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ESSAYS ON GLOBALIZATION, UNEMPLOYMENT, AND ECONOMIC
GEOGRAPHY

presented by
JOHN FRANC I S

has been accepted towards fulfillment
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ESSAYS ON GLOBALIZATION, UNEMPLOYMENT, AND ECONOMIC
GEOGRAPHY

By

John Francis

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Economics

2001

ABSTRACT
ESSAYS ON GLOBALIZATION, UNEMPLOYMENT, AND ECONOMIC
GEOGRAPHY
By

John Francis

This dissertation presents three essays examining the role that falling trade costs and the
resulting agglomerations have on unemployment. In addition, the role of regional (or
national) labor market characteristics on agglomeration patterns is also examined.

The first essay extends the Krugman (1991) new geography model to include
asymmetries in regional labor markets. The particular labor market considered is a two-
region variant Of the Shapiro-Stiglitz (1984) model where the rate of job breakup or
shirker detection may vary between regions. It is shown that in the presence Of such
asymmetries agglomeration can occur even in the absence of transport costs.
Furthermore, when transport costs are present it can be determined in which region
agglomeration is most likely to occur. The essay also examines the spatial pattern Of
unemployment in both the symmetric and asymmetric cases.

The second essay presents a two-country, two-sector new geography model where
workers are imperfectly monitored is used to examine the relationship between falling
trade costs and unemployment. It is shown that as trade costs fall over time the world
naturally falls into an industrialized core and an agricultural periphery. Globalization has
a positive effect on employment in the core in both the short and long term. The

periphery suffers employment losses in the short term but can gain in the long term. The

impact of labor market asymmetries on both the likelihood of agglomeration occurring in
a specific country and unemployment is also examined.

The final essay extends the Krugman (1991) new geography model to include
search frictions in the labor market. The particular labor market considered is a two-
region variant of the Diamond (1982) model. It is shown that if the matching function
exhibits constant returns to scale the pattern of agglomeration is identical to the fill]-
employment model and there is no change in unemployment as a result of agglomeration.
If the matching function exhibits increasing returns to scale agglomeration can be
sustained no matter the level of trade costs and unemployment falls as a result of
agglomeration. It is also shown that regions with higher rates of tenure will be more

likely to receive an agglomeration.

 

TABLE OF CONTENTS

LIST OF TABLES .................................................................................... v
LIST OF FIGURES .................................................................................. Vi
CHAPTER 1
THE PROBLEM ....................................................................................... 1
CHAPTER 2
A TWO-REGION MODEL WITH INIPREFECT MONITORING ............................ 7
CHAPTER 3
A TWO-COUNTRY MODEL WITH IMPERFECT MONITORING ...................... 34
CHAPTER 4
A TWO-REGION MODEL WITH SEARCH FRICTIONS .................................. 66
CHAPTER 5
CONCLUDING REMARKS ..................................................................... 101
APPENDIX ......................................................................................... 1 04
BIBLIOGRAPHY ................................................................................. 106

iv

TABLE OF CONTENTS

LIST OF TABLES .................................................................................... V
LIST OF FIGURES .................................................................................. vi
CHAPTER 1
THE PROBLEM ....................................................................................... 1
CHAPTER 2
A TWO-REGION MODEL WITH IMPREFECT MONITORING ............................ 7
CHAPTER 3
A TWO-COUNTRY MODEL WITH IMPERFECT MONITORING ...................... 34
CHAPTER 4
A TWO-REGION MODEL WITH SEARCH FRICTIONS .................................. 66
CHAPTER 5
CONCLUDING REMARKS ..................................................................... 101
APPENDIX ......................................................................................... 104
BIBLIOGRAPHY ................................................................................. 106

iv

LIST OF TABLES

Table 2-1: Simulation Parameters, (p. 18)
Table 2-2: Break and Sustain Points for Various Parameter Values, (p. 22)
Table 3-]: Simulation Parameters, (p.43)
Table 4-1 .' Simulation Parameters, (p. 76)
Table 4-2: Break and Sustain Points for Various Parameter Values, (p. 81)

Table 4-3: Break Points for Varying Degrees of Homogeneity in the Matching Function,
(p. 87)

Figure 2-1:
Figure 2-2:
Figure 2-3:
Figure 2-4:
Figure 2-5:
Figure 2-6:
Figure 3-1:
Figure 3-2:
Figure 3-3:
Figure 3-4:
Figure 3-5:
Figure 3-6:
Figure 3- 7:
Figure 3-8:

Figure 3-9:

(p. 60)

LIST OF FIGURES

Labor Dynamics with Symmetric Regions, (p. 20)

Bifurcation Diagram with Symmetric Regions, (p. 21)

Labor Dynamics with Asymmetric Regions, (p. 25)

Bifurcation Diagram with Asymmetric Regions, (p. 26)

Unemployment with Symmetric Regions, (p. 29)

Unemployment with Asymmetric Regions, (p. 31)

Labor Dynamics with High Trade Costs, (p. 46)

Labor Dynamics with Low Trade Costs, (p. 47)

Labor Dynamics with Intermediate Trade Costs, (p. 48)

Bifurcation Diagram with Symmetric Countries, (p. 49)

Efficiency Wage and F all-Employment Bifurcation Diagrams, (p. 50)
Unemployment Along the Efficiency Wage Bifurcation, (p. 52)

Labor Dynamics for Asymmetric Countries and High Trade Costs, (p. 57)
Labor Dynamics for Asymmetric Countries and Low Trade Costs, (p. 59)

Labor Dynamics for Asymmetric Countries and Intermediate Trade Costs,

Figure 3-10: Bifurcation Diagram for Asymmetric Countries, (p. 61)

Figure 3-11: Unemployment with Asymmetric Countries, (p. 62)

Figure 4-1:

(p. 78)

Figure 4-2:

80)

Labor Dynamics for CRS in the Matching Function and Symmetric Regions,

Bifurcation for CRS in the Matching Function and Symmetric Regions, (p.

vi

Figure 4-3: Labor Dynamics for IRS in the Matching Function and Symmetric Regions,
(p. 84)

Figure 4-4: Bifurcation for IRS in the Matching Function and Symmetric Countries, (p.
86)

Figure 4-5: Labor Dynamics for CRS in the Matching Function and Asymmetric
Regions, (p. 92)

Figure 4-6: Bifurcation for CRS in the Matching Function and Asymmetric Regions, (p.
93)

Figure 4- 7: Labor Dynamics for IRS in the Matching Function and Asymmetric Regions,
(p. 96)

Figure 4-8: Bifurcation for IRS in the Matching Function and Asymmetric Regions, (p.
97)

vii

Chapter 1:

The Problem

How does globalization affect unemployment? This question is not new to any who have
witnessed the political debates over the new global economy or the formation Of fi'ee
trade areas such as NAFTA in North America. To many economists the answer to this
general question seems Obvious: lower costs of trade mean an increase in the volume of
trade which will benefit some sectors while harming others, but in the long term, after
displaced workers have had time to retrain, there will be a net improvement in
employment. However, given the ferocity of these debates in political circles one can
conclude that not everyone has chosen to subscribe to this point of view. In particular,
labor groups have raised their concerns of losing out to low wage competition from the
less developed world. What is somewhat surprising is that a fairly small number Of
economists have researched directly the relationship between the falling costs of trade
and their resulting effects on integration and employment. The results in the existing
literature are mixed. Hanson (1998) shows that a fall in trade costs has a positive effect
on unemployment in border towns in Mexico. However, he ignores any impact that
falling trade costs may have in non-border towns. Milner and Wright (1998) show that,
in theory, employment should expand in the exportables sector and contract in the
irnportables sector in response to trade liberalization in a specific factor model of trade.
But, empirically, the data used in their study Show that employment has expanded in all
sectors]. Brecher and Choudhri (1994) Show that Pareto gains from trade and trade

liberalization may be infeasible in the presence of unemployment. Revenga (1997)

 

' The data used in this study are confined to the country Of Mauritius.

Shows that trade reform in Mexico between 1985-88 has had a negative impact on
manufacturing employment. Agenor and Aizeman (1996) show that when trade is
liberalized and taxes are adjusted so that the govemment’s budget does not change the
resultant effect on employment is ambiguous. SO, even in the limited literature that does
exist on this subject there is no clear-cut conclusion among economists.

The goal of this thesis, then, is to examine the relationship between the falling
costs of trade and unemployment at the national level. The models employed for this task
draw on the new geography framework first proposed by Krugman (1991). This choice
seems appropriate since changes in trade costs and the resulting effects on the economy
can be modeled in a tractable manner. The basic story in the new geography literature is
that the interaction between trade costs and scale economies will create incentives for
firms to agglomerate production into a small number Of locations. The intuition is
straightforward. Firms will want to set up factories where demand is highest since that
will minimize trade costs. However, demand will be highest in larger markets since a
considerable share of demand comes from the manufacturing labor force. These forces
are referred to as backward linkagesz. These linkages will be reinforced by the fact that it
will be more advantageous for a worker to reside in a larger market where trade costs
apply to a smaller share of consumption goods. These forces are referred to as forward

linkages3. Consequently, the reinforcing forward and backward linkages induce both

 

2 Perhaps the term “supplier linkages” would be more appropriate since backward linkages refer to the
reasons that suppliers would want to locate in a large market.

3 Perhaps a better term here would be “demander linkages” since forward linkages refer to reasons why the
demanders of manufactures would want to locate in a large market.

L *wflfl__—_—_—

manufacturing firms and workers to locate into a small number of regions given that trade
costs are sufiiciently low4.

In the story told above what drives the forward and backward linkages is that
workers are free to move between regions. If the goal is to construct a trade model where
labor is not internationally mobile then a slightly different approach is warranted.
Furthermore, with immobile labor agglomeration, as it is defined above, cannot occur.

SO, again, a slightly different concept is necessary. The approach taken in this paper,
attributed to Krugman and Venables (1995), is to use an intermediate good to play the
role that mobile labor normally would in creating the forward and backward linkages. A
country with a large manufacturing base provides firms locating there a greater variety Of
intermediates. This gives firms locating there lower costs of production, or a forward
linkages. A large base of final goods manufacturers also provides a large local market for
intermediate goods producers, or a backward linkage. What results is not a concentration
of people into a small number of locations but a concentration of manufacturing.

In both of the frameworks mentioned above a core-periphery pattern emerges.
That is, a core base of regions (or countries) produce the bulk of the world’s
manufacturing goods and export these goods to the agricultural periphery. So, a natural
divergence in production patterns emerge solely fiom falling transportation costs. This is
a fimdamental result in the new geography literature and has been used to explain the

differences between the developed and the less developed countries of the world.

 

4 There have been numerous extensions of the basic Krugman (1991) fi‘amework. The most notable of
these are Krugman and Venables (1995, 1996), and Venables (1996) extension to an open economy where
instead of footloose labor firms are linked vertically. For a complete survey of the literature see Krugman
(1998) and Fujita, et a]. (1999).

5 The linkages here may seem confiised from the earlier story. However, here final goods producers are the
demanders and intermediate goods producers are the suppliers.

In all three models presented in the following pages the new geography
framework is merged with one of two types of unemployment. First, in Chapters 2 and 3
a variant of the efliciency-wage/worker—discipline model first proposed by Shapiro-
Stiglitz (1984) is used. And second, a variant of the search fiamework developed by
Diamond (1982) is used in Chapter 4. One benefit Of using these particular forms of
unemployment is that it allows one to examine the effects that labor market asymmetries
have on the patterns of agglomeration. This is a subject that, to this point, has been
absent from the new geography literature. In fact, most articles in this field assume that
countries (or regions) are identical in every way except for the distribution of labor
between industries. Given that such asymmetries do exist in the real worldé,
incorporating these attributes into a new geography model seems relevant to the
literature.

The model presented in Chapter 2 is a two-region model where manufacturing
workers and firms are free to locate in either region. And, as mentioned above,
unemployment arises through the imperfect monitoring Of employed workers. If labor
markets are symmetric it is shown that the pattern of agglomeration is identical to that of
the Krugman (1991) model. However, if tenure is permitted to vary between regions the
region with longer rate of tenure will be more likely to be the recipient of an
agglomeration. In addition, it is shown that unemployment is decreasing in regional
agglomeration.

The model presented in Chapter 3 uses a slightly different framework to analyze

agglomeration patterns and unemployment between countries when labor is

 

6 For instance, in the European Union rates of job tenure range from 4.4 years in Denmark to 10.7 years in
Germany. See OECD (1998).

intemationally immobile. Here, an intermediate good is used to play the role that mobile
labor plays in a region model7. Again, unemployment in this model arises out Of the
imperfect monitoring of employed workers. The results are similar to those of Chapter 2.
If labor markets are symmetric then labor dynamics are identical to those of Krugman

and Venables (1995). However, if tenure is permitted to vary from country to country the
country with longer rate of tenure will be more likely to be the recipient Of an
agglomeration of industry. In addition, it is shown that unemployment is decreasing in
industry agglomeration. However, if trade costs fall to very low levels unemployment is
lower for both countries compared to an equilibrium where neither country specializes in
manufacturing goods.

The model presented in Chapter 4 returns to a two-region model where both firms
and workers are free to locate in either region. Unemployment in this model arises fiom
search frictions in the labor market. The results of this model depend on the homogeneity
Of the matching function. If the matching function exhibits constant returns to scale and
labor markets are symmetric, again the labor dynamics mimic those Of Krugman (1991).
However, the unemployment rate is unchanged with changes in the labor distribution.
Hence, there is no employment benefit to agglomeration. If, the matching fimction
exhibits increasing returns to scale agglomeration can be sustained no matter the value of
trade costs. And, unemployment is strictly decreasing in agglomeration. SO, there is an
employment benefit to agglomeration. Regardless Of the homogeneity of the matching
fimction, if tenure is permitted to vary between regions the region with longer rate of

tenure will be more likely to be the recipient of an agglomeration.

 

7 This fi'amework was first presented in Krugman and Venables (1995).

There are a several general conclusions one can draw from these three models.
First, when industry agglomerates unemployment will be at least as low as when industry
does not agglomerate in “core”, industrialized regions. SO, one can conclude that, at least
in this framework, globalization has at best a positive impact and at worst no impact on
employment in developed nations. Second, in the short term unemployment will increase
in peripheral, less developed nations, but in the long term unemployment rates will
converge to those of the developed world. Third, labor market asymmetry has an
influence on agglomeration patterns: agglomeration is more likely to occur in regions (or
countries) where tenure is long relative to other regions. This reveals an oversight in
much Of the new geography literature that ignores individual regional characteristics

which alter the results of models with symmetric regions.

Chapter 2:

A Two-Region Model with Imperfect Monitoring

1. Introduction

One theme that is common to most new geography models is that regions are assumed to
be identical in every way except for population size. It is conceivable that regional
asymmetries may encourage agglomeration economies even in the absence of trade costs.
In particular, labor markets may not be identical in every location. Job tenure rates do
vary significantly between regions. For instance, in the European Union (EU) rates of
job tenure range fiom 4.4 years in Denmark to 10.7 years in Germany]. The bases of
such differences can be attributed to cultural reasons as well as variations in public
policy. NO matter the source, these differences do exist in the real world.

This chapter, then, extends the Krugman (1991) framework to include
asymmetries in regional labor markets. The particular model Of unemployment used here
is a variant of the efiiciency-wage/worker-discipline model first proposed by Shapiro-
Stiglitz (1984). In this setting, workers’ incentive to Shirk will provide an additional
push (pull) towards (against) agglomeration. The region with the smaller incentive to
Shirk will tend to be more attractive since employment will be higher there. The
incentive to Shirk depends on both job tenure and the speed at which shirking workers are
detected. The longer the job tenure and the shorter the time it takes to get caught shirking
the smaller is the incentive to Shirk and the more attractive the region.

Given the description above it is clear that labor dynamics will be somewhat

altered from the Krugman (1991) model. Furthermore, the nature of the labor dynamics

 

‘ OECD, (1997)

are changed. In the efficiency wage model presented below employed workers are
temporarily immobile. Hence, labor dynamics are completely determined by the location
decision of unemployed workers. That is, in which region do unemployed workers
choose to search for employment. If all regions are identical then the incentive to Shirk is
the same everywhere and labor dynamics are unchanged from the Krugman (1991)
model. However, if regional labor markets vary it will be more likely that workers
agglomerate into the region with the smaller incentive to Shirk. That is, the regions
where job tenure is highest and shirker detection is most rapid.

Since unemployment is included to examine labor market asymmetries the model
is also equipped to determine the effects that changes in trade costs and agglomeration
have on economywide unemployment. It is shown below that, regardless of symmetry,
the lower are transportation costs the lower is unemployment. A more significant result
is that, in the symmetric case, no matter the value of transportation costs the
unemployment rate is decreasing in regional concentration. Hence, in a concentrated
equilibrium unemployment is at its minimum and in a diversified equilibrium where
workers are evenly distributed across regions unemployment is at its maximum The
asymmetric case is somewhat more complex. However, the major result still holds: as
trade costs fall and the economy moves toward a concentrated equilibrium the
unemployment rate declines.

Section II of this chapter describes the model. Section 111 describes the method
used to simulate the model. Section IV determines the labor dynamics Of the symmetric

case and section V describes the labor dynamics of the asymmetric case. Section VI

discusses the unemployment consequences Of these labor dynamics. And, section VII

offers some concluding remarks.

II. The Model

The model builds on the fi'amework first developed by Dixit-Stiglitz (1977) and its
extensions by Krugman (1979, 1980, 199l)2. Consider an economy in which there are
two types Of production: agriculture and manufactured goods; two factors of production:
farm labor and manufacturing labor; and two regions. Farm labor is assumed to be
perfectly immobile between regions3, and manufacturing labor can locate in either region.

The size of each type of labor force is normalized to one.

A. Agriculture

It is assumed that farm labor is evenly distributed throughout the economy with ‘/2 located
in each region. Agriculture is produced under constant returns to scale. The unit labor
requirement is one and agriculture is taken as numeraire so that its price (and the wage of
farm labor) is equal to unity. In addition, the simplifying assumption that agriculture can

be transported between regions at no cost is made4.

B. Preferences

All individuals share the utility function

 

2 Matusz (1994, 1996,1998) presents a model of monopolistic competition with efficiency wages. However,
geography is absent from his analysis.

Since land is not included as a factor of production, this assumption is equivalent to assuming that farm
labor is tied to the land.
4 This is a crucial assumption. Including trade costs on the agricultural good in these types of models can
alter the results of the model significantly. For more on this see Davis (1998), Fujita et a1. (1999), and
Rauch (1999).

 

 

(1) U = XLXK’ — e

where XM is consumption of an aggregate of manufactured goods, XA is consumption of
agricultural goods, and e is workers’ diSutility Of efion. It is assumed that e is positive
for manufacturing workers who exert effort and zero for both shirking and farm workers.
Hence, individuals will always spend a fraction y of their incomes on manufactured
goods and a fraction (1 - y) of their incomes on agricultural goods. The manufactures

aggregate is given by the CES subutility function

(2) X=[:(x )7 +:3(x )‘T

where nk is number of varieties produced in region k, x u; is the consumption of variety i
produced region k, and 0' > 1 is the elasticity of substitution between varieties. Given
equation (2), it is evident that individuals desire variety and will purchase some amount
Of each variety produced. The price index over manufactured goods for an individual
residing in region k is given by

l

(3) Hk=[nkpk—G +njp}_‘r° loil—o

where pk is the price Of a single variety produced in region k and ‘I.’ > 1 are iceberg trade
costs; in order for one unit Of the good to arrive at its destination I units must be shipped.
There are two notable characteristics of equation (3). First, the higher the fraction of
products produced in region k the smaller is IIk. Hence, when manufacturing is more

concentrated in region k the price Of manufactures as a whole is lower in region k, and

consequently the price of manufactures as a whole is higher in the other region. Second,

10

the higher are trade costs the higher is 11],. SO, manufacturing goods are more expensive
when transport costs are large.

Solving the utility maximization problem and substituting demands back into (1),
utility for a manufacturing worker in region k can be expressed in its indirect form as5
(4) Uk =1“wle;Y —e

where F = yy (1 — y)“ .

C. Manufacturing Production

The production of each variety of manufactured goods (regardless of the region in which
it is produced) requires both a fixed and a marginal input of manufacturing labor. In
region k, let E“, be the amount of labor required to produce xik units of output. Then

(5) AK =Ot+Bxik

where OL,B > O are the fixed an marginal input requirements respectively. Since
individuals desire variety Via a CBS sub-utility function with elasticity of substitution 0',
each firm will behave as a monopolist of its own variety who faces a demand curve with
constant elasticity of demand 0'. SO, to maximize profits each firm will set price so that
the Lerner index is inversely proportional to o. Noting that each firm’s marginal cost is [3

times the wage Of manufacturing workers in their respective locations, all firms in region

k will then set price

(6) p. ={—G—)Bwk

0—1

 

5 Since agriculture is taken as numeraire the indirect utility of a farm worker in region k is given by
replacing wk with unity in equation (4). However, this measure is not essential for the analysis that follows.

11

In addition, new firms may freely enter the market and will do so until profits are driven
to zero. A firm’s average cost can be expressed as [(Ot + BXII)Wkl/ x ik. In equilibrium, it

must be the case that this expression is equal to the price charged by the firm. Equating
this with equation (6) and solving for x ik yields a scale of production that is independent

of both the wage and the region in which production takes place

(7) x=%(0'—1)

So, all firms are of identical Size regardless of the region in which they are located.
Substituting equation (7) into equation (5), the amount Of labor that each firm will hire is
given by

(8) l = (sci

which is, again, identical for all firms regardless of their location. One implication of
equations (7) and (8) is that if there is an increase in demand for manufactures the only
way to meet this demand is for additional firms to enter the market and, consequently, for

employment to rise.

D. The Manufacturing Labor Market

The market for manufacturing labor is a two region variant of the Shapiro-Stiglitz (1984)
efficiency wage model. Workers in both regions receive disutility e from exerting effort.
In addition, workers are imperfectly monitored by their employers. Hence, there is the
possibility that a worker will Shirk her responsibilities if she thinks that she can get away
with it. In order to discourage such behavior workers receive a wage above the market
clearing wage and any worker caught shirking is immediately dismissed by the firm. The

threat of losing her job will prevent any worker fiom shirking in equilibrium.

12

Furthermore, in any steady state equilibrium there must be no incentive for an
unemployed worker to relocate in hopes of greener pastures in the other region. Thus,
unemployed workers must be indifferent to the region in which they are searching for
employment. Let p be the exogenous discount rate which is assumed to be identical for
all individuals regardless of their location. In region k, let qk be the rate at which shirking
workers are caught, and let bk be the rate at which non-shirking workers lose their jobs.
These exogenous parameters are permitted to vary between regions. In addition, let h, be
the endogenous rate at which workers are hired. Then, the asset value equations for a
region k worker are
(9) M =th: —V:)
(10) pV,:l = kaH;7 — e + bk(V,:’ — V1?)
(11) pV: = I‘wkII;Y + (bk + qk )(Vku — V:)
where Vku is the expected lifetime utility of an unemployed worker in region k, V," is the
expected lifetime utility of a non-shirking worker in region k, and V: is the expected
lifetime utility Of a shirking worker in region k. This assumes that an unemployed
worker has no source Of income.

First, the conditions under which workers have no incentive to Shirk must be
determined. A necessary and sufficient condition to guarantee this will be the case is
Vkn 2 Vi. Solving equations (9) — (1 1) and setting V’1 2. V: the no-shirking condition

can be expressed

(12) kaII;l _>_i[p+bk +qk +hk]

k

13

Next, the location decision of an unemployed worker must be determined. An

unemployed worker will choose to locate in the region in which she has higher expected
lifetime utility. Hence, the location decision is determined by A E V,u /V,u . If this

variable exceeds unity unemployed workers will choose to locate in region 1 and if it less

than unity unemployed workers will choose to locate in region 2. In solving equations

(9) — (11) it can be shown that

(13) V1:,=(I‘wkII;7 —e)'1k

(p + bk + hk )p
In equilibrium, the no shirking condition, equation (17), is satisfied with equality.
Combining this with equation (13)

:.h_k
P Qk

(l4) Vku =

Hence, the location variable can be expressed

(15) A=_lll_.q_2
hz ql

TO complete equation (15) an expression for hk must be determined. In any steady state

equilibrium the regional flow into employment must equal the regional flow out of
employment. At any given point in time there are Ink manufacturing workers employed
in region k. The flow into employment in region k is then hk [Lk —Tnk] where Lk is the
number of manufacturing workers located in region k. The flow out of employment is
the rate at which employed workers lose their jobs. This is given by kank . Equating

these flows and solving for hk gives

(16) hk .—.————_b"€‘_1k
Lk - ink

14

After some algebra and noting that the unemployment rate in region k is given by

111. E i.t(Lk , n k)=1 — In k / Lk , the job acquisition rate can be expressed

 

(17) hk =bk|:1—Hk]=bkn(l’lk)

“k
Note that the job acquisition rate is decreasing in the unemployment rate. Now the

location variable can be written

(18) _—-—-

 

Equation (18) completely determines the regional labor dynamics of the model.
In the Krugman (1991) model there are three effects determining labor dynamics which
manifest themselves into the real wage. First, the home market effect: the wage will tend
to be higher in the larger market since firms in the smaller market must have a labor cost
advantage to combat their disadvantage in higher transport costs6. Second, the price
index effect: workers in the larger market will face lower prices since they pay transport
costs on a smaller proportion Of their consumption goods. And third, the extent of
competition: competition in the larger region may become so fierce that it is beneficial to
locate near farm labor in the smaller region. These effects may appear to be absent from
equation (18), however, here they have manifest themselves into the unemployment rate.
The first two will tend to lower unemployment in the larger region while the latter will
tend to lower unemployment in the smaller region. But in the present analysis there is a
fourth force at work, a shirking effect which drives workers into the region where there is

a smaller incentive to Shirk. So, although labor dynamics are slightly altered fi'om the

 

6 For a complete discussion of this see Krugman (1980).

15

fiill-employment model all of the determinants of these dynamics are present in the

current model.

E. Regional Income and Demand

To complete the model regional incomes and demands for each individual variety must
be determined. The total income Of persons located in region k is given by

(19) vk = .5+ wknk'i

where the first term is income of farm labor and the second term is the income Of
manufacturing labor. Since preferences are Cobb-Douglass, region k expenditure on
manufactures is given by

(20) Ek = ka

Then, demand for manufactures in region k can be expressed

(21) xk =p;°[E,rI;:" + EJIIf‘R‘TJ

where the first term inside the brackets represents local demand and the second term
represents non-local demand. Note that if incomes were the same in both regions a
region R firm would see a larger proportion of its demand coming from local consumers
than from non-local consumers since locals need not pay the costs Of transport on locally
produced goods. Hence, demand will favor local products. Equilibrium is now

characterized by equations (3), (6), (12), (18), (l 9), (20), and (21) which can be used to

solve for the equilibrium values Of pk, wk, IIk, nk, Yk, Ek, and L1.

16

[11. Model Simulation
Solving the model analytically proves to be an intractable problem. However, it is
straightforward to use numerical simulation techniques to examine the characteristics Of

the equilibrium given particular values Of the model’s underlying parameters.

A. Methodology

The following describes the procedure used to simulate the model. Substituting equation

 

G )0 =1, the price

(6) into equation (3) and Choosing units Of measurement so that ( 1
G _.

index over varieties for individuals residing in region k can be expressed as

~ 1

(22) IIk = [nkwr’ + njw;‘°tl‘°]1-3
Substituting this and equation (16) into equation (12) yields the two nO-shirking
conditions as functions of 11;, and wk given L]. Then, substituting equation (19) into
equation (20) and substituting this result along with equation (22) into equation (21)
gives two demand equations as functions of nk and wk given LL Hence, there are four
equations in the four unknowns nk and wk given the distribution Of labor between regions.
These solutions can then be substituted into equation (18) to trace out A as a function of

L). From this point forward this fiinction will be referred to as the labor dynamics (LD)

curve.
B. Parameterization

The values Of the parameters that appear in both the full-employment model and the

current model (i.e. y and 0') are identical to those used in Krugman (1991). Therefore,

17

any results Obtained here that differ from those of Krugman can be attributed solely to the
addition of efficiency wages to the manufacturing labor market. Table 2-1 lists the

values of the parameters used in the simulation that are the same in both regions.

Table 2-1: Simulation Parameters

 

rcpebq a

 

 

.30 4 .04 .385 .13 .5 7.413x10'8

 

 

The expenditure share of manufactures is .30. Hence, individuals spend 30% Of their
incomes on differentiated goods and 70% on agriculture. The elasticity of demand is
equal to 4, which corresponds to a markup of price over marginal cost Of roughly 33%.
The choice of p = .04 is roughly consistent with recent real rates of interest in the EU 15
according to OECD (1996). The choice Of e implies the aggregate rate of unemployment
will fall somewhere between 9.8% and 10.6%. Again, this is consistent with recent EU 15
figures. Finally, the value of OI determines firm size which will, in turn, play a role in
determining the number of varieties produced in each region. Given the normalization of
the labor force the choice of OL = 7.413 x 10'8 = (2.9652 x 10'7)/0' is equivalent to a firm

size of 507.

 

7 The last term of the expression for or is to assure that firm size does not change when the elasticity of
demand changes. This makes the present model easier to compare with a full-employment version where
firm size can be eliminated fi'om the analysis.

18

IV. Labor Dynamics with Symmetric Regions
When labor markets are symmetric bk = b and qk = q for k = 1,2. Thus, the location

variable is given by

1’1 “2

Since all of the efficiency wage parameters affect each region in exactly the same way
there is an equal incentive to Shirk in both regions. So, it is as if the shirking effect is
absent. As a result, the same forces that determine labor dynamics in the full-
employment model will determine labor dynamics in the current model.

Although b and q are absent from the location decision variable, they do appear in
the nO-shirking condition. SO, values for these parameters must be assigned. Since jobs
arrive according tO a Poisson process, l/b is the average job tenure in the manufacturing
sector. Setting b = .13 implies the average job lasts roughly 7.7 years. This is
approximately the average tenure in the EU 158. Similarly, 1/q is the amount of time it
takes for a shirking worker to get caught. Setting q = .5 implies it takes two periods for
this to occur. It is not clear whether this is an appropriate value to use here; however, the
dynamics of the model are insensitive to changes in q.

A discussion of the dynamics of the model when there are no trade costs (i.e. 1: =
l) is useful here. When there are no trade costs both the manufacturing wage and the
price Of manufactures are the same in both regions. Otherwise, the product market will
not clear. Since the efiiciency wage parameters affect all workers in exactly the same

manner the unemployment rate will be identical in both regions regardless of each

 

8 This number is a weighted average of median tenure rates in the EU 15 according to OECD (1997) where
the weights are each country’s proportion of total EU 15 population.

19

region’s size. Given the definition of the location variable in equation (23) there is
nothing to encourage or discourage the population to deviate fiom its initial distribution.
So, when there are no trade costs location doesn’t matter and the LD curve is horizontal

atA=1.

Figure 2—1 : Labor Dynamics with Symmetric Regions

 

1.15 ;
t=1.3
1.10 , ————————— .— '
I \\\ ”fl."
\ t=1.5
1.05 r ~~ ------- ‘ \ _. \\\ _.////
| " \
. . - " _ I: 1.67
A100 ----- fi-———-;:\, _./-:/ ,,/
' K” w’“{ ----- «— TTTTTTT
\ 1\ 1:1 8
0.95 .1 ..........
-,""/ \\
\\‘~ \\\\\ t=2
0.90 1 '
0.85 ‘1' "A— '— . #7 A TIT F." _7" "‘_ 3 Ti? fi' 77"" WT "'F—"__ ' '—' V _
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

L1

Figure 2- 1 depicts the LD curve for several different values of trade costs. When
trade costs are high the LD curve is downward sloping suggesting that the extent of
competition dominates the price index and home market effects. Here an even
distribution Of labor is the only equilibrium. Then, as trade costs fall the LD curve begins
to flatten out until, at an intermediate level, there are multiple equilibria. For some labor
distributions the price index and home market effects are dominated by the extent of

competition and for others the reverse is true. So, the current distribution of labor will

20

determine whether agglomeration occurs or not. Finally, as trade costs fall fiuther the
extent of competition finally succumbs to the price index and home markets effects for all
distributions of labor and agglomeration is the only stable equilibriumg. The region in

which agglomeration occurs is determined entirely by the initial distribution of labor").

 

1.00 l /. 1(5)

._ : _____________________________________________________ . ......... f'
1 3(8)

 

 

0.00 ‘15)

 

 

1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.0(

T

Figure 2-2: Bifurcation Diagram with Symmetric Regions

To fully understand the structure of equilibria it is useful to look at the bifurcation
diagram shown in Figure 2-2. The solid lines represent stable equilibria and the dashed
lines represent unstable equilibria. When trade costs are high the symmetric equilibrium

is the only equilibrium that can be sustained. Then, when transport costs fall they reach a

 

9 A symmetric distribution of labor is an equilibrium. However, it is unstable. Any deviation fiom this
equilibrium will shoot the economy to an agglomerated equilibrium.

10 Note that if trade costs continue to fall the LD curve will eventually flatten out once again. For a detailed
explanation see Fujita et al. (1999).

21

threshold below which a concentrated equilibrium can be sustained in addition to the
symmetric equilibrium Adhering to the terminology in Fujita et. a1. (1999), this is called
the sustain point and is labeled r(S) in Figure 2-2. As trade costs fall further a second
threshold is reached below which the symmetric equilibrium breaks down and
concentration is the only sustainable equilibrium. This is called the break point and is
labeled r(B) in Figure 2-2. Table 2-2 lists the break and sustain points for several values

ofo and y.

Table 2-2: Break and Sustain Points for Various Parameter Values

 

y —.3 y =.5 y =.7

 

 

1(3) 1(8) 1(3) 1(3) 1(3) 1(8)
o = 4 1.63 1.718 2.455 3.761 5.858 94.68
0' = 6 1.317 1.348 1.646 1.96 2.303 7.42

0= 8 1.21 1.229 1.41 1.569 1.759 3.412

 

 

The results thus far are identical to those of Krugman (1991). In fact, it is
straightforward to determine break and sustain points in filll-employment model for the
same values of o and y as in Table 2-2. When this is done the break and sustain points
are identical in both models. This should be expected since exactly the same forces

determine labor dynamics in both models.

22

V. Labor Dynamics with Non-Symmetric Regions

The analysis now turns to the case where either the rate of job breakup or the rate of
shirker detection differs between regions. Why might these parameters be diflerent in
regions that are otherwise identical? First, as Shapiro-Stiglitz ( 1984) notes, the breakup
rate is ultimately linked to the employment package ofiered by firms. In the model
presented here the package includes only the wage. However, in the real world this may
include any number of benefits such as health insurance, vacation time, and so on, which
are absent from the present analysis. Suppose that these services are simply available for
employees to use at no additional labor co st. Then, it is plausible that the level of these
services will differ between regions based on history. Furthermore, reactions of the
public sector to unemployment may also differ from location to location especially if
local governments are permitted to determine their own policy”. Second, the rate of
shirker detection may differ by similar reasoning. Cultural reasons may determine the
level of detection that firms in a particular region settle on. In some areas workers may
appear to their employers as more dependable and honest than workers in other regions.
Or, employers may be more trusting in some regions than in others. For these reasons, it
is conceivable firms in one region will settle at a different level of detection than the

firms in another region.

A. Differences in the Rate of Job Breakup
Suppose that the rate at which non-shirking workers lose their jobs is not identical in both

regions. The location variable is then given by

 

” This is certainly the case in the EU where each country decides its own public policy as well as in the US
where policies are often vary from state to state.

23

 

(24) A=_E1_.TI(P'1)

11(112)

Unlike the symmetric case, in the absence of transportation costs location does matter.
This is due entirely to the shirking effect which, unlike the other forces driving labor
dynamics, does not depend on transportation costs. There will be a larger incentive to
Shirk in the region with the higher breakup rate. In the absence of transportation costs the
wage will be the same in both regions. Otherwise, the product market will not clear”.
So, in order to satisfy the no shirking condition it must be the case that employment is

higher in the low breakup rate region. Furthermore, it must be the case that bknflrk) is

largest in the low breakup rate region13 . Hence, it will always be more attractive to
search in the region with the smaller value of bk.

When transportation costs are incurred (i.e. T > 1) there will then be four effects at
work: the home market effect, the price index effect, the extent of competition, and the
shirking efl'ect. However, the shirking effect will not work in a symmetric fashion as the
others do. It will work in favor of concentration into the low breakup rate region and
against concentration in the high breakup rate region. Again it is easiest to analyze the
model with the use of numerical simulations. It is assumed that the breakup rate is
smaller in region one. The diagrams that follow were generated with bl = .12, b; = .15,
and all other parameters as listed in Table 2-1. Figure 2-3 depicts the labor dynamics
curve for various levels of trade costs. The first characteristic to note about this diagram

is that it has the same basic form as Figure 2-1. However, there is one noteworthy

 

‘2 This is a direct result of the CES demand structure. If the price of manufactures (and thus the wage) is
higher in one region than the other then demand for a single variety in that region will be smaller than in
the other region. However, the price that clears the market must be the same in both locations since all
firms have identical scale. Inspection of equation (21) will confirm this.

‘3 This can be confirmed by substituting equation (17) into equation (12) and setting w] = w.

24

difference: the curves are no longer symmetric around L1 = .5. In fact, all symmetry is

now lost.

1.207

 

 

 

 

0.90 . . w- . -— . . .
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
L1

Figure 2-3: Labor Dynamics with Asymmetric Regions

Consider the high transport cost case, r = 2. In this case, as in the symmetric model,
there is only one stable equilibrium. However, the equilibrium lies at a labor distribution
that is skewed in the direction of region 1, where the breakup rate is lower. Here, the
home market and price index effects as well as the extent of competition work in exactly
the same way as in the symmetric model pulling the economy towards a diversified
equilibrium. However, the shirking effect is now pushing concentration into region 1.
So, it is not surprising that the stable equilibrium is skewed in this direction. Now
consider the low transport cost case, 1: = 1.3. Here, as in the symmetric case, there are
two stable equilibria: concentration in either region. But now the unstable equilibrium is

skewed in the direction of region 2. Again, this result should be expected. With a low

25

level of transport costs the extent of competition is weak which pushes the stable
equilibria to the endpoints. Since the shirking effect is drawing workers into region 1 this
skewness simply suggests that it more likely that the population agglomerates into region

1 rather than region 2, given a random initial distribution of labor.

1.1 '1
1.0 11(8)
0.91
0.81;

0.7%
0.6 i

L1 0.5 E
0.4 4
0.3 —‘ ------

0.21 x
0.1 I , -.
0'0 . 212(8)

 

 

 

-o.1L —% , . T . ~ . WT- ._.
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

T

Figure 2-4: Bifurcation Diagram with Asymmetric Regions

Figure 2-4 shows the bifurcation diagram for the non-symmetric case. As
transportation costs fall, the LD curve begins to flatten out pushing the stable equilibrium
fin'ther and further towards concentration into region 1. This is a sensible result since as
transport costs fall the need to locate near final demand weakens and concentration
becomes more likely. Then, when transport costs fall further to the region one sustain
point, 11(8), concentration in region 1 is the only solution. As transport costs fall even
firrther to the region 2 sustain point, 1:2(S), the LD curve becomes upward sloping and

concentration in either region can be sustained.

26

It is important to note that in a world of falling transport costs the equilibrium that
the economy will tend to is with all manufacturing located in region 1. The only way
agglomeration in region 2 could be sustained is if trade costs were initially below the
region 2 sustain point and the population was sufficiently skewed towards region 2.

While the latter of these is certainly not out of the realm of possibilities, the former is.

B. Differences in the Rate of Shirker Detection
Now attention turns to the case where the rate of shirker detection is permitted to vary

between regions. In this case, the location variable can be expressed

(25) A=q—2.—fi‘—'
C11 ”2

Again, in the absence of trade costs location does matter. There is a shirking effect at
work here just as when the breakup rate is non-symmetric. There will be a smaller
incentive to Shirk in the region with the higher rate of shirker detection. Hence,
employment will tend to be higher in that region. So, with no trade costs, it is always
more beneficial to search in the region with the higher rate of shirker detection. When
transportation costs are incurred the shirking effect will draw workers into the region
with the higher detection rate causing similar asymmetries as those in the previous sub-
section. In fact, the diagrams one can derive in this case are similar to Figures 2-3 and 2-
4. In addition, the intuition behind the shapes of these diagrams is identical. The only
difference is the source of the shirking effect: in this case it comes from a higher rate of
shirker detection and in the previous case it comes fiom a lower rate of job breakup. In

light of this, a formal discussion will be suppressed.

27

V. Unemployment

How will the equilibrium behavior discussed above affect the economy’s unemployment
rate? The economy’s unemployment rate is given by

(26) 11A =1 —2(nl + n2)

The answer to the question posed above depends on whether 11;, increases or decreases
with a change in the distribution of labor. This, in turn, depends on whether the shirking
effect is present or absent. The unemployment dynamics of the model, then, differ

between the symmetric and asymmetric cases.

A. Unemployment with Symmetric Labor Markets

Figure 2-5 depicts the aggregate unemployment rate as a function of the proportion of
workers located in region 1 for both high and low trade costs when labor markets are
symmetric. There are two important features of this diagram. First, the unemployment
rate is always lower when trade costs are lower. Looking at the derivative of the
aggregate unemployment rate with respect to trade costs when the economy is not

agglomerated14

dHA

 

(27)

 

d'c dt
OSLISI

The positive sign follows from the price index effect mentioned above. If transportation
costs increase then demand for manufactures must decrease everywhere since
manufacturing goods are now more expensive. So, lower transportation costs will always

result in lower rates of unemployment.

 

'4 Although explicit expression cannot be obtained for the derivatives discussed in this section their signs
(and sometimes their relative magnitudes) can be determined through a little intuition.

28

 

9.0% 1* 1 r
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.0

 

 

 

I -fi‘hfifi—T l I " I ”—fi— _.- I_‘

L1

Figure 2-5: Unemployment with Symmetric Regions

Second, a regionally concentrated equilibrium minimizes the unemployment rate
and an even distribution of labor maximizes the unemployment rate. Suppose that the
distribution of labor in the economy is currently where L1 = O, i.e. complete concentration
into region 2. At this point, the derivative of unemployment with respect to labor

entering region 1 is given by

duA =_—dn2 >0
L1=O

 

(28)

Any deviation away from an agglomerated equilibrium will cause manufactures to be
more expensive for everyone in the economy. This will cause the demand for region 2
varieties to decline. Hence, the sign of this derivative is positive. Now consider the case

where 0 < L] < .5. Now the derivative can be expressed

29

(29) all
dL1

 

_? 99mg
dL, dL.

There are two forces influencing the signs of the two terms inside the brackets. First, a
shift in population into region 1 makes manufactures less expensive for region 1 residents
which tends to make both terms positive. Second, the shift in population makes
manufactures more expensive for region 2 residents which tends to make both terms
negative. Demand will always favor local products because individuals do not have to
pay transportation costs on locally produced goods. Hence, local effects will dominate
non-local efiects. The first term is, then, positive and the second term is negative. The
magnitudes of these effects will depend on the size of the region. Since region 2 is the
larger region it follows that the second term dominates the first and the net sign of the
derivative is positive. Now suppose that the distribution of labor is such that .5 S L1 < 1.
In this case the two terms inside the brackets have the same signs as before. But now
region 1 is the larger region so the first term dominates the second and the sign of the
derivative in equation (29) is negative. All of this together would imply the shape of the

curve given in Figure 2-5.

B. Unemployment with Non-Symmetric Labor Markets
The spatial pattern of unemployment changes drastically when asymmetries in the labor
market are introduced. Figure 2-6 shows the labor distribution/unemployment curve for

the non-symmetric case.

30

11.5% 5.
1

11.0% 1
i

1

10.5% J:
10.0% --

<
:5.

9.5% J

9.0% 1'

 

8.5% ~

8.0% L .__ . . . , . . ,__
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

L1

 

Figure 2-6: Unemployment with Asymmetric Regions

This diagram only shares one feature with Figure 2-5: when transport costs fall the
unemployment rate is lower. This can be explained in exactly the same manner as in the
symmetric model: when transportation costs fall manufactures are now less expensive
for everyone in the economy so demand will rise in both regions, thus, reducing
unemployment. However, the spatial variation in unemployment is now very different.
There are two notable disparities fiom the symmetric case. First, concentration into
region 1, where the breakup rate is lower, results in a lower rate of unemployment than
concentration into region 2. This is due to the shirking effect. A lower rate of job
breakup will result in a smaller incentive to Shirk and higher employment. Second, if
transportation costs are high there is an upward sloping portion to this curve, and if
transport costs are low enough the curve is strictly downward leping. Again, it is useful

to use some intuition on the signs of some derivatives. Suppose that the economy is

31

concentrated in region 2. i.e. L1 = 0. Then, the derivative of economywide
unemployment with respect to workers entering region 1 is again as given in equation
(28). However, the intuition concerning the sign is a little different. There are two
effects at work when workers migrate into region 1. First, the number of varieties
produced in region 2 should fall since manufacturing products have become more
expensive as a whole. This will tend to increase the unemployment rate. Second, since
the incentive to Shirk is lower in region 1 a higher proportion of the defecting workers
will be employed than if they remained in region 2. This will tend to decrease the
unemployment rate. Which of these dominate depends on the level of transportation
costs. If transportation costs are high the first effect will dominate and the
unemployment rate will to rise slightly. However, if transport costs are low the price
index effect will be weak and the unemployment rate will fall. If L1 is between 0 and 1
then the derivative with respect to workers entering region 1 is as given in equation (29).
The signs of the two terms in brackets are the same as in the symmetric case. However,
which term dominates not only depends on region size but also on transport costs and the
shirking effect. If transport costs are very high and the region with the smaller incentive
to Shirk is small then the larger region will dominate. In this situation the price index
effect will be particularly strong and local demand bias will be very high which will
undermine the shirking effect. However, when the smaller region reaches a critical size
the shirking effect will take over and unemployment will fall as residents enter the region
with the smaller incentive to Shirk. With a lower level of transport costs local demand
bias will be weak and the smaller incentive to Shirk will dominate for all possible labor

distributions. These imply the shapes of the curves in Figure 2-6.

32

VI. Conclusion

The analysis above uses a new geography model that includes unemployment in the form
of an efficiency wage to show that that the presence of labor market asymmetries is an
additional source of agglomeration that has not yet been considered in the literature.
When the values of the efficiency wage parameters are not identical in all regions the
model can predict in which region manufacturing is most likely to locate. Unless trade
costs are very low initially, which is highly unlikely, manufacturing production will
always gravitate to the region with the lower rate of job breakup, or the higher rate of
shirker detection.

The model also determines the effects of agglomeration on unemployment in both
the symmetric and asymmetric cases. As trade costs fall and labor begins to gravitate
into a single region, the unemployment rate declines. Furthermore, if the economy
reaches complete agglomeration the unemployment rate will tend to its minimum
regardless of the symmetry (or asymmetry) of the model. This highlights an additional
benefit to an economy that agglomerates. Not only will incomes be higher as shown by

Krugman (1991), but employment will also rise.

33

Chapter 3:

A Two-Country Model with Imperfect Monitoring

1. Introduction

The goal of this chapter’s model is to examine the relationship between the falling costs
of trade and unemployment at the national level in different countries. The approach
taken in this paper, attributed to Krugman and Venables (1995), is to use an intermediate
good to play the role that mobile labor played in the model of Chapter 2 in creating the
forward and backward linkages. The model builds on this framework to include a form
of the efliciency-wage/worker-discipline model first proposed by Shapiro-Stiglitz (1984)l
and used in Chapter 2. Quite surprisingly, this particular form of unemployment provides
an additional force encouraging manufacturing to concentrate into a small number of
countries due to the effects that agglomeration has on employment. As a result, the labor
dynamics are altered in such a way that the agglomeration of manufactures is more likely
to occur in a world with efficiency wages than in a full-employment environment! The
model also shows that lower trade costs cause unemployment to fall in all countries if
agglomeration economies fail to arise. However, in the event that agglomeration does
take place countries where agglomeration arises reap large employment gains and
countries that are the victim of a manufacturing exodus suffer large employment losses in
the short term. Which countries gain and which countries lose is completely determined
by industrial history. That is, which countries historically have produced a large amount
of manufactures and which have not. In the long term, however, all countries can enjoy

employment gains from globalization if trade costs fall far enough.

 

1 For other mergings of monopolistic competition and the worker discipline model see Matusz (1996,1998).

34

The model also examines the case where labor markets are not identical across
countries. In particular, the situation where rates of job tenure differ between countries is
taken up. In such an asymmetric world the model shows that countries with higher tenure
rates are more likely to be the recipients of an agglomeration of industry. The higher
rates of tenure lead to a fall in the rate of unemployment that will deter workers from
shirking. This will attract manufacturing making it more likely that industry
agglomerates there. So, although industrial history is still a driving force, differences in
national labor markets can have an impact on the pattern of agglomeration.

Section 11 describes the model. Section IH describes the simulation techniques
used to obtain the model’s conclusions. Section IV examines the simulation results for a
symmetric world. Section V examines the simulation results in an asymmetric world.

And section VI provides some concluding remarks and directions for fiiture research.

11. The Model

Consider a world in which there are two countries; one factor of production: labor; and
two goods: agriculture and manufactures. Labor is permitted to move between sectors
but not across international borders. The size of each country’s labor force is normalized

to one.

A. Agriculture
Agriculture is produced in a perfectly competitive environment. However, workers in
this sector, as well as the manufacturing sector, face the possibility of unemploymentz.

The unit labor requirement is one and agriculture is taken as numeraire so that both the

 

2 The labor market will be described in detail below.

35

price of agriculture and the wage paid to farmers is equal to unity. For simplicity it is

assumed that agriculture can be traded at no cost3 .

B. Preferences

All individuals in the economy share the utility function

(1) U = XXX 57 —- e

for O < y < 1, where XA is consumption of agriculture, XM is consumption of an aggregate
of manufactured goods, and e > O is workers disutility of effort. Hence, consumers will
always spend 7 of their income on agriculture and 1 - y of their income on manufactures.

The manufactures aggregate is given by the CES subutility fimction

["1 2.1 "2 9:131
(2) XM = L;(Xi1) ° +§(xiz) G J

where nk is the number of manufacturing varieties produced in country k, and 0' > 1 is the
elasticity of substitution between varieties. Hence, the model incorporates the love-of-

variety approach“. The price index over manufactures in country k can then be expressed

(3) 11k = [nkpkMH + n j(1)1141)” ]'-°
where P11” is the price of a single variety of the manufacturing good in country k, and r is

the iceberg trade cost of shipping a unit of manufactures from one country to the other.
That is, in order for one unit of the good to arrive at its destination 1 units must be

shipped. There are two noteworthy characteristics of equation (3). First, the higher the

 

3 Including trade costs on the agricultural good in these types of models can shrink the range of parameters
for which agglomeration can be sustained. However, it will not change the results presented here. For
more on this see Davis (1998), Fujita et al. (1999), and Rauch (1999).

4 See Dixit-Stiglitz (1977) and Krugman (1979, 1980).

36

fraction of products produced in country k the smaller is I’Ik. Hence, if manufacturing is
more concentrated in country k than country j the price of manufactures is lower in
country k than in country j since consumers need not pay trade costs on a larger
proportion of the total manufactures produced. Second, the larger is r the larger is l'lk.
So, manufacturing goods are more expensive when transport costs are large. After
solving the utility maximization problem a sector r worker’s indirect utility in country k
can be written

(4) U; =1“w;r1;y —e

for r = {A,M} where F = y’ (1 — y)H .

C. Manufacturing Production

Manufacturing production in country k requires the use of a composite input that is a
Cobb-Douglas combination of labor and intermediate goods. For simplicity it is assumed
that the price index over intermediate goods is identical to that of final manufactures.
Hence, the price index of both intermediate goods and final goods is given by equation

(3)5. The production function for the composite input in country k can be expressed
(5) Ck = mix;e
where G) = 0‘9 (1 — 0)0']. Afier solving the cost minimization problem the unit cost for

the composite input in country k can be expressed

(6) Pi=w3HIi9

 

5 This is a simplification proposed by Krugman and Venables (1995) making it possible to include
intermediates in production without explicitly modeling the intermediates sector. Using this approach,
intermediate goods and final goods are the same good, XM.

37

Production for the final good, then, requires a fixed and a marginal input of this
composite good. The amount of the composite good required for firm i in country k to
produce xik units of the final good can be written

(7) Cik = or + Bxik

where on and B are the fixed and marginal inputs respectively. So, the total cost of
producing xik units of the final good can be expressed

(8) TC... = €in = (a + Bx... )P5

In this monopolistically competitive environment each firm will View itself as a
monopolist facing a demand curve with elasticity 0'. So, each firm will set price o/(o - 1)
over marginal cost. Choosing units of measurement for the composite good such that

B = (o — l) /6 all firms in country k will set price for the final manufacturing good

(9) P.“ =wEHL‘9

So, the price of the final good is identical to that of the composite good. In equilibrium
price must equal average cost. Setting equation (9) equal to average cost and solving for
the firrn’s scale of production yields

(10) x = ow

Hence, all firms produce an identical scale of output that is independent of both input
prices and location. Given the production function and that firms earn zero profits in
equilibrium, it is evident that firms will devote a fraction 0 of their total revenue to the
wage bill. Hence,

(11) OPRMnkx = wankEk

38

where E k is the number of workers hired by a manufacturing firm located in country k.
Choosing units of measurement for the final good so that x = 1/0, this can be solved for
E k to get

[—0
While the scale of output is independent of location, the number of workers hired by
firms is not. A low cost for labor or a large cost for intermediates will tend to increase
the amount of labor and decrease the quantity of intermediates used in production.
However, firms the world over will use the same number of units of the composite input.
Thus, firms in each country will produce the same amount of output, but with a different

mix of inputs.

D. Labor Markets

Workers in both sectors receive disutility e of exerting effort. In addition, workers are
imperfectly monitored. So, workers have an incentive to Shirk if they believe that they
can avoid being detected. To deter this behavior workers are paid in excess of their
marginal products and are immediately discharged if caught shirking. The threat of being
fired will eliminate all shirking in equilibrium. Let p be the exogenous discount rate, let
q be the exogenous rate at which shirking workers are detected, and let b be the
exogenous rate at which non-shirking workers lose their jobs. In addition, let hk' be the
endogenous rate at which sector r workers are hired in country k. Then, the asset value

equations for a sector r worker in country k are

(13) W.” =hL(V,:" —V.:")

39

(14) lef’ = T‘le‘l;y — e + b(Vkur — Vi")
(15) pVi’ =FWLH;’ + (b + q)(V1l’r - V?)
where V: is the expected lifetime utility of an unemployed sector r worker in country k,
Vi" is the expected lifetime utility of a non-shirking sector r worker in country k, and
V: is the expected lifetime utility of a shirking sector r worker in country k. This
assumes that, if hired, an unemployed worker will not Shirk and that an unemployed
worker has no alternative source of income.

A necessary and sufficient condition so that workers do not Shirk is Vi" Z V:'.
Solving equations (13) — (15) and adhering to this inequality yields the no-shirking
condition (NSC) for sector r in country k

(16) mm: 23[p+b+q+h;]
q

To complete equation (16) an expression for hk' must be obtained. First, consider the
manufacturing sector. In any steady state equilibrium the flow into employment must
equal the flow out of employment. At any given point in time there are E knk
manufacturing workers employed in country k. The flow into employment in country k
is then hkM [Mk — E k nk] where Mk is the number of workers in the manufacturing sector
in country k. The flow out of employment is the rate at which employed workers lose

their jobs. This is given by bl knk. Equating these flows and solving for hkM gives

blknk

l7 bl“:—
( ) k Mk—lknk

Substituting this into equation ( 16) and doing some algebra yields the NSC for the

manufacturing sector in country k

40

l-n—

(18) rwfg‘n: 2§k+q+bmfl

where 11:“ = (Mk — 6 kn k )/ Mk is the unemployment rate in the manufacturing sector in

country k. Note that when trade costs fall the left hand side of this inequality rises.
Hence, the unemployment rate the ensures that this equality is satisfied must fall.

In the agriculture sector, since there is a total of one unit of labor for the economy,
the flow into employment is equal to hf: (1 — Mk — Ak ) where A, is the number of

employed workers in the agriculture sector. The flow out of employment is bAk.

Equating these and solving for the hiring rate yields

(19) h: =

 

1 — M k — A k
Substituting this into equation (14) and doing some algebra yields the NSC for the

agriculture sector in country k

(20) rnrzglp+q+bm£l

where u: =(1— Mk — Ak )/ (1 — Mk) is the unemployment rate in the agricultural sector

in country k.

E. Income and Demand

In country k, national income can be expressed
(21) Yk = Ak + wktknk
where the first term is the income of agricultural workers and the second term is the

income of manufacturing workers. Due to the Cobb-Douglas form of both the utility

41

function and the production fimction for the composite good, total expenditures on
manufactures in country k is given by

(22) Ek = ka + (1 — 0)P:‘nkx

where the first term is expenditure by consumers and the second term is expenditure by

firms. Then, the demand for a single country k variety can be expressed

(23) xk = (1),“)"[E,r1::'l + E j(r1j /r)°"]

where the first term inside the brackets represents domestic demand and the second term
represents foreign demand. Firms earn zero profits when the scale of production, xk, is
equal to that in equation (10). Equilibrium is now characterized by equations (3), (9),
(12), (18), (20), (21), (22), and (23) which can be used to solve for the equilibrium values
of Pi” , wk, nk, Z k , Yk, Ek, ITk, and Ak, given the distribution of labor, Mk, between

sectors in each country.

F. Steady State Equilibrium

In any steady state equilibrium, unemployed workers must be indifferent to the sector in
which they are searching for employment. So, the expected lifetime utility of an
unemployed worker must be the same in each sector. In the appendix it is shown that this
is equivalent to having equal hiring rates in each sector. Hence, in addition to the system
of equations above being satisfied, it also must be true that in any steady state equilibrium

where both agriculture and manufactures are produced in both countries

(24) hi” =h£

42

for k = 1,26.

IH. Model Simulation

A. Methodology

Analytical results are rare in new geography models. So, outcomes are attained largely
through numerical simulations. The first step in simulating the model is to reduce it to a
tractable number of equations. Equation (3) gives two price indices. Substituting
equation (21) into equation (22), and combining the result with equation (23) yields two
demand equations. Equations (18) and (20), then, are the four no-shirking conditions

(one for each sector in each country). Finally, equation (24) gives the two steady state
equations. Hence, the model can be reduced to ten equations in the ten unknowns w k ,

Hk, Ak, Mk, and nk for k = 1,2.

B. Parameterization

Table 3-1 lists the values of the parameters used in the simulation.

Table 3 -1 .' Simulation Parameters

 

 

 

 

 

 

6 In addition, there are steady state equilibria where equation (24) is not satisfied. These are equilibria
where a country devotes all of its resources to the production of a single good (i.e. manufactures or
agriculture). The dynamics spelled out below make it clear that these need not be considered when
deriving the diagrams that determine all of the steady state equilibria, including those where equation (24)
is not satisfied.

43

The expenditure share in manufactures is .4. Hence, individuals spend 40% of their
incomes on differentiated goods and 60% on agriculture. The elasticity of demand is
equal to 5, which corresponds to a markup of price over marginal cost of 20%. The
production share in intermediates is equal to .5. Thus, half of firms’ revenue goes to
intermediates and half to labor. The choice of p = .05 is roughly consistent with recent
real rates of interest in the developed world. Since jobs arrive according to a Poisson
process, l/b is the average job tenure in the manufacturing sector. So, b = .13
corresponds to a job lasting an average of 7.7 years, the average in the European Union7.
Finally, the choice of e implies the aggregate rate of unemployment will fall in the

neighborhood of 10%.

IV. Simulation Results

A. Labor Dynamics

Since the steady state condition requires that the hiring rate be equal in both sectors,
anything that increases the manufacturing hiring rate relative to the agricultural hiring
rate in the larger region will encourage agglomeration and anything that decreases the
manufacturing hiring rate relative to the agricultural hiring rate in the larger region
discourages agglomeration. So, a logical question to ask is how will a shift in the
distribution of labor affect the relative magnitudes of the manufacturing and agricultural
hiring rates? The forces at work here can be separated into four effects. One of these

works against the agglomeration of manufactures into a single country and will be

 

7 See OECD (1997).

44

 

referred to as the anti-agglomeration effect. And the other three work in favor of the
agglomeration of manufactures into a single country and will be referred to as the pro-
agglomeration effects. Suppose that there is a shift in the labor distribution into the
manufacturing sector in country k. First, there is the extent of competition. Increasing
the number of varieties in a single region will lower the price index since more varieties
are now produced there. This will reduce the demand for each individual variety and will
tend to lower the manufacturing hiring rate relative to that of agriculture. This is the anti-
agglomeration effect. Second, the lower price index reduces the cost of the intermediate
good. So, firms’ expenditure on intermediates will increase. This tends to increase both
the manufacturing wage and the manufacturing hiring rate relative to those of agriculture.
This is the forward linkage mentioned in section 1. Third, an increase in the amount of
labor producing manufactures in country k increases expenditure in country k since more
varieties are being produced there. This tends to increase the demand for each individual
variety and increase the manufacturing hiring rate relative to that of agriculture. This is
the backward linkage mentioned in section 1. Fourth, an effect absent fi'om the full
employment model, the fall in the price index will increase employment in both sectors.
This generates a further increase in expenditure through an increase in national income.
This will tend to increase the manufacturing hiring rate relative to that of agriculture.
These last three effects at work are the pro-agglomeration effects. Which effects
dominate depends on the value of trade costs.

Figure 3-1 shows, for each country, the locus of labor distributions where the
hiring rate is identical in both sectors when trade costs are high (I = 3). The thin line is

country 1’s curve and the thick line is country 2’s curve. If Mk = 0 then country k’s

45

entire labor force produces agriculture, and if Mk = 1 country k’s entire labor force

produces manufactures.

1.0.
0.9
0.81
0.7

0.6 f
0.5 ~

M2

0.4 -

0.3 -

 

0.2 «,

0.1 l

 

 

0.04 ,, . . . - .. .._._ .._. WWI .
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

M1
Figure 3-1: Labor Dynamics with High Trade Costs

For distributions of labor that lie below each country’s curve the hiring rate is larger in
the manufacturing sector so unemployed workers will shift their search efforts towards
manufacturing until the hiring rates are equalized. For distributions of labor that lie
above each country’s curve the hiring rate is larger in the agricultural sector so
unemployed workers will shift their search efforts towards agriculture until the hiring
rates are equalized. It is clear fiom the diagram that when trade costs are high there is a
single, globally stable equilibrium where both countries have 7 (= .4) of the labor force in
the manufacturing sector and the remainder in the agricultural sector. This will be

referred to as a symmetric equilibrium. Here, the pro-agglomeration forces are not

46

strong enough to combat the increased competition in the larger regionFigure 3-2 shows

the same type of diagram when trade costs are low (I = 1.5).

   

 

r
0.0 i#_ ___..._

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
M1

Figure 3-2: Labor Dynamics with Low Trade Costs

Here there is a saddle path leading to the same symmetric equilibrium However, this
equilibrium is now unstable. Any deviation from the symmetric equilibrium will result in
one country specializing in agriculture and the other country supplying the total world
demand of manufactures in addition to the remaining demand for agriculture. Such
equilibria will be referred to as specialized equilibria. The particular equilibrium that will
prevail depends entirely on the initial distributions of labor in both countries. The

country with the larger initial base of manufacturing labor will receive the agglomeration.

47

Hence, if trade costs fall low enough a catastrophic core-periphery pattern will emerge
where one country produces all of the world’s manufactures.

Finally, Figure 3-3 shows the diagram for an intermediate value of trade costs (I =

2.15).

1.0 7
0.9 7
0.8
0.7; '\
0.6

0.5 7

M2

0.4 5

0.3 L

0.2 '
0.1 i

0.0. -- — - -——-— . --- . - , --fi . _. ;*
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

M1

Figure 3-3: Labor Dynamics with Intermediate Trade Costs

Here there are three stable equilibria: the symmetric equilibrium where y (= .4) of the
labor force in the manufacturing sector and the remainder in the agricultural sector,
country 1 specializes in agriculture, and country 2 specializes in agriculture; and two
unstable equilibria at an intermediate distribution of labor between these extremes. Here
a catastrophic core—periphery bifurcation will not arise unless one country’s
manufacturing base is considerably larger than the other’s. Otherwise, a symmetric

equilibrium will prevail.

48

B. The Structure of Equilibria

Figures 3-1 to 3-3 suggest that as trade costs fall a threshold level is reached where the
stable, symmetric equilibrium breaks down. Call this level of trade costs the break point,
1:03). In addition, there is a threshold level of trade costs where a specialized equilibrium
can be sustained. Call this level of trade costs the sustain point r(S). Furthermore, as
evidenced by Figure 3-3, there are levels of trade costs where both classes of equilibria
are feasible. Figure 3-4 summarizes these facts with a bifiircation diagram showing the

equilibrium distributions of labor as a fimction of the level of trade costs.

1.0;

|
0.9 E

0.8 I
0.7 7
0.6 —

0.5 *-
M1, M2

 

 

M1, M2

0.4 ~~

 

0.3 l
0.2 1 M1
0.1 1;
0.0 M1 1(3)
l

'0.1 I _‘ fil— T ”I v“? . “—— —' '_ T'i ___—_fi—‘_~_ _'—T'—‘ l l l ~'_'—_{'

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

T

 

 

Figure 3-4: Bifurcation Diagram with Symmetric Countries

49

Here it is assumed that the initial distribution of labor is such that country 1 will
specialize in agriculture if trade costs fall sufliciently lows. The thick lines represent
stable equilibria and the thin lines represent unstable equilibria. What Figure 3-4 shows
is that as trade costs fall over time two countries who are similar in every way except for
their industrial histories will naturally divide themselves into an industrialized core and
an agricultural periphery. The core will consist of the country that historically has had
the larger manufacturing base and the periphery will consist of the country that

historically has had the larger agricultural baseg.

1.0 7-
0.9

0.8 A

 

 

 

0.7 1
0.6 l

0.5 i
' M1 ,M2

 

M1, M2

0.4 ..
0.3 l

0.2 —'

l
0.1 :
1 M1
0.0 ‘

 

 

 

 

 

'0.1 l"" ——"'"T"— f ‘ w “*‘I fi— ' ' ‘fi 1 r 1“" ‘fi

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Figure 3-5: Efficiency Wage and F ull-Employmenl' Bifurcation Diagrams

 

8 The case where each country’s role is revered yields a diagram identical to figure 4 with the exception
that M1 and M2 are reversed.

9 It may be the case that two countries industrial histories have them in a symmetric equilibrium when trade
costs initially fall below the break point. In this case the country that first deviates fi'om this equilibrium in
the direction of manufacturing will become the core and the other country will become the periphery.

50

The diagram given in Figure 3-4 is very similar to the bifurcation diagram that
can be derived fiom a full-employment version of this model. Figure 3-5 superirnposes
the bifurcation diagram from the full-employment model onto figure 3-4. The thick lines
are the efficiency wage bifurcation (i.e. Figure 3-4) and the thin lines are the full-
employment bifurcation. To avoid confusion in comparing this with figure 3-4 note that
stable and unstable equilibria are no longer differentiated in figure 3—5. There are two
striking differences between the structure of equilibria in the two models. First, both the
break and sustain points are larger in the efliciency wage model. This implies that
industry agglomeration is an equilibrium for a larger range of trade costs when there is
unemployment due to imperfect monitoring than in a fiill-employment world. This is due
to the effect mentioned above that is not present in the filll-employment model: a fall in
the price index increases employment which will increase demand for manufactures even
further. Hence, starting fiom a random distribution of labor and a random value of trade
costs agglomeration of manufacturing is more likely in the efficiency wage world than in
the fiill-employment world.

Second, in the efficiency wage bifurcation the amount of labor devoted to
manufactures in country 2 in the specialized equilibrium is smaller than in the full—
employment model for positive values of trade costs (i.e. ‘c > 1). Furthermore, as trade
costs fall the two labor distributions converge. In the efficiency wage model there is
some level of unemployment that would exist even in the absence of trade costs.
However, if trade costs rise the demand for manufactures falls due to the wedge that trade
costs drive between prices from one country to the other. Hence, in equilibrium fewer

workers are required to produce this demand. The diflerence in these two curves can

51

 

then be interpreted as the amount of unemployment that arises from the trade cost wedge

in prices between regions.

C. Unemployment

How will the structure of equilibria discussed above affect unemployment at the national
level in each country? The aggregate unemployment rate in country k can be expressed
(25) Uk =1—Ak —€knk

The answer to this question, then, depends on what effects changes in trade costs and the
resulting shifts in the distribution of labor have on the number of agricultural workers,

firm size, and the number of varieties produced.

 

 

 

6% —————. —-——- j ——.._ _ . . . ,
1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.0(

T

Figure 3-6: Unemployment Along the Efficiency Wage Bifurcation

52

Figure 3-6 shows the aggregate unemployment rate in both countries along the
bifurcation depicted in figure 3—4. Again, the thick lines represent stable equilibria and
the thin lines represent unstable equilibria. The lines labeled U1,U2 are the symmetric
equilibria. The unstable lines labeled U1 and U2 are the unstable equilibria that arise at an
intermediate level of trade costs. And, the stable lines labeled U1 and U2 are the core-
periphery equilibria. There are several significant features of this diagram First, if the
distribution of labor remains fixed at the symmetric equilibrium, unemployment is strictly
increasing in trade costs. This is evident from the strictly upward slope of the
unemployment curve along the symmetric equilibria. When trade costs fall real wages
increase which allows the manufacturing sector to expand increasing employment in this
sector. Unemployment must be identical in both sectors since wages are the same in both
sectors or else both no-shirking conditions will not be satisfied. This allows employment
to expand in the agriculture sector. Since, employment expands in both sectors the
aggregate unemployment rate must fall. In short, increased employment in the
manufacturing sector creates demand for agriculture allowing both sectors to expand.

Second, if the distribution of labor remains fixed at a specialized equilibrium the
aggregate unemployment rate is strictly increasing in trade costs. Again, this can be seen
by the strictly upward slope of the unemployment curves for both countries along the
specialized equilibria. The intuition is similar. In country 1, as trade costs fall real wages
increase which increases the level of employment required to deter shirking in the
agriculture sector. Since agriculture is the only industry in country 1 this will increase
aggregate employment in country 1. In country 2, the intuition is the same as in the

symmetric equilibrium. When trade costs fall real wages rise which allows the

53

manufacturing sector to expand. Unemployment must be the same in both sectors since
wages are the same in both sectors or both no-shirking conditions will not be satisfied.
This allows employment to expand in the agriculture sector. Since, employment expands
in both sectors the aggregate unemployment rate must fall.

Third, when country 1 specializes in agriculture country 2’s unemployment falls
compared to the symmetric equilibrium and country 1’s unemployment may rise or fall
depending on the value of trade costs. If country 1 specializes in agriculture then real
wages with respect to manufactures will rise in country 2 and fall in country 1. Since
demand favors local products the net result will be an increase in worldwide demand for
manufactures. Since country 2 is the only producer of manufactures employment must
rise in the country 2 manufacturing sector. Again, these new workers create demand for
agriculture which allows the agriculture sector to expand in country 2. Since
employment increases in both sectors the aggregate unemployment rate will fall in
country 2. In country 1 there are two competing forces at work. First, the real wage of
agriculture workers falls. To keep the no shirking condition satisfied either the wage
must rise or employment must fall in the country 1 agriculture sector. Since agriculture is
taken as numeraire this tends to reduce employment. On the other hand, the increased
employment in country 2 creates more demand for agriculture which tends to increase
employment in country 1. When trade costs are high the former effect dominates and
unemployment rises when the economy moves from a symmetric to an agglomerated
equilibrium. When trade costs are low enough the latter effect dominates and
unemployment falls when the economy moves from a symmetric equilibrium to an

agglomerated equilibrium.

54

Finally, as trade costs approach zero the unemployment rates of the two countries
converge. As trade costs fall real wages converge since the nominal wage is identical in
both countries. If real wages are converging then the employment levels required to deter
shirking will also grow closer to one another until they are identical when trade costs fall
to zero (i.e. 1: = 1).

What all of this suggests is that, in the short term, if a catastrophic core-periphery
bifurcation does occur the country that receives manufacturing firms will enjoy an
employment benefit while the country that loses manufacturing firms will suffer an
employment penalty. As was discussed above, the country that historically has had a
large manufacturing base (i.e. the developed world) will gain while the country that has
historically had a large agricultural base (i.e. the less developed world) will lose. So, the
initial agglomeration will further separate the less developed countries of the world from
the industrialized countries of the world. However, if trade costs continue to fall the
unemployment rates of the core and the periphery will begin to converge, but will not
completely converge unless the costs of trade fall to zero. So, as trade costs fall over
time there is a period of natural divergence followed by a period of natural convergence.
It is clear that no matter where the world is in this cycle the developed world gains
employment from globalization. The answer is less clear for the less developed world. It
depends on where the world is in this cycle. However, in the very long term if trade costs
continue to fall to very low levels the less developed world will see a gain in

employment.

55

V. Cross-Country Asymmetry

The analysis now turns to the situation where the rate of job tenure differs between
regions. Why might job tenure dijfer between countries that are otherwise identical?
First, as Shapiro-Stiglitz (1984) notes, the breakup rate, and hence tenure, is ultimately
linked to the employment package offered by firms. In the model presented above the
employment package includes only a wage. In the real world, the package will include
any number benefits that the firm chooses to offer its employees. If these services are
simply available for employees to use at no additional labor cost, it is conceivable that the
level of these services could difier between countries based on each country’s particular
history. Second, reactions of the public sector to unemployment may also differ fiom
country to country where local governments determine distinct policy reactions. Given

these, it is probable that tenure rates will differ from one country to the next.

A. Labor Dynamics

In efficiency wage models such as this the inverse of the breakup rate, b, is the expected
rate of tenure. So, by letting the breakup rate vary between countries the effects of
varying job tenure can be analyzed. How will this affect the labor dynamics of the
model? When the breakup rate is not the same in both countries there is a greater
incentive to Shirk in the country with the higher breakup rate (i.e. lower tenure). Hence,
there is a fifth force at work in determining the labor dynamics of the model: a shirking
effect. The shirking effect will tend to draw manufacturing into the high tenure country

through its effect on employment. The shirking effect leads to higher employment in the

56

high tenure country"). Since demand favors local over non-local products this allows
manufacturing to expand more in the high tenure country than in the low tenure country.
Hence, the high tenure country will tend to have a larger share of manufactures than the

low tenure country.

0.9
0.8 9
0.7 1
0.6 1'

0.5 1

M2

 

 

Figure 3- 7: Labor Dynamics for Asymmetric Countries and High Trade Costs

Without loss of generality, suppose that the breakup rate is lower in region 1. The
results that follow were obtained through numerical simulations with bl = .1, b2 = .16,
and all other parameters as listed in Table 3-1. Figure 3-7 shows the locus of labor
distributions for which the hiring rate is identical in both sectors when trade costs are
high (I = 3). The thin line is country 1’s curve while the thick line is country 2’s curve.

Just as in figure 3-1, distributions of labor that lie below each country’s curve will result

 

'0 This can be confirmed through inspection of equation (18).

57

in a larger hiring rate in the manufacturing sector so unemployed workers will shift their
search efforts towards manufacturing until the hiring rates are equalized. And,
distributions of labor that lie above each country’s curve will result in a larger hiring rate
in the agricultural sector so unemployed workers will shift their search efforts towards
agriculture until the hiring rates are equalized. Here, there is a single, globally stable
equilibrium, just as in figure 3-1. However, there is one notable difference: when
country 1 has a higher tenure rate than country 2 the globally stable equilibrium is
skewed with a higher proportion of the labor force in country 1 devoted to manufactures
than in country 21 1. However, the equilibrium is not far from the symmetric equilibria
discussed above. Hence, equilibria in the neighborhood of a symmetric equilibrium will
be referred to as nearly symmetric equilibria. This slight asymmetry should be expected
since the shirking effect allows manufacturing to expand slightly further in country 1 than
in country 2.

Figure 3-8 shows the case when trade costs are low (1: = 1.5). As in figure 3-2,
there is a saddle path leading to an unstable equilibrium. However, while it is still nearly
symmetric it is not the same equilibrium as in figure 3-7. Here the unstable equilibrium
is skewed with a higher proportion of the labor force engaged in manufacturing in
country 2 than in country I”. This result is, again, due to the shirking effect. Given the
skewness of the nearly symmetric equilibrium, if the world begins at a random
distribution of labor in both countries it is more probable that country 2, the low tenure
country, will specialize in agriculture and country 1, the high tenure country, will

specialize in manufacturing. So, while industrial history is still the major component

 

” The equilibrium labor distributions are L, = .402787 and L2 = .397052.
'2 The equilibrium labor distributions are L, = .379425 and L2 = .421593.

58

determining which country will receive the agglomeration of manufacturing, differing

labor market parameters do have an effect.

1.0 7
0.9 7
0.8 7
0.7 7
0.6 7

0.5 7

M2

0.4 7

0.3 7

 

0.2 -

0.1 g
i

0.0 4T . em ._ __,_,

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
M1

 

 

Figure 3 -8: Labor Dynamics for Asymmetric Countries and Low Trade Costs

Finally, figure 3-9 shows the case of an intermediate value of trade costs (1: =
2.15). As in figure 3-3 there are three stable equilibria: a nearly symmetric equilibrium,
country 1 specializes in agriculture, and country 2 specializes in agriculture; and two
unstable equilibria at an intermediate distribution of labor between these two extremes.
Again, a catastrophic core-periphery bifurcation will not arise unless one country’s
manufacturing base is sufficiently larger than the other’s. However, the higher tenure in
country 1 tips the scales in their favor. That is, if agglomeration into country 2 is to be
sustained they will need a higher proportion of the manufacturing base than country 1

does to sustain agglomeration there.

59

1.0 7
0.9 -
0.8 .
0.7 ~
0.6 -

g 0.5 — ‘1
0.4 —

0.3 7 L’

0.2 7

 

 

0.1 7

 

 

o_o . . . — — -— . . . 1
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
M1

Figure 3-9: Labor Dynamics for Asymmetric Countries and Intermediate Trade Costs

B. The Structure of Equilibria

To get a complete understanding of the structure of equilibria in the asymmetric case it is
useful to look at the bifurcation diagram given in figure 3-10. Again, thick lines
represent stable equilibria while the thin lines represent unstable equilibria. When trade
costs are very high there is only one stable equilibrium for a given value of trade costs.
These are the nearly symmetric equilibria with country 1 having slightly higher
proportion of its workers in manufacturing than country 2 and are represented by the
thick black lines. Then, when trade costs fall to the country 1 sustain point, 11(8), a
stable equilibrium in which country 1 produces all of the world’s manufactures and
country 2 specializes in agriculture can be sustained. As trade costs fall further to the
country 2 sustain point, 12(8), an additional stable equilibrium in which country 2

produces all of the world’s manufactures and country 1 specializes in agriculture can also

60

be sustained. These equilibria are represented by the thick gray lines. If trade costs fall
below the break point, 1(B), the nearly symmetric equilibrium is no longer stable. These

unstable equilibria are represented by the thin black lines.

1.0 7

0.9 1

 

0.8 7

 

0.7 --

 

Mk

 

 

 

 

 

M1, M2 72(5) “(8)

'0.1 lm— " T ‘_”’*-" "ii —T** 1 T 1 “ “ r —' 1 " '——T——" 1
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

 

Figure 3-10: Bifurcation Diagram for Asymmetric Countries

There are two other classes of equilibria depicted: one where country 1 has a higher
proportion of its workforce in manufacturing than country 2 and one where the reverse is
true. These are the unstable equilibria that arise when trade costs take on an intermediate
value and are represented by the thin gray lines. Just as in the case of symmetric
countries, as trade costs fall over time the world will naturally divide itself into an
industrialized core and an agricultural periphery. However, the sustain point is now
larger in country 1, the high tenure country, than in country 2 because the shirking effect

allows manufacturing to expand further in the high tenure country. Hence, for a random

61

distribution of labor and a random value of trade costs it is more likely that

agglomeration will arise in country 1 than in country 2.

C. Unemployment

How will the structure of equilibria in an asymmetric world affect the equilibrium levels
of unemployment in each country? Again, the unemployment rate for country k is
expressed as in equation (25). Figure 3-11 shows the equilibrium unemployment rates in
each country along the stable equilibria depicted in figure 3-10. The thick black lines are
the nearly symmetric equilibria; the thick gray lines are the equilibria where country 1
produces all of the world’s manufactures; and the thin black lines are the equilibria where

country 2 produces all of the world’s manufactures.

 

 

 

 

 

18% 7 U2
16% -
14% --
U2
¥
12%
.1:
3 U2
10% — /
8% -~
U1
" U1
6% ‘ U1
4% ”" UT ' ' ' ” 1 ' IT 7777‘ IA‘ 7”- Ififir 7’" ’ I

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

1:

Figure 3-11: Unemployment with Asymmetric Countries

62

There is one major difference between figure 3-11 and figure 3-6. When
countries are asymmetric if trade costs fall low enough unemployment will be lower in
country 1, the high tenure country, for all classes of stable equilibria. This is a direct
result of the effect that the lower rate of job breakup in country 1 has on the
unemployment rate that will deter workers fiom shirking. A lower breakup rate lowers
the unemployment rate that satisfies the no-shirking condition. So, one would expect that
the unemployment rate would be higher in the low tenure country. There is one
exception to this when manufacturing production is located entirely in country 2 and
trade costs are high. In this case, trade costs are sufficiently high so that the higher price
index in country 1 has a larger effect on the unemployment rate then does the lower rate
of job tenure. However, as trade costs fall this trend reverses and the result is, as one
would expect, that unemployment is lower in country 1.

Assuming that the developed world has higher rates of tenure than the developing
world the pattern is similar to the symmetric case. Over time as trade costs fall there is a
period of divergence followed by a period of convergence. However, absolute
convergence now cannot occur even if trade costs fall to zero. No matter where in the
cycle the world is currently the developed world will experience positive employment
gains from globalization. Again, for the developing world the impact of globalization on
employment depends on where the world lies: in the stage of convergence or the stage of

divergence.

63

 

VI. Conclusion

The model presented in this chapter constructs a two-country new geography model to
examine the relationships between falling trade costs and unemployment. It is shown that
as trade costs fall over time the world will naturally divide itself into an industrialized
core and an agricultural periphery. The core will consist of countries with a traditionally
large manufacturing base (i.e. the developed world) and the periphery will consist of
countries with a traditionally large agricultural base (i.e. the less developed world). In
such a model where unemployment is caused by imperfect monitoring there is an
additional push towards agglomeration in the form of expanding employment. As a
result, agglomeration is more likely to occur in a world where there are efficiency wages
than in a world devoid of unemployment.

It is also shown that in world of imperfect monitoring and symmetric countries
unemployment is increasing in trade costs for fixed distributions of labor. However, if
the world reaches a point where agglomeration occurs the industrialized core gains and
the less developed periphery loses from the initial bifurcation. However, if trade costs
continue to fall, the unemployment rates of the two will begin to converge.
Unequivocally, falling trade costs due to globalization have a positive effect on the core
countries of the developed world. Whether current global trends are good for the less
developed world depends on which stage the world is currently experiencing: divergence
or convergence. However, in the extreme long term, globalization will help both groups
as trade costs fall lower and lower.

Finally, the model shows that if country’s labor markets differ in terms rates of

job tenure it can tip the scales of agglomeration in their direction. Countries with higher

64

tenure are more likely to be on the receiving end of an agglomeration of manufacturing
than are countries with lower tenure rates. Furthermore, countries with higher tenure
rates will reap a larger benefit if agglomerations do arise within their borders. Even if
free trade is attained, the low tenure countries will always have a disadvantage in terms of
employment. In addition, the same conclusions must be reached about the effects of
globalization on employment. Globalization will undeniably have a positive employment
effect in the both developed and developing worlds in the long term. However, the short
term effects in the less developed countries depends on where the world economy is the

cycle of divergence and convergence.

65

Chapter 4:

A Two-Region Model with Search Frictions

I. Introduction

The goal of this chapter, again. will be to extend the Krugman (1991) framework to
include unemployment. The particular form of unemployment used here is a variant of
the Diamond (1982) model that accounts for search fi'ictions in the labor market. The

impact of this augmentation on the labor dynamics of the model varies depending on the

 

homogeneity of the stochastic matching technology. It is shown below that when the
matching function exhibits constant returns to scale the forces that shape agglomeration
patterns are identical to those in the Krugman (1991) model. Hence, agglomeration is no
more nor less likely than in a world of full-employment. However, if the matching
fimction exhibits increasing returns to scale then agglomeration not only becomes more
likely but can be sustained for any combination of the model’s parameters. In this case
there is a stark difference between the full-employment world and one where workers

must seek out job opportunities.

The impact on unemployment of adding search frictions to the labor market also
varies depending on the homogeneity of the matching technology. If the matching
function exhibits constant returns to scale the number of matches is constant regardless of
the size of each region. Hence, agglomeration has no impact on the economy’s
unemployment rate. However, if the matching technology exhibits increasing returns to

scale the number of matches increases as the population of a given region grows. In this

66

case agglomeration will provide an additional economic benefit through lower rates of

unemployment.

The case where rates of job turnover are permitted to vary fiom region to region is
also discussed. The source of such asymmetries is not modeled, however these
asymmetries do exist in the real world. It is shown that regions with lower rates of job
separation will attract workers by offering higher expected lifetime utilities. Hence,
agglomeration is more likely to occur in such regions in regions with higher turnover. In

addition, such agglomerations will result in lower economywide unemployment

 

regardless of the returns to scale in the matching technology.

Section II of the paper describes the model. Section III discusses the simulation
techniques used to derive the model’s results. Section III derives the model’s results
when the matching technology exhibits constant returns to scale. Section IV derives the
model’s results when the matching technology exhibits increasing returns to scale.
Section V derives the model’s results when labor markets are not symmetric between
regions. And finally, section VI offers some concluding remarks and suggestions for

fiirther research.

II. The Model

The model builds on the fiamework first developed by Dixit-Stiglitz (1977) and its
extensions by Krugman (1979, 1980, 1991). Consider an economy in which there are
two types of final goods: Agriculture (A) and manufactures (M); three factors of

production: farm labor, type A labor, and type B labor; and two regions. Farm workers

67

are assumed to be perfectly immobile between regions‘, while type A and type B workers
may locate in either region. All workers are endowed with one unit of leisure that is
inelastically supplied as labor services. Agriculture is produced using only farm labor
while production of manufacturing goods requires an intermediate input consisting of

both type A and type B labor. The size of each type of labor force is normalized to one.

A. Agricultural Production

Farm workers are assumed to be evenly distributed throughout the economy with 1/2
located in each region. Agriculture is produced under constant returns to scale. The unit
labor requirement is one and agriculture is taken as numeraire so that its price and the
wage of farm workers is equal to unity. In addition, the simplifying assumption that

agriculture can be transported between regions at no cost is madez.

B. Preferences

All individuals in the economy share the utility fimction

( 1) U = X’AH

for 0 < y < 1, where X is consumption of an aggregate of differentiated goods, and A is
consumption of agriculture. Hence, consumers will spend a proportion y of their incomes
on manufactured goods and a proportion (l- y) of their incomes on agriculture. The

differentiated goods aggregate is given by the CES subutility function

 

' This assumption is equivalent to assuming that farm labor is tied to the land.

2 Including trade costs on the agricultural good in these types of models can alter the results by shrinking
the range of parameters for which agglomeration is an equilibrium. For more on this see Davis (1998),
Fujita et al. (1999), and Rauch (1999).

68

 

“1 °_—_1 “2 9:1 3:1
(2) X=[§(Xn)° +§(x12)°]
where m is number of varieties produced in region k, xik is the consumption of variety i

produced in region k, and 0' > 1 is the elasticity of substitution between varieties. From
equation (2) it is evident that individuals desire variety and will consume some amount of
each variety that is produced. The price index over manufactured goods for an individual

residing in region k is given by

1
(3) IIk = [nkpr’ + njp;_°r"°]1:

where pk is the price of a single variety produced in region k, and r > 1 are iceberg
transportation costs; in order for one unit of the good to arrive at its destination 1.’ units
must be shipped. There are two noteworthy features of this price index. First, the higher
the share of manufactures produced in region k the smaller is the region k price index.
Hence, the price of manufactures as a whole is decreasing in regional agglomeration.
Second, the higher are trade costs the larger is the price index and the more expensive are
manufactures as a whole. Solving the utility maximization problem and substituting
demands back into (1), utility for a type j worker in region k can be expressed in its
indirect form as

(4) ij = ijkII;y

for j = {A,B,F} where r = 17(1— 10H.

69

 

C. Manufacturing Production

Firms producing manufactures require the use of a Leontief composite input, 0k, with
fixed coefficients of each type of labor

(5) e. = masts}

where E jk is the amount of type j labor in region k used in the production of the
composite input. Let ij be the wage of a type j worker for j = {A,B} employed in
region k. Then, the unit price of 0k is wAk + ka. A fixed and marginal input of 0k is
used in production. The amount of 0 required for firm i in region k to produce mik units
of manufacturing output is given by

(6) 91k = or + Bmik

where 0t and [5 are the fixed and marginal inputs respectively. Since products are
differentiated each firm will view itselfas a monopolist with respect to their own variety.
Each firm faces an elasticity of demand of 0 so firms will set price o/(o—l) over marginal

cost. The price set by region k firms, then, can be expressed

(7) pk = [L]B(WAR + ka)

0' — 1
New firms are free to enter the market and will do so until profits are driven to zero. The
equilibrium condition, then, is that the price charged by each firm must equal firms’
average cost. The average cost of a firm in region k is given by [(OL + Bx,k )(wAk + ka)]/
xik. After setting this expression equal to equation (7) and choosing units of
measurement for the final manufacturing good such that CL = 1/6 the scale of each firm is

given by

70

 

 

 

 

1 0—1
(8) “61“?)

Note that all firms produce the same amount of output regardless of factor prices or
location. Substituting equation (8) into equation (6) gives each firm’s demand for the
composite input

(9) 6 =1

So, each firm will require the amount of the composite input that is produced by a single

type A-type B worker match.

 

D. The Search Process

Type A and type B workers must seek one another out in order to produce the composite
input. When two workers in region k become matched they produce one unit of 9;, each
period until they become separated which happens at rate per unit time 5. There are LAk
potential type A workers and LB], potential type B workers in region k devoted to
production of 01,. Let Ujk be the number of unemployed type j workers in region k.
Workers are brought together by the stochastic matching function m(UAk,UBk). It is
assumed that m(- ) has the following characteristics:

(10A) m(0,UBk) = m(UAk,0) = 0

(10B) m(UAk,UBk) is increasing in UAk and UBk

(10C) m(UAk,UBk) is homogeneous of degree n 2 1

(10D) m(UAk,UBk)/[ij is decreasing in Ujk

(10E) m(UAk,UBk) S min{UAk,UBk} V UAk,UBk 6 [0,1]

71

Let W; and W]: be the expected lifetime wealth of employed and unemployed

type j agents in region k respectively. Then, the asset value equations for type A workers
in region k are given by

(11) rwli. =q..(UA..UB.)(Wf. —Wli.)

(12) erk = FwAkl'IE” — 3(W:k — Wfk)

U . -
m(UA" ’ 3") IS the rate at which type A searchers become

 

where qu(UAk ’UBk )=

Ak

matched with type B searchers in region k. Similarly the asset value equations for type B

 

workers in region k are given by
(13) rwdic =CIBk(UAk9UBk)(W§k _WBlr)
(14) 7w;k =I’kal'I;7 —s(w§k —w;)

UBk)= m(UAk9UBk)

Bk

where q Bk (U M ,

 

is the rate at which type B searchers become

matched with a type A searchers in region k.

Using basic linear algebra techniques equations (1 1) & (12) and (13) & (14) can
be solved for WJ.’k for i = E,U. Then, the surplus of finding a job for each type of worker
can be expressed

I‘wAkl'l;y
r+s+qu(UAk,UBk)

 

(15) WE. —W:d. =

I’kaI'I;y
r+S +qu(UAk9UBk)

 

(16) W751. -W$i =

A pair of matched workers bargains over the total surplus generated by the match. That

is, they bargain over W fk — Wfk + WEEk — W1; . It is assumed that they arrive at the Nash

72

bargaining solution where the surplus is shared equally between the two parties. So,

setting equations (15) and (16) equal to one another one can solve for the relative wage

W_Ak=r+s+qu(UAk’UBk)

(17)
war r+S+qu(UAk’UBk)

This equation completely defines the bargaining solution.

E. The Location Decision
In addition to the bargaining condition, in any steady state equilibrium the number of
matches must equal the number of separations for both types of workers
(18A) m(UAk,UBk) = (LA, — U,k )5
(18B) m(U...UB..) = (L... — UBk )s

The location decision of unemployed workers is made by comparing the expected
lifetime utility of searching in each region. After a bit of algebra, the location variable

for a type j worker, A j = W11} / W5 , can be expressed

(19) A.=[£]—Y le [qjl(UAlaUBI)][r+S+qj2(UA2,UBZ)
J H2 sz in(UA2’U132) r+s+qjl(UAl,UBl)

If this measure exceeds unity unemployed workers will migrate into region 1, and if this

 

 

measure is less than unity unemployed workers migrate into region 2. Only when

equation (19) equals unity will the economy be in a steady state equilibrium.
E. Regional income and Demand
The total income of persons located in region k is given by

(20) Yk :'5+wAk (LAk TUM)+ ka(LBk _UBk)

73

where the first term is the income of farm workers, and the final two terms are the
incomes of employed type A and type B workers respectively. Since preferences take the
Cobb-Douglas form, region k expenditure on differentiated products is

(21) E. = 1Y1.

Then, demand for region k products can be expressed

(22) mk = pf lEJIE“ + E 1.01;" /7)°“J

where the first term in brackets represents local demand and the second term represents
non-local demand. Firms will make zero profits if they produce at the scale given in
equation (8). Note that if expenditure is equal in both regions region k firms will see a
larger proportion of its demand coming from local consumers versus non-local
consumers. Hence, demand will favor local products since individuals do not have to pay
transport costs on these goods. Equilibrium is now characterized by equations (3), (7),
(17), (18), (19), (20), (21), and (22) which can be used to solve for the equilibrium values

Ofpka Hka wAka ka) Yka , Eka UAka and UBk-

III. Model Simulation

A. Potential Steady State Labor Distributions

With two types of manufacturing workers the set of possible labor distributions is very
large. In fact, in the model described above it is infinite. Since a steady state solution is
the desired result it would be prudent to narrow the set of all labor distributions to only

those that are potential steady state equilibria. Proposition 1 accomplishes this task.

74

Proposition 1: In any steady state equilibrium L,“ = L31.
Proof: In any steady state equilibrium equation (19) must equal unity for j = A,B.
Solving each of these equalities for the relative price index yields

(23) [EL]- =[Wj2][qj2(Ujl9Uj2)][r+s+qjl(Ujl’Uj2)] forj=A,B

2 wjl (ljllUji’szi r+s+qj2(Ujl9Uj2)

 

 

This gives the price index as a function of the parameters of the model and the type j
variables. Since the left-hand side of this is identical for all workers in the economy, the
right-hand side for type A workers must equal the right-hand side for type B workers

Using this and substituting the relative wage fiom equation (17) gives

(24) {qA2(UAI9UA2)]=(qB2(UBl’UBZ))

QA1(UA17UA2) (131(U317U32)

 

 

Substituting q jk (U jk , U 11. )2 mlU jk , U jk )/ U ,1. for j = {A,B}, equation (24) reduces to

UAl/UB] = UA2/U32. Since there are the same number of matched workers of each type in
each location if LA], = LBk then UAk = U31. and the economy is in a steady state. If LA], >
L3], then UAR > U31. and UN < Um. Hence, UM/UB] ¢ UAZIUBZ so this cannot constitute a

steady state equilibrium. A similar argument yields the same result when LA}, < LBk.

Q.E.D.

Intuitively, this result makes perfect sense. If there are not the same number of workers
of each type in each region than it would always make sense for a worker to migrate to
the region where she is scarce since she would have a higher likelihood of becoming

employed there and her share of the bargaining solution would be larger. Given this

75

result attention can be now be drawn only to those cases where there are the same number

of workers of each type in both regions.

B. Methodology & Parametrization
Given the distribution of labor and the matching technology, equation (18) alone
determines the level of employment in each region. After noting that nk = LAk — UAR =
LBk - UBk, combining equations (20)-(22) yields two equations in WA] and WM. By
varying the distribution of labor, these solutions can be substituted into equation (19) to
trace out A as a fimction of LAI (= L3,). From this point forward this curve will be
referred to as the labor dynamics (LD) curve.

Table 4-1 lists the values of the parameters and the specific matching technology

used to simulate the model.

Table 4-1: Simulation Parameters

 

srch m(-)

 

 

.13 .04 .3 4 .75 m(UAk,UBk)=C((.UAk- Uak)/(IJA1+UBk))“

 

 

The inverse of the rate of worker separation is the implied rate of job tenure. The choice
of s = .13 implies that the average job lasts around 7.7 years. This is approximately the

average of the median tenure rates in the EU 15. The discount rate is chosen to be the
approximate real rate of interest. The choice of y = .3 implies that consumer’s spend 30%

of their incomes on differentiated products. Setting 0' = 4 implies that firms’ markup

76

 

over marginal cost is 33%. The choice of [5 results in each firm producing exactly 1 unit
of output. It can be easily verified that the matching technology in table 1 satisfies all of
the assumptions in equation (10) if C S 1. Since in any possible steady state UAR = UBk
this fiinction simplifies to mCUAk) = C (U Ar)". If the matching function exhibits constant
returns to scale then n = l and the matching function is linear. If the matching

technology exhibits increasing returns to scale then n > 1 and the fiinction simplifies to

C(UAk/2)".

III. Constant Returns to Scale in the Matching Technology
Under constant returns to scale the matching function is linear. Hence, qik = C for all j =
{AB} and k = {1,2}. Equation (17) then implies that wAk = ka. The location variable,

A = A1 = A2, now simplifies to the relative real wage

(25) Ami-2.121:
wp/H;l

A. Labor Dynamics

Before discussing the simulation results it is useful to note what would happen if trade
costs were non-existent, i.e. 1: = 1. When there are no trade costs both the wage and the
price of the differentiated good are the same in both locations. Otherwise, the product
market will not clear. This can be confirmed by inspection of equation (22). In addition,
this will be true no matter the degree of homogeneity that the matching function
possesses. Hence, real wages are the same everywhere and the location variable is equal

to unity for all distributions of labor. In this situation there is nothing to encourage or

77

 

 

 

discourage the population to deviate from its initial labor distribution. So, when there are

no trade costs location doesn’t matter and A = 1 for all potential steady state distributions

of labor.

.' F13

F166

   

_u
,u
.

;" ::::

t=2

 

 

0.94 4—4 . -4 . . . -
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

LA1,LB1
Figure 4—1 : Labor Dynamics for CRS in the Matching Function and Symmetric Regions

Figure 4-1 depicts the LD curve for several different values of trade costs. When
trade costs are high the location variable, A, exceeds unity when less than half of the
population resides in region 1 and is less than unity when more than half of the labor
force is located in region 1. Hence, the extent of competition dominates the price index
and home market effects; and a symmetric equilibrium with an equal distribution of labor
between regions is the only solution. Then, as trade costs fall to an intermediate level (I

= 1.66) the LD curve begins to flatten out and there are then three classes of equilibria: a

78

 

symmetric equilibrium, two agglomerated equilibria where all manufacturing workers are
located in a single region, and two non-symmetric equilibria where there is an uneven
distribution of workers between regions. Since the LD curve is downward sloping in the
neighborhood of the symmetric equilibrium it is stable. Hence, if the initial distribution
of labor is close to symmetry the economy will end in a symmetric equilibrium. Since A
< O in the neighborhood of L1 = O and A > O in the neighborhood of L1 = l the
agglomerated equilibria are stable. So, if the initial distribution of labor is sufficiently

asymmetric manufacturing will concentrate into a single region. Since the LD curve is

 

upward sloping in the neighborhood of the asymmetric equilibria they are both unstable.
So, for some labor distributions the price index and home market effects are dominated
by the extent of competition and for others the reverse is true. The initial distribution of
labor, then, will determine whether agglomeration occurs or not. Finally, as trade costs
fall to a low level (1' = 1.33) A is less than unity when less than half of the population
resides in region 1 and is greater than unity when more than half of the labor force is
located in region 1. Hence, the extent of competition is dominated by the price index and
home market effects; and an agglomerated equilibrium is the only solution. Note that the

region in which agglomeration occurs is determined entirely by the initial distribution of

labor3 .

B. The Structure of Equilibria
To fully grasp the steady state labor dynamics of the model it is useful to look at the

bifiircation diagram illustrated in figure 4-2, which shows the model’s equilibria as a

 

3 Note that if trade costs continue to fall the LD curve will eventually flatten out once again. For a detailed
explanation see Fujita et al. (1999).

79

fimction of the level of trade costs. The thick lines represent stable equilibria and the thin
lines represent unstable equilibria. When trade costs are very high the symmetric
equilibrium is the only equilibrium that can be sustained. Then, as trade costs fall they
reach a threshold level below which a concentrated equilibrium can be sustained in

addition to the symmetric equilibrium.

1.1 7
1.0 I 1(5)
l

0.9

 

0.8 J
0.7 1

0.6 1

 

1(3)

 

0.5 '

LA1 , L31

0.41
0.3 1|
0.2 ".
0.11
0.0 l T(S)

-o.1 L-—

1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20

 

 

 

T

Figure 4-2.‘ Bifurcation for CRS in the Matching Function and Symmetric Regions

Adhering to the terminology in F ujita et. al. (1999), this is called the sustain point and is
labeled 1:(S). Then, as trade costs fall yet further a second threshold level of trade costs is

reached below which the symmetric equilibrium breaks down and agglomeration is the
only sustainable equilibrium. This is called the break point and is labeled T(B). Table 2

gives break and sustain points for several combinations of y and o.

80

Table 4-2: Break and Sustain Points for Various Parameter Values

 

y = .3 y =.5 'y =.7

 

 

1(3) 1:(S) 1(3) 1(8) r(B) 1(8)
6:4 1.63 1.72 2.46 3.76 5.86 94.68

0'=6 1.32 1.35 1.65 1.96 2.30 7.42

6=8 1.21 1.23 1.41 1.57 1.76 3.41

 

 

Note that as the share of manufactures in consumption, y, grows so do the break
and sustain points. Hence, a larger share of manufacturing in production will increase the
range of trade costs for which agglomeration can be sustained. This is a result of a
strengthening of the forward and backward linkages. A larger share of manufacturing in
consumption will result in higher demand and, thus, higher wages (forward linkage); and
a larger local market (backward linkage). In addition, a lower elasticity of substitution
will also strengthen the forward and backward linkages resulting in a larger range of trade
costs for which agglomeration can be sustained. A lower 0' results in a greater degree of
product differentiation which will result in greater price markups and, thus, wages
(forward linkage); and a larger market (backward linkage).

The results above are identical to those that can be obtained in a full-employment
world. This should not be an unanticipated result. The same forces that determine labor

dynamics in the fiill-employment model are the forces that determine dynamics in the

81

 

present model. Furthermore, since unemployment is a non-factor in the location decision

under CRS it will not strengthen nor weaken any of these forces.

C. Unemployment

What effect will agglomeration have on economywide unemployment? Unemployment
in each region is completely determined by the steady state equations (18A) and (18B).
Hence, economywide unemployment can be determined by the sum of the unemployment
levels determined by these equations. Proposition 2 establishes the impact that
agglomeration has on this sum when the matching fmetion exhibits constant returns to

scale.

Proposition 2: If the matching technology exhibits constant returns to scale the
economywide unemployment rate is identical in all steady state equilibria.

Proof: Equation (18) determines unemployment is each region. Totally differentiating
this equation one can obtain dUAl/dLAl = s/(s + dm(-)/dUA1) and dUA2/dLA1 = -s/(s +
dm(-)/dUA2). Since m(~) exhibits constant returns to scale and is increasing dm(-)/dUAk =

C where C is some positive constant". Hence, dm(o)/dUA1 = dm(-)/dUA2 which implies
that dUAl/dLAI + dUA2/dLA1 = 0. Thus, the reshuflling of labor between regions in any
possible steady state results in no change in the number of unemployed workers in the

economy. Q.E.D.

 

4 Note that this is not only true for the matching function listed in table 1, but for all increasing
homogeneous of degree 1 fiinctions with both arguments equal to one another.

82

The intuition here is straightforward. Constant returns to scale in the matching fimction
implies that increasing (decreasing) the number of unemployed workers will increase
(decrease) the number of matches proportionately. With a constant rate of separation this
implies that a shift in the population will increase the number of unemployed workers in
the target region by exactly the amount that the number of unemployed workers
decreases in the source region. So, aggregate unemployment must be constant. Under

CRS there is no employment benefit for the economy if agglomeration occurs.

IV. Increasing Returns to Scale in the Matching Technology

 

Under increasing returns to scale in the matching function the location variable does not
simplify. The variables qJ-k and q, are no longer equal to one another. Hence, the

location variable is as given in equation (19).

A. Labor Dynamics

When increasing returns to scale in the matching function are introduced an additional
force encouraging agglomeration arises. The rate at which an unemployed type j worker
finds employment is increasing in ij5. So, there is a job search effect working in favor
of agglomeration. Hence, the expected lifetime utility of searching in the larger region
will tend to be higher than in the smaller region. So, one would expect that
agglomeration will be an equilibrium for a larger range of parameters than in the CRS

case. Once again, it is usefiil to note what would happen if trade costs were non-existent,

 

5 Let 13]], be the number of employed type j workers in region k, then

dq- d n n_ n “—
(1L: =dij [CO/2) (ij —Ejk) l]=C(l/2) (n—IXij __Ejk) 2 >0.

 

83

i.e. r = 1. The results are identical to the CRS case. When there are no trade costs both
the wage and the price of the differentiated good are the same in both locations.
Otherwise, the product market will not clear. Hence, real wages are the same everywhere
and the location variable is equal to unity for all distributions of labor. In this situation
there is nothing to encourage or discourage the population to deviate from its initial labor
distribution. So, when there are no trade costs location doesn’t matter and A = 1 for all

potential steady state distributions of labor.

1.16 —.
1.14 1 7:13
1.12 1 1

1.10 g
1.08 1
1.06
1.04 1
1.02 i

r=1.66

I:

0.987
0.967
0.947
0.927
0.90—
0.88 7
0.86 . 1 T »-~—-7----——-—r-——— . 7 , .
0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
LA1,LB1

Figure 4-3: Labor Dynamics for IRS in the Matching Function and Symmetric Regions

 

 

 

 

Figure 4-3 depicts the LD curve for the three values of trade costs used in the
CRS simulation. The matching function is identical to the previous simulations with the
exception that n now takes the value 1.1. These curves have the same basic shapes as

those generated in figure 4-1. However, the LD curves have flattened out somewhat.

84

 

When trade costs are high (I = 2) the picture is similar to the LD curve when there is an
intermediate level of trade costs in the CRS case. Here, there are then three classes of
equilibria: a symmetric equilibrium, two agglomerated equilibria, and two non-symmetric
equilibria. Since the LD curve is downward sloping in the neighborhood of the
symmetric equilibrium it is stable. Hence, if the initial distribution of labor is close to
symmetry the economy will end in a symmetric equilibrium. Since A < O in the
neighborhood of L1 = 0 and A > 0 in the neighborhood of L1 = l the agglomerated
equilibria are stable. So, if the initial distribution of labor is sufficiently asymmetric
manufacturing will concentrate into a single region. Since the LD curve is upward
sloping in the neighborhood of the asymmetric equilibria they are both unstable. So, for
some labor distributions the price index and home market effects are dominated by the
extent of competition and for others the reverse is true. The initial distribution of labor,
then, will determine whether agglomeration occurs or not. For both an intermediate level
(I = 1.66) and a low level (I = 1.33) of trade costs A is less than unity when less than half
of the population resides in region 1 and is greater than unity when more than half of the
labor force is located in region 1. Hence, the extent of competition is dominated by the
price index and home market effects; and an agglomerated equilibrium is the only
solution. Note once again that the region in which agglomeration occurs is determined

entirely by the initial distribution of labor.

B. The Structure of Equilibria
These results are made clearer when looking at the bifurcation diagram shown in figure

4-4, which, again, shows the model’s equilibria as a function of the level of trade costs.

85

The thick lines represent stable equilibria and the thin lines represent unstable equilibria.
When trade costs are very high there are three equilibria: a symmetric equilibrium and
agglomeration in either region. This is true no matter how large trade costs are. Hence,
the sustain point under increasing returns to scale is infinite as long as the degree of
increasing returns is not minuscule6. As trade costs fall a threshold level is reached
below which the symmetric equilibrium breaks down and agglomeration is the only
sustainable equilibrium. This is the break point and is labeled 1(B). However, the break

point is larger than when the matching function exhibits constant returns to scale.

 

 

1.1

 

1.0 ,
0.9 ;
0.8 7
0.7 -.

0.6 «
7(3)

 

0.5

LA1 ,La1

0.4 l
0.3 i

0.1 <

 

1
"0.1 ““"'”—" 1 fl T r r' 1 r 1 1 1 m 1
1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20

 

T

Figure 4-4: Bifurcation for IRS in the Matching Function and Symmetric Countries

 

6 lnfmite sustain points arise for values of n as small as 1.005.

86

Comparing these results to the constant returns case (or full-employment) it is
clear that agglomeration is an equilibrium for a larger range of parameters when the
matching function exhibits increasing returns. In fact, it is an equilibrium for all
parameter values if the initial distribution of labor is sufficiently asymmetric. In addition,
it is the only equilibrium for a larger range of parameters than the CRS case evidenced by
the larger break point. In fact, as the degree of homogeneity in the matching firnction
increases the job search effect gets stronger which will increase the break point. This
result is summarized in table 4-3 which shows the break point for various degrees of

homogeneity in the matching function.

Table 4-3: Break Points for Varying Degrees of Homogeneity in the Matching Function

 

 

n l 1.1 1.2 1.3 1.4 1.5 2

1(B) 1.64 1.74 1.85 1.96 2.07 2.18 2.76

 

 

The intuition behind these results is clear. In the CRS case when workers migrate
fiom one region to the other there is a proportional increase in the number of varieties
produced and then wages adjust according to the home market effect, the price index
effect, and the extent of competition. This is also what happens in a full-employment
world. A shift in the labor force results in a proportional increase in the number of
products produced since the unemployment rate is the same for all distributions of labor.

However, with increasing returns to scale there is a more than proportional increase in the

87

number of products produced due to the job search effect since the unemployment rate is

lower in the larger region.

D. Labor Market Efficiency

Partial equilibrium models of search based unemployment show that inefficiencies exist
in the labor market due to extemalities that arise during the matching process. Since the
product market does not affect employment and, thus, has no impact on the matching

process these inefficiencies are identical to those found in the present model. The reason

 

for these externalities is that when a match occurs the expected lifetime utility increases
for both parties. However, a worker will ignore the increase in her partner’s expected
income. This neglect will cause the unemployment rate to be either too high or too low
depending on the properties of the matching function.

The one situation where the labor market is efficient is when both parties
contribute equally to the matching process and the matching function exhibits constant
returns to scale. Since the matching function given in table 1 is symmetric and LA], = L3],
in any potential steady state equilibrium, when the matching function exhibits constant
returns to scale the labor market will generate an efficient outcome. This is not the case
under increasing returns in the matching fimction where the unemployment rate is too

low since workers have higher marginal products compared to incomes7.

 

7 For a detailed analysis of these extemalities see Diamond (1982).

88

C. Unemployment
How will agglomeration affect economywide unemployment when the matching fimction
exhibits increasing returns to scale? The answer to this question has already been alluded

to. However, proposition 3 establishes the results formally.

Proposition 3: If the matching technology exhibits increasing returns to scale the steady
state economywide unemployment rate is non-increasing in regional agglomeration.
Proof: Suppose that there are an equal number of workers in each region (Ln = .5).
Then, UAI = UA2 which implies dm(-)/dUA1 = dm(7)/dUA2. Hence, dUAl/dLAl +
dUA2/dLA1 = 08 meaning that a very small change from a symmetric equilibrium does not
affect the unemployment rate. Now suppose that one of the regions is larger than the
other. Without loss of generality, suppose that LA] > .5 . Then, Um > UA2. Since m(-) is
homogeneous of degree k and increasing dm(~)/dUAk is an increasing firnction of UM.
Hence, dm(-)/dUA1 > dm(-)/dUA2 which implies that dUAl/dLAl + dUA2/dLA1 < 0. Thus,

making the larger region even larger will decrease the number of unemployed workers in

the economy. Q.E.D.

Again, the intuition is straightforward. Increasing returns to scale in the matching
technology implies that increasing (decreasing) the number of unemployed workers will
increase (decrease) the number of matches more than proportionately. This implies that a
shift in the population will increase the number of unemployed workers in the target

region by less than the amount that the number of unemployed workers decreases in the

 

8 Expressions for these derivatives are given in the proof of proposition 2.

89

source region. So, aggregate unemployment is decreasing in regional concentration.
Under increasing returns to scale there is a positive employment benefit to regional

agglomeration.

V. Regional Asymmetry

The analysis now turns to the situation where the separation rate differs between regions.
Why might this parameter vary between regions that are otherwise identical? First, as
Shapiro-Stiglitz (1984) note, the breakup rate is ultimately linked to the employment
package offered by firms. In the model presented here the package includes only the
wage. However, in the real world this may include any number of benefits such as health
insurance, vacation time, and so on, which are absent from the present analysis. Suppose
that these services are simply available for employees to use at no additional labor cost.
Then, it is plausible that the level of these services will differ between regions based on
history. Furthermore, reactions of the public sector to unemployment may also differ
from location to location especially if local governments are permitted to determine their

own policyg.

A. Labor Dynamics with Asymmetrical Separation and CRS in the Matching Technology
Suppose that the separation rate is lower in region one than in region two. Then, the

location variable is given by10
(25) A: wfl/I‘l} r+s,+1
wj2 /H; 1' 7’17 S1 +1

9 This is certainly the case in the EU where each country decides its own public policy as well as in the
US. where policies often vary from state to state.
‘0 Recall that qfl, = 1 for all j and all k when the matching fiinction exhibits CRS.

 

 

90

The figures that follow were derived with $1 = .11, S2 = .15, and all other parameters as
listed in table 4-1 when the matching function exhibits constant returns to scale. Again, it
is useful to note what would happen if trade costs were absent. The results are very
different fi'om the symmetric case. Just as before, both the wage and the price of the
differentiated good are the same in both locations. Otherwise, the product market will
not clear. Hence, real wages are the same everywhere. However, since 3; < 52 equation
(25) suggests that in the absence of trade costs unemployed workers will always want to
migrate into region 1 where the separation rate is lowest. This additional pull into region

one occurs because the separation rate is ultimately linked to tenure: lower rates of job

 

separation mean longer tenure. So, the expected lifetime utility of working in region one
will exceed that of region two even if wages are prices are identical everywhere. Hence,
this will be referred to as the tenure effect.

Figure 4-5 shows the analog of figure 4-1 when the separation rates are
asymmetric. The shapes of the curves are similar to the symmetric case. However, the
structure of equilibria is a bit different. When trade costs are high (I = 2) there is one
stable equilibrium, and when trade costs are low there are two stable equilibria with
agglomeration in either region. These are also what result in the symmetric case.
However, at an intermediate value of trade costs value of every point on the LD curve
exceeds unity. Hence, agglomeration into region one is the only equilibrium.

It is useful to examine these results more carefully. First note that the symmetric
equilibrium, as in figure 4-1, is no longer symmetric. That is, there is no equilibrium
where L1 = .5. When trade costs are high the only stable equilibrium has slightly more

than half of the workforce locating in region 1' where the separation rate is lower. This is

91

a logical result considering that the lower separation rate tends to draw more workers into

region one.

1.12 —,

r=1.3

 

 

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

T

Figure 4-5: Labor Dynamics for CRS in the Matching Function and Asymmetric Regions

When trade costs are low the unstable equilibrium has less than half the workforce
locating in region one and any deviation fi'om this equilibrium will shoot the economy
into an agglomerated equilibrium in one region or the other. This, again, is a logical
result when the lower separation rate in region one is taken into account. If the economy
begins at a random distribution of labor it will be more likely that the economy
agglomerates into the region with lower rate of separation than in the region with the
higher rate of separation. Finally, when trade costs take on an intermediate value the
only equilibrium is agglomeration into region one. This occurs since the extra pull of

workers into region one prevents any equilibria where a larger proportion of the labor

92

 

force is located in region two until trade costs fall significantly lower than in the
symmetric case. So, for all values of trade costs the forces driving the labor dynamics of
the model make it more likely that the economy have a larger proportion of the workforce
located where the expected length of tenure is longer.

To fiilly grasp the structure of equilibria it is again usefiil to look at the
bifurcation diagram, figure 4-6, which shows the equilibria of the model as a fimction of
trade costs. The solid lines represent stable equilibria and the thin lines represent

unstable equilibria.

 

11 (S)

 

 

LA1
O
01

1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40

T

Figure 4-6: Bifurcation for CRS in the Matching Function and Asymmetric Regions

As transportation costs fall, the LD curve begins to flatten out pushing the stable
equilibrium further and fiirther towards concentration into region one. Then, as transport

costs fall fiirther to the region one sustain point, 11(8), concentration in region 1 is the

93

only solution. As transport costs fall yet further to the region 2 sustain point, 12(8), the
LD curve becomes upward sloping and concentration in either region can be sustained.
Note that unless the initial distribution of labor is highly skewed with more workers in
region 2 as trade costs fall over time the economy will naturally agglomerate itself into

region 1.

B. Unemployment with Asymmetric Separation and CRS in the Matching Technology
How will the asymmetries discussed above affect the economy’s aggregate
unemployment rate? With asymmetric separation, the equation that defines the
unemployment rate is different in each region is

(264) m(U...UB.)=(LA. —U...)s1

(26B) m(UAk>UBk):(LBk —UBk)SZ
Proposition 4 establishes the effects of labor migration when labor markets are

asymmetric and the matching function exhibits constant returns to scale.

Proposition 4: If s I < S2 and the matching function exhibits constant returns to scale the
economywide unemployment rate is decreasing in L,“ (= L31).

Proof: Equation (25) determines unemployment is each region. Totally differentiating
this equation one can obtain dUAl/dLAl = sl/(sl + dm(-)/dUA1) and dUA2/dLA1 = -S2/(s2 +
dm(o)/dUA2). Since m(-) exhibits constant returns to scale and is increasing, dm(-)/dUAk =
C where C is some positive constant. Hence, dm(-)/dUA1 = dm(~)/dUA2 = C. Then,
dUAl/dLAI + dUA2/dLA1 = sl/(sl + C) - s2/(s2 + C) = (s. — s2)C/(31 + C)(s2 + C) < 0.

Q.E.D.

94

Hence, as workers move into the region with the lower separation rate the aggregate
unemployment rate falls. The intuition here is straightforward. When a contingent of the
population moves into region 1 the lower separation rate there implies that fewer of these

workers will remain unemployed causing a reduction in economywide unemployment.

C. Labor Dynamics with Asymmetrical Separation and IRS in the Matching Technology
How will these results change if the matching firnction exhibits increasing returns to

scale? The location variable is now given by

(27) A.=£E_L]—Y[wfl q11(UAwUm) r+82+q12(U.67U82)]
J H2 WJZ q12(UA2’UBZ) r+S1 +qj1(UA19UB])

Hence, the job search effect discussed above now comes into play. One would then

 

 

expect that, as in the symmetric case, agglomeration is an equilibrium for a larger range
of parameters when the matching function exhibits IRS than when it exhibits CRS.
Again, it is usefirl to note what would happen if trade costs were absent. Just as with the
CRS case, both the wage and the price of the differentiated good are the same in both
locations. Otherwise, the product market will not clear. Hence, real wages are the same
everywhere. However, the job search effect suggests that in the absence of trade costs
unemployed workers will always want to migrate into region 1 where the separation rate
is lowest. So, if there are no trade costs workers will agglomerate into region 1.

Figure 4-7 shows the LD curve for both high and low trade costs. The shapes of
the two curves are similar to the CRS case, however the structure of equilibria is quite

different. When trade costs are high (T = 2.1) there are four equilibria: agglomeration in

95

each region, and two non-symmetric equilibria one with a larger concentration of
manufactures than the other. The two agglomerated equilibria as well as the non-
symmetric equilibrium with the smaller concentration of manufacturing workers are
stable. The remaining equilibrium is unstable. So, once again when trade costs are high
agglomeration can be sustained if the initial distribution of labor is sufliciently
asymmetric (in this case very asymmetric). Otherwise, the economy will end up with
more than half but not all of its manufacturing labor in region 1. This is a sensible result
since that the lower separation rate tends to draw more workers into region one and the

job search eflect tends to draw workers into the larger region.

1.20-

t‘1.3
1.15
1.10 1

< 1.05 l 1:21
1

1.00 f —————————————————————————————————————————————
l
0.95 1
J

0,90 im """""T'I _ T' 7"”_TT ‘__—_ ”T ' ' WI' ' "I " " __'_ ’_"TT‘_

30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
LA1

0.00 0.10 0.20 0.

Figure 4- 7: Labor Dynamics for IRS in the Matching Function and Asymmetric Regions

96

When trade costs are low (I = 1.33) the unstable equilibrium has less than half the
workforce locating in region one and any deviation from this equilibrium will shoot the
economy into an agglomerated equilibrium in one region or the other. This is a sensible
result when the lower separation rate in region one and the job search effect are taken into
account. If the economy begins at a random distribution of labor it will be more likely
that the economy agglomerates into the region with lower rate of separation than in the
region with the higher rate of separation.

To fiilly grasp the structure of equilibria it is again useful to look at the

bifurcation diagram, figure 4—8, which shows the equilibria of the model as a function of

 

trade costs.

1.1 3

1.0. J

 

0.9 -«
0.8
0.7 ,
0.6

 

0.5 5

LA1

0.4 1
0.3 -
0.2

0.1 .

 

0.1 1,._______ ---.__-. __ ..__ . . . .
1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60

f 1*

T

Figure 4-8: Bifurcation for IRS in the Matching Function and Asymmetric Regions

97

The solid lines represent stable equilibria and the thin lines represent unstable equilibria.
Just as with CRS in the matching technology the sustain points are infinite. Hence, for
any parameter values agglomeration into either region can always be sustained. As trade
costs fall, the LD curve begins to flatten out pushing the stable equilibrium further and
further towards concentration into region one until the only stable equilibria are
concentration in either region. Note once again that unless the initial distribution of labor
is highly skewed with more workers in region 2 as trade costs fall over time the economy

will naturally agglomerate into region 1.

D. Unemployment with Asymmetric Separation and IRS in the Matching Technology
How will the asymmetries discussed above affect the economy’s aggregate
unemployment rate? Proposition 5 establishes the effects of labor migration when labor

markets are asymmetric and the matching fimction exhibits increasing returns to scale.

Proposition 5: If S; < S2 and the matching function exhibits increasing returns to scale
the economywide unemployment rate is decreasing in L,” (= L31).

Proof: Suppose that there are an equal number of workers in each region (LA) = .5).
Then, Um = UA2 which implies dm(-)/dUA1 = dm(-)/dUA2. Hence, dUAl/dLAl +

dUA2/dLA1 < 0 just as when the matching function exhibits CRS. Now suppose that LA) >
.5. Then, UA] > UA2. Since m(-) is homogeneous of degree k and increasing, Ck =
dm(o)/dU,1kH is an increasing function of UAR. Hence, C] > C2. Then dUAl/dLAl +

dUAz/dLA] = S]/(S] '1' C1) - Sz/(Sz + C2) = S1C1- SzCz/(Sj + C])(Sz + C2) < C1(Sl - 82)/(Sl ‘1'

 

H Note that Ck is not a constant. This notation is used convenience.

98

C1)(Sz + C2) < 0. Now suppose that LA. < .5. Then, C1 < C2. So, dUAl/dLAI + dUA2/dLA1
= S]/(S] + C1) - Sz/(Sz + C2) = SIC] - SzCz/(Sl + C|)(Sz + C2) < 82(C1— C2)/(81+ C1)(Sz + C2)

< 0. Q.E.D.

Thus, for any distribution of labor moving workers into region one will decrease
unemployment. The intuition here is somewhat similar to the constant returns case.
When a contingent of the population moves into region 1 the lower separation rate there
implies that fewer of these workers will remain unemployed causing a reduction in

economywide unemployment. However, as region 1 grows in population the number of

 

matches rises causing unemployment to fall even further. So, one would expect that
unemployment would be lower in an agglomeration when the matching function exhibits

increasing returns versus when the matching function exhibits constant returns.

VI. Conclusions
The analysis above has shown that when labor market search frictions are added to a new
geography model the results depend entirely on the returns to scale of the matching
technology. With a CRS matching fimction labor dynamics are identical to the full-
employment model and economywide unemployment is unchanged by shifts in the
distribution of the population. With an IRS matching firnction unemployment decreases
as the population concentrates into a single region. Thus, agglomeration becomes more
likely due to this employment effect that, in turn, makes the price index efl°ect stronger.

It is also shown that under constant returns to scale in the matching technology no

matter the distribution of labor the unemployment rate is constant. So there is no

99

employment benefit to agglomeration. However, if the matching function exhibits
increasing returns to scale employment rises as a region increases in size. Hence,
agglomeration will result in a decline in economywide unemployment.

Finally, it is shown that allowing for asymmetric separation rates between regions
will alter the labor dynamics by making it more likely that the region with the lower rate
of separation receives the agglomeration. Furthermore, it is shown that agglomerating
into the region with the lower rate of separation will, no matter the degree of

homogeneity in the matching function, increase employment.

 

100 j

Chapter 5:

Concluding Remarks

The preceding chapters have presented three models which examine both the relationship
between the falling costs of trade and unemployment; and the role that regional (or
national) labor market characteristics, in particular rates of tenure, have in determining
patterns of industrial agglomeration. There are a several general conclusions one can
draw from these three models. First, when industry agglomerates into industrial regions
as a result of falling trade costs unemployment rates will be at least as low as when
industry does not agglomerate in “core”, industrialized regions. So, one can conclude
that, at least in this framework, globalization has at best a positive impact and at worst no
impact on employment in developed nations. This allays at least some of the fear that
globalization will cause workers in developed countries to lose out from low-wage
competition in the less developed world. Second, in the short term unemployment will
increase in “periphera ”, less developed regions, but in the long term unemployment rates
will converge to those of the developed world. Globalization forces less developed
countries to suffer short term costs that they would have otherwise incurred. However,
they can reap long term benefits. One question that remains unresolved is whether the
long term gains outweigh the short term costs. Third, differences in regional labor
market characteristics do affect agglomeration patterns: agglomeration is more likely to
occur in regions (or countries) where tenure is long relative to other regions. This reveals
an oversight in much of the new geography literature that ignores individual regional

characteristics. While a core-periphery pattern does still emerge, it may be possible to

101

determine which regions are most likely to receive agglomerations based on factors other
than population size.

It is important to note some limitations of this analysis. First, admittedly, these
models present a very specific framework. There are specific utility and production
fmetions in all three models. So, overly general conclusions may be a bit of a reach.
However, understanding the forces at work in these models can give some insight into
how at least a piece of the economy operates. So, while these models suggest that
globalization will have a positive impact on employment in the developed world it does
not mean that other forces absent from the model will not counteract them I the real
world. Second, in all three models the assumption that agriculture can be traded at no
cost is made. This is akin to assuming that trade costs on differentiated goods are higher
than trade costs on homogeneous goods. If this assumption is taken away the results of
these models will change dramatically. If trade costs on homogeneous goods are small
then the range of parameters for which agglomeration can be sustained will shrink. But,
if trade costs on homogeneous goods are high enough agglomerations will disappear
altogether]. So, there is the question of whether trade costs, in reality, are higher for
differentiated or homogeneous goods. Rausch (1999) shows that traditional measures of
trade costs are higher for homogeneous goods. He also suggests that non-traditional
measures (e. g. non-tariff barriers) are also higher for homogeneous goods. However, he
admits that his methods of measuring non-traditional costs are far fiom ideal. Many
economists have suggested that non-tariff barriers are much higher for differentiated
goods. Hence, it is not clear Whether the total costs of trade are higher for homogeneous

goods or differentiated goods. This is a topic that warrants fiirther empirical analysis.

 

‘ For a detailed analysis of this issue see Davis (1998) and Fujita, et. al (1999).

102

There are several directions in which this research can progress. First, this
framework could be extended to multiple countries where blocks of countries are be
permitted to form trading alliances so that it is cheaper to trade with a member than with
a non-member. What sorts of unemployment patterns would emerge from such a model?
Could the less developed countries gain by forming trading agreements with one another?
With developed countries? Second, can other regional characteristics affect
agglomeration patterns in ways similar to labor market characteristics? Of particular
interest is whether policy can attract firms into a region giving rise to agglomeration
forces. Ludema and Wooton (2000) have shown that this in fact is the case in a model of
tax competition. Since unemployment is often a concern in attracting firms the
framework developed here would seem ideal to study such problems. Third, the fact that
labor market asymmetries have an affect on location size is a testable hypothesis. So, it
would be useful to integrate such asymmetries into any empirical model attempting to

test the viability of the new geography fiamework.

103

APPENDIX
Proposition: In any steady state equilibrium hr,” = hkA.
Proof of Proposition 1: In any steady state equilibrium, by definition, the expected
lifetime utility of an unemployed worker in the manufacturing sector must be identical to
the expected lifetime utility of an unemployed worker in the agricultural sector. First, an

expression for V1,” for r = {M,A} must be attained. Rearranging equations (14) and (15)

kal'l;Y — e + kak‘"
P+bk

 

(A1) Vi" =

kaH: + (bk + (1k )Vkur

(A2) VE’ =
p+b1+q1

 

Then, setting V'1r 2 V: to assure that the NSC is satisfied gives

(A3) kaI'I;y 2i[p+bk +qk]+pV,:Ir

k

Subtracting equation (13) from equation (14)
(A4) p(v,"r — v,ur )= rwkny — e — (h; + 6k )(v:r — V3)

Solving for (V;Ir - Vfi" ) and substituting this into equation (13)

(A5) Vi" _ (kal'lf’ —e}iL

_ (p+bk +hk)p

Since the NSC must be satisfied in any equilibrium, rearranging equation (16) gives

 

(A6) rwkn: —e=3(p+ b+h;)
q

Substituting this into (A5) gives

104

(A7) V1" =—e—h;
Pq

In steady state equilibrium VkUM = VkuA . It is evident from equation (A7) that this can be

true only if my = hf. Q.E.D.

105

BIBLIOGRAPHY

Agenor, Pierre-Richard and Joshua Aizeman, “Trade Liberalization and Unemployment,”
Journal of International Trade and Economic Development , V (1996), 265-86.

Brecher, Richard A. and Ehsan U. Choudhri, “ Pareto Gains from Trade, Reconsidered:
Compensating for Jobs Lost,” Journal of International Economics , XXXVI
(1994), 223-238.

Davis, Donald, “ The Home Market, Trade, and Industrial Structure,” American
Economic Review , LXXXVIH (1998), 1264-1276.

Dixit, Avanish and Joseph Stiglitz, “Monopolistic Competition and Optimum
Product Diversity,” American Economic Review , LXVII (1977), 297-308.

F ujita, Masahisa, Paul Krugman and Anthony Venables, The Spatial Economy,
(Cambridge, MA: MIT Press, 1999).

Hanson, Gordon, “Regional Adjustment to trade Liberalization,” Regional Science
and Urban Economics , XXVIII (1998), 419-44.

Krugman, Paul, “Increasing Returns, Monopolistic Competition, and International
Trade,” Journal of International Economics , IX (1979), 469-479.

_, “Scale Economies, Product Differentiation, and the Pattern of Trade,”
American Economic Review , LXX (1980), 950-59.

_, “Increasing Returns and Economic Geography,” Journal of Political
Economy , IC (1991), 483-499.

_, “Space: The Final Frontier,” Journal of Economic Perspectives , XII (1998), 161—

174.

106

Krugman, Paul and Anthony Venables, “ Globalization and the Inequality of
Nations,” Quarterly Journal of Economics , CX (1995), 857-880.

_, “Integration, Specialization and Adjustment,” European Economic
Review , XL (1996), 959-967.

Ludema, Rodney D. and Ian Wooton, “Economic Geography and the Fiscal Effects
of Integration,” Journal of International Economics, L11 (2000), 331-357.

Matusz, Steven, “International Trade, The Division of Labor, and Unemployment,”
International Economic Review, XXXVII (1996), 71-84.

_, “Calibrating the Unemployment Effects of Trade,” Review of
International Economics , VI (1998), 592-603.

Milner, Chris and Peter Wright, “ Modelling Labour Market Adjustment to Trade
Liberalisation in an Industrializing Economy,” Economic Journal , CVII (1998),
509-528.

OECD, Employment Outlook (Paris: OECD, 1998).

Rausch, James E., “ Networks Versus Markets in International Trade,” Journal
of International Economics , XLVII ( 1999), 7-35.

Revenga, Ana, “ Employment and Wage Effects of Trade Liberalization: The Case
Of Mexican Manufacturing,” Journal of Labor Economics , XV (1997), 820-843.

Shapiro, Carl and Joseph Stiglitz, “ Equilibrium Unemployment as a Worker
Discipline Device,” American Economic Review , LXXIV (1984), 433-444.

Venables, Anthony, “ Equilibrium Locations of vertically Linked Industries,”

International Economic Review , XXXVII (1996), 341-35.

107

 

 

 

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