Rules of origin and consumer-hurting
free trade agreements∗
Hiroshi Mukunokia

Hirofumi Okoshib,cAbstract
This study examines how the rules of origin (RoO) of a free trade agreement (FTA)
affect firms’ pricing strategies. The value-added criterion (VAC) of the RoO requires firms
to add more than a certain level of value within an FTA when firms use inputs originatingfrom outside the FTA. The VAC may work as a price floor, and the resulting increases inprices can benefit all firms if it induces an offshoring firm to manipulate its output price.
Meanwhile, a consumer-hurting FTA formation is possible, even if all firms make tariff-freeexports. Furthermore, such an FTA formation may worsen total welfare.
Keywords: Rules of origin; Free trade agreement; Pricing strategy
JEL classification: F13; F15; L11∗ We appreciate Carsten Eckel and Andreas Haufler for their comments and suggestions.

Hiroshi
Mukunoki acknowledges the financial support of the JSPS KAKENHI (Grant Numbers JP16H03620 and
JP17K03706). Hirofumi Okoshi acknowledges financial support from Deutsche Forschungsgemeinschaft(German Science Foundation, GRK1928).
a Gakushuin University, Faculty of Economics, Mejiro 1-5-1, Toshima-ku, Tokyo 171-8588, Japanb Corresponding author. University of Munich, Munich Graduate School of Economics, Seminar for
Economic Policy, Akademiestr. 1/II, D-80799 Munich, Germanyc Okayama University, Faculty of Economics, 3-1-1 Tsushima-naka, Kita-ku, Okayama, 700-8530, Japan

1

Introduction

Economic integration has boosted worldwide fragmentation and resulted in increased
international trade over the last few decades. One of the main vehicles of economic
integration is the proliferation of regional trade agreements (RTAs). As of September 2020,
there were 306 RTAs in force worldwide.1 Although trade liberalization through RTAs
seems to reduce trade costs, decrease consumer prices, and benefit consumers, the effect is
not as simple as it seems.2 Among others factors, it has been suggested that rules of origin(RoO), which are indispensable in implementing free trade agreements (FTAs), complicate
the effects of trade liberalization. If firms export their products by utilising preferential
tariffs in an FTA, then firms must comply with RoO and prove that the exported products
are produced within the FTA.
For instance, some empirical studies investigating the impact of FTAs have cast a
sceptical eye on the fruitfulness of trade liberalisation because of RoO. Conconi et al.
(2018) showed that the RoO used in NAFTA significantly reduce imports of intermediate
products from non-member countries relative to member ones, which implies that, in order
to meet the RoO, there is input relocation from more efficient input production countries
to less efficient ones. Takahashi and Urata (2010) and Hayakawa et al. (2013) found that
not all firms utilise FTA tariffs owing to RoO, which indicates that the impact of forming
an FTA is heterogeneous across firms and may be overestimated. Unfortunately, despite
the practical importance, little empirical investigation has been undertaken because thecomplexity of RoO makes it difficult to conduct empirical research on the impact of FTA
formation with RoO.3 Thus, identifying the impact of FTAs with a particular focus on RoO
remains an important research topic that could provide useful policy implications. This
paper theoretically tackles this issue and provides new insights that have been overlookedin the literature.
1 The cumulative number of RTAs in force was 83 in 2000, 137 in 2005, and 214 in 2010.
See
http://rtais.wto.org/UI/charts.aspx
2 Goldberg and Pavcnik (2016, p. 164) pointed out that ‘the world may not be as liberalized as it seems
and that failure to document significant effects of trade policies may instead be due to measurement andidentification challenges rather than the absence of such effects.
3 The existing research analysing the impact of FTA formations with RoO on prices include Cadot et al.
(2005) and Hayakawa et al. (2019).

1

Among the several methods for checking the origin of products, the valued-added
criterion (VAC) is the focus of this study. Let p denote the export value of the productand c denote the value of input materials not originating in the FTA; then, the VAC
typically requires that the value-added ratio,

p−c
p , be larger than a specified level.

Thismethod of calculating the value-added content is called the ‘transaction value method.’
Estevadeordal and Suominen (2003) reported that among the 87 FTAs they analysed, 68
employed this method, at least in a particular product category. Because the value-added
ratio is associated with an exporting firm’s pricing as well as its input sourcing, the VAC
may induce exporting firms to increase the value-added ratio by increasing their export
prices. These price increases, in turn, soften market competition and lead to increases in
the prices of other firms. In other words, the VAC can be a commitment device to increase
output prices.
Krishna and Krueger (1995) mentioned the possibility of the RoO-induced manipulationof output prices. They compared the transaction value method of the VAC with thecost-based method, by which the value-added content is calculated as the proportion of
the value of input materials originating in the FTA relative to the total value of input
materials. They suggested that firms prefer the transaction value method because a higher
price lowers the restrictiveness of the VAC. Some policy papers have also pointed out thatfirms are incentivised to manipulate output prices under the VAC. For instance, Falvey and
Reed (1998, p. 213) indicated that the VAC ‘. . . allows room for [the] manipulation of prices,’
and Reuter (2012, p. 214) also pointed out that ‘most rules of origin are on a percent-of-value
basis. . . . By overinvoicing the value added, the MNE can more easily meet a rule-of-origin
test and qualify for duty-free entry for its products into another country in the free tradearea’. These studies, however, did not analyse the welfare effects of FTAs when the VAC of
the RoO leads to the manipulation of output prices.4
Against this backdrop, this study examines how RoO affect firms’ incentives to set the
4 Although there is no direct empirical evidence that supports our arguments, some empirical studies

have found that firms in an FTA use significantly increase trade prices, and this increase is not necessarily
attributed to an increase in variable costs to comply with RoO. See, for example, Cadot et al. (2005) andHayakawa et al. (2019). These studies do not identify how the price-increasing effect of FTAs is attributed tothe manipulation of export prices to meet the VAC of RoO, but at least the price-increasing nature of FTAs isconsistent with our theoretical prediction.

2

prices of final goods in an oligopoly model with one input-offshoring firm and one firmusing the inputs produced inside the FTA. We demonstrate that there is a case in which
an FTA formation with RoO increases the prices of all goods, even when all firms export
tariff-free products within the FTA. This is because a firm that uses inputs outside the
FTA has an incentive to increase its product price to comply with the VAC of the RoO. In
other words, the firm can credibly commit to setting high export prices with RoO. Thus,
the VAC of RoO may work as a price floor, below which the firm using non-FTA inputs
cannot comply with the RoO. In response, the other exporting firm, which is a rival in
the product market, also increases its export prices. Because of this price-increasing effect,
more stringent RoO can benefit all firms. If the induced increases in export prices outweighthe tariff-elimination effect that should reduce the consumer price, the FTA formation will
hurt consumers even though tariffs against all firms are eliminated in the equilibrium.
In other words, an FTA with stringent RoO can be ‘consumer-hurting FTA’, rather than‘consumer-benefiting FTA’, in the sense that its formation decreases the consumer surplusof the liberalising countries. Furthermore, such stringent RoO may make an FTA formation
welfare reducing for those countries inside it, even compared to their welfare before the
FTA.
Extant theoretical studies have focused on how RoO change input sourcing (Ju andKrishna, 2005), the degree of market integration inside an FTA (Ishikawa et al., 2007),the productivity cut-off of exporting for users and non-users of FTA tariffs (Demidova
and Krishna, 2008), and the patterns of foreign direct investment (Mukunoki, 2017). Jinji
and Mizoguchi (2016a,b) have analysed the optimal choice of RoO. However, these studies
have not considered price manipulation to comply with RoO. The closest research to thecurrent study is another paper of ours, Mukunoki and Okoshi (2020), which focuses ontransfer-price manipulation of a multinational firm to comply with the VAC of an RoO.
This work complements the current study in that both focus on different levels of pricemanipulation.
The rest of the paper is organised as follows. Section 2 introduces our model and derives
the optimal strategy for firms. Section 3 explores the effects of FTA formation on consumer
surplus and the profits of firms. Section 4 examines the changes in total welfare. Section3

5 discusses the robustness and extensions of the baseline model. Section 6 concludes thepaper.

2Model

Two firms (I and O) produce differentiated products only in a home country (H) andsell them in country H and a foreign country (F). Countries H and F are potential FTA
partners. The reason why the two firms are located in country H is that we assume the costof production in country H is substantially low, enough to attract both firms to produce
their products in that location, because of low wages or the availability of labour with thespecific skills needed to produce these firms’ goods.5 For simplicity, we abstract from themarket in H as the primary focus of this paper is on the firms’ export-pricing strategies.
Even if we explicitly consider the market in country H, the qualitative nature of our results
remains unchanged. See Section 5.3 for further details.
The production of final products requires inputs made either in country H or incountries outside the two countries. One unit of input is transformed into one unit ofoutput at a constant marginal cost, which is normalised to 0.6 The input market is under
perfect competition, and the prices of the ‘inside inputs’ produced in country H are given
by c, while the prices of the ‘outside inputs’ produced outside the two countries are lower,
given by c − ∆ (∆ ∈ (0, c)). We assume that only firm O is an offshoring firm that can use
inputs imported from outside the two countries. Firm I always uses the inputs producedin country H because the firm lacks knowledge about foreign input markets and cannot
cover the cost of searching for appropriate suppliers.7
The indirect utility of the representative consumer in country F is V ( p I , pO ) = V̄ −a ( p I + pO ) +( p I )2 +( pO )2− bp I pO + Y, where V̄ is a positive constant,2

pi is the price of

product i manufactured by firm i ∈ { I, O}, b is the degree of product substitutability, and5 If the market size in country H is sufficiently large, the two firms will also choose to produce in country

H, though the market in H is not explicitly considered in our model.
6 In Section 5.1, we discuss the robustness of our results when firms incur a positive marginal cost.
7 Considering firm I’s procurement of the outside inputs complicates the model without changing themain results of the baseline model. See Section 5.4 for details.

4

Y is the consumption of the numéraire good. The utility maximisation yields:

xi = a − pi + bp j ,(1)

where xi is the demand for product i in country F, and j ∈ { I, O} ( j 6= i ).
A specific import tariff, τ, is imposed on both products by country F. There are no
tariffs on the inputs. The FTA formation removes τ, but zero tariff is applied only if firms
comply with RoO. Firm O may use the local inputs to meet the RoO, and thus, its marginal
cost is either c or c − ∆. Firm i’s profit is given by
Πi = ( pi − ci − λi τ ) xi ,(2)

where c I = c and cO ∈ {c, c − ∆}. λi is an index that takes zero if firm i meets the RoO
after an FTA formation and takes one otherwise.
For the RoO, we consider a VAC that requires the firms to add at least α fraction of
the value of the exported products within the FTA countries. Since firm I never uses theimported inputs, it always meets the VAC upon the FTA formation and enjoys tariff-freeaccess to country F.8 However, firm O needs to use either (i) the local inputs or (ii) theoutside inputs, and it sets its export price such that the following is satisfied:α ( pO ) ≡pO − ( c − ∆ )
≥ α.
pO

(3)

Because α ( pO ) increases with pO , even if firm O procures the outside inputs, α( pO ) exceeds
the required level (α) if pO is high enough.

Equilibrium
Given that (3) is not binding, the equilibrium price of good i is obtained by maximising (2):
(2 + b) a + 2ci + bc j + 2λi + bλ j τ( j 6 = i ),p̃i =4 − b2(4)

8 We abstract from the fixed costs of the RoO. The effect of introducing fixed costs on the results is

discussed in Section 5.2.

5The equilibrium sales of good i are xei , and the equilibrium profit and consumer surplus
f = V ( peI , peO ) − Y, respectively. By (4), we can
e i = ( xei )2 = ( pei − ci )2 and CS
become Πcharacterise the equilibrium in the following regimes.
• No Agreement (N): Before the FTA formation, a tariff is imposed on both goods (λ I =λO = 1). Firm O uses outside inputs cO = c − ∆. By substituting these parametersN =into (4), we obtain the equilibrium prices, denoted as pO(2+b)( a+c+τ )−2∆
and p NI =4− b2(2+b)( a+c+τ )−b∆.
4− b2

• Non-compliance (NC): After the FTA formation, firm O uses the outside input, andthe tariff is imposed only on firm O’s product. By substituting λ I = 0, λO = 1,(2+b)( a+c+τ )−2(∆−τ )4− b2(2+b)( a−c+bc)c)−b(∆−τ ). If τ satisfies τ ≥ τ exit ≡, firm O exits theand p NC= (2+b)(a+
I
4− b2
2− b2
NC =
and cO = c − ∆ into (4), the equilibrium price becomes pO

market.
• Input relocation (IR): After the FTA formation, firm O uses inside inputs to comply
IR =with the RoO. With λ I = λO = 0 and cO = c in (4), the equilibrium price is pO(2+b)( a+c)(2+b)( a+c)
and p IR
.
I =
4− b2
4− b2

Alternatively, suppose that firm O uses the outside inputs (cO = c − ∆) after the FTA
formation and still complies with the RoO. There are two sub-cases.
• Non-binding RoO (NB): Both firms set the unconstrained, optimal prices, which
NB =are given by substituting cO = c − ∆ and λ I = λO = 0 into (4), yielding pO(2+b)( a+c)−2∆a+c)−b∆and p NB
= (2+b)(4−. The VAC is non-binding if
I
4− b2
b2
NB − ( c − ∆ )pO(4 − b2 )(c − ∆)NBα ( pO ) ==1−≡ α NB ≥ α
NB(2 + b)( a + c) − 2∆pO

(5)holds.
• Binding RoO (B): If α NB < α holds, the RoO are binding and firm O sets the price,B , such that α p B = α is satisfied. The equilibrium prices become
pO
O
B
pO
=

(c − ∆)( a + c) b(c − ∆)and p BI =+.
(1 − α )22(1 − α )6(6)

If α is high enough to satisfy αexit ≡(2+b)( a−c+bc)+(2−b2 )∆, then firm O exits the market,(2+b) a+bc

where α NB < αexit holds.
Because (3) is binding, the prices in Regime B are different from the prices given by (4).
2B = α(c−∆) (2 + b ) a + bc − (c−∆)(2−b ) .
The profits of firm O in Regime B are given by ΠO
1− α2(1− α )The profits of firm I are given by Π BI = ( p BI − c)2 . The consumer surplus in Regime B is
B ) − Y.
given by CS B = V ( p BI , pO

The profits and consumer surplus under Regime ω ∈ { N, NC, IR, NB, B} are givenby Πiω and CSω , respectively. The total welfare of member countries is given by W ω ≡ω + Πω + TRω , where TRω is the tariff revenue under Regime ω. We have TR IR =CSω + ΠOITR NB = TR B = 0.

Firms’ choices of FTA use and input relocation
NB > max[ Π NC , Π IR ] holds. Thus, firm O
When the RoO are non-binding (α ≤ α NB ), ΠO
O
O

always chooses Regime NB, and both firms use the FTA without changing their pricing
and sourcing strategies. The FTA formation lowers the prices of all goods and benefits
consumers and all firms.
However, when the RoO are binding (α > α NB ), firm O chooses among Regimes NC, IR,
NC ≥ Π IR holds if τ ≤ ∆, whereas Π IR > Π NC holds if τ > ∆.9and B. We confirm that ΠOOOOWhen the tariff that is eliminated by complying with the RoO is lower than the additional
marginal cost from input relocation, firm O prefers Regime NC to Regime IR, and viceversa.
B takes an inverse U-shaped form in α ∈ [ α NB , αexit ]. Specifically,
We confirm that ΠO
2
B = Π NB at α = α NB , Π B takes the maximum at α = αmax ≡ (2+b) a+bc−(2−b )(c−∆) , andΠOOO(2+b) a+bc+(2−b2 )(c−∆)
B = 0 at α = αexit . This result implies that there is a unique cut-off level of the VAC,
ΠO
B > Π NC holds with α NB < α < α NC and Π NC ≥ Π B , with α NC ≤ α.
α NC , such that ΠOOOO
B > Π IR holds with α NB < α < α IR
Similarly, there is a unique cut-off level, α IR such that ΠOOIR ≥ Π B with α IR ≤ α. Note that α IR < α NC holds if τ > ∆ holds and α NC ≤ α IRand ΠOO
9 Given τ < τ exit such that Π NC > 0, we have Π NC − Π IR = ( ∆ − τ )OOO
NC T Π IR ⇐⇒ ∆ T τ.
that ΠOO

7

2 − b22(2τ exit − τ + ∆). This means

Case with 𝜏 > Δ
Regime 𝑁𝐵

Regime 𝐵

Regime 𝐼𝑅

𝛼
𝛼 #$

𝛼 !"

0

𝛼 %&'(

1Case with 𝜏 ≤ Δ
Regime 𝑁𝐵

Regime 𝐵

Regime 𝑁𝐶

𝛼
0

𝛼 !)

𝛼 !"

𝛼 %&'(

1

Figure 1: RoO and Equilibrium Regime
NC and Π IR are positive and independent of α, α NC < αexit
otherwise. Furthermore, as ΠOOand α IR < αexit hold. This means that firm O never exits the market of country F. The
following proposition summarises the choice of firm O.
Proposition 1. After an FTA formation, (i) the RoO are non-binding (Regime NB) if α ≤α NB holds; (ii) firm O complies with the RoO with price manipulation (Regime B) if α NB <α < min[α NC , α IR ] holds; (iii) firm O complies with the RoO with input relocation (RegimeIR) if ∆ < τ and α IR ≤ α hold; and (iv) firm O does not comply with the RoO (RegimeNC) if ∆ ≥ τ and α NC ≤ α hold.
The equilibrium choice presented in Proposition 1 is depicted in Figure 1.

3

Profit-enhancing RoO and consumer-hurting FTA

In the previous section, we characterise the regime that becomes the equilibrium outcome.
In this section, we examine how a formation of FTA affects firms and consumers. Under
Regimes NB, IR, and NC in the post-FTA equilibrium, the prices set by the firms and theirprofits are independent of the stringency of the VAC of the RoO, either because the VAC is
8

0

1

Figure 2: RoO and Profit of Firm O
non-binding or because firm O does not use the FTA tariff.
Under Regime B in Figure 1, however, firm O sets the price to satisfy the VAC, regardless
NB . Then, firmof how firm I sets the price of its product, and the price is higher than pO

I’s optimal reaction is to raise its own price. If α is not very high, these increases in prices
raise the profits of both firms. We have the following proposition.
Proposition 2. Under Regime B, the profits of all firms increase as the VAC becomes more
stringent for α ∈ [α NB , αmax ).
In other words, the RoO function as a price floor and become a commitment device
for firms to weaken price competition. If α is very high, however, the price increase is too
NB . That is, firm O’s profits have an inverse
large for firm O, and its profit will fall below ΠOU-shape, which is shown in Figure 2 in the case of ∆ ≤ τ. Since the pre-FTA profit of firm
N , lies somewhere between Π NC and Π NB , an FTA formation increases firm O’s profit
O, ΠO
O
O

unless α is very high. Firm I always gains from an FTA formation because it benefits not
only from tariff elimination but also from a price increase in the rival’s product in Regimes
B and IR. If firm O chooses Regime NC, only firm I benefits from tariff elimination.
9

𝐶𝑆𝑝!" > 𝑝!#𝑝$" > 𝑝$#𝐶𝑆 !"𝐶𝑆 #$ or 𝐶𝑆 !%
𝐶𝑆 !

𝐶𝑆 "

𝛼 !" 𝛼'𝛼"∗ 𝛼 #$ or 𝛼 !%1𝛼Figure 3: RoO and Consumer Surplus
Moreover, the price-increasing effect of binding RoO substantially changes the effects
of FTA formation on consumers. Under non-binding RoO (NB), input relocation (IR),or non-compliance (NC), an FTA formation is consumer-benefiting because it decreases
prices. It also benefits firms that use the FTA. However, the price-increasing effect of the
RoO might overturn the positive effect for consumers, as the following proposition states.
Proposition 3. When the post-FTA equilibrium regime is Regime B, there exists a unique
cut-off level for the VAC, α∗B , such that an FTA formation raises the prices of all
goods, benefits all firms, and hurts consumers for α > α∗B , even though all imports
become tariff free with the FTA. As long as the initial tariff is not very large, we haveα∗B ∈ (α NB , min[α NC , α IR ]) and a profit-increasing, consumer-hurting FTA becomes theequilibrium outcome if α∗B < α < min[α NC , α IR ]) holds.
Figure 3 shows the relationship between α and consumer surplus, where CSω is theconsumer surplus under Regime ω ∈ { N, NC, IR, NB, B}. In Regime B, the equilibrium
prices increase in α. The price of good O is higher than the pre-FTA level if α > α0 holds(α0 is defined in the proof of Proposition 3). The price increase of good I is smaller than
10that of good O because it is the second-order effect induced by the price increase of theother good. The price of good I also exceeds the pre-FTA level if α > α∗B holds. The cut-off
level of α, above which the FTA becomes consumer-hurting, lies somewhere between α0
and α∗B . Since the degree of the increase in the price of good O is larger than that of goodB > p N and p B < p N .
I, consumers can become worse off, even with pO
I
I
O

4

Welfare effects of FTA with RoO

Here, we explore the welfare effect of forming an FTA and how it is related to the stringencyof the RoO. In line with traditional models, it is easily confirmed that the total welfare ofmember countries is improved when the RoO change neither firm O’s pricing nor its input
sourcing. Thus, an FTA formation always improves total welfare inside the FTA if the
post-FTA equilibrium regime is Regime NB. However, as analysed, a stricter VAC of the
RoO can influence firm O’s pricing or input sourcing.
From Proposition 3, the overall impact of the FTA formation that leads to Regime B
on total welfare is not obvious, and it reduces the total welfare of member countries with
α > α∗B , even though all imports become tariff free. Even if α < α∗B holds and the FTA
formation decreases the price of good I, it can reduce total welfare because the negative
effect of an increase in the price of good O can dominate the positive effect of a decrease inBBN∗
the price of good I. Because we confirm that ∂W∂α < 0 holds, W < W at α = α B means
W∗
B
N
that there is a cut-off level of the VAC, αW
B (< α B ), such that W < W if and only if α > α B
10holds under Regime B. The level of αW
B is depicted in Figure 3 in the case of ∆ ≤ τ.

In an extreme case with b = 0, there are no interactions between firms. In this case, anincrease in pO does not affect the equilibrium level of p I , and an FTA formation worsens
welfare only if α is sufficiently large (shaded area of Regime B in Figure 4). As b becomes
higher, an increase in pO increases the equilibrium level of p I , and an FTA formation ismore likely to be welfare reducing. The following proposition summarises the welfare
effect when the post-FTA regime is Regime B.
ω
2 B
10 From (5), ∂α NB > 0 is obtained. Furthermore, ∂Π̃O > 0 and ∂ Π̃O > 0 implies α∗ is increasing in b. We
∂b
∂b
∂α∂b
∂Π B
∂Π B
∂2 Π B
confirm that (∂α)O2 < 0, holds for α ∈ [α NB , αexit ], where ∂αO > 0 at α = α NB and ∂αO < 0 at α = αexit . The

detailed calculation is available upon request.

11

1

Regime NB

Regime B

0

Regime IR
1

Figure 4: RoO and Welfare
Proposition 4. When the post-FTA equilibrium regime is Regime B, there exists a uniqueW
cut-off level of the VAC, αW
B , such that an FTA formation worsens total welfare if α B < α <min[α NC , α IR ] holds.
We should also note that even if the post-FTA equilibrium regime is either Regime IR
or Regime NC, an FTA formation may worsen welfare. Regime IR has a similar thresholdWbW
IR such that the FTA worsens the total welfare if b ∈ ( b IR , 1]. This area is depicted in

Figure 4 as the shaded area in Regime IR.11 If τ is only slightly greater than ∆, then the
FTA formation is always harmful for the member countries (see the proof of Proposition 5for details). This is because the input relocation increases the marginal cost of productionof firm O with limited declines in consumer prices. Therefore, an FTA that leads to Regime
IR results in welfare reduction in this case.
Proposition 5. When the post-FTA equilibrium regime is Regime IR, if the initial tariff level
2IRN
11 We always have ∂ (W −W )
2
(
∂b
)
p

τ≥

< 0 and (W IR − W N )|b=1 < 0, and (W IR − W N )|b=0 > 0 also holds if{2( a − c) + ∆}{2( a − c) + 7∆} − {2( a − c) + ∆} > 0.

12

is large, there exists a unique cut-off level of b, bW
IR (∈ (0, 1)), such that an FTA formation
worsens total welfare if b ∈ (bW
IR , 1) holds. If the initial tariff level is small, an FTA formation
always worsens total welfare.
Similarly, if the post-FTA equilibrium outcome is Regime NC, then there also exists
a unique level of product substitutability, bW
NC , such that an FTA formation reduces total
12 In Regime NC, the production cost of firm O is lower than thatwelfare for b ∈ (bW
NC , 1].

of firm I. Because the tariff is eliminated only for good I in this regime, the productionand exports of good O decrease while those of good I increase. This ‘trade diversion’ effectcauses inefficiency, so an FTA can be welfare reducing. As the two goods become closer
substitutes, the substitution effect between the two goods becomes larger, and an FTA that
leads to Regime NC is more likely to become welfare reducing.
Proposition 6. When the post-FTA equilibrium regime is Regime NC, there exists a unique
cut-off level of b, bW
NC (∈ (0, 1)), such that an FTA formation worsens total welfare if b ∈( bW
NC , 1) holds.

5

Discussion

Our benchmark model has employed some key assumptions to simplify the model. First,
we assume that only one of the two firms (firm O) is able to access cheaper offshore
inputs, even though firms have the same technology to produce final goods. As both
existing theoretical and empirical studies provide evidence that offshoring firms are moreproductive than onshoring firms, it is natural to introduce cost differences among them.
Second, we assume that the marginal cost of transforming inputs into final goods is zero.
One may question the assumption as it means that firm O re-exports the product at priceω > c without adding any value. Third, we abstract from the fixed costs of the RoO.
pO
O

It is believed that one of the reasons why not all firms use FTA tariffs is the bothersome
documentation process.13 Fourth, we did not consider the market in country H. Finally, we
2NCN
12 Since ∂ (W −W ) < 0, (W NC − W N )|NC − W N )|W
b=0 > 0, and (Wb=1 < 0 hold, b NC always exists in this(∂b)2

range.
13 For example, Francois et al. (2006) estimated that the tariff-equivalent costs of using preferences underthe ACP-EU Partnership Agreement ranged between 4% and 4.5%.

13

assume that only one of the two firms can use the inputs imported from countries outside
the FTA.
Here, we show that qualitative nature of our results remains unchanged if we relax
these assumptions.

5.1

Labour cost and productivity difference

Let us modify the model by introducing labour to transform inputs into final goods.
Both firms can hire labour from a perfectly competitive labour market at wage w, but
the unit-labour requirement is different. Let li be the unit-labour requirement of firm i, andl I > lO holds as we suppose that firm O is more productive. Then, the marginal cost forfirm i is rewritten as Ci = ci + wli . The term wli can also be interpreted as the input costsof the domestic materials.
By replacing ci with Ci in the benchmark model, we can obtain the optimal prices. As
NB
NB = pO −(c−∆) ,the VAC is calculated as α pO
p NB
O

α

NB

(4 − b2 )(c − ∆)
= 1−
(< 1)
(2 + b)( a + c) − 2∆ + (2 + b)wlO + bw(l I − lO )(7)

NB , itis derived. Because including the labour cost and productivity difference increases pO

raises the level of α NB and expands the range of α that realises Regime NB. Intuitively, since
the labour costs contribute to piling up the regional value-added as well as an increase in
the price–cost margin, it becomes easier for firm O to meet the VAC of the RoO, and it
widens the range of α in which the RoO is non-binding. For the same reason, including
labour costs should increase α IR and α NC because the adjustment of the export price needed
to meet the VAC of the RoO is smaller with the domestic labour costs, and it becomes easierfor firm O to comply with the RoO in Regime B.
For α ∈ (α NB , min[α IR , α NC ]), Regime B becomes the equilibrium outcome and changes
in α affect firm O’s pricing and profits as those in the benchmark model do. Therefore,
the main results remain unchanged with this alternative setup. The benchmark analysis
corresponds to the case with wlO = wl I = 0.
Furthermore, as the difference in productivity (l I − lO ) increases, α NB , α IR , and α NC
14

increase, and it becomes easier for firm O to comply with the RoO. This property is
consistent with Demidova and Krishna (2008), which suggests that only firms whose
productivity is above a cut-off level invoke RoO and use FTA tariffs.

5.2

Fixed costs of meeting RoO

Let us consider a case where firms must bear the fixed costs of meeting RoO. Firms incur
fixed costs only when they apply for FTA tariffs. In Figure 2, the curves representing the
profits of firm O under Regimes NB, B, and IR are shifted downward by the fixed costs,
but the curve under Regime NC remains unchanged.
The presence of fixed costs makes the use of FTA tariffs less attractive. For instance,
NC > Π IR can hold even if τ > ∆ holds and firms are more likely to choose
ΠOO

non-compliance with the RoO. In addition, an FTA formation is more likely to bewelfare-reducing because the fixed costs shrink the profit gained from the FTA formation.
Furthermore, if we consider the productivity difference described above, only firm O
complies with the RoO and uses the FTA tariff in equilibrium.

However, Regime B

will remain as an equilibrium outcome, and the qualitative nature of our results remains
unchanged as long as the fixed costs are not very large.

5.3

Market in country H

For simplicity, we ignore the market in H, as the primary focus of this paper is on firms’
export pricing strategies. When the post-FTA equilibrium is Regime NB, B, or NC, theeffects of an FTA formation are the same as the baseline model, even if we consider themarket in country H. This is because firm O’s marginal cost remains c − ∆, and the prices,
consumer surplus, and profits earned in country H are independent of the FTA formation
as long as the two markets are segmented and firms can make independent decisions ineach market.
When the post-FTA equilibrium is Regime IR, however, an FTA formation changes themarket outcomes in country H because it changes firm O’s marginal cost from c − ∆ to c.
The cost increase of firm O decreases firm O’s profits earned in country H, decreases

15

consumer surplus in country H by increasing the equilibrium prices, and reduces thewelfare in country H, although the profits of firm I in country H increase. These effects
make a consumer-hurting, welfare-reducing FTA more likely, and they make firm O’s input
relocation less likely. Even if we take these additional effects into account, the qualitative
nature of our results remains unchanged.

5.4

Both firms can procure inputs outside the FTA

We have assumed that only firm O can procure outside inputs. Given that the outside
inputs are supplied in a perfectly competitive market, there will be a case in which both
firms can procure outside inputs. In this case, firm I chooses whether to comply with the
RoO. If firm I does, it either manipulates its output price or changes the sources of inputs
from countries outside the FTA to countries inside the FTA when the VAC of the RoO isthe binding constraint.
The modified model should share the basic properties with the baseline model, suchas the effects of an increase in α on the prices, profits, and total welfare. However, eachfirm’s choice of regimes will be more complicated. For instance, suppose initially, the VAC
is non-binding for both firms and each firm operates under Regime NB. Then, supposethat an increase in α forces one of the two firms to manipulate its output price to meet the
VAC. Because the price commitment of one firm increases the price set by the other firm, it
becomes easier for the other firm to meet the VAC, and it may remain in the NB regime.
This implies that the cut-off levels for firm i (i ∈ { I, O}), αiNB (s j ), αiIR (s j ), and αiNC (s j ),depend on the rival’s choice of regime, s j ∈ { NB, B, IR, NC } (j ∈ { I, O}, j 6= i). For instance,
the above discussion suggests that αiNB ( NB) < αiNB ( B) holds. If we have αiNB ( NB) < α <αiNB ( B), the two firms make heterogeneous choices and one firm chooses Regime B and theother firm chooses Regime NB. Irrespective of whether one firm or both firms are under
Regime B. However, an increase in α will have qualitatively the same effects on the prices,
profits, and total welfare. Therefore, the main results remain unchanged.

16

6Conclusion

This study has revisited the welfare effects of an FTA when exporting firms must meet a
VAC to comply with RoO. When the value-added threshold is neither very low nor very
high, a firm manipulates its output price to satisfy the VAC. In this case, the RoO work
as a price floor and soften product market competition. The resulting increase in prices
can hurt consumers while benefiting firms. Because of this price-increasing effect, an FTA
formation with RoO might hurt consumers, even though all trade within the FTA is tariff
free. Moreover, the total impact of the conflicting effects may be negative if the required
threshold is sufficiently high. Furthermore, even if all firms keep the input procurementfrom efficient countries and enjoy tariff-free trade, the similarity of goods and the degreeof restriction of the VAC play core roles in explaining whether the FTA is harmful or not.
These results suggest that a VAC of RoO can transform a consumer-benefiting (orwelfare-improving) FTA into a consumer-hurting (or welfare-reducing) FTA. The RoO
of FTAs should be designed such that they do not induce firm manipulations of output
prices. One policy option is to employ the net-cost method, by which a calculation of thevalue-added ratio is unrelated to output prices.
There is room for further research. This study has assumed that the prices of inputs
are exogenously given, but it would be interesting to consider how the VAC changes input
prices. Another possible extension is to consider firms’ location choices of inside or outside
the FTA. The development of empirical analysis is left as the most important future task.

Appendixes
Proof of Proposition 3
B and p B are increasing in α, while p N and p N are independent of α. We haveBy (6), both pO
I
I
O

B
N
pO
− pO

p BI − p NI
4 − b2 (c − ∆) − (1 − α) {(2 + b) ( a + τ ) + 2(c − ∆) + bc}=,(4 − b2 ) (1 − α )b 4 − b2 (c − ∆) − (1 − α) {(2 + b) ( ab + 2τ ) + 2b(c − ∆) + b2 c}=.
2 (4 − b2 ) (1 − α )17B > p N and p B > p N hold if and only if
By these equations, pOIIO
4 − b2 ( c − ∆ )α > α ≡ 1−and
(2 + b) ( a + τ ) + 2(c − ∆) + bc
b 4 − b2 ( c − ∆ )∗α > αB ≡ 1 −(2 + b) ( ab + 2τ ) + 2b(c − ∆) + b2 c0hold, respectively.

(4− b2 ) ( c − ∆ ) τ
Because we have α∗B − α0 = {(2+b)(a+τ )+2(c−∆)+bc}{(2+b)(ab+2τ )+2b(c−∆)+b2 c} > 0, both
B > p N and p B > p N hold if and only if α > α∗ holds. There is a case where this cut-off
pO
B
I
I
O

level, α∗B , satisfies α∗B < min[α NC , α IR ], implying a price-increasing FTA when Regime B
becomes the equilibrium outcome. For instance, we know that αmax always satisfies α NB <αmax < min[α NC , α IR ]. If we compare α∗B and αmax , we have
αmax − α∗B =b3 {(2 + b) a + bc − (2 − b2 )(c − ∆)} − 4(2 + b)(2 − b2 )τ
.
{(2 + b) ( ab + 2τ ) + 2b(c − ∆) + b2 c}{(2 + b) a + bc + (2 − b2 ) (c − ∆)}Thus, as long as the tariff satisfies τ <b3 {(2+b) a+bc−(2−b2 )(c−∆)}, αmax > α∗B holds, and we4(2+b)(2−b2 )have α∗B < min[α NC , α IR ] because αmax < min[α NC , α IR ] always holds.
Proof of Proposition 5
The welfare comparison between Regime IR and N yields:
W IR − W N =2(1 − b)(2 + b)2 Γ − ∆{2a(2 + b)2 (3 − 2b) + (12 − 9b2 + 2b4 )∆}.
2(2 − b )2 (2 + b )2

where Γ ≡ τ 2 + {2( a − c + bc) + ∆(1 − b)}τ + ∆(3 − 2b)c. We can confirm that2(τ − ∆){2( a − c) + τ + ∆} − ∆{2( a − c) + ∆ − 2τ },8−∆(18a + 5∆)(W IR − W N )|b=1 =< 0, and18−2(1 + b)(2 + b)4 τ 2 + Φ∂2 (W IR − W N )
=
< 0,
(∂b)2
(2 − b )4 (2 + b )4

(W IR − W N )|b=0 =where Φ ≡ −2τ {2b2 (2b3 + 15b2 + 40b + 40)c + 32( a − c) + ( a − ∆)b2 (2b3 + 15b2 + 20b +20)} − 2∆{3c(16 + 16b − 8b2 − 16b3 − 7b4 − b5 ) + 6b2 (7b2 + 8) + 16( a − ∆)} + τ {−12∆(τ −18

∆) − 20∆τ − 6ab2 τ (b2 + 8b + 24)} − 2ab{96τ − (40b + 40b2 + 15b3 + 2b4 )∆} < 0 (∵ τ > ∆).
The sign of (W IR − W N )|b=0 is ambiguous, and it is increasing in τ. (W IR − W N )|b=0 >p0 holds if and only if τ̃ ≡ {2( a − c) + ∆}{2( a − c) + 7∆} − {2( a − c) + ∆} < τ holds.
IR > W N holds forIn this case, there exists a unique level of b, bW
IR ∈ (0, 1), such that W
IR = W N holds at b = bW , and W IR < W N holds for b > bW .
b < bWIR , W
IR
IR
IR

N

Moreover, ∂W ∂b−W |b=0 ≥ 0 holds if and only ifτ̂ ≡∆( a + 2c)< τ.
2c − ∆

By substituting τ = τ̂ into (W IR − W N )|b=0 , we get(W IR − W N )|τ =τ̂, b=0 =∆{2(4c − ∆) a2 − 8(2c2 − 4∆ + ∆2 ) a + 8c2 − 12∆c2 + 14∆2 c − 3∆3 },8(2c − ∆)2which takes a minimum at a = ã ≡W N )|τ =τ̂, b=0, a=ã =2(c2 −4∆c+∆2 ), and the minimum level is given by (W IR −4c−∆∆(2c−∆)2 (18c−5∆)
4c−∆

IR

N

> 0. This implies that τ̃ < τ̂ and ∂W ∂b−W |b=0 < 0whenever (W IR − W N )|b=0 < 0 holds. Therefore, if τ ≤ τ̃ holds, we have W IR ≤ W N for
any b ∈ [0, 1).

Proof of Proposition 6
The welfare gains from the FTA formation under Regime NC are computed as
W NC − W N =τ [2{(4 − 3b2 − b3 ) a − 2(2 − b2 )b∆} − 2(1 − b)2 (2 + b)2 c + (4 − 3b2 − 2b3 )τ ].
(2 − b )2

We have[2( a − c ) + τ ] τ> 0,
8(4∆ + τ )τ< 0, and(W NC − W N )|b=1 = −18∂2 (W NC − W N )
Θτ
=
−
< 0,
(∂b)2
(2 − b )4 (2 + b )4
(W NC − W N )|b=0 =where Θ ≡ (2b5 + 9b4 + 64b3 + 56b2 + 96b + 16)τ + (4b3 + 30b2 + 86b + 80)b2 c + 32( a − c) +2b{(48 + 56b + 32b2 + 9b3 + b4 ) a − 2(20 + b2 )b2 ∆} > 0. Thus, there exists a unique cut-off
19

NC > W N holds for b < bW , W NC = W N holds atlevel of b, bW
NC
NC ∈ (0, 1), such that W
NC < W N holds for b > bW .
b = bW
NC , and W
NC

20

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