Foreign Worker Participation in Labor Markets and Its Effects on the Economy’s Welfare
Akira Shimada
Faculty of Economics, Nagasaki University
Abstract
Using a small open economic model with dual labor markets, we investigate how changes inforeign workers’ accessibility to labor markets affect the economy’s welfare. We assume that only apart of the foreign workers can enter the labor markets due to impediments to foreign worker
participation in labor markets. In actual economies, foreign workers cannot participate in the labormarkets as freely as native workers. We assume two cases, one in which the union and the policy
authority behave non-cooperatively, and another in which they behave cooperatively. We show thatthe economy’s welfare, i.e., the sum of the union’s and policy authority’s utilities, increases in bothcases, as more unskilled foreign workers enter the secondary labor market, while the economy’s
welfare does not always increase as more skilled foreign workers enter the primary labor market.
This is because, in the case of cooperation, it is possible that the decreases in the union’s utility arelarger than the increases in the policy authority’s utility. Our results imply that if we want to increase
the economy’s welfare by increasing unskilled foreign worker participation in the secondary labormarket, we have to eliminate the discriminations that prevent their participation in this labor market.
We also have to implement policies that mitigate the decreases in the union’s utility caused by theincreases in union membership of skilled foreign workers, in order to encourage their employment.

JEL Classification: F41, F22, J42

Keywords: International migration of labor; Dual labor markets; Small open economic model01. Introduction
Today, many countries are experiencing large inflows of foreign workers.1 Foreign worker
inflow influences receiving countries in a variety of ways. It affects not only native worker
employment, but also aggregate supply through changes in employment and aggregate demandthrough changes in private and public spending. Therefore, analyzing the impact of foreign worker
inflow on the receiving countries has become an important economic issue.
Although conclusions pertaining to the effects of foreign worker inflow are not uniform, it is often
argued that the negative effects are larger than the positive effects. Many countries are attempting to
reduce the inflow of foreign workers.2 For this purpose, they are mainly implementing immigration
control laws and government regulations. However, such measures are not always effective in
reducing the inflow because workers are moving across different countries to seek better working
conditions and it is very difficult to manipulate workers’ rational behavior.3 This implies that theforeign worker inflow cannot be easily controlled.
Then, if foreign worker inflow has larger negative effects than positive effects on the receiving
countries and we only have imperfect control of foreign worker inflow, is it impossible for us toalleviate its negative effects and improve the economy’s welfare?
Previous studies on the economic impact of immigration have assumed that although foreign
workers are not always employed; however, once they enter a country, all of them can freely enter

1

See Böhning and Oishi (1995), Zlotnik (1998), and Stalker (1994, 2000) for a discussion of trends ininternational migration of labor.
2

It is far more difficult to let immigrated foreign workers leave the country than to reduce their inflow.

3

Shimada (2003) discussed the possibility of reducing the inflow of unskilled foreign workers byconsidering the rationality of their behavior.
1

labor markets of the immigrated country.4 However, in practice, many impediments such as thediscriminatory behavior of unions or the discriminatory structure of labor markets against foreign
workers makes it difficult for them to participate in labor markets of the immigrated country.
Therefore, foreign workers only have a limited access to labor markets.5 Several studies on theeconomic impact of immigration do not take sufficient account of this fact.
Foreign worker employment depends not only on the amount of foreign worker inflow but also on
the number of workers who can enter labor markets. In other words, foreign worker employment isaffected by the ratio of foreign workers entering labor markets to those entering a country as well as theamount of foreign worker inflow.

Even if the size of foreign worker inflow is large, theiremployment will be small in a case where their access to the labor market is limited.
Moreover, today, many policy authorities cannot completely ignore the interest of foreign workers
and therefore, pay some attention to their employment.6

Even if we accept foreign workers

4

It is assumed in Agiomirgianakis (1998, 2000) that all foreign workers can gain union membership,

and the union tries to attain full employment for all union members. Shimada (2003) follows thisassumption and assumes that all unskilled foreign workers can enter the competitive labor market of
the immigrated country.
5

In actual economies, many unions are unwilling to grant membership to foreign workers, because theobjectives of foreign workers tend to be different from those of the native workers. Even if theforeign workers can gain union membership, their interest will rarely be reflected in the union’s
objective.
6

It goes without saying that we are speaking about the foreign workers who have immigrated legally.

As Agiomirgianakis (2000) indicates, the policy authorities may ignore the interest of foreign workers
giving priority to the interest of native workers, and it is true that policy authorities in some countries2

reluctantly and if their existence might have negative economic effects, it is undesirable for the society
to leave many of them jobless. A large number of unemployed foreign workers have negative
non-economic effects on the society. They might lead to worsening of the public order.
Accordingly, foreign workers’ accessibility to labor markets affects the policy authority’s utility,
and thus the behavior, leading to changes in the union’s behavior. This implies that the economy’s
welfare, i.e., the sum of the union’s and the policy authority’s utilities, depends on the degree of foreign
workers’ accessibility to labor markets. Even if foreign worker inflows in the two countries are samein size, each economy’s welfare will be affected in different ways depending on those workers’
accessibility to those countries’ labor markets.
Therefore, this paper focuses on the effects of foreign workers’ accessibility to labor markets on theeconomy’s welfare. In particular, we consider whether it is possible or not to improve the economy’s
welfare by encouraging foreign workers’ participation in labor markets.
For this purpose, we utilize an open macroeconomic model for the analysis because internationalmigration of labor is closely connected with open macroeconomies. However, till date, internationalmigration has been mainly studied by approaches that do not use macroeconomic models and it has notbeen sufficiently analyzed in the context of macroeconomics, except by Agiomirgianakis (1998, 2000)
and Agiomirgianakis and Zervoyianni (2001).7

have a discriminatory attitude toward foreign workers. However, in the days of growing international
mobility of labor, the policy authorities cannot continue to have such attitudes.
7

Main approaches that explain international migration without using macroeconomic models are as

follows: Microeconomic studies of migration by Todaro (1969), Harris and Todaro (1970), Todaro
and Maruszko (1987) assume that international migration occurs as a result of individual optimization.
Partial equilibrium studies on migration by Greenwood and McDowell (1986) and chapters 2, 3, and 6
3

We assume a small open economy with dual labor markets where two kinds of labor, skilled andunskilled, are traded. We give the amount of foreign worker inflow exogenously. Although weshould examine how changes in the size of foreign worker inflow affect receiving countries, which isan important problem, the size of foreign worker inflow remains constant throughout the analysis
because this paper aims at clarifying how changes in foreign workers’ accessibility to labor markets
affect the economy’s welfare. We assume two cases - in one case the union and the policy authority
behave non-cooperatively and in another case they behave cooperatively.
We aim to draw conclusions as to whether increases in skilled (unskilled) foreign worker
participation in the primary (secondary) labor market increase the economy’s welfare. From these
conclusions, we attempt to derive implications as to how skilled and unskilled foreign workers shouldbe treated in order to increase the economy’s welfare.
Our analysis shows that given the size of unskilled foreign worker inflow, we can increase theeconomy’s welfare as more unskilled foreign workers enter the secondary labor market in both
non-cooperative and cooperative regimes. This can be explained as follows: In the non-cooperative
regime, both the union’s utility and the policy authority’s utility increase as more unskilled foreign
workers enter the secondary labor market. In the cooperative regime, although there are cases whereby Stalker (2000) focus on the labor markets of different countries and provided an explanation thatinternational migration is generated by wage differentials among countries. According to new
economics of migration by Stark (1991), international migration is determined not by an individual but
by a family. Stark (1984) and Stark and Taylor (1991) advocate the relative deprivation hypothesis.
Other approaches for explaining the international migration include the dual labor market theory, theworld systems theory, the network theory, and the cumulative causation. See Massey, Arango, Hugo,
Kouaouci, Pellegrino, and Taylor (1993, 1998) for a survey of theories in international migration.
4

the policy authority’s utility decreases as more unskilled foreign workers enter the secondary labormarket, effects of increases in unskilled foreign workers’ accessibility on the union’s utility arestronger than those on the policy authority’s utility, making the economy’s welfare higher as moreunskilled foreign workers enter the secondary labor market.
Our analysis also shows that given the size of skilled foreign worker inflow, the economy’s welfare
does not always increase as more skilled foreign workers enter the primary labor market and gain
union membership. This can be explained as follows: The policy authority’s utility increases as
more skilled foreign workers enter the primary labor market and gain union membership in both
non-cooperative and cooperative regimes. In the non-cooperative regime, decreases in the union’s
utility are smaller than increases in the policy authority’s utility due to increases in the skilled foreign
workers’ participation in the primary labor market, which implies that the economy’s welfare increases
as more skilled foreign workers enter the primary labor market and gain union membership.
However, in the cooperative regime, there are cases where decreases in the union’s utility are larger
than increases in the policy authority’s utility; hence, the economy’s welfare decreases as more skilled
foreign workers enter the primary labor market and gain union membership.
These results imply that the impediments for unskilled foreign workers should be removed to allow
them to enter the secondary labor market and encourage their participation in this market rather thankeeping them away. By doing so, we can increase the economy’s welfare in both the regimes.
These results also imply that if we want to increase the economy’s welfare by increasing skilled
foreign worker participation and their employment in the primary labor market, the policy authority
should implement policies that mitigate decreases in the union’s utility arising from increases in skilled
foreign workers’ membership. Such policies are required to encourage the employment of highly
skilled foreign workers who cannot be replaced by the skilled native workers.
The rest of this paper is organized as follows: Section 2 presents a small open economic model5

with primary and secondary labor markets. We assume that only a few of skilled (unskilled) foreign
workers can enter the primary (secondary) labor market. Section 3 examines the effects of changes inforeign workers’ accessibility to labor markets on the economy’s welfare in the case where the union
and the policy authority behave non-cooperatively. Section 4 examines those effects assuming thatthe union and the policy authority behave cooperatively.

Section 5 contains the concludingcomments.

2. The Model
We assume a small open economy with dual labor markets, where skilled labor is traded in the
primary labor market and unskilled labor is traded in the secondary labor market. The small open
economy interacts with the rest of the world through international trade of goods and internationalmigration of labor. The small open economy consists of skilled workers, unskilled workers, a firm,
and a policy authority.
In the primary labor market, all skilled workers are organized in a single union that sets nominal
wages unilaterally. Skilled worker employment is determined by the profit-maximizing conditions of
the firm.8 On the other hand, in the secondary labor market, nominal wages and employment of
unskilled labor are determined competitively, since on an average, unskilled workers are less unionizedthan skilled workers.98

In other words, nominal wages and employment of skilled workers are determined in such a way asassumed in the monopoly union model. See Dunlop (1944) and Oswald (1985) for the monopoly
union model.
9This paper follows the assumption made by Agiomirgianakis and Zervoyianni (2001). However,skilled (unskilled) labor is not always traded in the non-competitive (competitive) labor market.
6Since the workers are divided into skilled and unskilled workers, we assume two kinds ofinternational labor flows. Skilled workers move between the primary labor markets and unskilledworkers move between the secondary labor markets of the small open economy and the rest of theworld. These flows are usually generated by differentials of real-consumption wages (nominal wages
divided by the consumer price index) or expected real-consumption wages (real-consumption wages
multiplied by the employment probability), as assumed by Agiomirgianakis (1998, 2000),
Agiomirgianakis and Zervoyianni (2001), and Shimada (2003). However, this paper restricts theanalysis to immigration and assumes that fixed amounts of skilled and unskilled foreign workers flow
into the small open economy.10
The firm in the small open economy employs skilled and unskilled workers and produces a single
kind of product that is not only demanded in the small open economy but also in the rest of the world.
The small open economy has a money market. Money is the only financial asset held by theresidents of the small open economy. We disregard international mobility of financial capital and theholdings of interest-bearing assets.

Kemnitz (2003) assumes that high-skilled labor is traded in the competitive labor market, whilenominal wages and employment of low-skilled labor are determined by bargaining between the union
and the firm.
10

In an analysis of the welfare consequences of international migration of labor in a small open

economy, Agiomirgianakis (2000) restricted the analysis to emigration to avoid complications arisingfrom discrimination against immigrants. However, the purpose of this paper is to investigate how theeconomy’s welfare is affected by immigrants’ accessibility to labor markets that is dependent on
discrimination against them. Therefore we consider the case of immigration.
7

The model is summarized by Eqs. (1) - (7).11 Variables are expressed in logs unless otherwise
defined.
y = a1l1 + a2l2 , a1 , a2 > 0, a1 + a2 < 1.
1− a2
a2
1 − a2a2
l1 = ln a11−a1 −a2 a 2 1−a1 −a2 −( w1 − p ) −( w2 − p ).
1 − a1 − a 2
1 − a1 − a2l 2 = ln a1a1
1− a1 − a2

a2

1− a1
1− a1 − a2−

1 − a1a1( w2 − p ) −( w1 − p).
1 − a1 − a2
1 − a1 − a2z ≡ e + p * − p.
q ≡ p + cz, 0 < c < 1 2.
wic ≡ wi − q, i = 1,2.
m = p + y.
y = bz , b > 0.

(1)

(2)

(3)
(4)
(5)
(6)
(7)

Eq. (1) is the production function, where y is output, l1 is skilled worker employment, l2 isunskilled worker employment, and a1 , a2 are constants not expressed in logs.

Assuming

Cobb-Douglas production technology and a fixed amount of capital, output of a small open economy
is positively related to skilled and unskilled labor employed. Eqs. (2) is the labor demand functions
for skilled and unskilled workers, where w1 is skilled worker nominal wages, w2 is unskilledworker nominal wages, and p is the price of product produced in the small open economy. They
are derived from the profit maximization of the firm. Eqs. (2) shows the complementary relationshipbetween skilled and unskilled workers. Eq. (3) is the definition of the real exchange rate, where e isthe nominal exchange rate measured as units of domestic currency per unit of foreign currency, p* isthe price of the product produced in the rest of the world. Eq. (4) is the definition of the consumer
price index, where c is a constant not expressed in the log. The consumer price index is a weighted

11Structural equations of this paper are based on Agiomirgianakis and Zervoyianni (2001). They

assume a small open economy with dual labor markets for the analysis of macroeconomic
consequences of illegal immigration.
8

average of the price of the product produced in the small open economy and the domestic currency
price of imports. Eqs. (5) is the definitions of real-consumption wages where skilled worker
real-consumption wages is w1c , and unskilled worker real-consumption wages is w2 c . Eq. (6) is themoney market equilibrium condition, where m is the money stock.

The policy authority

manipulates the money stock. Eq. (7) implies that aggregate demand for output in the small open
economy is positively related to the real exchange rate, where b is a constant not expressed in the log.
A depreciation of the real exchange rate, that is increases in z , by improving competitiveness, shifts
the world demand toward the product produced in the small open economy. We assume that b islarger than 1.12

12

We have another interpretation of Eq. (7). The trade balance of the small open economy TB canbe expressed as,
TB = α1 z − α 2 ( y − y * ), α1 ,α 2 > 0,
where y * is the output of the rest of the world on which the small open economy has no influencesand α1 , α 2 are constants not expressed in logs. If the real exchange rate has stronger (weaker) effects
on the trade balance than the difference in output, α1 is larger (smaller) than α 2 . Assuming no
capital mobility, trade must be balanced, which requires the following equation:y − y * = bz ,where b denotes α1 α 2 .

Since output of the rest of the world is given to the small open economy,

we can assume y * to be 0 without qualitative changes in the results. This gives us Eq. (7).
Whether b is larger than 1 or not is an empirical problem.

However, according toAgiomirgianakis (1998, footnote 9), for most countries empirical evidence suggests that real exchange
rate has stronger effects on the trade balance than the difference in output and this allows us to assume
that b > 1.
9

In this paper, as mentioned already, factors that initiate labor migration are not assumed and theamounts of foreign worker inflow are given exogenously.13 In particular, the small open economy
experiences skilled foreign worker inflow by ∆1 and unskilled foreign worker inflow by ∆ 2 , where∆1 and ∆ 2 are positive constants not expressed in logs. We assume that all foreign workers arelegal.
We also assume that all skilled foreign workers cannot enter the primary labor market and all
unskilled foreign workers cannot enter the secondary labor market, regardless of their willingness to do
so. In other words, only a fraction of θ1 , 0 < θ1 < 1 of skilled foreign workers can enter the
primary labor market and gain union membership and only a fraction of θ 2 , 0 <θ 2< 1 of unskilled
foreign workers can enter the secondary labor market.14 These assumptions reflect on the fact that in
actual economies there are barriers that make it difficult for foreign workers to enter the labor markets.
The coefficients θ1 and θ 2 measure the degree of skilled and unskilled foreign workers’
accessibility to the primary and secondary labor markets respectively.

13

It is probable that foreign workers’ accessibility to labor markets affects the amount of foreign worker

inflow. For example, higher accessibility to labor markets may attract more foreign workers.
However, this paper does not assume such a possibility, since accessibility to labor markets is not themost important factor that changes the size of foreign worker inflow.
14

It is probable that the size of foreign worker inflow changes foreign workers’ accessibility to labormarkets. For example, the larger size of foreign worker inflow may increase foreign workers’
accessibility to labor markets, since foreign workers may have larger influence on labor market as thesize of foreign worker inflow becomes larger. However, in this paper, we have no need to consider
such a possibility, since the size of foreign worker inflow is assumed to be constant throughout thisanalysis.
10

Assumptions of labor immigration and foreign workers’ limited accessibility to labor markets leadto the following definitions of the effective skilled labor force (union membership) l1S and theeffective unskilled labor force l2S :l1S ≡ ln( L1 + θ1∆1 ),l2S ≡ ln( L2 + θ 2 ∆ 2 ),where L1 is the effective native skilled labor force (union membership in the absence of skilled
foreign workers’ immigration) and L2 is the effective native unskilled labor.

L1 and L2 arepositive constants not expressed in logs.
In the primary labor market, the union tries to maximize its utility function of the form,
U = −{l1 − ln( L1 + θ1∆1 )}2 + gw1c , g > 0,(8)where g , which is a constant not expressed in the log, reflects the relative weight assigned by theunion to employment versus skilled worker real-consumption wages. Eq. (8) says that the union
attempts to attain full employment for its membership and also make skilled worker real-consumption
wages as high as possible. The union’s employment target is equal to its membership. This implies
that once skilled foreign workers get union membership, they are treated as equally as skilled native
workers by the union.
We assume that the policy authority tries to provide employment to not only all workers in labormarkets but also to a part of foreign workers who cannot enter labor markets. This assumption
reflects on the fact that, today, it is necessary for many policy authorities to pay some attention toforeign worker employment for non-economic reasons, although foreign worker employment mightlead to negative effects on the native worker employment. It also attempts to accomplish theconsumer price index target, which is assumed to be 0. The policy authority’s objective function is of
the form,
V = −{l1 − ln( L1 + τ 1∆1 )}2 − {l2 − ln( L2 + τ 2 ∆ 2 )}2 − hq 2 , θ1 < τ 1 < 1, θ 2 < τ 2 < 1, h > 0,11(9)

where h, which is a constant not expressed in the log, reflects the relative weight assigned by thepolicy authority to employment versus the consumer price index. Eq. (9) says that the policy
authority disapproves of the deviation of skilled worker employment from the sum of all skilledworkers in the primary labor market (the effective skilled labor force) and a part of skilled foreign
workers not in the primary labor market l1 − ln( L1 + τ 1∆1 ) , the deviation of unskilled worker
employment from the sum of all unskilled workers in the secondary labor market (the effective
unskilled labor force) and a part of unskilled foreign workers not in the secondary labor market
l2 − ln( L2 + τ 2 ∆ 2 ) , and the deviation of the consumer price index from its target q .
Through appropriate substitutions, the model of Eqs. (1)-(7) can be solved for
l1 , l2 , y, p, z, q, w1c and w2 c as functions of w1 , w2 and m.
1− a 2

a2

a1

1− a1

1− a 2

a2

1− a1

a1

l1 = ln a11− a1 − a 2 a21− a1 − a 2 − A + m − w1 , A ≡ a1 ln a11− a1 − a 2 a2 1− a1 − a 2 + a2 ln a11− a1 − a 2 a21− a1 − a 2 . (10.1)
l 2 = ln a11−a1 −a2 a2 1−a1 −a2 − A + m − w2 .

(10.2)

y = a1 (m − w1 ) + a2 (m − w2 ) + (1 − a1 − a2 ) A.

(10.3)

p = −a1 (m − w1 ) − a2 (m − w2 ) + m − (1 − a1 − a2 ) A.

(10.4)a1a
1 − a1 − a2(m − w1 ) + 2 (m − w2 ) +
A.
b
b
b

(10.5)

z=

ac
a c
c



q =  − a1 + 1 (m − w1 ) +  − a2 + 2 (m − w2 ) + m + (1 − a1 − a2 ) − 1 +  A.
b 
b 
b




(10.6)

ac
a c
c



w1c = 1 − a1 + 1 ( w1 − m) +  − a2 + 2 ( w2 − m) − (1 − a1 − a2 ) − 1 +  A.
b 
b 
b




(10.7)

ac
a c
c



w2 c =  − a1 + 1 ( w1 − m) + 1 − a2 + 2 ( w2 − m) − (1 − a1 − a2 ) − 1 +  A.
b 
b 
b




(10.8)

Substituting the labor demand functions (Eqs. 2) into the production function (Eq. l), we obtain theaggregate supply function that positively relates the product price to output. As the money stock12

increases, the curve equilibrating the money market (Eq. 6) shifts upward to the right, resulting inincreases in output and the product price (see Eqs. 10.3 and 10.4). Increases in the nominal wages ofskilled and/or unskilled workers shift the aggregate supply curve upward to the left, causing decreases
in output and increases in the product price (see Eqs. 10.3 and 10.4).
Increases in the money stock increase skilled and unskilled worker employment, since increases in
the money stock increase the product price and decrease skilled and unskilled worker real-productwages w1 − p, w2 − p (see Eqs. 10.1 and 10.2). Increases in skilled (unskilled) worker nominal
wages decrease skilled (unskilled) worker employment directly, while they increase skilled (unskilled)worker employment indirectly, since increases in skilled and/or unskilled worker nominal wages shift
the aggregate supply curve upward to the left and the product price increases. Since the former
effects are stronger than the latter effects, skilled (unskilled) worker employment decreases by
increases in skilled (unskilled) worker nominal wages (see Eqs. 10.1 and 10.2). Increases in skilled(unskilled) worker nominal wages decrease unskilled (skilled) worker employment directly, while they
increase unskilled (skilled) worker employment indirectly by increasing the product price. Since theformer and latter effects offset each other, unskilled (skilled) worker employment does not change byincreases in skilled (unskilled) worker nominal wages (see Eqs. 10.1 and 10.2).
Increases in the money stock and/or decreases in skilled and/or unskilled worker nominal wages
increase output. Accordingly the aggregate demand must increase if the money stock increases
and/or if skilled and/or unskilled worker nominal wages decrease. To increase the aggregate demand,the price of the product produced in the small open economy has to become relatively lower to theprice of the product produced in the rest of the world in terms of domestic currency. Therefore
increases in the money stock and/or decreases in skilled and/or unskilled worker nominal wages haveto be accompanied with depreciation, in other words, increases in z (see Eq. 10.5).
Increases in the money stock increase the consumer price index not only by increasing the product13

price and but also by increasing output and bringing about depreciation (increases in z ) (see Eq.
10.6).
On the other hand, decreases in skilled and/or unskilled worker nominal wages decrease theconsumer price index by decreasing the product price, while they increase the consumer price index bydepreciation (increases in z ) brought about by increases in output. Accordingly effects of decreases
in skilled and/or unskilled worker nominal wages on the consumer price index are ambiguous (see Eq.
10.6). However, under the assumption of b > 1, decreases in skilled and/or unskilled worker
nominal wages decrease the consumer price index.
Increases in the money stock decrease skilled and unskilled worker real-consumption wages by
increasing the consumer price index (see Eqs. 10.7 and 10.8).
Increases in skilled (unskilled) worker nominal wages increase skilled (unskilled) worker realconsumption wages directly (see Eqs. 10.7 and 10.8). Increases in skilled (unskilled) worker nominal
wages increase skilled (unskilled) worker real-consumption wages indirectly by decreasing output,
bringing about appreciation (decreases in z ) and decreasing the consumer price index. On the other
hand, increases in skilled (unskilled) worker nominal wages decrease skilled (unskilled) worker
real-consumption wages by increasing the product price and the consumer price index. Since theformer two effects are stronger than the latter effects, increases in skilled (unskilled) worker nominal
wages increase the skilled (unskilled) worker real-consumption wages (see Eqs. 10.7 and 10.8).
Since the effects of increases in skilled (unskilled) worker nominal wages on the consumer priceindex are ambiguous, those effects on unskilled (skilled) worker real-consumption wages are also
ambiguous (see Eqs. 10.7 and 10.8). However, under the assumption of b > 1, increases in skilled(unskilled) worker nominal wages decrease unskilled (skilled) worker real-consumption wages. Thisis because under this assumption, increases in skilled and/or unskilled worker nominal wages increase
the consumer price index.
14

3. Effects of Foreign Worker Participation in Labor Markets on the Economy’s Welfare
under Non-Cooperation between the Union and the Policy Authority
In this section, we examine how changes in foreign workers’ accessibility to labor markets affectthe economy’s welfare in a case where the union and the policy authority behave non-cooperatively.
In a non-cooperative environment, the union will set skilled worker nominal wages so as tomaximize its utility treating m and w2 as given, that is, it will solve,
max U subject to (10.1), (10.7), ∂m ∂w1 = 0 and ∂w2 ∂w1 = 0 .
w1This gives us the condition,l1 − ln( L1 + θ1∆1 ) = −gac1 − a1 + 1 .
2
b 

(11)

The policy authority will set the money stock so as to maximize its utility treating w1 and w2 asgiven, that is, it will solve,
max V subject to (10.1), (10.2), (10.6), ∂w1 ∂m = 0 and ∂w2 ∂m = 0.
mThis gives us the condition,
ac
a c

l1 − ln( L1 + τ 1∆1 ) + l2 − ln( L2 + τ 2 ∆ 2 ) + h1 − a1 + 1 − a2 + 2 q = 0.
b
b 


(12)

The equilibrium condition of the secondary labor market is,l2 = ln( L2 + θ 2 ∆ 2 ).

(13)

We obtain the effects of changes in skilled foreign workers’ accessibility to the primary labormarket on the economy’s welfare from Eqs. (11), (12) and (13).
∂U N
∂V N
∂U N ∂V N
< 0,
> 0,
+
> 0.
∂θ1
∂θ1
∂θ1
∂θ1

(14)

Eqs. (14) can be explained as follows: According to Eq. (11), the deviation of skilled worker
employment from union membership l1 − ln( L1 + θ1∆1 ) is a constant. On the other hand, as shown
by Eqs. (11) and (10.1), increases in θ1 decrease skilled worker nominal wages, since increases in θ1
15

increase union membership, that is, the target of skilled worker employment, which brings about
higher employment and lower nominal wages of skilled workers. Decreases in skilled worker
nominal wages decrease skilled worker real-consumption wages (see Eq. 10.7). These imply that in
the non-cooperative regime the union’s utility decreases as more skilled foreign workers enter the
primary labor market and gain union membership, i.e., ∂U N ∂θ1 < 0.
The deviation of skilled worker employment from the sum of all skilled workers in the primarylabor market and a part of skilled foreign workers not in the primary labor market l1 − ln( L1 + τ 1∆1 )decreases as we increase θ1 , since increases in θ1 increase l1 by Eq. (11) and l1 < ln( L1 + τ 1∆1 ).
This makes the policy authority’s utility higher. The deviation of unskilled worker employment fromthe sum of all unskilled workers in the secondary labor market and a part of unskilled foreign workers
not in the secondary labor market l2 − ln( L2 + τ 2 ∆ 2 ) is independent of θ1 (see Eq. 13). The
deviation of the consumer price index from its target q decreases as we increase θ1 , since theconsumer price index decreases as we increase θ1 by Eq. (12) and the consumer price index is
positive. 15

This also makes the policy authority’s utility higher.

These imply that in the

non-cooperative regime the policy authority’s utility increases as more skilled foreign workers enter
the primary labor market and gain union membership, i.e., ∂V N ∂θ1 > 0.
In the non-cooperative regime, the economy’s welfare, i.e., the sum of the union’s and policy
authority’s utilities, increases as we increase θ1.

This comes from the fact that increases in the policy

authority’s utility due to decreases in the deviation of skilled worker employment from the sum of all
skilled workers in the primary labor market and a part of skilled foreign workers not in the primarylabor market outweigh decreases in the union’s utility due to decreases in skilled worker

15

q = {1 h(1 − a1 + a1c b − a2 + a2c b)}{ln( L1 + τ 1∆1 ) − ln( L1 + θ1∆1 )+ ( g 2)(1 − a1 + a1c b) + ln( L2 + τ 2 ∆ 2 ) − ln( L2 + θ 2 ∆ 2 )}.
16

real-consumption wages, that is, ∂[−{l1 − ln( L1 + τ 1∆1 )}2 ] ∂θ1 > ∂ ( gwc ) ∂θ1 .

This makes

increases in the policy authority’s utility larger than decreases in the union’s utility when more skilled
foreign workers enter the primary labor market and gain union membership, implying ∂U N ∂θ1+ ∂V N ∂ θ1 > 0.
We also obtain the effects of changes in unskilled foreign workers’ accessibility to the secondary
labor market on the economy’s welfare from Eqs. (11), (12) and (13).
∂U N
∂V N
∂U N ∂V N
> 0,
> 0,
+
> 0.
∂θ 2
∂θ 2
∂θ 2
∂θ 2

(15)

Eqs. (15) can be explained as follows: As Eq. (11) shows, the deviation of skilled worker
employment from union membership l1 − ln( L1 + θ1∆1 ) is independent of θ 2 . On the other hand,increases in θ 2 decrease unskilled worker nominal wages, since increases in θ 2 make the effective
unskilled labor force larger (see Eqs. 13 and 10.2).

According to Eq. (10.7), decreases in unskilledworker nominal wages increase skilled worker real-consumption wages under the assumption ofb > 1. 16 These imply that in the non-cooperative regime the union’s utility increases as moreunskilled foreign workers enter the secondary labor market, i.e., ∂U N ∂θ 2 > 0.
As Eq. (11) shows, the deviation of skilled worker employment from the sum of all skilled workers
in the primary labor market and a part of skilled foreign workers not in the primary labor market
l1 − ln( L1 + τ 1∆1 ) is independent of θ 2 .

The deviation of unskilled worker employment from thesum of all unskilled workers in the secondary labor market and a part of unskilled foreign workers notin the secondary labor market l2 − ln( L2 + τ 2 ∆ 2 ) decreases as we increase θ 2 , since increases inθ 2 increase unskilled worker employment by Eq. (13) and l2 < ln( L2 + τ 2 ∆ 2 ).

16

This makes the

According to Agiomirgianakis (1998, footnote 9), for most countries empirical evidence suggests thatthe real exchange rates have stronger effects. This allows us to assume b > 1.
17

policy authority’s utility higher. The deviation of the consumer price index from its target q
decreases as we increase θ 2 , since increases in θ 2 decrease the consumer price index from Eq. (12).
This also makes the policy authority’s utility higher. These imply that in the non-cooperative regime
the policy authority’s utility increases as more unskilled foreign workers enter the secondary labormarket, i.e., ∂V N ∂θ 2 > 0.
The economy’s welfare increases as more unskilled foreign workers enter the secondary labormarket, i.e., ∂U N ∂θ 2 + ∂V N ∂θ 2 > 0, since ∂U N ∂θ 2 and ∂V N ∂θ 2 are both positive.
To summarize the results on the economy’s welfare in the non-cooperative environment, theunion’s utility decreases as more skilled foreign workers enter the primary labor market and gain union
membership, while it increases as more unskilled foreign workers enter the secondary labor market.
The policy authority’s utility increases as more skilled foreign workers enter the primary labor market
and gain union membership, and it also increases as more unskilled foreign workers enter thesecondary labor market. The economy’s welfare increases as more skilled foreign workers enter the
primary labor market and gain union membership, and it also increases as more unskilled foreign
workers enter the secondary labor market. Therefore our results imply that under non-cooperative
behavior by the union and the policy authority, we should remove the discriminatory behavior of theunion and the discriminatory structure of labor markets against skilled and unskilled foreign workers
and encourage their participation to primary and secondary labor markets, since by doing so more
foreign workers participate in labor markets and the economy’s welfare increases.

4. Effects of Foreign Worker Participation in Labor Markets on the Economy’s Welfare
under Cooperation between the Union and the Policy Authority
In this section, we examine how changes in foreign workers’ accessibility to labor markets affectthe economy’s welfare in a case where the union and the policy authority behave cooperatively.
In a cooperative environment, the union and the policy authority will set skilled worker nominal18

wages and the money stock so as to maximize the sum of their utilities treating w2 as given, that is,they will solve,

max U + V subject to (10.1), (10.7), (10.2), (10.6), ∂w2 ∂w1 = 0 and ∂w2 ∂m = 0.
w1 , mThis gives us the conditions,l1 − ln( L + θ1∆ ) + l1 − ln( L1 + τ 1∆1 ) +

g
ac 
ac
1 − a1 + 1  + h − a1 + 1 q = 0,
2
b  
b 

l1 − ln( L + θ1∆) + l1 − ln( L1 + τ 1∆1 ) + l2 − ln( L2 + τ 2 ∆ 2 )g
aca c 
aca c+ 1 − a1 + 1 − a2 + 2  + h1 − a1 + 1 − a2 + 2 q = 0,
2
b
b  
b
b 

(16)

(17)

As in a case of non-cooperation, equilibrium in the secondary labor market requires Eq. (13).
We obtain the effects of changes in skilled foreign workers’ accessibility to the primary labormarket on the economy’s welfare from Eqs. (16), (17) and (13).
∂U C ∂V C >
∂U C
∂V C
+
< 0,
> 0,
0.
∂θ1
∂θ1 <
∂θ1
∂θ1

(18)

Eqs. (18) can be explain as follows: Increases in θ1 decrease skilled worker nominal wages by
Eqs. (16) and (17), since increases in θ1 increase the target value of skilled worker employment
bringing about higher employment and lower nominal wages of skilled workers.17 Decreases in

17

From Eqs. (16) and (17), we can get the consumer price index.

q = − ( g 2)(−a2 + a2c b) {h(1 − a2 + a2c b)}+ {ln( L2 + τ 2 ∆ 2 ) − ln( L2 + θ 2 ∆ 2 )} {h(1 − a2 + a2c b)}.
The consumer price index does not depend on θ1.

Therefore, as Eq. (16) shows, increases in θ1

increase skilled worker employment. This can be confirmed by differentiating skilled worker
employment,

l1 = (1 2)[ln( L1 + θ1∆1 ) + ln( L1 + τ 1∆1 )− {( − a1 + a1c b) (1 − a2 + a2c b)}{ln( L2 + τ 2 ∆ 2 ) − ln( L2 + θ 2 ∆ 2 )}]− ( g 4){(1 − a1 + a1c b − a2 + a2c b) (1 − a2 + a2c b)},19

skilled worker nominal wages decrease skilled worker real-consumption wages by Eq. (10.7), leading
to decreases in the union’s utility. Increases in θ1 make the deviation of skilled worker employment
from union membership l − ln( L1 + θ1∆1 ) larger, since both skilled worker employment and union
membership increase by increases in θ1 and the former increases are smaller than the latter
increases.18 This also makes the union’s utility lower.19 These imply that in the cooperative regime
the union’s utility decreases as we increase θ1, i.e., ∂ U C ∂θ1 < 0.
Increases in θ1 make the deviation of skilled worker employment from the sum of all skilledworkers in the primary labor market and a part of skilled foreign workers not in the primary labormarket l1 − ln( L1 + τ 1∆1 ) smaller, since, as mentioned earlier, skilled worker employment increases
by increases in θ1.

This makes the policy authority’s utility higher. The deviation of unskilledworker employment from the sum of all unskilled workers in the secondary labor market and a part ofunskilled foreign workers not in the secondary labor market l2 − ln(L2 + τ 2 ∆ 2 ) and the deviation of
the consumer price index from its target q are independent of θ1. 20 These imply that in thecooperative regime the policy authority’s utility increases as we increase θ1, i.e., ∂V C ∂θ1 > 0.
Increases in θ1 decrease the union’s utility, while they increase the policy authority’s utility. We
are not able to determine which of these two effects are stronger. Therefore effects of increases in θ1with respect to θ1.
18∂l1 ∂θ1 = (1 2){∆1 ( L1 + θ1∆1 )}. ∂ ln( L1 + θ1∆1 ) θ1 = ∆1 ( L1 + θ1∆1 ) .

19

This contrasts with the effects on the union’s utility in the non-cooperative regime where thedeviation of skilled worker employment from union membership is independent of θ1.
20

This contrasts with the effects on the policy authority’s utility in the non-cooperative regime where

the deviation of the consumer price index from its target decreases as we increase θ1 making thepolicy authority’s utility higher.
20

on the economy’s welfare are ambiguous in the cooperative regime, i.e., ∂(U + V ) ∂θ1 <> 0. 21
CC

We also obtain the effects of changes in unskilled foreign workers’ accessibility to the secondary
labor market on the economy’s welfare from Eqs. (16), (17) and (13),∂U C∂V C >∂U C ∂V C
> 0,
0
,
+
> 0.
∂θ 2 <
∂θ 2
∂θ 2
∂θ 2

(19)

Eqs. (19) can be explained as follows: Increases in θ 2 increase skilled worker nominal wages
by Eqs. (16) and (17), since increases in θ 2 bring about the lower consumer price index lower, lower
employment and higher nominal wages of skilled workers under the assumption of b > 1.

Increasesin skilled worker nominal wages increase skilled worker real-consumption wages by Eq. (10.7). This
makes the union’s utility higher. On the other hand, increases in θ 2 make the deviation of skilledworker employment from union membership l1 − ln( L1 + θ1∆1 ) larger, since increases in θ 2
decrease skilled worker employment under the assumption of b > 1.

This makes the union’s utility

lower.22 The former effects are stronger than the latter effects. Therefore in the cooperative regime
the union’s utility increases as we increase θ 2 , i.e., ∂U C ∂θ 2 > 0.
Increases in θ 2 decrease the deviation of unskilled worker employment from the sum of all
unskilled workers in the secondary labor market and a part of unskilled foreign workers not in the

21∂(U C + V C ) ∂θ1= {ln( L1 + τ1∆1 ) − ln( L1 + θ1∆1 )}{∆1 ( L1 + θ1∆1 )} − ( g 2)(1 − a1 + a1c b){∆1 ( L1 + θ1∆1 )}.

As we increase θ1 , the sum of union’s and policy authority’s utilities increases if,ln( L1 + τ 1∆1 ) − ln( L1 + θ1∆1 ) − ( g 2)(1 − a1 + a1c b) > 0,and decreases if,ln( L1 + τ 1∆1 ) − ln( L1 + θ1∆1 ) − ( g 2)(1 − a1 + a1c b) < 0.
22This contrasts with the effects on the union’s utility in the non-cooperative regime where the21secondary labor market l2 − ln( L2 + τ 2 ∆ 2 ) , since unskilled worker employment increases by
increases in θ 2 by Eq. (13). They also decrease the deviation of the consumer price index from its
target q , since increases in θ 2 decrease the consumer price index and the deviation of the consumer
price index from its target value is positive under the assumption of b > 1.

These two effects makethe policy authority’s utility higher. On the other hand, increases in θ 2 make the deviation of skilledworker employment from the sum of all skilled workers in the primary market and a part of skilled
foreign workers not in the primary labor market l1 − ln( L1 + τ 1∆1 ) larger, bringing about the lower
policy authority’s utility, since skilled worker employment decreases by increases in θ 2 under theassumption of b > 1. 23 We are not able to determine whether the former two effects are stronger
than the latter effects. Therefore the effects of increases in θ 2 on the policy authority’s utility areambiguous in the cooperative regime, i.e., ∂V C ∂θ 2 <> 0. 24
Since the effects of increases in θ 2 on the union’s utility are stronger than the effects of increasesin θ 2 on policy authority’s utility, the economy’s welfare increases as we increase θ 2 in thecooperative regime, i.e., ∂ (U C + V C ) ∂θ 2 > 0.
To summarize the results on the economy’s welfare in the cooperative environment, the union
decreases its utility as more skilled foreign workers enter the primary labor market and gain union
membership, while it increases its utility as more unskilled foreign workers enter the secondary labor

deviation of skilled worker employment from union membership is independent of θ 2 .
23This contrasts with the effects on the policy authority’s utility in the non-cooperative regime where

the deviation of skilled worker employment from the sum of all skilled workers in the primary labormarket and a part of skilled foreign workers not in the primary labor market is independent of θ 2 .
In the case where θ1 , θ 2 and g satisfy l1 − ln( L1 + τ 1∆1 ) = 0, we obtain ∂V C ∂θ 2 > 0.

24

another case where θ 2 = 1 and h is sufficiently large, we obtain ∂V C ∂θ 2 < 0.
22In

market. The policy authority increases its utility as more skilled foreign workers enter the primarylabor market and gain union membership, while it is ambiguous whether the policy authority increases
its utility or not as more unskilled foreign workers enter the secondary labor market. The economy’s
welfare increases as more unskilled foreign workers enter the secondary labor market in thecooperative environment. The result on the effects of increases in the unskilled foreign worker
participation in the secondary labor market is the same as the one derived under non-cooperation.
However, it may happen that the economy’s welfare decreases as more skilled foreign workers enter
the primary labor market and gain union membership in a cooperative regime. This result contrasts
with the one derived under non-cooperation.
These results have the following implications:

Today, many developed countries areexperiencing large inflows of unskilled foreign workers and it is very difficult to control their inflows,since it is very rational for unskilled foreign workers to seek better working conditions. Accordingly
many developed countries are accepting unskilled foreign workers willingly or unwillingly. However
once we accept unskilled foreign workers, we should try to increase their accessibility to the secondary
labor market, since by doing so we can increase the economy’s welfare in non-cooperative andcooperative regimes. In other words, once we accept unskilled foreign workers, we should remove
the discriminatory structure of the secondary labor market, rather than keeping them away from thesecondary labor market because we do not want to accept them.
On the other hand, many developed countries are implementing policies to encourage skilled
foreign worker inflow. Our results suggest that such policies do not necessarily lead to increases inskilled foreign worker employment in the primary labor market, since there are cases where theeconomy’s welfare decreases due to increases in union membership of skilled foreign workers in thecooperative regime. This may partly explain why it is difficult for a country like Japan where theunion and the policy authority behave cooperatively to increase skilled foreign worker participation
23

and their employment in the primary labor market. For this purpose, especially to increase highly
skilled foreign worker participation and their employment whom we cannot replace with native
workers, the policy authority will have to manipulate its instruments to mitigate decreases in theunion’s utility due to increases in union membership of skilled foreign workers.

5. Conclusions
In this paper, we assumed a small open economy where the labor market has a dual structure. We
also assumed that foreign workers are not always able to enter domestic labor markets due to barriers
imposed on foreign workers. In such an economy, we examined how changes in foreign workers’
accessibility to labor markets affect the economy’s welfare and showed that the economy’s welfare
increases as more unskilled foreign workers enter the secondary labor market in both non-cooperativeand cooperative regimes, while the economy’s welfare does not always increase with an increase in thenumber of skilled foreign workers entering the primary labor market.
Our results suggest that in order to increase the economy’s welfare, we have to remove
impediments for unskilled foreign workers to encourage their participation in the secondary labormarket in either regime. Once we accept unskilled foreign workers, they have to be treated as equallyas unskilled native workers, even if we do not want to accept them. Discriminatory practices against
unskilled foreign workers that prevent them from entering the secondary labor market decrease theeconomy’s welfare.
Moreover, our results provide an explanation for the difficulties observed in increasing skilled
foreign worker participation and their employment in the primary labor market. If the policy
authority wants to increase the economy’s welfare by increasing skilled foreign workers’ participationand their employment in the primary labor market, it should implement policies that alleviate decreases
in union’s utility arising from increases in skilled foreign workers’ membership. For example,
24policies like giving subsidies to the unions that increase skilled foreign workers’ membership mightlead to increases in skilled foreign worker participation and their employment in the primary labormarket as well as increases in the economy’s welfare. Such policies will help increase employmentof skilled foreign workers possessing high skills and valuable experiences that skilled native workers
do not possess.

25

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