ISSN (Print) 0473-453X

Discussion Paper No. 1222

ISSN (Online) 2435-0982

ENVIRONMENTAL POLICIESAND STAGNATIONIN A TWO-COUNTRY ECONOMY

Masako Ikefuji
Yoshiyasu Ono

November 2023

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

November 2023

Environmental policies and stagnation
in a two-country economy*
Masako Ikefuji† and Yoshiyasu Ono‡
Osaka University

Abstract
Global warming is a serious and acute threat to our planet, but, when negotiating theallocation of permissible carbon emissions, conflicts of interest exist between developed anddeveloping countries. Developing countries insist that global warming is the result of prolonged
pollution emissions by developed countries, while developed countries demand that developing
countries make efforts comparable to their own to reduce carbon emissions. They bothgenerally believe that stricter emission limits will burden their economies because of the extra
abatement costs required. We use a two-country model with wealth preferences and find thatthe effects of a country’s emission limit on the two countries’ real consumption and pollution
emissions differ, depending on the combination of their business situations. If both countries
achieve full employment, one country’s stricter emission limit decreases both countries’ realconsumption, as expected. However, if one country faces aggregate demand stagnation and theother achieves full employment, a stricter emission limit imposed by the stagnant country
increases both countries’ real consumption.
JEL classification: F13, F41, F42, Q52, Q56, Q58
Keywords: persistent unemployment, wealth preferences, pollution, emission restriction, clean
technology transfer.

*)

This work was financially supported by the Asahi Glass Foundation, the JSPS KAKENHI Grants(JP20H05631, JP20H01477), and the program of the Joint Usage/Research Center for “Behavioral Economics”
at ISER of Osaka University.
†

Osaka School of International Public Policy, Osaka University, 1-31 Machikaneyama, Toyonaka, Osaka
560-0043, JAPAN. E-mail: ikefuji.osipp@osaka-u.ac.jp‡

Institute of Social and Economic Research, Osaka University, 6-1, Mihogaoka, Ibaraki, Osaka 567-0047,
JAPAN. E-mail: ono@iser.osaka-u.ac.jp

1. Introduction
Most countries have come to regard global warming as one of the most serious threats tohuman beings. This common understanding led 187 countries and regions to adopt the 2015
Paris agreement, an international treaty intended to limit global warming by reducing global
emissions. 3 However, when negotiating the allocation of permissible carbon emissions,conflicts of interest exist, particularly between developed and developing countries.
Developing countries insist that global warming is a result of prolonged pollution emissions by
developed countries, while developed countries demand that developing countries make efforts
comparable to their own to reduce carbon emissions. They both believe that stricter emission
limits will burden their economies due to the extra abatement costs required. This is particularly
the case when the countries face stagnation.
However, if a country faces aggregate demand stagnation, a stricter emission limit induces
firms to hire more labor to abate pollution, which mitigates deflation, urges households toconsume more, and stimulates business activity. Ikefuji and Ono (2021) find that this property
holds in a closed-economy setting with demand stagnation caused by households’ wealthpreferences.4 The current paper extends their analysis to an open-economy setting using a twocountry model with secular stagnation caused by wealth preferences.5 It incorporates pollution
emissions in the model, and examines one country’s own and international spillover effects of
its pollution emission limit on the two countries’ consumption and pollution emissions under
different combinations of their business activities: full employment in both countries,
stagnation in one country and full employment in the other, and stagnation in both countries.
The results show that the effects are mixed depending on the combination of their businessactivities.
For example, if one country faces aggregate demand stagnation and the other achieves full
employment, which may describe the current situation for developed and developing countries,
a stricter pollution emission limit by the stagnant country leads to greater consumption in both3
The USA withdrew from the agreement under the Trump administration, but returned in 2021 under the
Biden administration.
4

A secular demand stagnation model of this type was first presented by Ono (1994, 2001). Recent extensions
include Ono and Ishida (2014), Michau (2018), and Michaillat and Saez (2022). Using a model in which themarginal utility of wealth remains strictly positive, these authors find that secular demand stagnation occurs andexamine the effects of various monetary and fiscal policies. Illing et al. (2018); Mian et al. (2021); and Hashimoto
et al. (2023) also analyze wealth preference models.
5

See Ono (2006, 2014, 2018) for a two-country model with wealth preferences of this type.

1

countries. This is because a stricter emission limit induces domestic firms to hire more laborfor abatement, which mitigates deflation and stimulates households to increase consumption.
Consequently, the country’s current account worsens and its currency depreciates, which
implies an improvement in the other country’s terms of trade. Thus, if the latter achieves full
employment, it will also be better off — that is, there is no conflict of interest with respect toconsumption between the two countries. This is in contrast to the case where both countries arein full employment and a tradeoff exists between consumption and the environment; in thiscase, a stricter emission limit decreases pollution emissions at the cost of less output and lower
consumption.
Much has been written about the environment in an open-economy context.6 In the absenceof self-enforcing international environmental agreements, the question of whether free tradeliberalization is good or bad for the environment has particularly been noted, leading to manystudies that focus on the existence of carbon leakage. Carbon leakage refers to the situation
where a country’s unilateral climate policy causes other countries to increase carbon emissions.
These studies focus on how one country’s environmental policy affects the other country’s
production reallocation from clean to dirty sectors. For example, Copeland and Taylor (1994)
employ a two-country model with a continuum of goods and show that a higher pollution tax
imposed by the higher-income country causes more pollution-intensive production to move tothe lower-income country with a less stringent environmental policy (the pollution haveneffect).7
More recent studies discuss the possibility of negative carbon leakage, where a unilateralclimate policy may decrease carbon emissions in other countries through production
reallocation from dirty to clean sectors. These studies include Baylis et al. (2014) under perfectcompetition and Baccianti and Schenker (2022) under Cournot competition. Di Maria andSmulders (2004), Hémous (2016), Acemoglu et al. (2014), and Gerlagh and Kuik (2014)
introduce directed technical change to a North-South economy with clean and dirty sectors andshow that international technology spillovers from North to South are necessary for negative
carbon leakage to occur.

6

See the reviews by Jayadevappa and Chhatre (2000), Rauscher (2005), and Cherniwchan et al. (2017).

7

Babiker (2005) numerically analyzes the strategic interaction among energy-intensive production firms in a
Cournot oligopoly model and finds significant carbon leakage from the OECD countries to developing countries.
Levinson and Taylor (2008) estimate the pollution haven effect using data on U.S. manufacturing sector imports
from Canada and Mexico.

2

While we focus on how emission restrictions affect employment, real consumption, andpollution emissions in the policy-setting country and the other country, we also discuss positive
and negative carbon leakage in various combinations of the two countries’ employment
situations. We find that a stricter emission limit causes negative carbon leakage to occur whenboth countries face stagnation because it decreases the other country’s employment, output andpollution emissions. However, the policy-setting country may increase pollution emissions
despite a stricter emission limit because the stricter limit creates new employment forabatement, thereby stimulating aggregate demand, which leads to increased employment andoutput. An international transfer of superior abatement technology in this case also reduces therecipient country’s pollution emissions by decreasing employment and output. Thus, themechanism of negative carbon leakage presented in the current paper is quite different fromthe conventional one via intersectoral reallocation of production. It works through changes in
employment and output in the presence of aggregate demand shortages.
The remainder of this paper is organized as follows. Section 2 presents the model andcharacterizes the steady state under different combinations of full employment (F) andstagnation (S) in the two countries. Sections 3 and 4 investigate the effects of a pollution
emission limit when both countries attain full employment (FF), and when they face stagnation(SS), respectively. Section 5 considers the case where the policy-setting country is in stagnationand the other country is in full employment (SF) and vice versa (FS). Section 6 examines theeffects of transfers of abatement and cleaner production technologies in the four cases: FF, SS,
SF and FS. It also discusses the first-best policy for the stagnant country. Section 7 concludes.

2. The model
We consider an open economy with two countries, ℎ and 𝑓 , and firms of country ℎ
specialize in commodity 1 while firms of country 𝑓 specialize in commodity 2. The twocountries have the same population, which is normalized to unity.
Households
Households in the two countries have the following lifetime utility:𝑈𝑢 𝑐 ,𝑐

𝑣 𝑚

𝑞 𝑧

𝑧

exp

𝜌𝑠 𝑑𝑠,

𝑈𝑢 𝑐 ,𝑐

𝑣 𝑚

𝑞 𝑧

𝑧

exp

𝜌𝑠 𝑑𝑠,

0; 𝑞

0, 𝑞

0,

𝑢

0, 𝑢

0; 𝑣

0, 𝑣
3

(1)

where superscript 𝑗 (𝑗𝑢 𝑐 ,𝑐ℎ, 𝑓) of a variable implies that the variable belongs to country 𝑗,

is the utility of consumption on the two commodities 𝑐 and 𝑐 , 𝑣 𝑚of real money holdings 𝑚 , and 𝑞 𝑧𝑧

is the disutility of global pollution 𝑧

is the utility
𝑧 , such

as greenhouse gas.
We assume that 𝑢 . , . is homothetic; hence, once real aggregate consumption 𝑐 is given
at each point in time, the optimal levels of 𝑐 and 𝑐 satisfy𝑝 𝜔 𝑐

𝛾 𝜔 𝑐 , 𝑝 𝜔 𝑐

1

𝑝 𝜔 𝑐

𝑝 𝜔 𝑐

𝑐 ,

1

0, 𝛾′ 𝜔0,𝛾 𝜔𝛾 𝜔 𝑐 ,

(2)

where 𝜔 is the relative price of commodity 2 to commodity 1, 𝑝 𝜔 is the real price ofcommodity 𝑖 (𝑖1, 2), and 𝛾 𝜔 is the share of consumption expenditure on commodity 1.

Real prices 𝑝 𝜔 and 𝑝 𝜔 are respectively the same between the two countries because
both households have the same utility function, as shown by (1), and no tariff is imposed in thetwo countries.
As proved in Appendix A, the real and nominal prices satisfy
/

𝑝 𝜔

, 𝑝 𝜔

𝑝 𝜔

0,
𝑃

𝜔𝑝 𝜔 ,
𝑝 𝜔

𝜀𝑃 ,

𝛾𝑝

𝜋

𝜋 ,

0,
(3)

where 𝑃 is country 𝑗 ’s consumer price index, 𝑃 is the nominal price of commodity 𝑖measured in terms of country 𝑗’s currency, 𝜀 is the nominal exchange rate, and 𝜋 is the
inflation rate of 𝑃 . From the non-arbitrage condition between home and foreign assets, we
have
𝑅 ,

𝑅

where 𝑅 is country 𝑗’s nominal interest rate. Therefore, from the last equation of (3), we find
𝑅

𝜋

𝑟

𝑅

𝜋 ,

(4)

that is, the real interest rate 𝑟 is internationally the same.
As a result of the intratemporal optimal allocation of consumption given by (2), the utilityof consumption is represented as a function of only 𝑐 :
𝑢 𝑐

≡𝑢

,

4

,

because 𝑢 𝑐 , 𝑐

is homothetic and unaffected by the relative price 𝜔 if the consumer priceindex is properly defined. Thus, the lifetime utility given in (1) of a representative householdin each country is rewritten as follows:
𝑈

𝑢 𝑐

𝑣 𝑚

𝑞 𝑧

𝑧

exp

𝜌𝑠 𝑑𝑠,

𝑈

𝑢 𝑐

𝑣 𝑚

𝑞 𝑧

𝑧

exp

𝜌𝑠 𝑑𝑠,(5)

which is to be maximized subject to the flow and stock budget equations:
𝑎

𝑟𝑎

𝑤 ℓ

𝑐

𝑅 𝑚 ,

𝑎

𝑚

𝑏 ,

(6)

Where 𝑎 is total assets, 𝑏 is international lending-borrowing, 𝑤

𝑊 /𝑃

is the real

wage, and ℓ is the realized labor supply in country 𝑗. The first-order optimality condition is𝜌
where 𝜂 ≡𝑢𝑐 𝑐 /𝑢′ 𝑐

𝜂

𝜋

𝑅

,

(7)

is the elasticity of the marginal utility of consumption. The

transversality condition islim 𝑎 𝑡 exp

𝑟 𝑠 𝑑𝑠

→

0.

(8)

Firms
All firms are competitive, and firms in country ℎ (country 𝑓 ) produce commodity 1(commodity 2). They utilize labor ℓ (𝑗ℎ, 𝑓) to produce 𝑦 (𝑖1, 2) of commodity 𝑖 withconstant labor productivity 𝐴 , and emit pollution 𝑒 :𝑦𝑒Where 𝛿 (𝑖

𝐴 ℓ ,

𝑦

𝐴 ℓ ,

𝛿 𝐴 ℓ ,𝑒

𝛿 𝐴 ℓ ,

(9)1, 2) is the ratio of pollution emissions to output. Each government limits

pollution emissions per output to 𝜑 , so that net actual emissions 𝑧 and pollution abatement𝑒𝑧 satisfy𝑧

𝜑 𝑦

𝜑 𝐴 ℓ ,

𝑒

𝑧

𝛿

𝜑 𝐴 ℓ

𝜎ℓ ,

𝑧

𝜑 𝑦

𝜑 𝐴 ℓ ,

𝑒

𝑧

𝛿

𝜑 𝐴 ℓ

𝜎ℓ ,

(10)

where ℓ is labor input for abatement in country 𝑗 and 𝜎 is labor productivity of abatement ofpollution emitted when producing commodity 𝑖. Therefore, total employment ℓℓℓ )in country 𝑗 is
ℓ

1

ℓ ,

ℓ

5

1

ℓ .

(11)

Obviously, if 𝛿

𝜑 , implying that the unrestricted emission rate is lower than theemission limit set by the government, firms are not required to abate pollution; thus, theenvironmental policy is not in effect and ℓℓ in (11). However, in the following, we focus

on the case where the environmental policy is in effect (i.e., 𝛿𝜑 ).

Using (9)–(11), we find that firm output and profits in country 𝑗 (𝑗ℎ, 𝑓) are𝑦

𝐴 ℓ , 𝑝𝑦

𝑤 ℓ

𝑝𝐴

𝑤

ℓ , where 𝐴 ≡,𝑦

𝐴 ℓ , 𝑝 𝑦

𝑤 ℓ

𝑝 𝐴

𝑤

ℓ , where 𝐴 ≡

.

(12)

𝐴 is effective labor productivity with emission limit 𝜑 , which satisfies
0,

0,

0,

𝛿

𝜑

0;

(13)

that is, a stricter emission limit (𝜑 ↓) decreases effective labor productivity 𝐴 , whereas 𝐴
increases with an improvement in the production technology ( 𝐴 ↑ ), cleaner production
technology with less pollution emissions (𝛿 ↓), and an improvement in abatement technology(𝜎 ↑). Because of the linear technology, real wage 𝑤 must satisfy𝑤

𝑝 𝜔 𝐴 , 𝑤

𝑝 𝜔 𝐴 ,

(14)

so that profits are zero for all firms.
Markets
We assume, for simplicity, that both governments keep nominal money stock 𝑀 constantover time so that
𝑚

𝜋 𝑚

for 𝑗

ℎ, 𝑓.

(15)

Applying (4), (7), (14), and (15) to (6) yields each country’s current account:
𝑏

𝑟𝑏

𝑐

𝑝𝐴 ℓ ,𝑏𝑟𝑏

𝑐

𝑝 𝐴 ℓ .

(16)

The world total lending-borrowing is zero:
𝑏

𝑏

0.

For simplicity, we treat the case in the neighborhood of
𝑏 ,𝑏

0,0 ,

(17)

where we can ignore the effect through a change in the exchange rate on the real value of eachcountry’s net assets, which generally depends on the asset portfolio. This effect is beyond thescope of the present analysis.
From (2) and (12), the international markets of the two commodities satisfy

6𝜓 𝜔 𝑐𝑐where 𝜓 𝜔

𝐴 ℓ ,

𝜓 𝜔 𝑐

𝑐

, 𝜓

0, 𝜓 𝜔

𝐴 ℓ ,
, 𝜓

(18)
0.

In the labor market of each country, nominal wage 𝑊 perfectly adjusts when ℓadjusts in a sluggish manner depending on the deflationary gap when ℓ
If ℓ1, 𝑊 perfectly adjusts.

If ℓ

1,

𝛼 ℓ

1, while it

1. Thus,

1 .

(19)

Steady state
In steady state, 𝑐 and 𝑤

𝑊 /𝑃
𝑟

𝜌,

are constant so that we have from (4) and (7)

𝜋

for 𝑗

ℎ, 𝑓.

(20)

We therefore obtain, from (7), (10), (12), (16), (17), and (18),
ℓ

𝑐

,

ℓ

𝑝 𝜔 𝐴 ℓ ,𝑧

𝜑 𝐴 ℓ ,

𝜌

𝜋

𝑧

𝑐

𝑝 𝜔 𝐴 ℓ ,𝜑 𝐴 ℓ .
for 𝑗

ℎ, 𝑓.

Moreover, if both countries achieve full employment (ℓ

(21)
1, ℓ

1) in the steady state, wehave from (21),𝑐𝑝 𝜔 𝐴 ,
𝜑 𝐴 ,

𝑧
𝜌

𝑐

𝑧

𝜑 𝐴 .

for 𝑗

ℎ, 𝑓.

𝑝 𝜔 𝐴 ,

(22)

However, if households have insatiable preference for money (or financial wealth)holdings; namely,
lim 𝑣 𝑚

𝛽

→

0,

(23)

aggregate demand shortages can occur, as found by Ono (1994, 2001).8 More precisely, inorder for the solution of 𝑚 and 𝑚 in (22) to exist, it must hold that

8

𝜌

,

𝜌

,

See Ono et al. (2004) for an empirical analysis of insatiable preferences for money (or financial wealth).

7

where 𝜔 is obtained from the first equation in (22). Therefore, full employment is reached ineach country if and only if
𝑝 𝜔 𝐴

𝑢

,

𝑝 𝜔 𝐴

𝑢

.

Otherwise, stagnation occurs in each country. Therefore, we find the conditions for eachcombination of the two countries’ business activities to appear as follows:9
FF (ℓ

1, ℓ

1 : 𝑝 𝜔 𝐴𝑢

, 𝑝 𝜔 𝐴

𝑢

,

SS (ℓ

1, ℓ

1 : 𝑝 𝜔 𝐴𝑢

, 𝑝 𝜔 𝐴

𝑢

,

SF (ℓ

1, ℓ

1 : 𝑝 𝜔 𝐴𝑢

, 𝑝 𝜔 𝐴

𝑢

,

FS (ℓ

1, ℓ

1 : 𝑝 𝜔 𝐴𝑢

, 𝑝 𝜔 𝐴

𝑢

,

(24)

where F and S imply full employment and stagnation, respectively, and the first and second
letters denote the employment situation of countries ℎ and 𝑓, respectively.

3. Full employment in both countries
Let us first consider the case where both countries achieve full employment (case FF) andanalyze the effects of country ℎ’s emission limit 𝜑 on the two countries’ real consumption
and pollution emissions. Obviously, the effects of country 𝑓’s emission limit 𝜑 on the twocountries’ real consumption and pollution emissions are symmetrically treated.
Using 𝑝 𝜔 and 𝑝 𝜔 in (3), (13), and the steady-state conditions in case FF given by(22), we obtain the effects of changes in 𝐴 and 𝜑 on the two countries’ real consumption andpollution emissions:
0,

𝐴
𝑝

0,

𝑝
0 for 𝑗

|

𝜑

.

|

9

0,

𝐴
.

0,

ℎ, 𝑓,
1

(25)
0,

0.

Ono (2014, 2018) shows these conditions for the four cases to appear.

80,These are summarized as follows:
Proposition 1: When both countries attain full employment, a country’s stricter emission limit
and higher effective productivity yield the following effects on the real price (𝑝) and output (𝑦)of each product, pollution emissions (𝑧), and real consumption (𝑐) in the two countries:

Policy-setting country (F)
𝑝

𝑦, 𝑧

𝑐

The other country (F)𝑝𝑦, 𝑧Stricter emission limit

0Higher effective productivity

0𝑐(F) implies full employment.

Proposition 1 shows the standard properties of the own and spillover effects of country ℎ’s
stricter emission limit 𝜑 . It naturally lowers 𝐴 and decreases country ℎ ’s production,
pollution emissions and real consumption. Consequently, the relative price of commodity 1
rises and country 𝑓’s real consumption decreases through a deterioration in its terms of trade.
Its pollution emissions are unchanged because its output is unchanged at the full-employment
level. Thus, there is naturally a tradeoff between the environment and both countries’ realconsumption.

4. Stagnation in both countries
We now turn to the case where both countries face persistent unemployment in the steadystate, that is, case SS in (24), and examine the effects of a change in country ℎ’s emission limit
𝜑 on the two countries’ consumption, employment, and pollution emissions. Obviously, theeffects of a change in country 𝑓’s emission limit 𝜑 are symmetrically treated.
When aggregate demand shortages appear (ℓ1) in both countries, from (19) and (20),their consumer price indices 𝑃 keep declining, making 𝑣 𝑚converge to 𝛽, as shown by(23). Then, the Euler equation (7) reduces to
𝜌

𝛼 ℓ

1

⟹

ℓ

In this state, from (15), (19), and (20),9ℓ 𝑐 , ℓ ′ 𝑐

0.

(26)

𝜋
Because 𝑚

𝛼 ℓ

1

0.

𝑎 from (6) and (17), 𝑎 continues to expand at the following rate:
𝜋

𝜌

𝛽/𝑢 𝑐

0.

Nevertheless, the transversality condition given by (8) is valid because 𝑟(20), and the expansion rate of 𝑎 , which is𝜌, as shown by

𝜋 , is lower than 𝜌, as seen from the above

equation.
Substituting ℓ 𝑐given by (26) into ℓ in (18) yields

𝜓 𝜔 𝑐

𝑐

𝐴 ℓ 𝑐

⟹ 𝑐

𝑔 𝑐 ; 𝜔, 𝐴 ,

𝜓 𝜔 𝑐

𝑐

𝐴 ℓ 𝑐

⟹ 𝑐

𝑔 𝑐 ; 𝜔, 𝐴 .

(27)

The intersection of the two functions in (27) gives the two countries’ real consumption in thestagnation steady state. As proved in Appendix B, for the intersection to exist, it must be valid
that
Ω≡ 1
Let 𝑐 𝜔; 𝐴 , 𝐴

𝛾 𝑝𝐴 ℓ ′ 𝑝 𝐴 ℓ ′1

𝛾𝑝 𝐴 ℓ ′ 𝑝 𝐴 ℓ ′

1

0.

(28)

represent 𝑐 at the intersection of the two functions in (27):𝑐 𝜔; 𝐴 , 𝐴

for 𝑗

ℎ, 𝑓.

Totally differentiating the two equations in (27) and rearranging the results gives 𝜕𝑐 /𝜕𝜔:;,𝑝 𝐴 ℓ ′

1

𝛾′

.

(29)

The steady-state 𝜔 is determined so that the current account 𝑏 given by (16) is in balance. We
assume the Marshall-Lerner condition: country ℎ’s current account improves if 𝜔 increases (orequivalently, country 𝑓’s current account improves if 𝜔 decreases). Thus, substituting 𝑐 in(27) into 𝑏 in (16), differentiating the result with respect to 𝜔, and applying (3) and (29) tothe result yields
𝑝𝐴 ℓMarshall-Lerner condition:
where 𝜕𝑐 /𝜕𝜔 is given by (29), in which 𝛾

1

𝑝𝐴 ℓ

0 from (2) and Ω

0,

(30)

0 from (28). Therefore, we

have
𝑝𝐴 ℓ

1 𝑝 𝐴 ℓ10.

This property and (28) give the following properties:𝑝𝐴 ℓ

10, 𝑝 𝐴 ℓ

1

0,

0.

(31)

Totally differentiating the two equations in (27), rearranging the results, and using (31)
gives
10

;

Ω

,

;

Ω
From (16), where 𝑟

𝑝 𝐴 ℓ ′
,

1

𝛾

𝑝ℓ

𝑝ℓ 1

𝛾

0.

0,
(32)

𝜌, which is seen from (20), (17), (31), and (32), we have

𝑝𝐴 ℓ

,

;

1

ℓ

𝑝ℓ

ℓ

0.

(33)

From this property and the Marshall-Lerner condition (30), we obtain
/
/

0.

(34)

In other words, a decrease in the effective productivity of commodity 1 (𝐴 ↓) leads to a higher
relative price for commodity 2. From (31), (32), and (34), we obtain
;

,

;

∙

𝑝𝐴 ℓ

,

/

0,

0.

(35)

Note that the effects of a change in 𝐴 on 𝜔 and 𝑐 in case SS, shown by (34) and (35),are opposite to those in case FF, shown by (25), where both countries achieve full employment.
In case FF, a decrease in 𝐴 lowers the output of commodity 1 because full employment is inplace, and raises its relative price (𝜔 ↓→ 𝑝 𝜔 ↑). The former effect dominates the latter sothat real consumption 𝑐𝑝 𝜔 𝐴 decreases. In case SS, a decrease in 𝐴 deteriorates

country ℎ’s current account 𝑏 , as shown by (33), and leads country ℎ’s currency to depreciate
so much that the relative price of commodity 1 declines (𝜔 ↑→ 𝑝 𝜔 ↓), as shown by (34).
Consequently, in country ℎ, employment and output increase, which stimulates consumption𝑐 , and the current account balance is restored. Country 𝑓’s consumption 𝑐 decreases in bothcases FF and SS but the mechanism is quite different. In case FF, a decrease in 𝐴 raises therelative price of commodity 1, deteriorates country 𝑓’s terms of trade, and reduces 𝑐 , while incase SS, it increases the relative price of commodity 2 and reduces country 𝑓’s employment
and consumption.
We next examine the effects on pollution emissions 𝑧 and 𝑧 in case SS. Because countryℎ’s output 𝑦 is 𝐴 ℓ from (12), and real consumption 𝑐 equals 𝑝 𝑦 from (16) where 𝑏
0 and (17), using 𝑝 𝜔 in (3), (34), and the first equation in (35), we find
𝑐

11

0.

(36)

From (10), the two countries’ pollution emissions 𝑧 and 𝑧 are
𝑧

𝜑 𝑦 ,

𝑧

𝜑 𝐴 ℓ 𝑐 .

Therefore, from (13), (35), and (36) we obtain
|

.

𝑦

𝜑

0,

𝜑 𝐴 ℓ

𝜑

⋛ 0,

0,
0.

Noting that a stricter emission limit 𝜑 decreases effective productivity 𝐴 from (13), wesummarize the above results as follows:
Proposition 2: When both countries face aggregate demand stagnation, a country’s stricter
emission limit and higher effective productivity yield the following effects on the real price (𝑝)and output (𝑦) of each product, pollution emissions (𝑧), and real consumption (𝑐) in the twocountries:
Policy-setting country (S)The other country (S)

𝑝

𝑝

𝑦

𝑧

𝑐

𝑦

𝑧

𝑐

Stricter emission limit
Higher effective productivity(S) implies stagnation.
Proposition 2 shows that in case SS a reduction in a country’s emission limit decreases theother country’s consumption and output, thereby reducing its pollution emissions. A stricter
emission limit yields negative carbon leakage by deteriorating the other country’s businessactivity.

5. Environmental policies under asymmetric business activities
This section considers the asymmetric case where country ℎ faces stagnation and the othercountry achieves full employment, which is case SF in (24). We examine the effects of changes
in the two countries’ emission limits on their real consumption and pollution emissions.
In case SF, where ℓ𝜓 𝜔 𝑐

1 and ℓ𝑐

1, from (18) we find
𝐴 ℓ 𝑐

𝜓 𝜔 𝑐

⟹ 𝑐
𝑐

12

𝐴 ,

𝑔 𝑐 ; 𝜔, 𝐴 ,where 𝜔 is determined so that the current account given by (16) is in balance. Therefore, using(17), the definition of 𝜓 𝜔 in (18), and (20), we find𝑐𝑐𝑏where ℓ 𝑐

,
𝑐

ℓ 𝑐

,

𝑝 𝜔 𝐴 ℓ 𝑐

0,

(37)

is given by (26). The three equations determine 𝑐 , 𝑐 and 𝜔. By partiallydifferentiating the current account 𝑏 with respect to 𝜔, using 𝑝 𝜔 in (3), and assuming the
Marshall-Lerner condition, we obtain𝑝𝐴 ℓ

the Marshall-Lerner condition:

1

ℓ
ℓ

1

0,

0,

ℓ

𝑝𝐴 ℓ

𝐴 ℓ

0,

(38)

where the last property is found to hold from the other two properties.
The stagnant country’s environmental policy
Let us initially consider how a change in the stagnant country ℎ’s emission limit affects
the two countries’ real consumption and pollution emissions. Given the relationship between
𝐴 and 𝑐 represented by the second equation in (37), we find that 𝑏 given by the third
equation in (37) satisfies
ℓ

0.

ℓ

The Marshall-Lerner condition in (38) and the above property give/0,

implying that a decrease in 𝐴 leads to an improvement in country 𝑓’s terms of trade (𝜔 ↑).
This benefits country 𝑓 because it is in full employment. It also benefits the stagnant country
because a higher 𝜔 (or equivalently, a lower relative price of commodity 1) improves therelative competitiveness of commodity 1 to commodity 2 and increases the stagnant country’s
output and real consumption.
Let us mathematically obtain the properties mentioned above. From (12) and (37), theoutput of commodity 1 is𝑦.

Therefore, totally differentiating the three equations in (37) and using (38) leads to

13

ℓ

𝑝

ℓ

0,

𝑐
ℓ
ℓ

𝛾𝑝

0,
0.

(39)

From (13), a stricter emission limit of country ℎ lowers 𝐴 . Therefore, the effects of a decrease
in 𝐴 obtained above can be reinterpreted as the effects of a stricter emission limit of countryℎ, which is stagnant in the present case.
As for pollution emissions 𝑧 and 𝑧 in case SF, from (21) we have𝑧

𝜑 𝑦 , 𝑧

𝜑 𝐴 .

(40)

Using (13), (39), and (40), we obtain the effects of a change in 𝐴 on 𝑧 and 𝑧 when 𝜑 isconstant, and the effects of a change in 𝜑 on them which include the effects through changes
in 𝐴 . They are
|

.

𝑦

𝜑

0,

|

𝜑

𝐴 ⋛ 0,

.

0,

0.

(41)

The following proposition summarizes the results of (39) and (41).
Proposition 3: When a country faces stagnation and the other country achieves full
employment, the stagnant country’s stricter emission limit and higher effective productivity
yield the following effects on the real price (𝑝) and output (𝑦) of each product, pollution
emissions (𝑧), and real consumption (𝑐) in the two countries:
Policy-setting country (S)The other country (F)

𝑝

𝑝

𝑦

𝑧

𝑐

𝑦

𝑧

Stricter emission limit

00Higher effective productivity

0

0

𝑐

From Proposition 3, if a country faces aggregate demand stagnation and the other country
achieves full employment (which may currently be the case for developed and developing
countries), a stricter emission limit by the stagnant country deteriorates the exchange rate and14lowers the relative price of its output, which increases its employment and real consumption.
The other country, which is in full employment, also achieves higher real consumption because
its terms of trade improve. Thus, there is no international conflict of interest with respect toreal consumption. However, the stagnant country’s pollution emissions may increase in spiteof a stricter emission limit because its output increases.
The full-employment country’s environmental policy
Next, we obtain the effects of the full-employment country’s stricter emission limit. In thepresent setting, the full-employment country is country 𝑓, whose emission limit is 𝜑 , and thestagnant country is country ℎ. Therefore, we examine the effects of changes in 𝐴 and 𝜑 .
Totally differentiating the three equations in (37) and rearranging the results leads to
𝑝𝐴 ℓ
ℓ

ℓ

where ℓ𝑝𝐴 ℓ

0 from (26), and 𝜕𝑏 /𝜕𝜔

0,

ℓ

𝛾𝑝

ℓ

ℓ

ℓ

1

1

0,
1

𝛾

𝑝

⋛ 0,

(42)

0 from (38). A rise in 𝐴 lowers the relative price ofcommodity 2, which deteriorates the relative competitiveness of commodity 1 and worsens
country ℎ’s employment and real consumption. The effect on 𝑐 is ambiguous because a risein 𝐴 reduces the relative price of commodity 2 but expands its output in country 𝑓 under full
employment. If both countries achieve full employment, the latter effect dominates the former,
benefiting country 𝑓. However, when country ℎ faces stagnation, the reduction in 𝜔 is so largethat the former effect may dominate the latter; that is, the effect on 𝑐 is ambiguous, as shownby the last equation in (42). From (13), country 𝑓’s stricter emission limit decreases 𝐴 ; hence,
its effects are opposite to those mentioned above.
As for the two countries’ pollution emissions, from (13), (40) and (42), we obtain

|

𝜑 𝐴 ℓ

𝑐

.

𝜑

0,
0,

0,
𝐴

𝜑

0.

A decrease in 𝜑 , implying a stricter emission limit by country 𝑓, naturally reduces country
𝑓 ’s pollution emissions but expands country ℎ’s pollution emissions because it increases
country ℎ’s production; that is, carbon leakage occurs.
15

Noting that country 𝑓 is the policy-setting country and attains full employment in thepresent case, we summarize the above results as follows:
Proposition 4: When one country achieves full employment and the other country faces
stagnation, the full-employment country’s stricter emission limit and higher effective
productivity yield the following effects on the real price (𝑝) and output (𝑦) of each product,pollution emissions (𝑧), and real consumption (𝑐) in the two countries:
Policy-setting country (F)The other country (S)

𝑝

𝑝

𝑦

𝑧

𝑐

𝑦

𝑧

𝑐

Stricter emission limit
Higher effective productivity

A stricter emission limit by the full-employment country reduces its output, resulting inless pollution emissions. It raises the relative price so that the stagnant country’s commodity ismore competitive, causing its output, pollution emissions, employment and real consumption
to increase. Thus, carbon leakage occurs, and world pollution emissions may increase eventhough the full-employment country reduces its pollution emission limit. The country’s output
is less, but its relative price rises so that its real consumption may increase.

6. Discussion
Let us finally discuss the effects of clean technology transfer on the source and recipient
countries’ real consumption and pollution emissions, and the first-best pollution emission limitof the stagnant country.
Clean technology transfer
In international negotiations of global warming countermeasures, a typical policy option
is to transfer clean technologies. This lowers pollution emissions generated by production (𝛿 ↓)and improves the efficiency of abatement (𝜎 ↑) in the recipient country. This subsection
examines how such technology transfers affect real consumption and pollution emissions in
the two countries. The effects of the transfers are regarded as the effects of an improvement in16

the recipient country’s effective productivity, as is clear from (13). Thus, having Propositions
1–4 in mind, we summarize the effects as follows:
Proposition 5: If country ℎ transfers a superior clean technology to country 𝑓 so that 𝛿
decreases and/or 𝜎 increases, the following effects appear in the two countries:
Source country
Cases
FF

𝑝

𝑦, 𝑧

Recipient country
𝑐

𝑝

𝑦, 𝑧

𝑐

0

SS
SF
FS

0

Note that when the recipient country is in full employment (cases FF and SF), it emits
more pollution, even though the source country transfers a superior technology of abatement
and a cleaner production technology. This happens because the recipient country leaves its
pollution emission limit per output unchanged. The recipient country’s firms can then reduce
the amount of labor for abatement and reallocate the extra labor to production, thus increasing
effective productivity. If a stricter emission limit is set so that effective productivity does notchange when the technology is transferred, real consumption is unchanged in both countries
and the recipient country emits less pollution. Thus, the source country should require therecipient country with full employment to impose a stricter emission limit when transferring
superior abatement and cleaner production technologies.
A large number of clean technology transfers have been implemented through Clean
Development Mechanism (CDM) projects under the Kyoto Protocol in order to assist
developing countries in achieving sustainable development (see Dechezleprêtre et al., 2009).
Jaraitė et al. (2022) evaluate the CDM in Indian manufacturing and find that firms registeredwith CDM projects increase carbon emissions as well as outputs — findings consistent with
our results in the case where the recipient country is in full employment. There is also empiricalevidence that the impact of CDM on carbon emissions and sustainable development in recipient
countries is ambiguous and politically charged.10 This suggests that source countries should

10
Zhang et al. (2018) show that the impact of CDM projects on carbon emissions becomes negative in Chinaas the levels of energy-use technology and carbon emissions reduction technology become higher. Various

17require recipient countries to impose stricter limits on polluting emissions when transferring
clean technologies.
When the recipient country faces stagnation (cases SS and FS), a technology transfer
decreases its pollution emissions even if its emission limit is unchanged. This is because thetransfer increases the recipient country’s effective productivity, which improves its current
account, raises the relative price of its product, and decreases its output and pollution emissions.
Among the above four cases, case SF is arguably the most likely — a transfer from adeveloped country under stagnation to a developing country with full employment. Such atransfer harms the source country because the relative price of its product increases and its
output decreases. The recipient country’s real consumption may decrease even though its
output and pollution emissions increase because the relative price of its product declines. Thus,
from Proposition 3, it is better for the stagnant country to lower its own emission limit than totransfer a clean technology because the former increases real consumption in both countries.
In this case, however, pollution emissions in the stagnant country may increase because its
output is stimulated. If the stagnant country transfers a clean technology, it should do so under
the condition that the recipient country sufficiently decreases its pollution emission limit, as
mentioned below Proposition 5.
First-best policy
Propositions 2 and 3 show that the stagnant country’s stricter emission limit creates new
employment for abatement, which increases real consumption, output, and pollution emissions
in that country, whether the other country is in full employment or stagnation. Moreover, thecountry can achieve the same output with less pollution emissions by lowering the emission
limit enough to make firms allocate all residual labor to abatement, leading to less pollution
emissions with the same output level. Therefore, the stagnant country can achieve the first-best
combination of real consumption and pollution emissions by lowering its emission limit. Moreprecisely, we have the following proposition:
Proposition 6: The stagnant country’s first-best policy is to decrease its emission limit enoughto achieve full employment. If the emission limit is stricter than the optimal level under full

impacts of CDM projects on sustainable development (social equality, economic growth, and environmental
protection) are discussed in Mori-Clement (2019).

18

employment, the emission limit that just allows the country to reach full employment is thefirst-best optimal. If the emission limit is looser than the optimal level under full employment,
the first-best optimal level equals the optimal level under full employment, which is stricter
than the emission limit that just achieves full employment.

7. Conclusions: international emission coordination
In the case of full employment in both countries, a country’s small restriction on pollution
emissions should benefit both countries if pollution emissions are very harmful andsignificantly spill over beyond its borders. This is because in this case the harm due to adecrease in net productivity is smaller than the benefit due to less pollution emissions.
However, when negotiating the optimal emission limit of each country, a conflict of interest
arises because their optimal emission limits differ.
If a country is in stagnation, a stricter emission limit creates new employment forabatement, which stimulates the country’s real consumption and production, depreciating theexchange rate and lowering the relative price of its product. Thus, if the other country is in full
employment, that country receives the benefit of improved terms of trade and increases realconsumption — that is, there is no conflict of interest between the two countries. The stagnant
country should further decrease its emission limit until it reaches full employment. Once bothcountries achieve full employment, however, they face a conflict of interest when determining
their individual emission limits, as discussed above.
The first-best policy must be strict enough to achieve full employment in both countries
because if there is unemployment, both countries are better off by allocating all the unemployed
to abatement. The necessary negotiation is based on the assumption that both countries achieve
full employment.

Appendices
Appendix A: Proof of (3)Under homothetic utility 𝑢 . , . , once real aggregate consumption 𝑐 is given at each point
in time, the optimal levels of 𝑐 and 𝑐 satisfy
,

,

/

,

,

/

𝜔,

19

(A1)

from which we obtain (2). The consumer price index is chosen so that a change in the relative
price 𝜔 will not affect the level of 𝑢 . , . . Inserting 𝑐

∗

and 𝑐

∗

, given in (2), into 𝑢 . , . then

gives
𝑐∗,

𝑢

𝑐∗
,

Because 𝑢 /𝑢𝜔𝜙 𝑐∗ 𝑢≡𝑢 𝑐∗ ,

,

𝑢

𝑢

0.

(A2)

𝑝 𝜔 /𝑝 𝜔 from (A1), the second equation in (A2) yields

𝑝 𝜔

0,

𝑝 𝜔

𝛾𝑝

0,

which are shown in (3).
Appendix B: Proof of (28)Given 𝑐 , if 𝑐 is such that ℓ 𝑐

1 in the first equation of (27), the demand forcommodity 1 (the left-hand side) is lower than its supply (the right-hand side). Otherwise, full
employment should be reached. Thus, for the stagnation steady state to exist, the left-hand sideof the equation must be less inclined with respect to 𝑐 than the right-hand side. The second
equation must also satisfy the same property. Therefore, using 𝜓 and 𝜓 in (18), and 𝑔 and
𝑔 in (27), we obtain
; ,

ℓ

; ,

0,

ℓ

0.

(A3)

Moreover, the two functions satisfy
if 𝑐0, then 𝑐𝑔 0; 𝜔, 𝐴

0

𝑐 ;

if 𝑐

0, then 𝑐𝑔 0; 𝜔, 𝐴0𝑐 ;because household consumption must be positive even if the other country’s consumption iszero. From these properties, the two functions are illustrated as shown in Figure 1. Therefore,
if the intersection point of the two functions exists, at that point it must be valid that.
From (A3), this condition is equivalent to (28).

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22

𝑐

𝑐

𝑔 𝑐 ; 𝜔, 𝐴1𝑐𝑔 𝑐 ; 𝜔, 𝐴2

E
𝑔 0; 𝜔, 𝐴2O𝑐𝑔 0; 𝜔, 𝐴1

Figure 1: Interdependence of Consumption

23