Online Appendix for “tariﬀ elimination versus Tax Avoidance:
Free Trade Agreements and Transfer Pricing”
Hiroshi Mukunoki

Hirofumi Okoshi

B.1 Partial procurement of inputs
We have assumed that the MNE makes a binary choice about input procurement, that is, a“make all or buy all” choice. It would be more realistic to suppose that the MNE purchases
some proportion of parts from local suppliers and procures the rest from intra-ﬁrm transactions,which we refer to as scheme 𝑃.
Suppose that the MNE uses a continuum of inputs indexed in the [0, 1] space. Let 𝛽 ∈ [0, 1]
denote the proportion of inputs that ﬁrm 𝑀𝐻 procures from ﬁrm 𝑀𝑂 in country 𝑂. This meansthat the 1 − 𝛽 proportion of the input is procured within the FTA countries. The amount of theintra-ﬁrm trade becomes 𝛽𝑥, and the modiﬁed VA ratio is given by 𝑝−𝛽𝑟
𝑝 . The MNE maximizes
Π = 𝛽{𝑟 − (𝑤 − Δ)}𝑥 + 𝜋 + (1 − 𝑇) [{𝑝 − 𝛽𝑟 − (1 − 𝛽)𝑤}𝑥](B-1)

with respect to 𝑥, 𝑟, and 𝛽, and subject to 𝜋 𝐻 ≥ 0, 𝜋𝑂 ≥ 0, and 𝑝−𝛽𝑟
𝑝 ≥ 𝛼.
𝑃𝑃Since 𝜕Π𝜕𝑟 > 0 holds, the optimal transfer price, 𝑟 , is set at the level such that 𝑝 − 𝛽𝑟 −(1 − 𝛽)𝑤 = 0 is satisﬁed. We can also conﬁrm that 𝜕Π𝜕 𝛽 > 0 always holds, which implies thatthe MNE sets 𝛽 as high as possible. Therefore, the optimal 𝛽 becomes 𝛽 = max[0, 𝛽 𝑃 ], where
𝛼𝑝𝛽 𝑃 ≡ 1 − 𝑤 . Let 𝑥 𝑃 denote the corresponding optimal level of 𝑥. Then, the equilibrium post-tax
proﬁts in scheme 𝑃 are𝛼Δ( 𝑝 − 𝑐 𝑃𝑀 )𝑥 𝑃 + 𝜋,
Π = 1−𝑤𝑃(B-2)

where 𝑐 𝑃𝑀 ≡ 𝑤(𝑤−Δ)
𝑤−𝛼Δ is the modiﬁed perceived marginal cost, which falls between 𝑤 − Δ and 𝑤.
Even if the MNE can choose 𝛽, the optimal level of 𝛽 can be zero and the main results ofthe benchmark model remain unchanged. Given that the MNE sets the abusive transfer price as
𝑤𝑟 𝑃 , the VA ratio with 𝑟 = 𝑟 𝑃 becomes (1−𝛽)𝑤
𝑝 . If 𝑝 ≤ 𝛼 holds, the MNE can never comply with

the ROO when 𝛽 > 0.

1

Because 𝑤𝑝 < 1, there exists a unique cut-oﬀ of 𝛼, 𝛼 𝑃𝛽=0 , above which the MNE sets 𝛽 𝑃 = 0.
Thus, schemes 𝑁, 𝐼, and 𝐵 of the benchmark model are still the equilibrium outcomes when𝛼 ≥ 𝛼 𝑃𝛽=0 holds. When 𝛼 < 𝛼 𝑃𝛽=0 holds, the MNE chooses a positive 𝛽, and scheme 𝐵 isreplaced with scheme 𝑃.
Furthermore, if some key inputs must be produced outside the FTA for technical reasons,
there should be the upper bound of 𝛽, which is denoted by 𝛽. If 𝛽 < 𝛽 𝑃 holds, then the MNE
still manipulates the transfer price to comply with ROO even with 𝛽 > 0, although to a lesserdegree than in the case with 𝛽 = 0.

B.2 Concealment costs for transfer price manipulation
In the benchmark model, we have assumed that the MNE can costlessly manipulate the transferprice. Here, we show that the assumption is not critical to obtain the main results.
In practice, MNEs need to explain the plausibility of transfer pricing to shift proﬁts acrosscountries. As MNEs shift more proﬁts among countries, it becomes more diﬃcult to explain why
their intra-ﬁrm prices deviate from the appropriate prices, such as the prices charged at arm’slength transaction. Following the literature on transfer pricing, we introduce the “concealmentcost” in the case of oﬀshoring, which is increasing in the gap between the transfer price and theproduction cost of inputs:
𝐶 (𝑟, 𝑥 𝑂 ) =𝛿{𝑟 − (𝑤 − Δ)}2 𝑥 𝑂,2(B-3)

where the parameter 𝛿 captures the diﬃculty of concealing tax avoidance. For example, a higher𝛿 reﬂects a well-enforced tax authority. The post-tax proﬁts under oﬀshoring are modiﬁed as
Π𝑂 = {𝑟 − (𝑤 − Δ)}𝑥 𝑂 + 𝜋 + (1 − 𝑇) [( 𝑝 − 𝑟 − 𝜆 𝑀 𝜏)𝑥 𝑂 ] − 𝐶 (𝑟, 𝑥 𝑂 ),= 𝜋 + (1 − 𝑇)( 𝑝 − 𝑐𝐶𝑀 )𝑥 𝑂 ,(B-4)

where 𝑐𝐶𝑀 = (𝑤−Δ)+(1−𝑇)𝜆𝜏−𝑇𝑟+ 𝛿{𝑟−(𝑤−𝛿)}is the eﬀective marginal cost.
1−𝑇2(1−𝑇)
2

The concealment cost can prevent the MNE from transferring all the proﬁts from country
𝐻 to 𝑂. In other words, the MNE can choose the transfer price and ﬁnal good price, such that𝑝 > 𝑟 + 𝜆𝜏 holds, even in the absence of the ROO. Given that some of the MNE’s tax bases
2remain in country 𝐻, our welfare analysis needs several modiﬁcations.
First, the welfare eﬀect of an FTA formation in the absence of the ROO now depends
on country 𝐻’s tax, 𝑇. Substituting the optimal level of 𝑟 that maximizes Π𝑂 into 𝑐𝐶𝑀 , theperceived marginal cost in the equilibrium is calculated as 𝑐𝐶𝑀 = 𝑤 − Δ + 𝜆𝜏 − 𝑇2𝛿 . Thus, as
2

the tax diﬀerence between countries widens, the perceived marginal cost lowers. Since theMNE becomes less willing to increase 𝑟 because of the concealment cost, it has an incentive toincrease 𝑥 𝑂 and lower 𝑝, which saves the MNE’s tax payments in country 𝐻 by narrowing thegap between 𝑝 and 𝑟 + 𝜆𝜏. This incentive is reﬂected in the perceived marginal cost. Because theelimination of tariﬀs increases the gap between 𝑝 and 𝑟 + 𝜆𝜏, it gives the MNE an extra incentive
to increase 𝑥 𝑂 to avoid tax payments. The increase in 𝑥 𝑂 beneﬁts consumers, and, thereby,improves the joint welfare of member countries. Therefore, in the presence of concealment
costs, an FTA formation without the ROO is more likely to beneﬁt member countries as the tax
gap widens.
Second, 𝑝 > 𝑟 + 𝜆𝜏 implies that the VA ratio is positive, even for the absence of the ROO. Inthe benchmark model, the MNE always chooses zero VA ratio in FTA countries in the absenceof the ROO. This implies that the VA requirement of the ROO aﬀects neither the MNE’s transfer
pricing nor its location choice when 𝛼 is suﬃciently small. This is because the MNE has alreadysatisﬁed the required VA ratio in this case.
Even if we consider these two elements, the nature of our results does not change. Speciﬁcally, an FTA formation without the ROO may harm member countries, and ROO can transforma welfare reducing FTA into a welfare-improving one. The opposite case is also possible, wherethe ROO transform a welfare-improving FTA into a welfare-reducing one.

B.3 Total welfare of member countries
Let us start with an FTA formation without the ROO. The post-FTA equilibrium scheme isalways scheme 𝑂. The member countries cannot collect tax revenues both before and after the3FTA formation. The change in the total welfare by the FTA formation is given byd𝐹 𝑂 − 𝐶𝑆𝑂∗ − 𝑇 𝑅𝑂∗
b 𝑂 − 𝑊 𝑂∗ = 𝐶𝑆𝑊𝐹𝐹=−2(𝑎 − 𝑤 + Δ) + 3𝜏2(𝑎 − 𝑤 + Δ)
⋛ 0 ⇐⇒ 𝜏 ⋛≡ 𝜏𝑊 .
83(B-5)

As (B-5) shows, an FTA without the ROO generates a trade-oﬀ between an increase in theconsumer surplus and disappearance of tariﬀ revenues. When the initial tariﬀ rate is high, theconsumers’ gains exceed the tariﬀ revenues, and the FTA formation increases the total welfareof member countries. Therefore, an FTA formation without ROO beneﬁts member countries
when the initial tariﬀ rate is high (𝜏 > 𝜏𝑊 ) and hurts them when it is low (𝜏 < 𝜏𝑊 ).
Let us discuss how the presence of the ROO changes the welfare eﬀect of FTA formation. As
discussed in section 3.2, the ROO reduce consumers’ gains from an FTA formation in country
𝐹. However, the ROO also help generate tax revenues in country 𝐻 if the MNE changes its
input procurement from country 𝑂 to country 𝐻, or adjusts its transfer price to comply with therules. Thus, the rules can either increase or decrease the welfare gains from an FTA formation.
Total welfare under scheme 𝐼 is sum of the consumer surplus and tax revenue from theMNE:
e 𝐼 = (𝑎 − 𝑤) (1 + 2𝑇) .
𝑊
8(B-6)e 𝐼 ⋛ 𝑊 𝑂∗ ⇐⇒ 𝑇 ⋛ 𝑇e𝑊 ≡ 2(𝑎 − 𝑤)(Δ + 𝜏) − (𝜏 − Δ)(Δ + 3𝜏) .
𝑊2(𝑎 − 𝑤) 2(B-7)

2

We have

Total welfare under scheme 𝐵 also includes tax revenue from the MNE, given by"22#21𝑤−Δ𝑎𝑤−Δe𝐵 =𝑊
𝑎−−+ 𝑇𝛼.
81 − 𝛼𝑇42(1 − 𝛼𝑇)(B-8)

e 𝐵 = 𝑊).
b
At 𝛼 = 0, regime 𝐵 is identical to the post-FTA equilibrium without the ROO (𝑊Starting from 𝛼 = 0, an increase in the stringency of the ROO has two opposite eﬀects one 𝐵 . On the one hand, a stricter VA requirement reduces the transfer price, and, thereby,𝑊
increases the tax revenue that country 𝐻 collects. On the other hand, it diminishes consumers’
gains from an FTA formation by increasing the MNE’s perceived marginal cost and reducing
4

e 𝐵 and 𝛼.
the amount of exports. There is thus an inverted U-shaped relationship between 𝑊e𝐵𝑊
Speciﬁcally, the former eﬀect dominates the latter and 𝜕𝜕𝛼> 0 holds when 𝛼 is small, wherease𝐵𝑊the latter eﬀect dominates the former and 𝜕𝜕𝛼< 0 holds when 𝛼 is large.1 We can specify

e 𝐵 = 𝑊 𝑂∗ holds.2 When 𝛼𝑊 < min[𝛼 𝐼 , 𝛼 𝑁 ] holds, we havea threshold of 𝛼, 𝛼𝑊 , at which 𝑊e 𝐵 ⋛ 𝑊 𝑂∗ ⇐⇒ 𝛼 ⋛ 𝛼𝑊 .3 If the post-FTA scheme is scheme 𝑁, an FTA formation with the𝑊
ROO does not aﬀect the total welfare of member countries.
Suppose 𝜏 < 𝜏𝑊 , with which an FTA without the ROO reduces total welfare. Since stricter
ROO improve post-FTA welfare in scheme 𝐵, the post-FTA welfare can be larger than thepre-FTA welfare, even with 𝜏 < 𝜏𝑊 . The left ﬁgure of Figure B.1 provides a numerical example
to show that 𝛼𝑊 < min[𝛼 𝐼 , 𝛼 𝑁 ] holds.4 In the shaded area in scheme 𝐵, an FTA formation
improves the total welfare. Further, an FTA formation improves the total welfare in scheme 𝐼
if 𝑇 > 𝑇e𝑊 holds. Therefore, the ROO can transform a welfare-reducing FTA into a welfareimproving one because the increased tax revenue from the MNE compensates for the tariﬀ
revenue loss.
However, ROO may negatively aﬀect total welfare and transform a welfare-improving FTA
into a welfare-reducing one. The right ﬁgure of Figure B.1 corresponds to the case wherein𝜏 > 𝜏𝑊 , and the formation of an FTA without the ROO is beneﬁcial for member countries. The
dotted curve in scheme 𝐵 represents 𝛼𝑟 , above which we see the reversal of proﬁt shifting, asdiscussed in the previous section. The ﬁgure shows that an FTA stays feasible even if we takethe ROO into account, such that the ROO increase the gains of forming an FTA under schemee𝐵𝑊
𝐵 in the equilibrium because 𝜕𝜕𝛼> 0| 𝛼=0 holds. If both 𝛼 and 𝑇 are high, such that scheme

𝑁 is the equilibrium outcome, there is no welfare change from an FTA formation. Moreover, ife𝑥𝐵

1Let 𝛼 𝑥 be the threshold of 𝛼 such that the amount of exports is constant before and after the FTA is formed,2𝑊
f𝐵
f𝐵
f𝐵𝑊𝑥
= 𝑥 𝑂∗ . Since we have 𝜕𝜕𝛼| 𝛼=0 > 0, 𝜕𝜕𝛼< 0, and 𝑊2
𝜕𝛼 | 𝛼=𝛼 < 0, there exists a unique threshold,f𝐵𝑊𝑥𝛼𝑊= 0 holds.
0 ∈ [0, 𝛼 ), such that 𝜕𝛼 | 𝛼=𝛼𝑊0𝑥
2At 𝛼 = 𝛼 , an FTA formation does not change the MNE’s exports of the ﬁnal goods or consumer surplus. Wee 𝐵 − 𝑊 𝑂∗ | 𝛼=𝛼 𝑥 =can simplify the change in total welfare to the sum of tax revenue and the loss of tariﬀ revenue, 𝑊hnoi
𝐵
𝑎+𝑤−Δ+𝜏
𝜋𝐻− 𝜏𝑥 𝑂∗ = 𝜏𝑥 𝑂∗ 2(𝑤−Δ+𝜏)𝑇 𝛼 𝑥e− 1 > 0. This means that a threshold 𝛼𝑊 ∈ [0, 𝛼 𝑥 ) exists that satisﬁese 𝐵 = 𝑊 𝑂∗ .
𝑊e 𝐵 is an inverted U-shaped curve in 𝛼, we always have 𝑊
e 𝐵 > 𝑊 𝑂∗ at 𝛼 = min[𝛼 𝐼 , 𝛼 𝑁 ] because
3Although 𝑊𝐼𝑁𝑥
min[𝛼 , 𝛼 ] < 𝛼 holds. This means that an FTA formation always improves total welfare for 𝛼𝑊 < 𝛼 ≤min[𝛼 𝐼 , 𝛼 𝑁 ].
14The parameters are set as follows: 𝑎 = 1, Δ = 32, and 𝜏 = 14 . The left ﬁgure is drawn with 𝑤 = 21 , whereas
2the right ﬁgure uses 𝑤 = 3 .

5

Figure B.1: rules of origin and the welfare eﬀect of an FTA formation
the equilibrium outcome is scheme 𝐼 and 𝑇 ≤ 𝑇e𝑊 holds, the gains from increased tax revenue
are smaller than the loss from the lower consumer surplus. In this case, the ROO transform awelfare-improving FTA formation into a welfare-reducing one.

B.4 A tariﬀ on inputs
Because there is no market in country 𝐻, only tariﬀ revenues or tax revenues are the welfare
components of country 𝐻. Let 𝜉 be a tariﬀ on inputs in country 𝐻. If the MNE locates its
upstream aﬃliates in country 𝑂, the amount of the imported inputs from country 𝑂 becomes. Before the FTA formation, 𝜆 = 0. The MNE chooses to produce in country𝑥 𝑂 = 𝑎−𝑤+Δ−𝜉−𝜆𝜏
2𝐻 if√
Π 𝐼 ≥ Π𝑂 ⇐⇒ 𝜉 ≥ Δ + (𝑎 − 𝑤 − 𝜏)(1 − 1 − 𝑇) ≡ 𝜉 𝑀(B-9)

holds. 𝜉 𝑀 increases with 𝑇 and 𝜉 𝑀 |𝑇=0 = Δ. In scheme 𝐼, country 𝐻 earns no tariﬀ revenue,
but it earns corporate tax revenues, which are given by 𝑇 𝑅 𝐻𝐼 . Given the input production in𝑂country 𝑂, the input tariﬀ that maximizes country 𝐻’s tariﬀ revenue, 𝑇 𝑅𝑂
𝐻 = 𝜉𝑥 , is given by:

𝜕𝑇 𝑅𝑂𝐻=0𝜕𝜉

→

𝜉𝑇 =

6𝑎−𝑤+Δ−𝜏.
2(B-10)Because 𝜉𝑇 − 𝜉 𝑀 |𝑇=0 = 𝑎−𝑤−Δ−𝜏, we have 𝜉𝑇 > 𝜉 𝑀 |𝑇=0 if 𝑎 − 𝑤 − 𝜏 > Δ holds. There exists a
2threshold level of 𝑇, 𝑇𝜉 , such that 𝜉𝑇 < 𝜉 𝑀 holds if 𝑇𝜉 < 𝑇 is satisﬁed. If 𝑎 − 𝑤 − 𝜏 ≤ Δ holds,
𝜉𝑇 < 𝜉 𝑀 is always satisﬁed as long as 𝑇 > 0. Moreover, 𝑇 𝑅𝑂
𝐻 is an inverse U-shaped curve in𝜉. We can conﬁrm that𝐼𝑇 𝑅𝑂𝐻 𝜉=𝜉𝑇 ⋛ 𝑇 𝑅 𝐻 ⇐⇒ 𝑇 ⋚ 𝑇1 ≡(𝑎 − 𝑤 + Δ − 𝜏) 2.
2(𝑎 − 𝑤 − 𝜏) 2(B-11)

If 𝑎 − 𝑤 − 𝜏 ≤ Δ and 𝑇 < 𝑇1 hold, or if 𝑎 − 𝑤 − 𝜏 > Δ and 𝑇𝜉 < 𝑇 < 𝑇1 hold, country 𝐻
prefers the oﬀshoring scheme and sets its input tariﬀ at 𝜉 = 𝜉𝑇 . Otherwise, 𝑇 𝑅𝐻𝐼 is always higher
than 𝑇 𝑅𝑂
𝐻 , irrespective of the level of 𝑇 and 𝜉. In this case, country 𝐻 prefers the inshoring
scheme and sets the input tariﬀ at 𝜉 ≥ 𝜉 𝑀 to induce the MNE’s inshoring.
After an FTA is formed, by (B-9) and (B-10), the optimal input tariﬀ becomes larger.
However, Article XXIV of GATT prohibits an increase in the external tariﬀ above the pre-FTA
level. Therefore, by replacing Δ with Δ′ ≡ Δ − 𝜉, we qualitatively obtain the same results as thebenchmark analysis.

7