Agreements on product standards in a three-country model ofinternational oligopoly

Akihiko Yanase a, Hiroshi Kurata b, and Yaqiong Lin ca,cNagoya University

Tohoku Gakuin UniversitybVery preliminary. Do not quote without authors’ permission.

Abstract
This paper extends the comparative institutional analysis of agreements on productstandards developed by Costinot (2008, Journal of International Economics) to a threecountry world, in which there are two “member” countries of an agreement on standards anda “non-member” country. We examine the comparative performance of two principles; oneis a “National Treatment” (NT) principle, and the other is a principle of “Mutual Recognition”(MR). We consider an international oligopoly in which the traded goods generate
consumption externalities. We show that for low levels of externalities, the member
countries prefer MR to NT, while they prefer NT to MR for high levels of externalities.
Assuming the member countries conclude a standard agreement that yields higher benefits,
the non-member country becomes better off only when the member countries choose NT.
We also discuss whether the bilateral agreement on standards can be a “building block” ora “stumbling block” to a multilateral agreement by all three countries.
Keywords: International oligopoly; Consumption externalities; Product standards; National
treatment; Mutual recognition.
JEL classifications: F12; F13; F15; F18

11. Introduction
Agreements on non-tariff barriers have become increasingly important in recent times. As a resultof WTO negotiation and the growth of preferential trade agreements (PTAs), tariffs have become
sufficiently low, reducing tariffs is not so effective. Non-tariff barriers, many previously treated as
domestic regulations, often differ from country to country. As a result, such differences in non-tariffbarriers tend to disadvantage foreign firms (Estevadeordal, Suominen, and Teh, 2009; Maskus, Otsuki,
and Wilson, 2005). Therefore, recent PTAs tends to contain provisions on non-tariff barriers.1
In this paper, we focus on product standards in the non-tariff barriers. Product standards are set
to protect the health and safety of the public, and we have often witnessed the difference from country
to country. The WTO has two agreements concerning standards: the agreements on technical barriers
to trade (TBT) and sanitary and phytosanitary standards (SPS), to control the impact of countryspecific product standards on trade. In addition, recent PTAs include provisions on the TBT and SPS
Agreements. For example, Hofmann, Osnago, and Ruta (2017) point out that about 50% of the total
PTA in 2015 in force includes the TBT and SPS agreements.2
Despite the growing importance of product standards, the economic benefits of product standards
have not been understood. In particular, concerning agreements on product standards, Costinot (2008)
develops the two-country model to compare the performances of two principles on product standards:
national treatment (NT) and mutual recognition (MR). He focuses on the externalities of trading
products and shows that the NT is preferred to the MR when the volume of trade with high externalities
is large. However, analysis in the two-country model cannot focus on the effects of the agreements on

We call agreements with the tariff and non-tariff measures ``Deep Trade Agreement'' (Matoo,
Roche, and Ruta, 2020).
2
The numbers of agreements including the SPS and TBT are 152 and 147, respectively, out of the1

total number of PTAs in 2015 is 279 (Hofmann, Osnago, and Ruta, 2017).
2

product standards to the overall economy, including non-member countries. Furthermore, we cannot
consider whether the bilateral agreements can be "building block" or "stumbling block" to themultilateral agreements. On the other hand, Yanase and Kurata (2022) focus on the effects of the FTAs
with agreements on product standards in a three-country model. They demonstrate that the more
stringent product standards may or may not benefit the member countries while it is beneficial for the
non-member country. Takarada et al. (2020) set up a three-country model and examine if theharmonization of product standards expands from regional to multinational. They show that regional
harmonization is a "building block" when the negative externality is quite transboundary. Althoughthese studies consider the three-country model to examine the economic effects of agreements on
product standards, they focus only on the harmonization of product standards.
This paper extends Costinot's comparative analysis of the agreements to the three-country model.
We consider two member countries and one non-member country and focus on a situation where theconsumption of goods generates a negative externality. Product standard controls the externality: highstandard reduces the negative externality more. As Costinot (2008), we compare the performances of
the NT or the MR in the model. We also examine whether the member countries of the bilateralagreement prefer to conclude the multilateral agreement.
We demonstrate that the agreement on product standards can be preferable or not preferable formember and non-member countries, depending on the degree of the negative externality. In particular,
for member countries, the MR is reasonable for the low degree of externality, while the NT isreasonable for the high degree of externality. For the non-member countries, both MR and NT isreasonable for the low degree of externalities, while only NT is reasonable for the high degree ofexternalities. Furthermore, we find some externalities where the agreement of product standards isbeneficial for both member and non-member countries.

3

Our analysis is related to the literature on product standards. Fischer and Serra (2000), Sturn(2006), and Ishikawa and Okubo (2011) conduct their analysis in a two-country model. Takarada andKawabata (2021) set up a three-country model to examine the effects of the harmonization of productstandards. They do not focus on the MR. Our analysis is also related to the literature on the WTO
principle (Krishna, 1998; Bagwell and Staiger, 2001; Orneras, 2005, 2007; Saggi and Yildiz, 2010;Limão and Saggi, 2013). These studies consider agreements to reduce the tariff and not consider
agreements on product standards. Our study examines the effects of agreements on product standards
in a three-country model and provides new insight into these research streams.
The remainder of the paper is as follows. In Section 2, we set up a basic model. Then, section 3
considers the bilateral agreement and policy game with the NT and the MR. We examine the welfare
effect of the bilateral agreement on the member and non-member countries. In Section 4, we discuss
the possibilities of extending the bilateral agreement to the multilateral agreement. Finally, in Section
5, we provide brief concluding remarks.

2．The Model
2.1. The economic environment
There are three identical countries, A, B and C, with one firm per country, a, b and c, all producing
a homogeneous good. There are two types of good, H and L, that the firms can produce, distinguishedby production cost and the level of consumption pollution. For H type of good, firms’ unit production
cost is 0, but 𝜃 units of pollution are emitted per unit of consumption. For L type of good, unit
production cost is 𝑐, and no consumption pollution is generated. Pollution damage occurs at thelocation of consumption.
There is a continuum of consumers of measure one. Each consumer can buy at most one unit ofproduct. For consumers, both types of products are indifferent. Consumers are heterogeneous and4utility of type 𝑣 consumer living in country J (J=A, B, C) is given by𝑢(𝑣) = {𝑣 − 𝑝 − 𝜑𝐽
−𝜑 𝐽

if she buys the productif she buys nothing,(1)

where 𝑣 is uniformly distributed with support [0,1], p is the price of the good, and 𝜑 𝐽 is the pollution
damage.
Since consumers of type 𝑣 ≥ 𝑝 will buy the good, the demand for the product in country J is1

𝑄𝐽 = ∫𝑝 1 ∙ 𝑑𝑣 = 1 − 𝑝(2)From (2), the inverse demand in country J isP(𝑄𝐽 ) = 1 − 𝑄 𝐽(3)Pollution damage in country J depends on the consumption in each country:
𝜑 𝐽 = ∑𝑗=𝑎,𝑏,𝑐 𝜃𝑗𝐽 𝑞𝑗𝐽 ,(4)

where 𝑞𝑗𝐽 is firm j’s sales in country J and 𝜃𝑗𝐽 ∈ {0, θ} is the pollution damage per unit ofconsumption of firm j’s product.
Firm j’s profit earned in country J’s market (j=a, b, c and J =A, B, C) is given by
𝜋𝑗𝐽 = [𝑃𝐽 (𝑄𝐽 ) − 𝑐𝑗𝐽 ] 𝑞𝑗𝐽 = (1 − 𝑄𝐽 − 𝑐𝑗𝐽 )𝑞𝑗𝐽 ,(5)

𝐽where 𝑐𝑗 ∈ {0, c} is the unit production cost of the good produced in firm j and consumed in country𝐽

J and 𝑄 𝐽 = ∑𝑖=𝑎,𝑏,𝑐 𝑞𝑖 is the total consumption in country J. Tariffs or transport costs are notconsidered in this model.
𝐽

Country J’s government can regulate its market by setting standards 𝜎𝑗 ∈ {𝐻, 𝐿} for each firm j’s
product. (j= a, b, c). Each firm can sell in country J’s market if and only if its product’s type satisfies𝐽

the minimum quality standard. If 𝜎𝑗 = 𝐻, firm j can sell both H and L type, but firm will choose H
type because the unit production cost is 0. If 𝜎𝑗𝐽 = 𝐿, firm j must produce and sell the production of
L type.
The standards setting game with Cournot competition is represented by the following two stage

5

game:
Stage 1: Governments simultaneously choose their standards policy.
Stage 2: After observing the governments’ standards, firms simultaneously decide which type ofthe good and what quantity to sell in each market.
We solve the game by backward induction to derive the subgame perfect Nash equilibrium.

2.2. Cournot-Nash equilibrium
In stage 2, given the standards policy in the respective countries, the firms play Cournot game ineach country’s market. In country J’s market, firm j chooses 𝑞𝑗𝐽 to maximize 𝜋𝑗𝐽 = (1 − 𝑞𝑗𝐽 −∑𝑖≠𝑗 𝑞𝑖𝐽 − 𝑐𝑗𝐽 )𝑞𝑗𝐽 , taking 𝑞𝑖𝐽 , 𝑖 ≠ 𝑗, as given. From the first-order conditions for profit maximization,
the Cournot-equilibrium outputs can be obtained as 𝑞𝑗𝐽 = (1 − 3𝑐𝑗𝐽 + ∑𝑖≠𝑗 𝑐𝑖𝐽 )/4, 𝑗, 𝑖 = 𝑎, 𝑏, 𝑐. The
equilibrium sales and price in country J are then derived as 𝑄 𝐽 = (3 − ∑𝑗=𝑎,𝑏,𝑐 𝑐𝑗𝐽 )/4 and 𝑃(𝑄𝐽 ) =(1 + ∑𝑗=𝑎,𝑏,𝑐 𝑐𝑗𝐽 )/4, respectively.
We regard the governments’ objective function for the policy game in stage 1 as the social welfare
in the respective countries, which is the sum of consumer surplus, which can be calculated as 𝐶𝑆𝐽 =(𝑄𝐽 )2 /2 − 𝜑 𝐽 , and the domestic firm’s total profits from domestic sales and exports, which can be2

represented by 𝜋𝑗 = ∑𝐽=𝐴,𝐵,𝐶 𝜋𝑗𝐽 = ∑𝐽=𝐴,𝐵,𝐶(𝑞𝑗𝐽 ) . In light of the Cournot-Nash equilibrium outputs,
the equilibrium social welfare in country J is
𝐽

𝑆𝑊𝐽 =

(3−∑𝑗=𝑎,𝑏,𝑐 𝑐𝑗 )232− ∑𝑗=𝑎,𝑏,𝑐 𝜃𝑗𝐽𝐽𝐽

1−3𝑐𝑗 +∑𝑖≠𝑗 𝑐𝑖
4

J=A, B, C.
Throughout this paper, we put the following assumption.
Assumption. 0 < 𝑐 < 1/5

6+ ∑𝐼=𝐴,𝐵,𝐶(1−3𝑐𝑗𝐼 +∑𝑖≠𝑗 𝑐𝑖𝐼 )2
16

,

(6)

2.3. Noncooperative policy equilibrium without agreements
As a benchmark for the subsequent analysis, we consider outcomes under which the governments
noncooperatively determine their standards without making any agreements among countries. In theabsence of agreements on standards, in stage 1, country J’s government chooses the standards for the𝐽𝐽𝐽

products consumed in that country, (𝜎𝑎 , 𝜎𝑏 , 𝜎𝑐 ), to maximize country J’s social welfare (6), taking theother countries’ standards (𝜎𝑎𝐼 , 𝜎𝑏𝐼 , 𝜎𝑐𝐼 ), 𝐼 ≠ 𝐽, as given. There are three regimes for governments tochoose from:3
1. Full regulation (FR): (𝜎𝑎𝐽 , 𝜎𝑏𝐽 , 𝜎𝑐𝐽 ) = (𝐿, 𝐿, 𝐿)
2. No regulation (NR): (𝜎𝑎𝐽 , 𝜎𝑏𝐽 , 𝜎𝑐𝐽 ) = (𝐻, 𝐻, 𝐻) for 𝐽 = 𝐴, 𝐵, 𝐶;
3. Discrimination (D): ( 𝜎𝑎𝐴 , 𝜎𝑏𝐴 , 𝜎𝑐𝐴 ) = (𝐻, 𝐿, 𝐿) , ( 𝜎𝑎𝐵 , 𝜎𝑏𝐵 , 𝜎𝑐𝐵 ) = (𝐿, 𝐻, 𝐿) , and (𝜎𝑎𝐶 , 𝜎𝑏𝐶 , 𝜎𝑐𝐶 ) =(𝐿, 𝐿, 𝐻)
Since export profits depend only on other countries’ standards, country J chooses its standards inorder to maximize the domestic welfare, which is the sum of the consumer surplus and the domestic
firm’s profit from domestic sales. Take country A as the example, the domestic welfare is:
𝐶𝑆 𝐴 + 𝜋𝑎𝐴 =(3−∑𝑗=𝑎,𝑏,𝑐 𝑐𝑗𝐴 )232− ∑𝑗∈𝑎,𝑏,𝑐 𝜃𝑗𝐴

1−3𝑐𝑗𝐴 +∑𝑖≠𝑗 𝑐𝑖𝐴4+(1−3𝑐𝑗𝐼 +∑𝑖≠𝑗 𝑐𝑖𝐴 )2
16(7)

By comparing domestic welfare under the respective strategies for standards policy, we obtain thefollowing proposition.

Proposition 1. In the unconstrained noncooperative standards game without any international
agreements, the equilibrium standards regime implies that:

Strictly speaking, the discrimination regime should be interpreted as “negative discrimination”
because the government discriminates against the foreign firms by setting more stringent standards.
We may consider another type of discriminatory standards regime, namely, “positive discrimination”,
which the government sets less stringent standards on foreign products than the domestic product; forcountry A, positive discrimination means (𝜎𝑎𝐽 , 𝜎𝑏𝐽 , 𝜎𝑐𝐽 ) = (𝐿, 𝐻, 𝐻). However, we can verify that under
the assumption that 𝑐 < 1/5, positive discrimination will never be an equilibrium outcome. Thus,
throughout this paper, we regard the negative discrimination case as the discrimination regime.
3

7

No regulation for 0 ≤ 𝜃 < 𝜃 𝑈 ;Negative discrimination for 𝜃 𝑈 ≤ 𝜃 < 𝜃̅ 𝑈 ;Full regulation for 𝜃̅ 𝑈 ≤ 𝜃,𝑐(1−3𝑐)𝑐(18+𝑐)where 𝜃 𝑈 ≡ 4(1−𝑐) and 𝜃̅ 𝑈 ≡ 8(1+2𝑐) .

(Proof) See the Appendix.

Intuitively, when the level of pollution is very small, no regulation could help country A gets biggest
outcome. When the level of pollution gets bigger, country A has incentives to use discrimination
strategy to reduce pollution emitted by the consumption of product produced in country B and C.
Besides country A could also shift the profit from exporters to national producers. When the level ofpollution is too big, country A must use full regulation to reduce the pollution.

3. Bilateral Agreements on Standards Policy
In this section, we consider a situation in which two of the three countries, namely countries A andB, sign an agreement that requires a commitment on rigid rule regarding their standards policy. We
consider two rules for the standards agreements. One is “national treatment (NT)” and the other is“mutual recognition (MR)”. NT means that same standards should be applied to both domestic productand the product imported from the member country in the agreement. MR means that control over the
standard on exported product is transferred from the importer to the exporter member country,
meaning that the exporter country sets the standards, and the importer country has to accept it.
Although there is a bilateral agreement on standards policy, we assume that all countries choose
standards noncooperatively. That is, member countries A and B, facing a constraint imposed by NT
or MR, determine their respective standards to maximize their own welfare. Country C, which is an8

outsider of the agreement, also determines its standards noncooperatively. Because country C’s
optimal standards are independent of the other countries’ standards, Proposition 1 holds for country Ceven in the presence of bilateral agreements.

3.1. Policy game under NT
As in the unconstrained non-cooperative case, export profit only depends on the foreign standards
under NT. Therefore, for country A and B, the government’s problem in stage 1 is to decide on thestandards policy to maximize the domestic welfare given by (7), subject to the constraint that the same
standards should be applied to the domestic product and the product imported from the member𝐽𝐽

country; that is, the constraint is 𝜎𝑎 = 𝜎𝑏 ∈ {H, L}, 𝐽 = 𝐴, 𝐵.
The member countries A and B choose a strategy for standards policy from the following possible
choices:
𝐽

𝐽

𝐽

𝐽

𝐽

𝐽

1. Full regulation (FR): (𝜎𝑎 , 𝜎𝑏 , 𝜎𝑐 ) = (𝐿, 𝐿, 𝐿);
2. No regulation (NR): (𝜎𝑎 , 𝜎𝑏 , 𝜎𝑐 ) = (𝐻, 𝐻, 𝐻);
3. Discrimination (D): (𝜎𝑎𝐽 , 𝜎𝑏𝐽 , 𝜎𝑐𝐽 ) = (𝐻, 𝐻, 𝐿)
for 𝐽 = 𝐴, 𝐵. Here, D means that the member countries discriminate against the nonmember country
C regarding the choice of standards.
The equilibrium standards regime for the member countries under NT is represented by thefollowing proposition.

Proposition 2. Under a bilateral agreement of standards policy with NT, the member countries’
equilibrium standards regime implies that:
No regulation for 0 ≤ 𝜃 < 𝜃;
Discrimination for 𝜃 ≤ 𝜃 < 𝜃̅ 𝑁 ;9

Full regulation for 𝜃̅ 𝑁 ≤ 𝜃,𝑐(2−3𝑐)𝑐(5−2𝑐)where 𝜃 ≡ 8(1−2𝑐) and 𝜃̅ 𝑁 ≡ 4(1+𝑐) .
(Proof) See the Appendix.

3.2. Policy game under MR
Under MR, each member country transfers the right to control importer to the other member (i.e.,exporter) country. More specifically, country A controls (𝜎𝑎𝐴 , 𝜎𝑎𝐵 , 𝜎𝑐𝐴 ) and country B controls(𝜎𝑏𝐵 , 𝜎𝑏𝐴 , 𝜎𝑐𝐵 ). Each member country faces the constraint that the same policy should be applied todomestically consumed product and the product produced by the same firm and exported to anothermember country; that is, 𝜎𝑎𝐴 = 𝜎𝑎𝐵 and 𝜎𝑏𝐴 = 𝜎𝑏𝐵 must hold.
Unlike NT, each member country’s standards policy affects the export profit earned in anothermember country as well as consumer surplus and domestic profit. Thus, considering country A’s
problem in stage 1 for example, its problem is represented as to maximize
𝐶𝑆 𝐴 + 𝜋𝑎𝐴 + 𝜋𝑎𝐵 =(3−∑𝑗=𝑎,𝑏,𝑐 𝑐𝑗𝐴 )232− ∑𝑗∈𝑎,𝑏,𝑐 𝜃𝑗𝐴

1−3𝑐𝑗𝐴 +∑𝑖≠𝑗 𝑐𝑖𝐴4+(1−3𝑐𝑎𝐴 +∑𝑗≠𝑎 𝑐𝑖𝐴 )216+(1−3𝑐𝑎𝐵 +∑𝑗≠𝑎 𝑐𝑖𝐵 )216(8)
subject to 𝜎𝑎𝐴 = 𝜎𝑎𝐵 . The problem for country B, which faces the constraint 𝜎𝑏𝐴 = 𝜎𝑏𝐵 , can be similarly
defined. The member countries’ possible strategies are as follows:
1. Full regulation (FR): (𝜎𝑎𝐴 , 𝜎𝑎𝐵 , 𝜎𝑐𝐴 ) = (𝜎𝑏𝐵 , 𝜎𝑏𝐴 , 𝜎𝑐𝐵 ) = (𝐿, 𝐿, 𝐿);
2. No regulation (NR): (𝜎𝑎𝐴 , 𝜎𝑎𝐵 , 𝜎𝑐𝐴 ) = (𝜎𝑏𝐵 , 𝜎𝑏𝐴 , 𝜎𝑐𝐵 ) = (𝐻, 𝐻, 𝐻);
3. Discrimination (D): (𝜎𝑎𝐴 , 𝜎𝑎𝐵 , 𝜎𝑐𝐴 ) = (𝜎𝑏𝐵 , 𝜎𝑏𝐴 , 𝜎𝑐𝐵 ) = (𝐻, 𝐻, 𝐿).
From (8), we observe that under MR, country A’s optimal standards depend on country B’s
standards, and vice versa. This means that, unlike the previous policy regimes, we first need to derive
each member country’s best response strategies and then obtain the Nash equilibrium of the standards
game. As we will see, both member countries’ standards are strategic complements in the MR game.
10

This particular feature of MR creates room (in our setting with discrete policy choices) for multiple
equilibria, as represented by the following proposition (see also Fig.1).

Proposition 3. Under a bilateral agreement of standards policy with MR, the member countries’
equilibrium standards regime implies that:
No regulation for 0 ≤ 𝜃 < 𝜃;
Discrimination for 𝜃 ≤ 𝜃 < 𝜃̅ 𝑀 ;Discrimination or Full regulation for 𝜃̅ 𝑀 ≤ 𝜃 < 𝜃 ′ ;Full regulation for 𝜃 ′ ≤ 𝜃,
(30+7𝑐)𝑐where 𝜃̅ 𝑀 ≡ 8(1+2𝑐) and 𝜃 ′ ≡15(2−𝑐)𝑐8.

(Proof) See the Appendix.

Fig.1: equilibrium standards of policy game under MR

In order to compare the outcomes under MR with those under NT, we need to make a refinementof equilibrium in the MR game. As in Costinot (2008), we restrict our attention to Pareto-efficient or“most cooperative” equilibrium; If one equilibrium is strictly preferred to any other by both countries,
we assume that they can coordinate on this equilibrium.

11

Proposition 4. In the most cooperative equilibrium under MR regime, the member countries will
coordinate on Full regulation when 𝜃 ∈ [𝜃̅ 𝑀 , 𝜃 ′ ].
(Proof) See the Appendix.

In light of Proposition 4, the equilibrium standards regime under MR characterized in Proposition
3 can be revised as follows: each member country chooses No regulation for 0 ≤ 𝜃 < 𝜃 ;Discrimination for 𝜃 ≤ 𝜃 < 𝜃̅ 𝑀 ; and Full regulation for 𝜃̅ 𝑀 ≤ 𝜃.

3.3. Summary of equilibrium standards under different policy regimes
To summarize the analysis so far, we obtain country A’s equilibrium standards under different
policy regimes, as illustrated in Fig.2.

Fig.2: country A’s equilibrium standards

The equilibrium strategies in country B, which concludes bilateral agreements with country A under
NT and MR, are the same as those in country A, with (𝜎𝑎𝐵 , 𝜎𝑏𝐵 , 𝜎𝑐𝐵 ) = (𝐿, 𝐻, 𝐿) for 𝜃 𝑈 ≤ 𝜃 < 𝜃𝑈inthe unconstrained noncooperative (UN) equilibrium. Even when countries A and B conclude bilateralagreements on standards, country C's equilibrium strategies are the same as that of UN. From Fig.2,
we can observe that the respective countries’ equilibrium standards vary as the value of 𝜃 changes.
Table 1 summarizes the equilibrium standards (𝜎𝑎𝐴 , 𝜎𝑏𝐴 , 𝜎𝑐𝐴 ; 𝜎𝑎𝐵 , 𝜎𝑏𝐵 , 𝜎𝑐𝐵 ; 𝜎𝑎𝐶 , 𝜎𝑏𝐶 , 𝜎𝑐𝐶 ) under12

respective regimes.

0 ≤ 𝜃 < 𝜃𝑈𝑈𝜃 ≤𝜃<𝜃
𝑁

UN

NT

MR

(H,H,H; H,H,H; H,H,H)(H,H,H; H,H,H; H,H,H)(H,H,H; H,H,H; H,H,H)(H,L,L; L,H,L; L,L,H)(H,H,H; H,H,H; L,L,H)(H,H,H; H,H,H; L,L,H)(H,L,L; L,H,L; L,L,H)(H,H,L; H,H,L; L,L,H)(H,H,L; H,H,L; L,L,H)

𝑁

𝑈(H,L,L; L,H,L; L,L,H)(L,L,L; L,L,L; L,L,H)(H,H,L; H,H,L; L,L,H)

𝑈

𝑀(L,L,L; L,L,L; L,L,L)(L,L,L; L,L,L; L,L,L)(H,H,L; H,H,L; L,L,L)(L,L,L; L,L,L; L,L,L)(L,L,L; L,L,L; L,L,L)(L,L,L; L,L,L; L,L,L)𝜃≤𝜃<𝜃𝜃 ≤𝜃<𝜃𝜃 ≤𝜃<𝜃𝑀𝜃 ≤𝜃

Table 1: Summary of the equilibrium standards (𝜎𝑎𝐴 , 𝜎𝑏𝐴 , 𝜎𝑐𝐴 ; 𝜎𝑎𝐵 , 𝜎𝑏𝐵 , 𝜎𝑐𝐵 ; 𝜎𝑎𝐶 , 𝜎𝑏𝐶 , 𝜎𝑐𝐶 )3.4. the welfare implications of NT and MR for member and nonmember countries
In this subsection, having characterized the equilibrium outcome under NT and MR, we compare
their performance by analyzing member and nonmember countries’ social welfare 𝑆𝑊𝐽 = 𝐶𝑆𝐽 + 𝜋𝑗 ,J=A, B, C, and j=a, b, c.

Fig.3. welfare comparison of member countries.
The blue line in Fig.3 represents 𝑆𝑊𝐽𝑀 − 𝑆𝑊𝐽𝑈 , where 𝑆𝑊𝐽𝑀 and 𝑆𝑊𝐽𝑈 denote country J’s
13welfare under MR and UN, respectively, for J=A,B. First, we consider the performance of MR.
Compared to the benchmark of UN, when 𝜃 is extremely small, member countries impose negative
regulation and the outcomes under MR and UN are same. When 𝜃 𝑈 ≤ 𝜃 < 𝜃, where 𝜃 is a little
larger than before, under UN, country began to discriminate to reduce pollution and shift profit fromexporters to national producers. While because under MR, the control of standard over B’s producthas been transferred to B’s government. A and B impose same standard policy towards each other andthe discrimination policy towards C. However，compared with UN，the distortion of the market power
under MR is smaller. Also, under MR, country A could prompt the exporting to B. So, the outcome of𝑀

MR increases. For very large level of pollution, 𝜃 ≤ 𝜃 , member countries imposed a positive𝑀

regulation and outcomes become equivalent. As for the immediate range, when 𝜃̃ ≤ 𝜃 < 𝜃 , country
A and B should impose the positive standard, while governments still have the incentive to shift more
profits from C to themselves and prompt the exportation to each other. Consequently, the level ofpollution which they started to impose the regulation is too high. This is a “Race to the Bottom”,
similarly with Costinot (2008).
The red line in Fig.3 represents 𝑆𝑊𝐽𝑁 − 𝑆𝑊𝐽𝑈 , where 𝑆𝑊𝐽𝑁 denotes country J’s welfare under NT
for J=A,B. Then we analyze the performance of NT. Similarly with MR, when 𝜃 is extremely small𝑁and large, the outcome of NT and UN are equivalent. When 𝜃 ≤ 𝜃 < 𝜃 , Country A could only
impose discrimination standards on C and the outcome of NT increase. Also, country A couldn’t
𝑁

prompt the exporting to B and C. So, when 𝜃 starts getting larger, 𝜃 ≤ 𝜃 < 𝜃̃ country A overevaluate the negative externality and start to impose the regulation when the level of pollution is toolow. This patten is called “Green Protectionism”. Comparing the member countries’ performance
under MR and UN, we obtain the following proposition.

(7−2𝑐)𝑐
Proposition 5. Let us define 𝜃̃ ≡ 4(1+𝑐) . Then, for member countries J = A, B

14

MR ~ NT for 𝜃 < 𝜃𝑁𝑀and 𝜃 > 𝜃 ;𝑁

MR ≻ NT for 𝜃 ≤ 𝜃 < 𝜃̃;𝑀NT ≻ MR for 𝜃̃ ≤ 𝜃 < 𝜃 .

We next analyze the performance of country C, the nonmember country of bilateral agreements ofstandards, in different policy regimes, as illustrated in Fig.4.

Fig.4. welfare comparison nonmember countries.

First, we see the nonmember countries’ performance of MR. When the level of pollution is too small
or too large, the strategies under MR and UN are same, so the outcomes are equivalent. When 𝜃 𝑈 ≤𝜃 < 𝜃, country C under UN uses discrimination strategy and shift profit from A and B while A and B𝑁

are still imposing no regulation. So, the outcome under MR increases. When 𝜃 ≤ 𝜃 < 𝜃 , country A
and B both impose discrimination standards on C, and the outcome under MR is lower than it under
UN.

15

𝑁

For the outcome of NT, the analysis is similar with MR. But the range 𝜃 ≤ 𝜃 < 𝜃𝑁𝑈

is different.
𝑁

Because under NT, country A and B set Full regulation at a low pollution level, 𝜃 . When 𝜃 ≤ 𝜃 <𝑈

𝜃 , country C imposes discrimination policy, and C could shift profit from A and B. Thus, outcome
increases. Compare the performance under MR and NT, we obtain the following proposition.

Proposition 6. For nonmember country C,
𝑁𝑈𝑁

NT is beneficial for 𝜃 𝑈 ≤ 𝜃 < 𝜃 and 𝜃 ≤ 𝜃 < 𝜃 , but harmful for 𝜃 ≤ 𝜃 < 𝜃 .
𝑀

MR is beneficial for 𝜃 𝑈 ≤ 𝜃 < 𝜃, but harmful for 𝜃 ≤ 𝜃 < 𝜃 .

Summarizing the welfare comparisons of member and nonmember countries, we obtain thefollowing proposition.

Proposition 7.
Suppose that the member countries conclude a standards agreement that yields higher benefits. Then,(i) the regional agreement on standards policy benefits both member and nonmember countries for𝑈𝜃 𝑈 ≤ 𝜃 < 𝜃 and 𝜃̃ ≤ 𝜃 < 𝜃 ; (ii) the regional agreement benefits only the member countries for𝜃 ≤ 𝜃 < 𝜃̃

4. Multilateral Agreements on Standards Policy
In this section, we consider the case in which country C join the agreements. Thus, country A, B
and C’s standard policies are under the restriction of agreements. Similarly with section 2, we consider
two types of agreements, NT and MR.

16

4.1. Multilateral agreements on standards policy: NT
For all the countries, the government’s problem in stage 1 is still to decide on the standards policy𝐽𝐽𝐽

to maximize the domestic welfare given by (7), subject to the constraint,𝜎𝑎 = 𝜎𝑏 = 𝜎𝑐 , 𝐽 = 𝐴, 𝐵, 𝐶.
The government in each country has two possible choices; one is Full regulation (FR), which means(𝜎𝑎𝐽 , 𝜎𝑏𝐽 , 𝜎𝑐𝐽 ) = (𝐿, 𝐿, 𝐿), and the other is No regulation (NR), which means (𝜎𝑎𝐽 , 𝜎𝑏𝐽 , 𝜎𝑐𝐽 ) = (𝐻, 𝐻, 𝐻).
The equilibrium standards regime under NT is represented by the following proposition.

Proposition 8. Under a multilateral agreement of standards based on national treatment, theequilibrium standards regime implies
No regulation for 0 ≤ 𝜃 < 𝜃 ∗𝑁 ;Full regulation for 𝜃 ∗𝑁 ≤ 𝜃,
11

where 𝜃 ∗𝑁 = 24 𝑐(2 − 𝑐).
(Proof) See the Appendix.

We are interested in whether bilateral agreements can be a building block to multilateral agreements;that is, starting from a situation under a bilateral agreement, whether the countries have an incentive
to conclude a multilateral agreement. We begin with a comparison of member countries’ welfare under
the NT-based bilateral agreement, denoted by 𝑆𝑊𝐽𝑁 , with that under the multilateral agreement,
denoted by 𝑆𝑊 𝑁𝑀 , 𝐽 = 𝐴, 𝐵 . In light of Fig.3, the member countries are indifferent to theunconstrained noncooperative equilibrium and the bilateral agreements for 0 ≤ 𝜃 < 𝜃 𝑈 and 𝜃 ≥ 𝜃̅ 𝑀 .
Therefore, in what follows, we focus on the case of 𝜃 𝑈 ≤ 𝜃 < 𝜃̅ 𝑀 . The results are shown in Fig.5.

17

Fig. 5. The welfare comparison between bilateral and multilateral agreement under NT

Based on Fig. 5, We obtain the following Proposition:

Proposition 9. Under NT, compare member countries’ welfare in bilateral agreement and multilateralagreement,
𝑆𝑊 𝑁𝑀 = 𝑆𝑊𝐽𝑁 for 𝜃̅ 𝑈 ≤ θ < 𝜃̅ 𝑀 ;𝑆𝑊 𝑁𝑀 > 𝑆𝑊𝐽𝑁 for 𝜃 𝑈 < 𝜃 < 𝜃́ and 𝜃̅ 𝑁 < 𝜃 < 𝜃̅ 𝑈 ；𝑆𝑊 𝑁𝑀 < 𝑆𝑊𝐽𝑁 for 𝜃́ ≤ θ < 𝜃̅ 𝑁 ,where θ́ =13c2 −6c8(2c−1).

(Proof) See the Appendix.

For the nonmember country C, comparing its welfare under the NT-based bilateral agreement,
denoted by 𝑆𝑊𝐶𝑁 , with that under the multilateral agreement 𝑆𝑊 𝑁𝑀 , we obtain the following
proposition.

18

Proposition 10. Under NT, compare nonmember country’ welfare in bilateral agreement andmultilateral agreement,
𝑆𝑊 𝑁𝑀 = 𝑆𝑊𝐶𝑁 for 𝜃̅ 𝑈 ≤ 𝜃 < 𝜃̅ 𝑀 ;𝑁

𝑈

𝑆𝑊 𝑁𝑀 < 𝑆𝑊𝐶𝑁 for 𝜃 𝑈 ≤ 𝜃 < 𝜃 and 𝜃 < 𝜃 < 𝜃 ;𝑁

𝑆𝑊 𝑁𝑀 > 𝑆𝑊𝐶𝑁 for 𝜃 ≤ 𝜃 < 𝜃 .
(Proof) See the Appendix.

By comparison of welfare, we find that only when the welfare of member countries and nonmember
country’s increases under Multilateral agreements, a Bilateral agreement of NT could lead to a
Multilateral agreement under NT. Summarizing the above analysis, we could find that for all thecountries J =A, B, C under NT policy regimes - A Bilateral agreement of NT could lead to a
Multilateral agreement for 𝜃 ≤ θ < θ́.

4.2. Multilateral agreements on standards policy: MR
After country C joins agreements, because all the countries are symmetric, we could take country
A as example to make analysis. The economic problem in stage 1 is𝐽

𝑆𝑊 𝐴 = 𝐶𝑆 𝐴 + ∑ 𝜋𝑎
𝐽=𝐴,𝐵,𝐶=(3−∑𝑗=𝑎,𝑏,𝑐 𝑐𝑗𝐴 )232− ∑𝑗∈𝑎,𝑏,𝑐 𝜃𝑗𝐴

1−3𝑐𝑗𝐴 +∑𝑖≠𝑗 𝑐𝑖𝐴4𝐽+ ∑𝐽=𝐴,𝐵,𝐶

𝐽(1−3𝑐𝑎 +∑𝑖≠𝑎 𝑐𝑖 )216(9)subject to 𝜎𝑎𝐴 = 𝜎𝑎𝐵 = 𝜎𝑎𝐶 . Country A’s government has now two possible choices; one is Full
regulation (FR), which means (𝜎𝑎𝐴 , 𝜎𝑎𝐵 , 𝜎𝑎𝐶 ) = (𝐿, 𝐿, 𝐿), and the other is No regulation (NR), whichmeans (𝜎𝑎𝐴 , 𝜎𝑎𝐵 , 𝜎𝑎𝐶 ) = (𝐻, 𝐻, 𝐻) . The governments’ problems in countries B and C can beanalogously presented.
As with the MR policy regimes of bilateral agreement, multiple equilibria can exist as well. We
consider the “most cooperative” equilibrium of multilateral agreement. The results are represented as
19the following proposition.

Proposition 11. Under a multilateral agreement of standards based on MR, the “most cooperative”
equilibrium standards regime implies
No regulation for 0 ≤ 𝜃 < 𝜃 ∗𝑀 ;Full regulation for 𝜃 ∗𝑀 ≤ 𝜃,
where 𝜃 ∗𝑀 =𝑐(42+13𝑐)8(1+2𝑐).

(Proof) See the Appendix.

Let us denote country J’s welfare under the MR-based multilateral agreement by 𝑆𝑊𝐽𝑀 , andcompare its welfare under the bilateral agreement 𝑆𝑊 𝑀𝑀 , J=A,B,C. The results are shown in Fig.6.

Fig. 6. The welfare comparison between bilateral and multilateral agreement under MR

We begin with the discussion of member countries A and B. Because 𝜃 ∗𝑀 > 𝜃̅ 𝑀 , here we consider
the case of 𝜃 𝑈 ≤ 𝜃 < 𝜃 ∗𝑀 .The following results hold for J=A,B. And we obtain the Proposition 12.

20

Proposition 12. Under MR, compare member countries’ welfare in bilateral agreement andmultilateral agreement,
𝑆𝑊 𝑀𝑀 < 𝑆𝑊𝐽𝑀 for θ́ < θ < θ∗M ;𝑆𝑊 𝑀𝑀 > 𝑆𝑊𝐽𝑀 for θU ≤ θ < θ́.
(Proof) See the Appendix.

For the nonmember country C, 𝑆𝑊𝐶𝑀 denotes the welfare under Bilateral agreements and 𝑆𝑊 𝑀𝑀
denotes the welfare under Multilateral agreements. We obtain the following Proposition.

Proposition 13. Under MR, compare nonmember country’ welfare in bilateral agreement andmultilateral agreement
𝑆𝑊 𝑀𝑀 < 𝑆𝑊𝐽𝑀 for θU ≤ θ < 𝜃 and 𝜃̂ < 𝜃 < 𝜃 ∗𝑀 ;𝑆𝑊 𝑀𝑀 < 𝑆𝑊𝐽𝑀 for 𝜃 ≤ θ < 𝜃̂ ,2

12𝑐 −7𝑐𝜃̂ =.
4(𝑐−1)(Proof) See the Appendix.

By the above analysis, we know that when the welfare of member countries and nonmember
country’s increase under Multilateral agreements, a Bilateral agreement of MR could lead to a
Multilateral agreement. Then we could obtain that for all the countries J =A, B, C under MR or NT
policy regimes - A Bilateral agreement could lead to a Multilateral agreement for 𝜃 ≤ θ < θ́.
By summarizing the above analysis, we could obtain the following the Proposition:
Proposition 14. A Bilateral agreement could lead to a Multilateral agreement for 𝜃 ≤ 𝜃 < 𝜃́.

21

5. Concluding remarks
In Bilateral agreements, there is the range for the level of externality, where the regional agreements
could be beneficial for not only member countries but nonmember countries. Inside the agreement,
the outcome characterized by higher levels of externalities is larger under NT. And when the level ofpollution is lower, the outcome under MR will be larger. As for nonmember country,
When the level of pollution is relatively low, all the member countries form the regional agreement
and nonmember countries have the incentive to join the multilateral agreement. When the level ofpollution increases, the outcome for member countries and nonmember country will be higher in thebilateral agreement under MR, it’s better to keep the regional agreement. Under NT, when the level ofpollution increases, only member countries could get more benefits from multilateral agreements while
nonmember country doesn’t have the incentive to join the agreement.

22

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