficient MNE is larger than those of the less efficient firm if t∗ is sufficiently high (Ω > 0). Otherwise (Ω < 0), the margin of the more efficient MNE is smaller than those of the less efficient firm. Rearranging Eq. (10), we can also find the relationship between the difference in transfer price and the difference in upstream-marginal cost as follows.

m2 − m1 = γ 2 − γ 1 −

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3Ω (w2 + γ 2 − w1 − γ 1 ) (Ω + 4Γ)

Robustness

In this section, we investigate to what extent our results on transfer pricing are robust. Our basic model assumes constant marginal costs in the both production stages. In the literature, it is, however, often assumed that the cost function of the upstream production is convex. For example, see Zhao (2000). Replacing γ i xi by 12 γ i x2i , we can redefined the total net profit of MNE i (i = 1, 2) as π ti

µ ¶ 1 2 = (1 − t) mi xi − γ i xi + (1 − T ) (P − mi − wi ) xi . 2 12

We consider the slope of the reaction functions. The slope of the reaction function of headquarter i is dmi 1 βΩ + 2γ i (1 − t) = , dmj 4 βΓ + γ i (1 − t)

(12)

where Ω = −1 − 3t + 4t∗ and Γ = 1 − 3t + 2t∗ > 0. This implies that the sign of always the same as the sign of Ω if γ i 6= 0. can find the rate of t∗ at which

dmi dmj

t∗ =

dmi dmj

dmi dmj

is not

> 0 may hold even if Ω < 0. Using Eq. (12), we

= 0 as follows. γ (1 − t) 1 (1 + 3t) − i ≡ te∗i 4 2β

Unlike in the case of constant marginal cost, te∗i
0.

We also investigate the effect of transfer pricing cost. In Nielsen et al. (forthcoming), they assume that the transfer pricing cost is quadratic and based on the actual difference between the chosen price and the true price. Supposing the form of transfer pricing cost is

1 2

2

(m − γ) , we

can reexamine our analysis. In the result, the robustness of our results to transfer pricing cost can be confirmed.

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Concluding Remarks

We consider the competition among two decentralized MNEs and the transfer pricing set by the headquarters. For any given rate of the domestic corporate tax, it is found that the transfer prices of two MNEs may be strategic complements if the foreign corporate tax rate is high and may be strategic substitutes otherwise. We examine the question, “which MNE does have the higher transfer price?” When the cost difference is only in the upstream, the headquarter with the high cost upstream firm offers the higher transfer price. This price difference also occurs when the cost difference is only in the downstream as long as the foreign corporate tax rate is not relatively high to the domestic corporate tax. The difference in margin depends on total unit costs of MNEs. The more efficient MNE have larger margin than the less efficient MNE if the 13

foreign corporate tax rate is high and the more efficient MNE have smaller margin otherwise. In this paper, we do not consider the delegation decision. In Nielsen et al. (forthcoming), it is found that MNE, which complete with the local firm, does not delegate at the high rate of the foreign tax. The other issue that we do not investigate is the choices of corporate tax rates by the governments. These are left for the future research.

Appendix In this appendix, we show the second-order sufficient conditions for profit-maximization. The second-order sufficient condition for profit-maximization of downstream firm i (i = 1, 2) is holds as follows. ∂ 2 Πd1 ∂ 2 Πd2 = = 2P 0 = −2β < 0, ∂x21 ∂x22 µ 2 d¶µ 2 d¶ µ 2 d ¶µ 2 d ¶ ∂ Π2 ∂ Π1 ∂ Π1 ∂ Π2 2 2 − = (−2β) − (−β) = 3β 2 > 0, ∂x21 ∂x22 ∂x2 ∂x1 ∂x1 ∂x2 where ∂ 2 Πd1 ∂ 2 Πd2 = = P 0 = −β < 0. ∂x2 ∂x1 ∂x2 ∂x1 In the price-setting stage, the second-order sufficient for profit-maximization of MNE i (i = 1, 2) is ∂ 2 π ti ∂m2i

= (t∗ − t) = −

∂xi ∂xi ∂xi ∂xj + (1 − t) + (1 − t∗ ) P 0 ∂mi ∂mi ∂mi ∂mi

4Γ 0, = 9β 9β

where ∂ 2 π ti ∂mj ∂mi

= (t∗ − t) =

∂xi ∂xi ∂xj + (1 − t∗ ) P 0 ∂mj ∂mj ∂mi

Ω . 9β

This implies that we obtain interior solutions as long as we suppose FTC.

References [1] Brander, James A. and Barbara J. Spencer (1985) “Export Subsidies and International Market Rivalry,” Journal of International Economics 18, 83-100. [2] de Meza, David (1986) “Export Subsidies and High Productivity: Cause or Effect?,” Canadian Journal of Economics 19, 347-350. [3] Hines, James R. Jr. (2004) “Do Tax Havens Flourish?” NBER Working Paper 10936. [4] Nielsen, Søren Bo, Pascalis Raimondos–Møller and Guttorm Schjelderup “Taxes and Decision Rights in Multinationals,” Journal of Public Economic Theory, forthcoming. [5] Zhao, Laixun (2000) “Decentralization and Transfer Pricing Under Oligopoly,” Southern Economic Journal 67, 414-426.

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