Can We Reduce Unskilled Labor Shortage by Expanding the Unskilled Immigrant Quota?
Akira Shimada
Faculty of Economics, Nagasaki University
Abstract
We investigate whether we can employ an increased number of unskilled workers after we
expand the unskilled immigrant quota. For this purpose, we assume a small open economy withdual labor markets, i.e., a skilled labor market where labor is abundant and an unskilled labormarket where labor is scarce. In both the labor markets, wages are determined by the efficiency
wage hypothesis. We introduce the skilled (unskilled) immigrant quota in the skilled (unskilled)labor market. We show that even if we expand the unskilled immigrant quota, we cannot always
employ an increased number of unskilled workers. In particular, it is likely that unskilled worker
employment decreases with the expansion of the unskilled immigrant quota. This is because
unskilled native workers might decrease their labor supply with the increases in the quota. On
the other hand, we also show that the expansion of the skilled immigrant quota always increases
skilled worker employment. Our results suggest that the expansion of the unskilled immigrantquota does not necessarily alleviate unskilled labor shortage. In actual economies, we tend to
expand the skilled immigrant quota to increase skilled worker employment. However, such a
policy appears to be inapplicable in the case of unskilled worker employment.

JEL Classification: F22; J23; J24; J41; J42; J61

Keywords: Unskilled labor shortage; Skilled labor market; Unskilled labor market; Skilled
immigrant quota; Unskilled immigrant quota; Efficiency wages

01. Introduction
This paper investigates the effects of the skilled and unskilled immigrant quotas on skilled andunskilled worker employment assuming that skilled labor is abundant and unskilled labor is scarce.
Further, this paper attempts to clarify whether or not unskilled labor shortage can be reduced byexpanding the unskilled immigrant quota.
Many developed countries have been reluctant to accept unskilled foreign workers. This isbecause the policy authorities of these countries believe that the inflow of unskilled foreign labor
is likely to have negative impacts on the host countries, although according to previous studies,
this is not necessarily the case.1
Labor markets in developed countries have become increasingly segmented into the primaryand secondary sectors.2 This has induced many native workers in these countries to supply theirlabor to the primary sector, since by participating in this sector, they can secure well-paid skilledjobs. Consequently, the number of native workers who enter the secondary sector to securepoorly paid unskilled jobs has decreased. This has led to unskilled labor shortage in many1

According to the estimate by Borjas (1997), the inflow of large numbers of less-skilled

immigrants has an adverse impact on the labor market opportunities for less-skilled U.S. native
workers. On the other hand, Friedberg and Hunt (1995) argued that even if native workers are
the closest substitutes for immigrant labor, they have not been found to suffer significantly fromincreased immigration. Based on their theoretical analysis, Schmidt, Stilz, and Zimmermann(1994) and Zimmermann (1996) also derived the possibility that accepting unskilled immigrants
increases unskilled native worker employment.
2

See Puglises (1992) and Massy and Taylor (2004) for the growing segmentation of the labormarkets in developed countries.
1

developed countries. It is true that unskilled labor is often abundant in the large cities ofdeveloped countries and many unskilled native workers are unemployed in such cities. However,even in these countries, firms in many regions are unable to easily procure unskilled workers tofill their vacancies, and the unskilled labor available in the whole economy is not necessarilyadequate to fulfill the total demand for it. Further, a rise in native workers’ expectations ofobtaining more attractive jobs in the primary sector is increasing unskilled labor shortage (Stahl2001).
In response to this situation, the argument that we begin and expand the unskilled immigrantquota in order to formally accept a larger number of unskilled foreign workers is becoming morepersuasive.3 This argument arose from our past experience of encouraging the acceptance ofskilled foreign workers and increasing skilled worker employment by expanding the skilled

3

Similar to other industrialized nations, Japan is currently suffering from unskilled labor shortage.

Faced with this situation, Japanese industries suggest that the government extend the interpretationof technical and technological jobs and legally accept more foreign workers whose jobs have notbeen classified into skilled ones before. In particular, in order to eliminate current and futurechronic shortage of skilled workers in such sectors as manufacturing, construction and machineassembly, Nippon Keidanran (Japan Business Federation) (2007) is requesting the government toadmit non-Japanese workers who meet requirements such as knowledge of a certain level ofJapanese, conditional upon the introduction of a labor test.

Additionally, the Japanese

government is under pressure from Asian countries to accept nurses and caretakers, and it will
accept them by establishing quotas for them through Economic Partnership Agreements (EPAs)
with these countries.

This will lead to the establishment and/or expansion of quotas forless-skilled foreign workers.
2

immigrant quota. Another basis for this argument is that unskilled labor shortage has led to alarge inflow of illegal unskilled immigrants.4
In such a situation, can we actually reduce unskilled labor shortage by implementing a policy
similar to the one utilized to increase skilled worker employment? In other words, will unskilledworker employment increase by establishing and expanding the unskilled immigrant quota? As
mentioned earlier, unskilled labor is in shortage, whereas skilled labor is not necessarily inshortage. Accordingly, our question can be paraphrased as whether or not the same immigrantquota policy can be applied to labor markets wherein the availability of labor differs.
Many studies on immigrant quotas have attempted to clarify how the quota can be determinedby utilizing political economy theories. Shughart et al. (1986) explained it through the interest
group theory of government.

Labor unions lobby for the enforcement of the restrictive

immigration policy to prevent wage reductions during recessions, while employers lobby for the
reduced enforcement of the immigration policy to reduce upward pressures on wages during
expansions. Benhabib (1996) studied how immigration policies that impose capital and skill
requirements on immigrants will be determined under majority voting. Amegashie (2004) built amodel in which the number of immigrants is the outcome of a costly political lobbying contest
between a firm and a union. It explained how immigrant reservation wages, the firm’s productprice, union size, and lobbying cost affect immigrant quotas. In Bodvarsson et al. (2007), a
political market for an endogenous immigrant quota emerges as a consequence of the conflicting
interests of native workers in the substitute industry, native workers in the complement industry,and lobbying groups.

4

However, it is possible that the expansion of the quota increases the number of illegal unskilled

immigrants.
3

These analyses did not pay sufficient attention to the availability of labor in the labor market inwhich the quota is introduced. However, the availability of labor will change the effects of thequota on workers and firms. Therefore, it will be difficult for the government to improve theeconomy’s welfare without considering the availability of labor when it manipulates the quota.
It also changes the degree of the influence workers and firms can have in the process of quota
determination.
Therefore, this paper explicitly assumes that the availability of labor in the skilled and unskilledlabor markets differs and attempts to show whether or not the expansion of the unskilled
immigrant quota is effective for increasing unskilled worker employment.
For this purpose, we model a small open economy with dual labor markets consisting of theskilled labor market whose labor supply is abundant and the unskilled labor market whose labor
supply is scarce. We manipulate the skilled and unskilled immigrant quotas and examine theireffects on skilled and unskilled worker employment.
We demonstrate that the skilled immigrant quota always increases skilled worker employment.
Moreover, its expansion does not have any negative effects on unskilled worker employment.
On the other hand, the unskilled immigrant quota does not always increase unskilled worker
employment. In particular, it is likely that unskilled worker employment decreases with the
expansion of the unskilled immigrant quota. This is because the unskilled immigrant quota
decreases unskilled worker wages, and decreases in unskilled worker wages may reduce unskilled
native worker employment much more than the increase in unskilled immigrant employment.
Moreover, decreases in unskilled worker employment always negatively impact skilled worker
employment.
Our results suggest that the manipulation of the immigrant quota is asymmetric between theskilled labor market with abundant labor and the unskilled labor market with scarce labor. Many4

governments tend to expand the skilled immigrant quota to increase skilled worker employment.
However, a similar policy is not necessarily appropriate to reduce unskilled labor shortage, since
expanding the unskilled immigrant quota might result in aggravating it rather than alleviating it.
The remainder of the paper is organized as follows. Section 2 presents a small open economic
model with dual labor markets and efficiency wages. The availability of labor differs in theskilled and unskilled labor markets. We introduce the skilled and unskilled immigrant quotas in
the skilled and unskilled labor markets, respectively. Section 3 examines the effects of theskilled immigrant quota on skilled and unskilled worker employment. Section 4 examines theeffects of the unskilled immigrant quota on unskilled and skilled worker employment. The
concluding comments are presented in Section 5.

2. The Model
We consider a small open economy with dual labor markets consisting of skilled and unskilledlabor markets. Jobs in the skilled labor market are attractive and require a certain level of skill,whereas jobs in the unskilled labor market are unattractive and do not require skill. Althoughnative workers include skilled and unskilled ones, most of them have sufficient skills to be
employed in the skilled labor market. Accordingly, most of the native workers are in the skilledlabor market and the rest of them are in the unskilled labor market.
The small open economy is connected to the rest of the world through the skilled and unskilled
foreign worker inflow. To accept them formally, its government establishes skilled and unskilled
immigrant quotas, which are small as compared to the skilled and unskilled native labor forces.
The number of skilled native workers is large, and most of them are always willing to supply
labor since their wages are sufficiently high. Although whether or not they do so depends on
skilled worker wages, the ratio of these skilled native workers to all skilled native workers is near5

to 1. The remaining skilled native workers are not always willing to supply labor. They arevoluntarily unemployed and supply labor if there is a possibility of reemployment in steady state.
We formally accept skilled immigrants by establishing a skilled immigrant quota M 1 , which ismanipulated by the government. All skilled immigrants are always willing to supply labor; thisis the sole difference between skilled native workers and skilled immigrants, and firms consider
them to be the same in terms of input.5 Moreover, we assume that even if skilled native workers
and skilled immigrants are involuntarily unemployed, they do not attempt to enter the unskilledlabor market. In other words, there is no internal migration.
Accordingly, labor supply in the skilled labor market, i.e., the number of the skilled workers
who are always willing to supply labor L1 , can be abundant, which is equal to φ1 ( w1 ) N1 + M 1 ,0 < φ1 ( w1 ) ≤ 1, and φ1 '( w1 ) > 0 . Here, φ1 ( w1 ), which is usually near to 1, is the ratio of skilled

native workers who are always willing to supply labor to all skilled native workers, w1 is skilledworker wages, and N1 is the number of skilled native workers, which is assumed to be aconstant.6 Skilled labor supply increases with respect to their wages.7 In steady state, the5To put it more precisely, there are no differences between skilled native workers who do not havea record of voluntary unemployment and skilled immigrants.

See what follows for anassumption on the reemployment of unemployed workers in the skilled labor market.
6

In this paper, the product price does not change and is assumed to be 1; therefore, we need not

differentiate between real and nominal wages.
7

Greenwood and Hunt (1995) considered several channels through which immigrants affect native

worker employment and their wages, including the production structure channel, the local demand
channel, the net export demand channel, the labor force participation channel, and the migration
channel. In the labor force participation channel, they assumed that the labor force participation
6

remaining skilled workers {1 − φ1 ( w1 )}N1 are willing to supply labor if there is a possibility of
reemployment.8
In contrast to skilled native workers, the number of unskilled native workers is less, and someof them are not always willing to supply labor since their wages are not sufficiently high. In
other words, whether or not they do so depends on unskilled worker wages, and the ratio of these
unskilled workers to all unskilled native workers is not near to 1. The remaining unskilled native
workers are not always willing to supply labor. They are voluntarily unemployed and supply
labor if there is a possibility of reemployment in steady state. We formally accept unskilled
immigrants by establishing an unskilled immigrant quota M 2 , which is manipulated by thegovernment.9 All unskilled immigrants are always willing to supply labor; this is the solerate (defined as the employment-to-population ratios) depends on wages as well as local prices
and non-labor income. They expected that higher wages will lead to a higher participation rate.
Thus, as assumed in this paper, labor supply is increasing with respect to wages.
8

In general, all unemployed workers can get out of unemployment with some probability, which isequal to the accession rate. Unemployed skilled workers consist of voluntarily unemployedskilled native workers whose number is equal to {1 − φ1 ( w1 )}N1 and involuntarily unemployedskilled native and foreign workers whose number is equal to φ1 ( w1 ) N1 + M 1 − L1.

However, asassumed, flow out of unemployment in the skilled labor market does not include the former
workers. See what follows for an assumption on the reemployment of unemployed workers inthe skilled labor market.
9

Even if we cannot control the unskilled foreign worker inflow perfectly and we accept illegal

unskilled immigrants, the main results of the paper remain unchanged as long as their number is aconstant and small as compared to the demand for them.
7difference between unskilled native workers and unskilled immigrants, and firms consider them tobe the same in terms of input.
Accordingly, labor supply in the unskilled labor market, i.e., the number of unskilled workers
who are always willing to supply labor L2 , can be scarce, which is equal to φ2 ( w2 ) N 2 + M 2 ,0 < φ2 ( w2 ) ≤ 1, φ2 '( w2 ) > 0 . Here, φ2 ( w2 ), which is not necessarily near to 1, is the ratio of

unskilled native workers who are always willing to supply labor to all unskilled native workers,
w2 is unskilled worker wages, and N 2 is the number of unskilled native workers, which isassumed to be a constant. Unskilled labor supply increases with respect to their wages. In
steady state, the remaining unskilled workers {1 − φ2 ( w2 )}N 2 are willing to supply labor if there
is a possibility of reemployment.10
Assuming a Cobb-Douglas production technology and considering capital to be fixed, theoutput in a small open economy Y increases with rises in the employment of skilled labor L1
and unskilled labor L2 :Y = L1a1 La22 , a1 , a2 > 0, a1 + a2 < 1.
This suggests that skilled labor and unskilled labor are complements.
Firms are perfectly competitive and they demand skilled labor and unskilled labor in such a
way as to maximize profits, which is defined as π ≡ L1a1 La22 − w1 L1 − w2 L2 .

In the skilled labormarket, there is abundant labor supply. Accordingly, firms can demand skilled workers toestablish ∂π ∂L1 L ≤ L , L ≤ L = 0.
1

∂π ∂L2 L ≤ L , L ≤ L
1

1

2

1

2

On the other hand, since unskilled labor is scarce,2is positive.

Accordingly, firms demand unskilled workers as much as

2

10

As assumed, there are no involuntarily unemployed unskilled workers since unskilled labor is inexcess demand. Accordingly, flow out of unemployment in the unskilled labor market includes
only voluntarily unemployed unskilled native workers.
8

supplied.

Therefore, we derive the following demand functions for skilled and unskilledworkers:
1
1− a1
1

L1 = a( L2 )

1
1− a1

−

w1

1
1− a1

.

L2 = L2 .
The labor demand functions are rewritten by substituting L2 = φ2 ( w2 ) N 2 + M 2 into the above
functions:
1
1− a1
1

L1 = a1
1− a1{φ 2 ( w2 ) N 2 + M 2 }

−

w1

1
1− a1

(1)

.

L2 = φ 2 ( w2 ) N 2 + M 2 .

(2)Since firms are unable to completely identify shirking by the employed workers, they set wages
in a manner that prevents shirking (Shapiro and Stiglitz 1984). The instantaneous utility of arepresentative employed worker in the skilled (unskilled) labor market who does not shirk is equal
to the skilled (unskilled) worker wages minus effort e, which is a constant and does not differ
across labor markets. On the other hand, if he shirks, his instantaneous utility is equal to theskilled (unskilled) worker wages. However, in such a case, he will be identified and fired by thefirm at the probability ρ , which is a constant and does not differ across labor markets.
Moreover, some of the employed workers separate their jobs although they are not fired on the
grounds of shirking. This constitutes flow into unemployment. The separation rate in eachlabor market, which is defined as the ratio of separations due to reasons other than shirking to thenumber of employed workers, is given by β , which is a constant and does not differ across labormarkets.
Under these assumptions, the expected lifetime utility of a representative employed shirker inthe skilled labor market V ES1 is,rVES1 = w1 + ( β + ρ )(VU1 − VES1 ),(3.1)

where r is the discount rate and VU 1 is the expected lifetime utility of a representative
9

unemployed worker in the skilled labor market. The expected lifetime utility of a representative
employed non-shirker in the skilled labor market VEN1 is,rVEN1 = w1 − e + β (VU1 − VEN1 ).

(4.1)

In order to prevent shirking, firms have to set skilled worker wages that ensure the skilled labormarket non-shirking condition VEN1 = VES1 (≡ VE1 ).

The following is obtained by substituting

Equations (3.1) and (4.1) into this condition:
w1 = rVU 1 +

r+β+ρ

ρ

(5.1)

e.

Moreover, VU 1 is given by,
rVU 1 = w1 + α1 (VE1 − VU 1 ),(6.1)

where w1 is the unemployment benefit for the workers in the skilled labor market, which isassumed to be a constant, and α1 is the accession rate in the skilled labor market, which isdefined as the ratio of new hires, i.e., flow out of unemployment in the skilled labor market, to thenumber of unemployed workers in the skilled labor market.
Involuntarily unemployed skilled workers φ1 ( w1 ) N1 + M 1 − L1 as well as voluntarily
unemployed skilled native workers {1 − φ1 ( w1 )}N1 are willing to supply labor if there is apossibility of reemployment. However, since skilled labor is abundant, we assume that firms do
not employ the latter workers in steady state.

This is because even if there are no real

distinctions between voluntarily unemployed skilled native workers and involuntarily unemployedskilled workers, firms tend to underestimate the quality of a worker who has a record of voluntary
unemployment. Accordingly, in steady state, firms only reemploy involuntarily unemployedskilled workers in the skilled labor market.
Therefore, in steady state, α1 must be such that flow out of unemployment is equal to flow
into unemployment in the skilled labor market, i.e., α1{φ1 ( w1 ) N1 + M 1 − L1} = βL1.
10Solving thisfor α1 and utilizing Equations (3.1), (4.1), (5.1), and (6.1), steady state skilled worker wages arederived as follows:

w1 = w1 + e +[{φ1 ( w1 ) N1 + M 1} {φ1 ( w1 ) N1 + M 1 − L1}]β + r

ρ

e.

(7.1)

According to Equation (7.1), steady state skilled worker wages are dependent on skilled worker
employment.11
Similar to the case of the skilled labor market, the expected lifetime utility of a representative
employed shirker in the unskilled labor market VES2 is,rVES2 = w2 + ( β + ρ )(VU 2 − VES2 ),(3.2)

where VU 2 is the expected lifetime utility of a representative unemployed worker in the unskilledlabor market. The expected lifetime utility of a representative employed non-shirker in theunskilled labor market VEN2 is,rVEN2 = w2 − e + β (VU 2 − VEN2 ).

(4.2)

Substituting Equations (3.2) and (4.2) into the unskilled labor market non-shirking condition

VEN2 = VES2 (≡ VE2 ), we are able to derive,
w2 = rVU 2 +r+β +ρ

ρ

e.

(5.2)

Moreover, VU 2 is given by,

As in the case where there are no voluntarily unemployed skilled workers, i.e., φ1 ( w1 ) = 1,11

steady state skilled worker wages increase with respect to their employment and decrease withrespect to the skilled immigrant quota. However, the slope of the curve and the amount of theshift due to given changes in the skilled immigrant quota are different from those in the casewhere there are no voluntarily unemployed skilled workers.
11

rVU 2 = w2 + α 2 (VE 2 − VU 2 ),(6.2)

where w2 is the unemployment benefit for the workers in the unskilled labor market, which isassumed to be a constant, and α 2 is the accession rate in the unskilled labor market, which isdefined as the ratio of new hires in the unskilled labor market to the number of unemployedworkers in the unskilled labor market.
Unskilled labor is scarce and there are no involuntarily unemployed unskilled workers.
Accordingly, we assume that the voluntarily unemployed unskilled native workers{1 − φ2 ( w2 )}N 2 , equal to N 2 + M 2 − L2 from Equation (2), can be employed if there is apossibility of reemployment.
Therefore, in steady state, α 2 must be such that flow out of unemployment is equal to flow
into unemployment in the unskilled labor market, i.e., α 2 ( N 2 + M 2 − L2 ) = βL2 .

Solving thisfor α 2 and utilizing Equations (3.2), (4.2), (5.2), and (6.2), steady state unskilled worker wages
are derived as follows:
w2 = w2 + e +[( N 2 + M 2 ) {1 − φ2 ( w2 )}N 2 ]β + r

ρ

e.

(7.2)

According to Equation (7.2), steady state unskilled worker wages are independent of unskilledworker employment.

3. Effects of the Skilled Immigrant Quota on Skilled and Unskilled Worker Employment

In this section, we examine how the changes in the skilled immigrant quota affect skilled andunskilled worker employment.
Totally differentiating Equations (1) and (7.1) and solving the resulting equations for dL1 , theeffects of changes in the skilled immigrant quota on skilled worker employment are derived asfollows:
12dL1{1 (1 − a1 )}L1 (1 w1 ) B=,
dM 1 1 + {1 (1 − a1 )}L1 (1 w1 ) A

(8)

where

A≡

(e ρ )(α1 + β )[1 {φ1 ( w1 ) N1 + M 1 − L1}],
1 + (e ρ )α1[φ '1 ( w1 ) N1 {φ1 ( w1 ) N1 + M 1 − L1}]B≡(e ρ )α1[1 {φ1 ( w1 ) N1 + M 1 − L1}].
1 + (e ρ )α1[φ1 ' ( w1 ) N1 {φ1 ( w1 ) N1 + M 1 − L1}]

According to Equation (8), since A, B > 0, the skilled immigrant quota increases skilled worker
employment ( dL1 dM 1 > 0 ). The intuitions behind this result are as follows:

Equation (1)indicates that the demand for skilled workers decreases with skilled worker wages. If w1 ismeasured on the vertical axis and L1 is measured on the horizontal axis, the curve that describes
Equation (1) is downward sloping. On the other hand, the total differentiation of Equation (7.1)
indicates that in steady state, skilled worker wages increase with respect to skilled worker
employment and decrease with respect to the skilled immigrant quota. This suggests that the
curve for skilled worker wages, i.e., the non-shirking condition for skilled workers in steady stateis upward sloping and shifts downward to the right with increases in the skilled immigrant quota.
Therefore, skilled worker employment increases with the skilled immigrant quota.
As Equation (7.2) shows, unskilled worker wages are independent of the skilled immigrantquota. Accordingly, unskilled worker employment (Equation 2) is also independent of it, i.e.,

dL2
= 0.
dM 1

(9)

Equation (9) suggests that the government can manipulate the skilled immigrant quota without
considering its effects on unskilled worker employment.
To summarize the results derived in this section, the government can always increase skilledworker employment by expanding the skilled immigrant quota, and this has no negative impacts
13

on unskilled worker employment.

4. Effects of the Unskilled Immigrant Quota on Unskilled and Skilled Worker Employment

In this section, we examine how the changes in the unskilled immigrant quota affect unskilled
and skilled worker employment.
For this purpose, we totally differentiate Equation (7.2) and derive the effects of the unskilled
immigrant quota on unskilled worker wages.

(e ρ )(α 2 + β ){1 ( N 2 + M 2 )}dw2=.
dM 2 1 − (e ρ )(α 2 + β )[φ2 ' ( w2 ) {1 − φ2 ( w2 )}](10)

According to Equation (10), the effects of the unskilled immigrant quota on unskilled worker
wages are ambiguous. If the increases in α 2 due to the increases in w2 are smaller than theincreases in w2 , M 2 has to be larger to ensure Equation (7.2), suggesting that the unskilled
immigrant quota increases unskilled worker wages ( dw2 dM 2 > 0 ). This corresponds to thecase where unskilled native workers are sufficiently unresponsive to unskilled worker wages intheir labor supply decision, i.e., φ2 ' ( w2 ) is sufficiently small.

On the other hand, if theincreases in α 2 due to the increases in w2 are larger than the increases in w2 , M 2 has to besmaller to ensure Equation (7.2), suggesting that the unskilled immigrant quota lowers unskilledworker wages ( dw2 dM 2 < 0 ). This corresponds to the case where unskilled native workers are
sufficiently responsive to unskilled worker wages in their labor supply decision, i.e., φ2 ' ( w2 ) issufficiently large.
From these arguments, we observe that it is possible for unskilled native worker employment todecrease when we expand the unskilled immigrant quota. If φ2 ' ( w2 ) is sufficiently small andthe expansion of the unskilled immigrant quota increases unskilled worker wages, a larger numberof unskilled native workers supply labor with increases in the quota, i.e., d{φ2 ( w2 ) N 2 } dM 2 > 0 .
14

However, if φ2 ' ( w2 ) is sufficiently large and the expansion of the unskilled immigrant quota
lowers unskilled worker wages, a smaller number of unskilled native workers supply labor withincreases in the quota, i.e., d{φ2 ( w2 ) N 2 } dM 2 < 0 .
From the above results, we can infer that unskilled worker employment might decrease when
we expand the unskilled immigrant quota.
dL2 1 − (e ρ )(α 2 + β )[φ2 ' ( w2 ) {1 − φ2 ( w2 )}][{φ2 ( w2 ) N 2 + M 2 } ( N 2 + M 2 )]=.
dM 2
1 − (e ρ )(α 2 + β )[φ2 ' ( w2 ) {1 − φ2 ( w2 )}](11)

According to Equation (11), the effects of the unskilled immigrant quota on unskilled worker
employment are ambiguous. If the unskilled immigrant quota increases unskilled native worker
employment, the expansion of the unskilled immigrant quota always increases unskilled worker
employment. As mentioned earlier, this corresponds to the case where φ2 ' ( w2 ) is sufficiently
small.12 Moreover, even if the unskilled immigrant quota decreases unskilled native worker
employment, unskilled worker employment increases with the unskilled immigrant quota,
provided that the decreases in unskilled native worker employment are smaller than the increases
in the quota. This corresponds to the case where φ2 ' ( w2 ) is sufficiently large.13 However, if
the unskilled immigrant quota decreases skilled native worker employment and its decreases arelarger than the increases in the quota, unskilled worker employment decreases with the increases

12d{φ2 ( w2 ) N 2 } dM 2 > 0 implies 1 − (e ρ )(α2 + β )[φ2 ' (w2 ) {1 − φ2 (w2 )}] > 0.

Moreover, if thisis the case, 1 − (e ρ )(α 2 + β )[φ2 ' (w2 ) {1 − φ2 (w2 )}][{φ2 (w2 ) N2 + M 2} ( N2 + M 2 )] > 0.
Even if it is negative, d{φ2 (w2 ) N2} dM2 is approximately equal to − {1 − φ2 (w2 )}N2 ( N2 + M2 )13

for sufficiently large values of φ2 ' (w2 ). Since −{1− φ2 (w2 )}N2 ( N2 + M2 ) < 1, the decreases inunskilled native worker employment are smaller than the increases in the unskilled immigrantquota.

15

in the quota. This corresponds to the case where φ2 ' ( w2 ) is neither sufficiently small nor
sufficiently large.14 Therefore, we can conclude that it is likely that an expansion of the unskilled
immigrant quota decreases unskilled worker employment.
Totally differentiating Equations (1) and (7.1) and solving the resulting equations for dL1 , weshow how the changes in the unskilled immigrant quota affect skilled worker employment.
{a2 (1 − a1 )}( L1 L2 ) dL2
dL1=.
dM 2 1 + {1 (1 − a1 )}L1 (1 w1 ) A dM 2

(12)

According to Equation (12), the effects of the unskilled immigrant quota on skilled worker
employment are also ambiguous. Whether or not the unskilled immigrant quota increases skilledworker employment depends on whether or not it increases unskilled worker employment. The
intuitions behind this result are as follows: As mentioned earlier, the demand curve for skilledworkers is downward sloping, and shifts upward to the right with increases in unskilled worker
employment.

The curve that describes Equation (7.1) is upward sloping.

Accordingly, if

φ2 ' ( w2 ) is sufficiently small or sufficiently large and thereby, the unskilled immigrant quota
increases unskilled worker employment, the demand curve for skilled workers shifts upward to
the right with increases in the unskilled immigrant quota, resulting in increases in skilled worker
employment.

However, if φ2 ' ( w2 ) is neither sufficiently small nor sufficiently large andthereby, the unskilled immigrant quota decreases unskilled worker employment, the demand curve

As mentioned earlier, if φ2 ' (w2 ) is sufficiently small, both the numerator and the denominator

14of Equation (11) are positive. Further, if φ2 ' (w2 ) is sufficiently large, both the numerator andthe denominator of Equation (11) are negative. In either case, dL2 dM 2 > 0.

On the other

hand, if φ2 ' ( w2 ) is neither sufficiently small nor sufficiently large, it is likely that the numerator
is positive and the denominator is negative. In such a case, dL2 dM 2 < 0.
16

for skilled workers shifts downward to the left with increases in the quota, resulting in decreases inskilled worker employment. Therefore, we can conclude that it is likely that an expansion of theunskilled immigrant quota decreases skilled worker employment.
To summarize the results derived in this section, an expansion of the unskilled immigrant quota
does not always increase unskilled worker employment. Rather, it is likely to have negative
impacts on unskilled worker employment. Under the assumption that skilled labor and unskilledlabor are complements, it is possible that the unskilled immigrant quota decreases both unskilled
and skilled worker employment.

5. Conclusions

We investigated how the changes in the skilled and unskilled immigrant quotas affect skilled
and unskilled worker employment by assuming a small open economy with dual labor markets
where the skilled labor market is labor abundant and the unskilled labor market is labor scarce.
We showed that the expansion of the unskilled immigrant quota does not necessarily increase
unskilled worker employment.

It is likely that its expansion decreases unskilled worker

employment. This suggests that the expansion of the unskilled immigrant quota might lead tofurther shortage of labor in the unskilled labor market. In contrast, the skilled immigrant quota
always increases skilled worker employment.
Our results suggest that if we attempt to employ a larger number of workers in a certain labormarket by manipulating the immigrant quota, we have to consider whether the labor supply of thatmarket is abundant or scarce.

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