Tsukuba Economics Working Papers
No. 2014-002

A Simple Model of Competition Policies, Trade, and the Skill PremiumbyYoshinori Kurokawa
July 2014
This version: April 2020

UNIVERSITY OF TSUKUBA
Department of Economics
1-1-1 Tennodai
Tsukuba, Ibaraki 305-8571
JAPAN

A Simple Model of Competition Policies, Trade, and the
Skill Premium
Yoshinori Kurokaway
University of Tsukuba
April 6, 2020

Abstract
We develop a simple model of competition policies and trade, where …xed costs areshared within a cartel. The closed economy model shows that entry deregulation can
increase the skill premium by increasing …rm numbers and decreasing …rm size, while anantitrust policy has the opposite e¤ects. The numerical example with two asymmetriccountries shows that entry deregulation and antitrust policy in one country, respectively,
can increase and decrease the skill premia in both countries; however, the domestic skill
premium is changed by a greater percentage than the foreign one. Available U.S. data
show that our model seems empirically relevant.
Keywords: Trade, Entry policy, Antitrust policy, Skill premium, Firm numbers/size
JEL Classi…cations: F12, F16, J31, L13, L41, L51

I am very grateful to the editors, a referee, Tomohiro Ara, Ichiroh Daitoh, Colin Davis, Fumio Dei,
Difei Geng, Yunfang Hu, Koji Ishibashi, Hirokazu Ishise, Yoshitaka Itsumi, Naoto Jinji, Timothy Kehoe,
Morimitsu Kurino, Mamello Nchake, Takeshi Ogawa, Toshihiro Okubo, Gina Pieters, Ariell Reshef, Kim
Ruhl, Tetsuya Saito, Yoichi Sugita, Kazuhiro Yamamoto, Akihiko Yanase, Morihiro Yomogida, and seminar
participants at Keio, the 4th Spring Meeting of the JSIE, the 2014 JEA Spring Meeting, the 2014 NASM of
the Econometric Society, the IEFS Japan Annual Meeting 2014, and the Spring 2015 Midwest International
Trade Meetings for their useful comments. I also thank Daniel Sokol for the data help. Any errors aremine. This research is supported by a grant-in-aid from the Zengin Foundation for Studies on Economics
and Finance and by the JSPS KAKENHI Grant-in-Aid for Young Scientists (B) No. 25780157 (2013-2015).
yFaculty of Humanities and Social Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki
305-8571, Japan. Tel.&Fax: +81-29-853-7426. E-mail: kurokawa.yoshi.fw@u.tsukuba.ac.jp.

11Introduction

How competition policies interact with international trade has been one of the so-called“new issues” in the World Trade Organization (WTO). In 1996, the Singapore Ministerial Conference of the WTO set up the Working Group on the Interaction between Tradeand Competition Policy (WGTCP) to study this issue, with the participation of all WTO
members. The provisional decision to start negotiations was taken at the Doha Ministerial
Conference in 2001. In July 2004, however, the WTO General Council decided that thisissue would no longer form part of the Work Programme set out in the Doha Ministerial
Declaration and therefore no further work toward negotiations would take place within the
WTO during the Doha Round. As a result, the WGTCP is currently inactive.1
This paper now casts a doubt on this decision by the WTO and argues that the decision
might have been premature. This is because the interaction between domestic competition
policies and trade can result in a change in wage inequality in a trading partner even if
it is not the purpose of the policies, which implies the essential necessity of international
negotiations/coordination of competition policies among the trading countries.
To show this possible interaction between domestic competition policies and trade, thispaper now develops a simple, general equilibrium model in which competition policies— both
entry and antitrust policies— can change the skill premium for wages. It extends our initial
work (Kurokawa, 2010), which linked entry policy to the skill premium in a closed economy
model.2 There are two sectors: a …nal goods sector and an intermediate goods sector. Finalgoods are homogeneous goods produced under conditions of constant returns to scale andperfect competition. Intermediate goods are di¤erentiated goods produced under conditionsof increasing returns to scale and monopolistic competition. Monopolistically competitive…rms are Cournot competitors, and cartels of …rms are allowed in that a certain set of …rms
collude in decision-making. While cartels are detrimental in that they directly decrease
the degree of competition, e¢ ciency gains from a cartel exist in that the …xed costs areshared within a cartel.3 There are also two types of labor: high-skilled labor and lowskilled labor. The production of …nal goods uses a variety of intermediate goods/tasks
and high-skilled labor, and the production of intermediate goods uses low-skilled labor.4
One might interpret that high-skilled labor manages a variety of tasks, and each of tasks
is performed by low-skilled labor. A government can control the number and the size ofmonopolistically competitive …rms by exogenously changing the …xed costs of entry (entry
1

Regional trade agreements containing competition policy provisions have recently proliferated instead.
Our initial work (Kurokawa, 2010) examined the e¤ects of entry policy on the skill premium in a closed
economy model. We now examine the e¤ects of entry and antitrust policies in closed and open economy
models.
3
As will be mentioned later, one might think of automobile industries as an actual example that independent …rms that collude share …xed costs.
4
In this paper, a variety of intermediate goods are interpreted as a variety of tasks, a common interpretation in task-based model literature. For example, Mitchell (2005) and Grossman and Rossi-Hansberg (2008)
adopt this interpretation.
22policy) or the size of cartels (antitrust policy).
We …rst show, in a closed economy model, that entry deregulation that reduces the…xed costs of entry can increase the skill premium by increasing the number of …rms anddecreasing …rm size in the intermediate goods sector, which was also documented by our2010 paper. Antitrust policy that reduces the size of cartels, however, can decrease theskill premium by decreasing the number of …rms and increasing …rm size, which is a new
result of this paper. The key mechanism that drives these results is that entry deregulationthat lowers the …xed costs of entry increases the number of intermediate …rms, that is, thevariety of intermediate goods/tasks used by the …nal good. On the other hand, antitrust
policy that reduces the size of cartels increases the …xed costs per …rm since the …xed costs
are shared within a cartel, thereby decreasing the number of intermediate …rms, that is, thevariety of intermediate goods/tasks used by the …nal good. Then, entry deregulation andantitrust policies, respectively, increases and decreases the skill premium if varieties andhigh-skilled labor are complementary.
We next extend the model to a two-country model while our 2010 paper focused on aclosed economy model. The extended model shows that in the case in which the two countries are symmetric, entry deregulation that is conducted symmetrically in each country
can increase the skill premia symmetrically in both countries while antitrust policy that is
conducted symmetrically in each country can have the opposite e¤ect. Then entry deregulation and antitrust policy in each country contribute to this change in the skill premia
by, respectively, increasing and decreasing the total number of varieties common to bothcountries.
In the case in which the countries are asymmetric, though the e¤ects of competition
policies in one country on the skill premium in each country are not clear, our numericalexample illustrates a possibility that entry deregulation and antitrust policy in one country,
respectively, can increase and decrease the skill premia in both countries through trade.
The domestic skill premium, however, is changed by a greater percentage than the foreignone.
Finally, we show that available data from the U.S. are compatible with the main predictions and assumption of our model. It indicates that our model does appear to be
empirically relevant.
The main contributions of this paper are as follows. First, we attempt to internationallylink competition policies— both entry and antitrust policies— to the skill premium. It is
widely recognized that skill-biased technological change (e.g., Berman et al., 1994; Katz andAutor, 1999; Krusell et al., 2000) or trade (e.g., Feenstra and Hanson, 1996; Dinopoulos andSegerstrom, 1999; Acemoglu, 2003; Kurokawa, 2011) is an explanation for changes in theskill premium in wages.5 However, competition policies as a cause for changes in the skill
premium have received little attention in the wage inequality literature, although there is5

For example, see Kurokawa (2014) for a survey of trade and wage inequality.

3

an empirical fact that the number of …rms and the skill premium increased in the U.S. after
the Carter/Reagan deregulation was implemented in the late 1970s and early 1980s (e.g.,
see Kurokawa, 2010). Our 2010 paper, however, linked entry policy to the skill premium ina closed economy model.6 The current paper extends this work by linking internationallyboth entry and antitrust policies to the skill premium in a two-country model. Note that achange in …xed costs may be caused by technological change as well as competition policies
and that competition policies and trade may interactively a¤ect the skill premium as shownby our model. Therefore, competition policies may strengthen or weaken the e¤ects oftechnological change and trade.
Second, our paper adds to the literature on competition policies and trade. Probably
the most related work is Neary (2003a, 2003b). Neary (2003a) analyzes the e¤ects of anincrease in the number of …rms, due to a change in competition policy, on the relative
wage between the trading countries in a model of general oligopolistic equilibrium. Neary(2003b) analyzes the e¤ects of an increase in the number of …rms that is interpreted ascompetition policy on wages vs. pro…ts in a model of oligopoly in general equilibrium, andhe also extends it to the model with high- and low-skilled wages to analyze the e¤ects oftrade liberalization on the relative wage of high- to low-skilled workers— the skill premium.
Our paper analyzes the e¤ects of both an increase in the number of …rms and a change in
cartel size on the skill premium in a general equilibrium model of monopolistic competition.
To the best of our knowledge, our paper is the …rst to link competition policies to the skill
premium via trade.
Third, this paper emphasizes changes in both entry and antitrust policies as sources ofchanges in the …rm size. Past studies have emphasized technological change. For example,
Mitchell (2005) and Mobius and Schoenle (2006) argue that technological change, such as
the introduction of new ‡exible machines, changes the organization of production from mass
production to smaller customized batches, thus decreasing the size of plants/…rms. Our 2010
paper, however, argues that in addition to technological progress, entry deregulation that
reduces the …xed costs of entry can decrease …m size and increase the number of …ms. We
now argue, using a uni…ed framework, that both entry deregulation and cartel restriction
policies can change …rm size and the number of …rms.
The rest of this paper is organized as follows. Section 2 develops a simple model. In
Section 3, we examine the possible e¤ects of both entry and antitrust policies. Section 4extends our model to a two-country model. In Section 5, we discuss the empirical relevanceof our model. Section 6 concludes the paper and indicates opportunities for future research.
6

As far as we are aware, our initial work (Kurokawa, 2010) is only one study on the subject. It showedthat entry policy can a¤ect the skill premium.

4

2

Model

2.1

The setup of the modelOur 2010 paper extended the standard one-sector monopolistic competition model (Dixit
and Stiglitz, 1977) to a two-sector model and focused on the e¤ect of entry policy on theskill premium in a closed economy model. We now extend that focus to analyze the e¤ectsof entry and antitrust policies in closed and open economy models.
Consider an economy with an intermediate goods sector and a …nal goods sector. There
are two types of labor, high-skilled and low-skilled labor, with endowments of H and L,
respectively.
The intermediate goods sector is monopolistically competitive. There is a continuum[0; n] of di¤erentiated intermediate goods. Firms are Cournot competitors,7 and there is
free entry and exit. Each variety uses low-skilled labor, and the technology of each variety
is speci…ed by the following increasing returns to scale production function:x (j) = max [l (j)f; 0] ; 8j;

where x (j) is the output of variety j, l (j) is the input of low-skilled labor to produce variety
j, and f is the …xed costs in terms of low-skilled labor.
The …nal goods sector is perfectly competitive and homogeneous. The …nal goods use avariety of intermediate goods/tasks and high-skilled labor, and the technology is speci…edby the following constant returns to scale production function:
20
31=
1=
Zn
6
7
y = 4@ x (j) dj A + H 5 ;0where y is the output of …nal goods, and x (j) and H are the inputs of di¤erentiatedintermediate goods/task j and high-skilled labor. We assume that < 1 and that 0 << 1.

The elasticity of substitution between a composite of intermediate goods— which we callvarieties— and high-skilled labor is= 1= (1).

We note that one might interpret the above production structure of the intermediate
and …nal goods as follows. High-skilled labor manages a variety of tasks, and each of tasks
is performed by low-skilled labor. Lucas (1978) and Rosen (1982), for example, also build
models in which managerial skill enters the production function. We also note that for
simplicity, in our model the …nal goods sector uses only high-skilled labor; the intermediate
goods sector only low-skilled labor. We can generalize the model to a model in which eachsector uses both types of labor. It can be shown that as long as varieties and high-skilled
7

See Dixit (1979) and Singh and Vives (1984) for the analysis of Cournot competition in the case ofdi¤erentiated goods.

5labor are complementary, the main results hold.
Here, as in Seade (1980) and Ohyama (1999), we allow for cartels of …rms in that acertain set of …rms collude in their output decisions.8 For simplicity, we assume that thesize of each cartel is symmetric and is given by m (mn). Thus, the number of cartels

is n=m. Each cartel is assumed to determine its output so as to maximize its total pro…t,taking other cartels’outputs as given. Cartels are detrimental in that they directly decrease
the degree of competition. In this paper, however, there also exist e¢ ciency gains from a
cartel in that the …xed costs f are shared within a cartel and thus become f =m per …rm ina cartel.9 One might think of automobile industries as an actual example that independent…rms that collude share …xed costs (e.g., Toyota and Daihatsu; Nissan and Renault). Notethat each variety j is still produced by an individual …rm j (one of n …rms), not by a cartel(m of n …rms).
The demand side is as follows. A representative consumer has the endowments of highskilled and low-skilled labor: H and L.10 The utility function is given by:u(c) = c;where c is the consumption of the …nal goods. The budget constraint is given by:py c = wH H + wL L;
where py is the price of the …nal goods, wH is the wage for high-skilled labor, and wL is thewage for low-skilled labor.11
The market clearing (full employment) conditions for high-skilled labor and low-skilledlabor are:H = H;
Znl (j) dj = L:0

Finally, let us assume that a government can control …rm numbers, n, and …rm size,
L=n, by exogenously changing the …xed costs of entry f (entry policy) and the size of thecartels m (antitrust policy) in the intermediate goods sector.
8
As noted by Ohyama (1999), each cartel may also be considered as a merged …rm consisting of several
indivisible units of production.
9
In the Ichikawa and Kikuchi (2002) model of communications networks and trade, the …xed costs of
network provision are shared by users, and an increase in the number of users lowers the …xed costs per user.
10
The results for the case of a representative consumer (an aggregate consumer) are the same as those forthe case of two types of consumers: high- and low-skilled labor.
11
As will be shown later, we consider the long-run economy where the pro…t of each …rm becomes zero,and thus there is no pro…t in the consumer’s budget.

6

2.2

Firm numbers and the skill premium in equilibrium

By solving the model,12 we can derive the free-entry number of …rms n in the intermediate
goods sector with the regulated …xed costs at f and the regulated cartel size at m:
n=

L (1
)
:
f =m

(1)

We can also obtain the skill premium wH f ; m corresponding to the regulated …xed
costs at f and the regulated cartel size at m:
wH f ; m = nwhere n = L (1

(

1)=

p

1

L
H

;

(2)

) = f =m and p = 1= . For simplicity, we have assumed that …rms

are identical and equilibria symmetric. Thus, letting p (j) denote the price of intermediate
goods j, we have p (j) = p; 8j. Note also that we have normalized wL = 1 and thus therelative wage of high-skilled to low-skilled labor— the skill premium— is wH as above.

3

Competition Policies and the Skill Premium

We now establish the possible relationship between competition policies and the skill premium. From (1) and (2), we derive the following two propositions. Note that Proposition 1
reproduces the results that was documented by our 2010 paper, which analyzed the e¤ectof a decrease in …xed costs on the skill premium in a closed economy.
Proposition 1 (Entry deregulation, …rm numbers/size, and the skill premium) Supposethat the government decreases the …xed costs f . Then, we have the following.
(a) The number of …rms n increases, while the …rm size L=n decreases.
(b) The skill premium wH decreases if
if> 0, remains unchanged if= 0, and increases< 0.

Proof. (a) It is evident from (1) that decreasing the …xed costs f increases the number of…rms n, thereby decreasing …rm size L=n.
(b) Di¤erentiating (2) with respect to f yields:

dwH f ; m=df

12

+ or 0 or
z}|{

z

+

n(

1)=

p

1 (

}|

1)2

n 1= pSolving the model is standard and has been relegated to Appendix.

7

L
H

1

Lmf

{
2

:

Proposition 2 (Antitrust policy, …rm numbers/size, and the skill premium) Suppose thatthe government decreases the cartel size m. Then, we have the following.
(a) The number of …rms n decreases, while the …rm size L=n increases.
(b) The skill premium wH increases if
if> 0, remains unchanged if= 0, and decreases< 0.

Proof. (a) It is evident from (1) that decreasing the cartel size m decreases the number of…rms n, thereby increasing …rm size L=n.
(b) Di¤erentiating (2) with respect to m yields:

dwH f ; m=dm

+ or 0 or
z}|{

z

n(

1)=

p

1

(

}|
1)2

n 1= p

L
H

1

Lf

{
1

:

In these propositions, we have shown that entry deregulation that lowers the …xed costsof entry f increases the number of …rms, that is, the variety of intermediate goods/tasks nused by the …nal good. Then, the skill premium increases if< 0, that is, if a composite

of intermediate goods— varieties— and high-skilled labor are complementary (i.e., ful…llingvariety–skill complementarity).13 However, antitrust policy that reduces the size of cartelsm increases the …xed costs per …rm since the …xed costs are shared within a cartel. Thisdecreases the number of …rms, that is, the variety of intermediate goods/tasks n used by
the …nal good, thereby decreasing the skill premium under variety–skill complementarity.
We have also shown that entry deregulation decreases the size of …rms in the intermediate
goods sector that is measured by employment per intermediate …rm, L=n, while antitrust
policy increases it. We note that …rm size measured by …rm sales per intermediate …rm,px, is also decreased by entry deregulation and increased by antitrust policy. As do theskill premia and the size of …rms, the welfares also move to the opposite directions in thesetwo cases. An increase in n due to a decrease in f increases the quantity of the composite
1=Rn
good X =x (j) dj(as pointed out by Ethier, 1982) and thus the quantity of the0…nal good y.14 This increases the consumption c and thus the welfare u.15 On the other
hand, a decrease in n due to a decrease in m decreases the quantity of the composite good13

Kurokawa (2011) de…nes the case < 0 ( < 1) as the case in which varieties and high-skilled labor
are complementary. The number of inputs has a related role in other papers. For example, Blanchard andKremer (1997) de…ne the index of complexity that relates the increased number of inputs to more complexity
in production processes. Kremer (1993) theoretically shows that higher skilled workers will use more complex
technologies that incorporate a greater number of tasks.
14
Ethier (1982) documented that the increased number of inputs translates into higher productivity.
15
As shown by a model developed by Vives (1988), policies that lower the cost of entry need not increase
the welfare.

8X and thus the quantity of the …nal good y. This decreases the consumption c and thus
the welfare u.
The key mechanism driving the above results is very simple. Here, let us focus on thecase of entry deregulation. An increase in the number of varieties n, due to a decrease in the…xed costs of entry f , increases the quantity of the composite good X through an increasein productivity. This directly increases the marginal products and thus the demand of highskilled labor. If varieties and high-skilled labor are complementary ( < 0), it also increases
the relative demand and thus the relative wage of high-skilled to low-skilled labor wH . In
other words, an increase in the number of varieties n lowers the price of the composite good
( 1)=
Rn
=( 1)
PX =
p (j)
dj
. Under the complementarity, it causes the demand and thus0

the wage of high-skilled labor wH to increase. The similar argument also holds for the caseof antitrust policy. Here, we have linked an increase in the number of varieties to an increasein the skill premium through the complementarity between varieties and skill. As will be
discussed in Section 5, if we interpret varieties as varieties of tasks, intuitively it would beplausible to assume that high-skilled workers are more complementary to varieties of tasks
than low-skilled workers are.
Thus far, we have considered the case in which the government changes either the …xed
costs of entry f using an entry policy or the size of cartels m with an antitrust policy. We
now consider the case in which the government changes both the …xed costs of entry f andthe size of cartels m. Of course, the net e¤ect on the skill premium depends on which policy
dominates in changing the number of …rms n. We thus obtain the following proposition
regarding this net e¤ect.

Proposition 3 (Entry and antitrust policies, …rm numbers/size, and the skill premium) If
the government decreases the …xed costs f by a greater percentage than does the cartel size
m, and if varieties and high-skilled labor are complementary ( < 0), then the skill premium
wH increases because of an increase in the number of …rms n and a decrease in …rm size
L=n.
Proof. From (1), it is evident that if the …xed costs f decrease by a greater percentage
than does the size of cartels m, then the number of …rms n increases, thus decreasing the…rm size L=n. Then, given (2), it is evident that if
wH , noting that 0 << 0, then an increase in n increases< 1.

As a corollary of this proposition, we can see that if the government decreases the cartel
size m and the …xed costs f by the same percentage, then competition policies do not a¤ect
the skill premium wH because the number of …rms n does not change. In particular, if thegovernment prohibits cartel by regulating the cartel size from m to 1 and also decreases
the …xed costs from f to f =m, thereby changing m and f by the same percentage, then wecan consider this case as a change from the cartel equilibrium to the non-cartel equilibrium

9without altering the total number of …rms n. Needless to say, in this case the skill premium
wH remains unchanged.

4

A Two-Country Model: Competition Policies, Trade, andthe Skill Premium

We consider two countries, country 1 and country 2. Let these two countries trade intermediate varieties with each other, while …nal goods are nontradable. Labor is mobile
within each country but not across countries. There are no trade costs. Then the numberof varieties that the …nal sector can use increases; in fact, it increases merely from ni to
n1 + n2 (the sum of the autarky levels) in each country i, i = 1; 2. This increase is because
the number of varieties ni produced in each country remains unchanged before and after
trade, with the constant endowment of low-skilled labor Li .

4.1

Symmetric Countries

First, we consider the case of symmetric countries. Then, the skill premium corresponding
to the regulated …xed costs and the regulated cartel size in each country i, i = 1; 2, is:
1
wH
2
wH

1

2

1

2

1

2

1

2

f ;f ;m ;mf ;f ;m ;mwhere n1 = L1 (1

=

2 (

1)=

1

L1
H1

1

1

2 (

1)=

1

L2
H2

1

1

n +n

=

n +n

) = f 1 =m1 and n2 = L2 (1

;

(3)

;

(4)

) = f 2 =m2 . Note that due to thesymmetry, each of variables with superscript i is equal, for i = 1; 2 (e.g., L1 = L2 ). Note
1 = w 2 = 1 as the numeraire.
also that due to the symmetry, we have set wLL

We now determine the possible e¤ects of competition policies on the skill premium
through trade. Since the two countries are symmetric, we consider the case in which bothcountries conduct competition policies simultaneously and symmetrically. First, we determine the e¤ects of entry deregulation.
Proposition 4 (Entry deregulation, trade, and the skill premium) Suppose that the government in each country i decreases the …xed costs f i symmetrically. Then, the skill premia
1 and w 2 symmetrically decrease if
in both countries wH
H

and increase if> 0, remain unchanged if

= 0,

< 0.

Proof. Suppose that the government in each country i decreases the …xed costs f i symmetrically. Then the number of …rms ni increases symmetrically in each country i. Hence,
due to (1)= < 0 the term n1 + n2(

1)=

(1= ) symmetrically decreases in equations(3) and (4). Thus it is evident from equations (3) and (4) that the skill premia in both10

1 and w 2 symmetrically decrease if
countries wH
H

increase if> 0, remain unchanged if= 0, and< 0.

As can be seen from equations (3) and (4), entry deregulation in one country can contribute to a change in the skill premium in both countries through a change in n1 + n2 .
Here, we note that even if these two countries do not trade with each other, a symmetricdecrease in …xed costs in both countries can cause the skill premium to change in bothcountries. In that autarky case, however, entry deregulation in each country contributes
only to the change in the skill premium in own country. We also note that just moving fromautarky to trading equilibrium, without changing …xed costs, can change the skill premiumin both countries through an increase in the number of varieties.16
Similarly, we can also determine the e¤ects of antitrust policy.
Proposition 5 (Antitrust policy, trade, and the skill premium) Suppose that the government in each country i decreases the cartel size mi symmetrically. Then, the skill premia
1 and w 2 symmetrically increase if
in both countries wH
H

and decrease if> 0, remain unchanged if

= 0,

< 0.

Proof. The proof is similar to that for Proposition 4.
As does entry deregulation, through a change in n1 + n2 because of trade, antitrust
policy in one country can also a¤ect the skill premium in both countries. However, thee¤ects are opposite to those of entry deregulation.
Thus, it follows that if the government in each country decreases the …xed costs and thecartel size by the same percentage, then competition policies do not a¤ect the skill premiumin either country. This lack of change is because the number of …rms does not change ineither country and thus, neither does the total number of varieties.

4.2

Asymmetric Countries

Next, we consider the case of asymmetric countries. We assume that the two countries
have identical technologies and preferences but di¤er in their endowments of high-skilled
1 = w 2 does not necessarily hold.
labor and low-skilled labor, H i and Li , i = 1; 2. Then wLL
1 = 1 as the numeraire.
Therefore, we only set wL

Then, the skill premium corresponding to the regulated …xed costs and the regulated
16

Kurokawa (2011) analyzed the e¤ect of trade in varieties on the skill premium in both of the trading
countries.

11cartel size in each country i, i = 1; 2, is:1wH
f 1 ; f 2 ; m1 ; m2
2
wH
1 2
1
2
2 f ;f ;m ;mwLwhere n1 = L1 (1

=
0

= @

(

2 =(
n1 + n2 (wL)

1)

2 ) =(
n1 + n2 (wL

1) (

1)=

1)= 1

1
A

2
wL

) = f 1 =m1 and n2 = L2 (1

1

L1
H1

1

L2
H2

1

;

(5)

;

(6)

) = f 2 =m2 . Note that we have set

1 = 1 as the numeraire.17
wL

We now want to see the possible e¤ects of competition policies in one country on the skill
premium in the other country through trade. If the government in one country i decreases
the …xed costs f i , the number of …rms in that country ni surely increases. In this asymmetric2 ) =(
case, however, as can be seen there is now an extra term (wL1) in equation (5), and

1) and w 2 in equation (6).18 Due to these extra terms,
L2 ) =( 1) ( 1)= (1= ) decreases in equation (5)it is not clear whether the term n1 + n2 (wL
2 ) =( 1) ( 1)= (1= )=w 2 decreases in equation (6). Thusor whether the term n1 + n2 (wLL2 ) =(
there are now extra terms (wL

the e¤ects of entry deregulation in one country on the skill premium in each country are
not clear. For the same reason, the e¤ects of antitrust policy in one country are not clear,either. It should also be noted that even if the two countries have the same ratio of low2 in equation (6) the skill
to high-skilled labor (L1 =H 1 = L2 =H 2 ), due to the extra term wL

premia are not necessarily equal in these countries.
Here, we resort to a concrete numerical example to illustrate that there is a case in which
entry deregulation and antitrust policy in one country, respectively, increases and decreases
the skill premia in both countries and to also show the quantitatively di¤erent e¤ects of adomestic policy on the domestic and foreign skill premia. Note that the parameters are notcalibrated because our model is very simple and thus cannot perform full-scale calibrations
capturing many facts. Here, we just want to show this numerical example to highlight theexistence of such a case.
Example Consider the numerical example of asymmetric countries in which1f 1 = f 2 = 4; m1 = m2 = 2; = ; =2

1; H 1 = 200; L1 = 100; H 2 = 75; L2 = 50:

Then, from (5) and (6), we obtain:1
wH= 4:6875;172wH
2 = 8:33:
wL

If we introduce a tradable homogenous intermediate good as numeraire, due to its price equalization
1
2
across the two countries it is possible to have wL= wL= 1 even in the case of asymmetric countries
18
2
It can be shown that the low-skilled wage wL decreases (resp. increases) when the total value of thecomposite intermediate goods decreases (resp. increases).

12

We consider the following three cases.
1
1. If the government in country 1 decreases the …xed costs f 1 from 4 to 1, then wH
2 =w 2 also increases from 8.33 to 13.89. This
increases from 4.6875 to 15.625 and wH
Lshows that the decrease in the …xed costs in country 1 raises the skill premium incountry 1 by a greater percentage than that in country 2.
1
2. If the government in country 1 decreases the cartel size m1 from 2 to 1, then wH
2 =w 2 also decreases from 8.33 to 6.69. Thisdecreases from 4.6875 to 2.67 and wH
Lshows that the decrease in the cartel size in country 1 decreases the skill premium incountry 1 by a greater percentage than that in country 2.
3. If the government in each country i simultaneously decreases the …xed costs f i from1 increases from 4.6875 to 18.75 and w 2 =w 2 also increases from 8.33
4 to 1, then wH
HL

to 33.33. As we can see, the increase in the skill premium in each country is greaterthan that in the …rst case in which only country 1 conducts entry deregulation.

5

Empirical RelevanceIn this section, we discuss the empirical relevance of our model, although a de…nitive answer
must wait for serious empirical work.
Are the main predictions of our model empirically relevant? Table 1 shows available
empirical evidence from the U.S. for entry costs, cartels, …rm numbers/size, and the skill
premium. The data for the entry cost index and the total cartel cases are from Nicolettiand Scarpetta (2003) and the Workload Statistics provided by the Antitrust Division at the
U.S. Department of Justice (DOJ), respectively. Nicoletti and Scarpetta (2003) compiled
an index on product market regulation, and we measure the total cartel cases by the total
criminal cases (…led). The data for …rm numbers/size and the skill premium are from the
U.S. Annual Survey of Manufactures (ASM). We measure …rm numbers and …rm size by the
number of establishments and the number of workers per establishment, respectively. The
skill premium is measured by the relative wage of non-production to production workers.
We note that the table provides the data on the entry cost index and the total cartel cases
for 1978 and 1998, while it provides the ASM data for 1977 and 1997. This is because the
Nicoletti and Scarpetta (2003) index’s starting date is 1978 and its ending date is 1998, while
the ASM uses census data for the number of establishments and this census is conductedat 5-year intervals including the years 1977 and 1997.
=== Table 1 ===As shown in Table 1, from the late 1970s to the late 1990s entry costs decreased andcartel activities became more active. Over the same period, …rm numbers increased, …rm

13

size decreased, and the skill premium increased. These observations are indeed compatible
with the predictions that our model has derived under the assumption that a composite
of intermediate goods— varieties— and skill are complementary ( < 0). Recall that, inboth autarky and two-country models, a decrease in entry costs f is accompanied by anincrease in …rm numbers, a decrease in …rm size, and an increase in the skill premium,under the assumption of variety–skill complementarity. Recall also that more active cartel
activities (an increase in m) are also accompanied by an increase in …rm numbers and theskill premium and a decrease in …rm size. Thus the main predictions under the assumptionof variety–skill complementarity does appear to be empirically relevant.
What about the assumption of variety–skill complementarity? Is this assumption also
empirically relevant? A de…nitive answer must wait for estimating the elasticity of substitution between intermediate goods— which we call varieties— and high-skilled workers.
However, if we interpret varieties as varieties of tasks, intuitively it is plausible to assume
that higher skilled workers are more complementary to varieties of tasks than lower skilledworkers are. Indeed, this assumption can be compatible with the data on Stanford business school alumni. Using data on Stanford business school alumni, Lazear (2005, 2012)
empirically con…rmed that leaders are generalists who need not excel in any one skill but
are competent in many. He de…nes leaders as individuals who have a position de…ned as a
“C” level position (CEO, COO, CFO, etc.), a managing director, or similar, which would
be a high-skill position.

6

Conclusion and Extensions

This paper has developed a simple, general equilibrium model to examine the possible effects of both entry and antitrust policies on the skill premium in wages through a change
in …rm numbers/size. The closed economy model has shown that entry deregulation that
reduces the …xed costs of entry can increase the skill premium by increasing the numberof …rms and decreasing the …rm size. However, an antitrust policy that reduces the sizeof cartels can decrease the skill premium by decreasing the number of …rms and increasing
the …rm size. We have also extended the model to a two-country model. The extended
model has shown that in the case of symmetric countries, entry deregulation that is conducted symmetrically in both countries can increase the skill premia symmetrically in bothcountries while antitrust policy that is conducted symmetrically in both countries can havethe opposite e¤ect. In the case of asymmetric countries, though the e¤ects are not clear,
our numerical example has shown a possibility that entry deregulation and antitrust policyin one country, respectively, can increase and decrease the skill premia in both countries
through trade; however, the domestic skill premium is changed by a greater percentage than
the foreign one. Thus, in both symmetric and asymmetric cases, the interaction between
domestic competition policies and trade can change wage inequality in a trading partner

14

even if it is not the purpose of the policies. This implies that the international coordinationof competition policies are essentially necessary among the trading countries.
Several next steps could be pursued for future research. First, our model has implied
the essential necessity of international coordination of competition policies. We can thus
extend our model to explicitly analyze international policy coordination as does Ohyama(1997).19 Second, our paper has focused on the interaction between competition policies
and free trade. It would be interesting to introduce tari¤s/trade costs into our model andanalyze the interaction between the competiton and trade policies. Third, in our model the…xed costs are in terms of low-skilled labor. Thus an extension of our model is to introduce
the …xed costs of high-skilled labor, as well.
Fourth, this paper has provided a simple model with symmetric …rms as a …rst step. It
would also be interesting to extend our model to a heterogeneous …rm model. The results
regarding entry deregulation in a closed economy will remain unchanged. Upon applicationof the well-known argument by Melitz (2003), …rms whose productivities are above the cuto¤
productivity stay and produce in the intermediate goods market. If the …xed costs of entry
are decreased due to entry deregulation, then the number of producing …rms will increase,which increases the number of varieties available to the …nal goods. It raises the skill
premium if varieties and high-skilled workers are complements, and it decreases the average
size of …rms measured by emloyment. However, the results regarding entry deregulation inan open economy might not be clear even in the case of symmetric countries. Suppose that…xed costs are decreased due to entry deregulation in each country. Then the total numberof producing …rms in each country will increase, but the number of exporters in each country
might decrease. Hence, the total number of the domestic and imported varieties available to
the …nal goods in each country might not increase. As for antitrust policy, it would not besafe to assume that cartels are formed symmetrically among …rms in a heterogeneous …rm
setting. Modeling how cartels are formed among heterogeneous …rms will be a challenge.
Finally, we have discussed the empirical relevance of our model in Section 5, but a de…nitive answer must wait for serious empirical work. In particular, it would be important toestimate the elasticity of substitution between intermediate goods— which we call varieties—
and high-skilled workers like several studies (e.g., Krusell et al., 2000) have estimated theelasticity of substitution between capital and high-skilled workers.20
19

Ohyama (1997) considers the international coordination of entry policy in a model of monopolisticcompetiton. Yanase (2019) extends it to a model with non-homothetic quadratic preferences. For theinternational coordination of merger policy, see Richardson (1999) and Horn and Levinsohn (2001).
20
Kiyota and Kurokawa (2019) have recently provided a …rst statistical test on whether intermediate
goods are complements for skilled labor. Using a two-level CES production function and the panel data of
40 countries over 1995–2009, they show that the elasticity of substitution between intermediate goods andunskilled labor is signi…cantly greater than that between intermediate goods and skilled labor, suggesting
intermediate goods–skill complementarity.

15

Appendix: Solving the Model
A.1

The intermediate goods sector

First, we derive the free-entry number of …rms n in the intermediate goods sector with theregulated …xed costs at f and the regulated cartel size at m.21 For simplicity, we assume
that …rms are identical and equilibria symmetric. Thus we have p (j) = p and x (j) = x; 8j.
Given an arbitrary n, as in Seade (1980) and Ohyama (1999) each cartel maximizes thetotal pro…t of m …rms mpx

m(wL xwL f =m), taking other cartels’ outputs as given.

By setting wL = 1 as the numeraire and noting that an individual …rm is negligible in theaggregate economy,22 the output x n; f ; m , the price p n; f ; m , and the pro…tn; f ; mof each variety corresponding to this n are:x n; f ; m =

"

=(1

1

n

py n ( = ) 1
p n; f ; m =n; f ; m =

)

1

1

=

# 1=

H; 8j;; 8j;

x n; f ; m

x n; f ; m

f
; 8j:
m

As the price is independent of the number of varieties n, the price when the pro…t ofeach variety reaches zero because of free entry and exit is also:p=Then, the zero pro…t condition px n; f ; m1:

x n; f ; m

f =m = 0, with p = 1= , speci…es

the output of each variety:x n; f ; m =

f
m (1

)

:

Substituting this output into the equality of labor demand and supply in the intermediate
sector, n x n; f ; m + f =m = L, gives the free-entry number of …rms n:
n=

L (1
)
:
f =m

21

(A1)

Mankiw and Whinston (1986) are one of the notable theoretical studies on the free-entry number of…rms. It shows that there is a tendency toward excess entry from a social standpoint in homogeneous
product markets and that product di¤erentiation can reverse this tendency.
22
Our model with symmetric …rms cannot capture the cross-sectional fact that larger employers pay higher
wages at a given point in time (Brown and Medo¤, 1989). Extending our model to a heterogeneous …rms
model may capture this size–wage relationship in the cross-section. Holmes and Mitchell (2008) link thesize–skill relationship in the cross-section (where larger plants employ a larger/smaller fraction of skilledworkers) to changes in the skill premium over time. They show that if the size–skill relationship is positive,
an expansion of markets due to increased trade can raise the skill premium without technological change.

16

A.2

The …nal good sector

Next, we derive the solutions for the …nal sector.
Here, we …nd it useful to de…ne a composite good
0 n
11=
Z
X = @ x (j) dj A
0and its price pX . Then the pro…t of the …nal good sector becomes:py (X + H )1=

pX X

wH H:

By solving the cost minimization problem for the composite good X, its price pX becomes:

0 n
Z
@
pX =
p (j) =(

1)

dj A

1)=

p:

0

By symmetry p (j) = p, pX becomes:

pX = n (

1(

1)=

:

The market clearing condition for the …nal good and the …rst order conditions withrespect to X and H thereby yield:
wH = n(

1)=

L
H

p

1

:

As we have normalized wL = 1, the relative wage of high-skilled to low-skilled labor— theskill premium— is wH .

A.3

The skill premium

Finally, by combining the above solutions in the intermediate sector and in the …nal sector,
we obtain the skill premium wH f ; m corresponding to the regulated …xed costs at f andthe regulated cartel size at m:
wH f ; m = n(where n = L (11)=

) = f =m and p = 1= .

17

p

L
H

1

;

(A2)

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20Entry cost index (Nicoletti and Scarpetta, 2003)
Total cartel cases (DOJ)
Firm numbers (ASM)
Firm size (ASM)
Skill premium (ASM)

1978
4.0
31
1977
359,928
54.4
1.58

Table 1: Indirect evidence from the U.S.

21

1998
1.4
62
1997
373,54848.4
1.88