GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.83

Cost-reducing R&D investment, Labor market and trade

Tadashi Morita

September 2009GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Cost-reducing R&D investment, Labor market andtrade ∗
Tadashi Morita †Graduate School of Economics, Osaka University
September 3, 2009

Abstract
In this paper, I construct a two-country general equilibrium model inwhich oligopolistic firms export goods and undertake cost-reducing R&D investment. Each country imposes tariffs. A decrease in the tariff rates in bothcountries decreases cost-reducing R&D investment.
Keywords: R&D, Trade, Oligopoly
JEL classification: F12, F13∗

I am very grateful to Koichi Futagami for his considerable help. I have also benefited fromcomments and suggestion by Kenzo Abe, David Flath, Taiji Furusawa, Jota Ishikawa, Masao
Oda, Hisayuki Okamoto, Yoshiyasu Ono, Kazuhiro Yamamoto, Akihiko Yanase and seminar participants at Seinan Gakuin University, the Japan Society of International Economics Kansai, theJapanese Economic Association and the 2009 Asian Pacific Trade Seminars. This article waspreviously entitled, ”R&D and trade in a general equilibrium model”.
†
Graduate School of Economics, Osaka University, 1.7 Machikaneyama, Toyonaka, Osaka 5600043, JAPAN e-mail: gge013mt@mail2.econ.osaka-u.ac.jp1

1

Introduction

In 1980s and 1990s, R&D investment has increased dramatically in the OECD
countries. Braun (2008) explains that the ratio of industrial R&D expenditures to
GDP has risen from 1% in 1979 to 1.43% in 1990 and 1.72% in 2004. In addition,international market become more openness recently. For example, Gao (2006)
explains that average tariffs fell around 20% in 1995 to under 5% today. 1
The purpose of this paper is to investigate the relationship between the tradeliberalization and cost-reducing R&D expenditures: When international trade isfacilitated, does the cost-reducing R&D expenditures increase?
In this paper, I construct a two-country general equilibrium model in which
oligopolistic firms export goods and conduct cost-reducing R&D investment to reduce their marginal cost. Each country simultaneously imposes tariffs on import
goods at the same rate. In each country, there are two types of labor: skilled laborand unskilled labor. The firms employ skilled labor not only to produce goods
but also to conduct cost-reducing R&D investment while unskilled labor is used
only to produce goods. I show that when the countries reduce their tariff rates,
cost-reducing R&D investment decreases.

2

The model

There are two countries, Home and Foreign, indexed by l ∈ {H, F } and thesecountries are symmetric. The population size in each country is equal to L. There
are two types of labor in each country: skilled labor and unskilled labor. I assume
that s is the proportion of skilled labor. Thus, sL is the number of skilled laborand (1 − s)L is the number of unskilled labor.2 There are three types of goods;
an agricultural good, and manufacturing goods 1 and 2. The agricultural goodcan be produced in both countries. Manufacturing good 1 is produced only in the
Home country and manufacturing good 2 is produced only in the Foreign country.
The firm producing manufacturing good 1 is named Firm 1 and the firm producing
manufacturing good 2 is named Firm 2. I assume that Firms 1 and 2 compete
1

Some empirical papers investigate the relationship between trade liberalization and R&D
expenditures. Funk (2003) concludes that U.S manufacturing firms which sell their product tothe U.S market decrease the R&D investment when the trade liberalization is promoted. On theother hands, U. S manufacturing firms with foreign sale increases the R&D investment. Scherer
and Huh (1992) investigate that average U.S. high-tech firms reduce the R&D investment in the
short run when the trade liberalization is promoted.
2
I omit the process of skill acquisition and I assume that the supply of skilled and unskilledlabor are given.

2

strategically by using their product quantities, that is, they engage in Cournot
competition. Both countries levy tariffs on their imports of the manufacturing
good and the tariff rate is denoted by τ .

2.1

Consumer

The utility function of the representative consumer in each country is given by
U l (q1l , q2l , ml ) = ml + a(q1l + q2l ) −

¤
1£ 2
2
+ 2bq1l q2l , l ∈ {H, F } , b ∈ {0, 1} ,q1l + q2l2(1)

where ml is the consumption of the agricultural good in country l, q1l and q2l
respectively denote the consumption of the manufacturing goods produced by Firms
1 and 2, and a and b are positive parameters. The budget constraint of the consumer
in country l is as follows:
ml + p1l q1l + p2l q2l = El , l ∈ {H, F } ,(2)where ml is chosen to be the numeraire, p1l and p2l respectively denote the pricesof the manufacturing goods produced by Firms 1 and 2, and El is the expenditure
in country l. From the first-order condition of the consumer, I obtain the following
inverse demand functions:p1l = a − q1l − bq2l ,(3)

p2l = a − q2l − bq1l .

(4)

2.2

Production

2.2.1

Agricultural goods sector

Production of one unit of the agricultural good requires one unit of unskilled laborin both countries. I assume that the agricultural good market is perfect competitive
and the agricultural good can be traded freely. Thus, the wage rate for unskilledlabor in both countries is equal to unity.
2.2.2

Manufacturing goods sector

Firms 1 and 2 produce the manufacturing goods and conduct cost-reducing R&D
investment to decrease their marginal costs of production. Production of the manufacturing good requires both skilled and unskilled labor. The production of one
3

unit of the manufacturing good requires θ units of skilled labor and α(kl ) ∈ [0, ᾱ]units of unskilled labor in country l. kl denotes the number of the skilled laborthat is allocated to cost-reducing R&D investment in country l. I assume that∂α(kl )/∂kl < 0 and ∂ 2 α(kl )/∂kl2 ≥ 0. The profit of Firm 1 is then given by
π1 = p1H q1H + (p1F − τ )q1F − (q1H + q1F )(α(k1 ) + θwH ) − k1 wH ,(5)

where wH is the wage rate for skilled labor in the Home country. Due to the inverse
demand functions (3) and (4), the profit maximization of the firms leads to thefollowing levels of output and R&D investment:1[a − bq2H − (α(k1 ) + θwH )] ,
2

(6)

1
[a − τ − bq2F − (α(k1 ) + θwH )] ,
2

(7)

q1H =
q1F =

0

wH = −(q1H + q1F )α (k1 ).

(8)

I suppose that the wage rate of skilled labor is constant for the manufacturing goodfirms. Because I assume that Home and Foreign countries are symmetric, Firms 1
and 2 produce the same output level. Thus, both the level of R&D investment andthe wage rate for skilled labor are the same in the both countries: k1 = k2 ≡ k andwH = wS ≡ w. From (6) and (7), the output levels are given by1[(2 − b)a + bτ − (2 − b)(α(k) + θw)] ,4 − b21
q1F = q2H =[(2 − b)a − 2τ − (2 − b)(α(k) + θw)] ,4 − b2

q1H = q2F =

(9)
(10)

when q1H and q1F take positive values. Because the purpose of this paper is toinvestigate the effect of tariffs, I focus on the case in which positive amounts ofmanufacturied goods are traded between the countries.
The demand for skilled labor derives from R&D investment and production of
the manufacturing good. The demand for unskilled labor comes from productionof the manufacturing good and the agricultural good. Because the supply of skilledlabor is sL and that of unskilled labor is (1 − s)L, the labor market equilibrium
conditions in country H is given bysL = k1 + θ(q1H + q1F ),(11)(1 − s)L = mPH + α(k1 )(q1H + q1H ),

(12)

4

where mPH denotes the labor demand of the agricultural good sector in country H.

3

Equilibrium

From (8), (9), and (10), I obtain the wage rate for skilled labor as follows:0−α (k) [2a − τ − 2α(k)]w=.
(2 + b) − 2θα0 (k)(13)

From (13), I obtain the output level of Firm 1 as follows:
q1H + q1F =

A
,
B

(14)
0

where A ≡ 2a − τ − 2α(k) > 0, B ≡ (2 + b) − 2θα (k) > 0.
Inserting (13) and (14) into the skilled labor equilibrium condition, (11), yields
the skilled labor equilibrium condition as follows:sL = k +

θA
.
B

(15)

Totally differentiating (15) reveals that ∂k/∂τ takes a positive value (see the Appendix). This result is summarized as the following proposition.
Proposition 1. An increase in the tariff rate raises R&D investment.
An increase in the tariff rate lowers the profitability of exporting manufacturing
goods. Hence, both firms decrease their exports and the market becomes lesscompetitive. Given their increased market power, both firms raise prices and lower
output levels. Because of the skilled labor market equilibrium condition, moreskilled labor can be allocated to R&D investment. Consequently, both firms increase
R&D investment.
By differentiating (14) with respect to the tariff rate, τ , I obtain ∂(q1H +q1F )/∂τ < 0 (see the Appendix). Thus, this results in the following lemma.
Lemma 1. A decrease in the tariff rate raises the output level of both firms.
A decrease in the tariff rate has a direct effect and an indirect effect. A reductionin the tariff rate directly increases output levels of the firms by facilitating exports.
A fall in the tariff rate indirectly reduces output level of the firms. This is because
the stimulus to exports brought about by the lower tariff makes the market morecompetitive, to which the firms respond by reducing their R&D investment; this5then raises the marginal costs, which reduces output levels of the firms. However,the direct effect dominates the indirect effect.
I now investigate the effects of lowering the tariff rate on the wage rate of skilledlabor. Differentiating the wage rate of skilled labor with respect to τ , I obtain∂w< 0 (see the Appendix). This result is summarized as the following proposition.
∂τProposition 2. A decrease in the tariff rate increases the wage rate for skilledlabor.
From Lemma 1, a reduction in the tariff rate raises output levels of the firms.
Then, because the firms demand skilled labor more to produce their goods, thedemand of skilled labor increases the wage rate for skilled labor. Therefore, thewage gap between skilled and unskilled labor widens.

4

Welfare Analysis

In this section, I investigate the relationship between welfare and the tariff rate.
In the country H, the consumption of the agricultural good mH is derived frombudged constraint (2) as follows:
mH = EH − p1H q1H − p2H q2H .

(16)

The expenditure in the country H, EH , is consisted of wage rate, profit of the firm
1, and tariff revenue. Therefore, the expenditure in the country H is given by
EH = wsL + (1 − s)L + π1 + τ q2H .

(17)Then, substituting (17) to (16), I can derive the consumption of the agricultural
good as follow:
mH = (1 − s)L − α(k)(q1H + q2H ).

(18)

By using (18), I can gauge the welfare level in the country H
U H = (1 − s)L + (a − α(k))(q1H + q2H ) −

6

¤
1£ 2
2
+ 2bq1H q2H .
q1H + q2H2

(19)

Differentiating by τ and substituting the consumption of manufacturing goods (9)and (10), I get
·
¸
0
∂U H
1
b−2
2 + b − b2 α (k)θA 3b2 − 4=(a − α(k)) ++τ∂τ
4 − b2 b + 2
2+bB
4 − b21∂k0−[2(a − α(k)) + (q1H + q2H )] α (k)(2 + b)
∂τ
h
i ∂w
θ
0
−
2(a
−
α(k))(1
−
2θα
(k))
+
(1
+
b)τ
. (20)(2 + b)(2 + b − 2θα0 (k))∂τ
The first term takes a negative value. The second term and the third term takepositive values. Therefore, the effect of tariff rate is ambiguous. In order to getsome clear results. I present a numerical example. In this example, the function
α(k) is 3 − k. As for the parameters of the utility function I choose a = 7.5 andb = 0.74. The number of the population is L = 10 and the proportion of skilledlabor is s = 0.5. The parameter of the skilled labor’s productivity is θ = 0.3.
Figure 1 describes the relationship between the welfare level and the tariff rate τ .
As Figure 1 shows, there exists the tariff rate which maximizes the welfare level inthe contry H and optimal tariff rate is τ ∗ = −4.555. Therefore the both countries
subsidize the firms to their import goods.
6JGYGNHCTGNGXGN

34

32

30

28

-15

-10

-5

5

Ǽ

Figure 1: Numerical example

5Conclusion

In this paper, I constructed a two-country general equilibrium model in which
oligopolistic firms produce goods and undertake cost-reducing R&D investment. A
reduction in the tariff rate increases the wage gap between skilled and unskilled la7

bor. I also showed that a fall in the tariff rate decreases investment in cost-reducing
R&D. This result differs from its of Braun (2008) and Haaland and Kind (2008).
Their studies contributed analyzing relationship between the trade liberalization
and R&D investment. They do not consider that the increased demand for skilledlabor raised the wage rate of skilled labor because they do not incorporate the labor market. Therefore, although a fall in tariff rate raises firms’ output levels, themarginal cost of R&D does not change. However, I incorporate the labor market.
Therefore, I can obtain the opposite result.

A

Appendix

A.1

Proof of Proposition 1

By totally differentiating (15), I obtain the following equation:−θθCdτ + (1 + 2 )dk = 0,
B
B
0

00

where C ≡ −2α (k)B + 2θα A > 0. This equation can be rewritten as
dk
θB
= 2
> 0.
dτ
B + θC

A.2(A.1)

Proof of Lemma 1

To prove that an increase in the tariff rate decreases the output level of Firm 1, I
differentiate (14) with respect to τ to obtain·¸∂(q1H + q1F )1∂k= 2 −B + C
∂τ
B
∂τ
·
¸
1
θC
=
−1 + 2B
B + θC−B= 2< 0.
B + θCThus, the result follows.

8

A.3

Proof of Proposition 2

Differentiating the wage rate for skilled labor with respect to the tariff rate, τ ,yields the following:
i dk
dw
α (k)
1 h 000=− 2 α (k)AB + α (k)C
.
dτ
B
B
dτ
0

By inserting (A.1) into the above equation, I obtain the following equation:
0

00

dw
Bα (k) − θAα (k)
=
< 0.
dτ
B 2 + θC(A.2)

The denominator of the above equation is positive because B > 0 and C > 0. The
000

numerator of the above equation is negative because α (k) < 0 and α (k) > 0.
Therefore, ∂w/∂τ is negative.

References
Braun, Sebastian, (2008), ’Economic Integration, Process and Product Innovation,
and Relative Skill Demand,’ Review of International Economics, 16:5, 864873.
Funk, Mark, (2003), ’The Effects of Trade on Research and Development,’ Openeconomies review 14, 29-42.
Gao, Ting, (2007), ’Trade costs, international production shifting, and growth,’ European Economic Review, 51:2, 317-335.
Haaland, Jan I, and Hans Jarle, Kind, (2008), ’R&D policies, trade and process
innovation,’ Journal of International Economics, 74, 170-187.
Scherer, F, M and Huh Keun, (1992), ’Research Reactions to High-Technology Import Competition,’ Review of Economics and Statistics, 74, 202-212.

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