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CENTER FOR COMPUTATIONAL RESEARCH
IN ECONOMICS AND MANAGEMENT SCIENCE
Competition and Human Capital Accumulation:
A Theory of Interregional Specialization and Trade
Julio J. Rotemberg
Massachusetts Institute of Technology
Garth Saloner
Massachusetts Institute of Technology
and Harvard University
WP#3101-89
December 1989
Competition and Human Capital Accumulation:
A Theory of Interregional Specialization and Trade
Julio J. Rotemberg
Massachusetts Institute of Technology
Garth Saloner
Massachusetts Institute of Technology
and Harvard University
WP#3101-89
December 1989
M.I.T.
MAR
1J3RARIES
1
5 1990
!
Human
Competition and
A Theory
Capital Accumulation:
of Interregional Specialization and Trade
Julio J.
*
Rotemberg
Massachusetts Institute of Technology
Garth Saloner
Massachusetts Institute of Technology and Harvard University
Current version: December 13, 1989
Abstract
We
consider a model with several regions whose technological ability and
endowments are
identical
and
in
negligible. Nonetheless, certain
all
faw:tor
which transport costs between regions are non-
goods are sometimes produced by multiple firms
of which are located in the ssone region. These goods are then exported from
the regions in which their production
is
agglomerated. Regional agglomeration of
production 2Lnd trade stem from two forces.
the services of trained workers
is
First,
competition between firms for
necessary for the workers to recoup the cost of
acquiring industry-specific humain capital. Second, the technology of production
is
more
demand
efiicient
is
when
plamts are larger th£m a
insufficient to
niinimum
eflBcient scale
support several firms of that scale.
We
and
local
also study the
policy implications of our model.
*We wish to thank Ken Froot, D&vid Sch&r{itein, and Larry Sununer* for helpful convenationi and the National Science
Foundation and the Sloan Foundation for financial lupport.
Human
Competition and
A Theory
Capital Accumulation:
of Interregional Trade
Julio J.
Rotemberg
Garth Saloner
Regional agglomeration
ize in the
in the
production of goods
production of watches and chocolates; Silicon Valley
iaute couture, and movies originate disproportionately
the Swiss special-
pervasive:
is
in
computers; and shoes,
in Italy, Paris,
and Hollywood
respectively. Regional specialization extends even to product subcategories.
mobiles, liixury sedans tend to
come from Germany,
sports
czirs
from
Within auto-
Italy,
and
reliable
forms of basic transportation from Japan. While, as the Heckscher-Ohlin model has
some
of this regional agglomeration results
it is difficult
from differences
in factor
it,
endowments, much of
to explain in that mzmner. For example, regional specialization in industrial
products such as shoes and watches does not seem to be driven by the abundance of any
particular factor.
The standao-d
alternative explzmation of regional agglomeration (e.g. Mju^hall (1920),
Melvin (1969), Markusen and Melvin (1981) and Ethier (1982))
the output of an individual firm
is
Izo-ger
the larger
is
is
that, for given inputs,
the aggregate output of other
firms producing the szmae good in the saime region. So, for example, the level of inputs
required by a
new watchmaker
to produce a given output
Switzerland where there are other watch manufacturers.
have shown that external returns of
seem
to
A
this type
is
lower
Romer
if
that entrant locates in
(1986)
and Lucas (1988)
can also explain the fact that some nations
remain forever more advanced than others.
possible source of external economies of this kind
is
the spillover of knowledge
i.e.,
the possibility that knowledge acquired by one agent can be used by others. In order for
knowledge spillovers to provide a compelling explanation, however,
that they are
somehow
localized. If
an engineer
in
it
must be the case
Taiwjm can reverse engineer a product
of Silicon Valley as easily as an inhabitant of Silicon Valley, there
is
no good reason
for
regional concentration of computer companies.
Marshall (1920) posits instead that the external economies arise from proximity to
specialized inputs.
As noted by Helpman and Krugman
comparative advantage
is
incomplete.
The
for the
puzzle
is
(1985), unless there
is
a natural
production of these inputs in the region, this explanation
simply rolled back to the previous production stage:
Why
do
the producers of inputs locate in the region?
Our theory
is
that the location decisions of the firms and their input suppliers are
interdependent. Input suppliers find
it
advantageous to be located where they have
potential customers because competition
a
fair return. In
among their downstrecim customers
severa.!
assures
them
the absence of such competition, the relatively immobile suppliers would
be subject to the monopsony power of the downstream
power would be used to drive down input
monopsony
firms. Foreseeing that
would not
prices, potential input suppliers
choose to invest ex ante in the accumulation of the capital necessary to supply the inputs
efficiently.
This
critical role of
competition in securing a return to suppliers
is
one of the
elements in Porter's (1989) broad treatbe on regional agglomeration.
For concreteness, the particular input we focus on
•which
to cut
If
is
diamonds or the
skills
which
capital
a new chocolate concoction.
several potential employers, they will be paid as a
By
contrast,
if
there
is
only one potential employer,
impossible to write contracts that specify the level of training, there
(in this industry or elsewhere).
is
no reason
The hold-up problem described by
Willizjnson (1975)
Confronted with the prospect of a single potential employer, workers do not find
worthwhile to accumulate
human
themselves refrain from entering
The industry cam only
If
human
monopeonist to pay trained employees any more than untrained employees earn
for this
arises.
facilitate the creation of
among
function of their marginal product.
it is
industry specific
costly for individuals to acquire, such as the specific hand-eye coordination needed
trained workers can choose
and
is
there
is
a
capital.
if
Moreover,
if
entry by firms
is
it
costly, firms will
they can expect to be the only firm in the industry.
exist with several closely located competitors.
minimum
efficient scale
below which each firm cannot operate profitably,
the necessity of having severzd competing firms for an industry to be viable implies that the
region's output
itself
may be
may have
to be substantial. In particular,
insufficient to
accommodate the
among
of ensuring competition
We
produce for the world market.
regions with the
firms
is
it is
number
to have several of
in the
them
access to the
producing region
Then
the only
way
locate in one region
and
of firms.
show that trade emerges between
same endowments and
are transport costs and
requisite
demand
spatially sepjirated
same technology even though there
technologically feasible to produce
all
of a region's consumption
locally.^
Our theory
involves an externality.
The presence
firm to have access to suitable workers.
of other firms
is
necessary for each
However, unlike the alternative theory of trade
based on external returns, we do not require that the presence of other firms lower the
input requirement for producing output. Instead, the technology for producing output
the
same
in all regions.
Because ea^h firm needs other
firnas
to be present for workers to
might be though that omi model has multiple equilibria
b we
This would be true
and Saloner
(1985),
sequentially so that, through their ax:tions, they czm
other. This
makes
which production
of the
external returns
it
is
some
we model
trained,
it
of which no firm produces.
made
simultane-
firms as mzJting this choice
communicate
their intentions to each
impossible for equilibria with no production to coexist with others in
positive.
most important implications of the
is
in
become
insisted that the entry decisions of firms all be
ously. Instead, following Farrell
One
is
that nations can be
made worse
traditional theory of trade based
off as
a result of trade (see
on
Graham
(1923) and Ethier (1982)). In our model such losses from trade are possible as well. These
losses are intimately linked to the existence of multiple equilibria. In
some
agglomerated equilibria) only one region produces the good even though,
good
is
produced
can be worse
off.
in
equilibria (the
in autarky, the
both regions. At these agglomerated equilibria the importing region
In our
model
this
happens because there are transportation costs so that
an imported good costs more than a
locally
produced good. In Ethier (1982)
it
occurs
'Note that while monopiony power playi * role in our ttory, our formal model U rather different {rom tboee in the eiirlier
on monoptony and trade (Feeratra (1980), Markuien and Robion (1080), McCulloch and Yellen (1980)). In thote
model* monopioniitt are active in equilibrium. By contrait, in our model, the only •ectort that arc viable in •quilibrium have
several flrmi competing for labor.
literature
when one
can lead
region produces nothing other than the good subject to external returns. This
its
price in terms of the other
produced more
We show
efficiently)
good
to rise relative to autarky (even
because factor demands
rise in the
agents to
tell
ea^
other that they would
decision whether to
ers
from trade are not
mechanism that
allows the
produce the good subject to the exter-
like to
Formally, losses from trade can occur in our model
nality.^
it is
producing region.
that, in our context at least, the equilibria with losses
robust. They, again, depend crucially on the absence of any
though
if
workers must make their
become trained simultaneously. To capture the
possibility that
work-
can conmiunicate their intentions to each other we consider a variant of our model
which workers become trained
in sequence.
In this case, the equilibrium
is
in
unique and
trade can only be beneficial.
One
difference between our theory
in the role ascribed to antitrust policy.
policy can be socially desirable.
and the traditional external returns approa^
is
In the traditional theory, relaxation of antitrust
Cooperation among firms can lead them to internalize
whatever externality leads the production by one firm to lower the input requirements
of the others.
This
logic
has led Jorde and Teece (1988), for excimple, to conclude that
antitrust exemptions axe essential for certain
a world
By
tion.
contrast, in our theory as well as in Porter (1989), society benefits from competi-
willing they are to
make
Section
1
firms the potential suppliers of labor expect, the
promoting the creation of viable export industries.
in
presents the simple peirtial equilibrium setting in which workers decide
multaneously whether to acquire industry
in general equilibrium
of goods
we discuss
if
si-
Section 2 embeds this
identical regions.
That
the patterns of trade that emerge as the
and the nimiber of regions that trade
present our argument that
'The low
specific himicin capital.
and considers trade among ex ante
section has several subsections in which
we
more
industry specific investments. Thus a vigorous antitrust policy
can play an important role
number
high-technology industries to succeed in
scale.
The more competition among
model
US
varies. In
one of these subsections
workers decide whether to become trained
in
sequence.
welfare-low activity equDibria in the rather different pecuniary externality modelt of Murphy, Shleifer and Viahny
(1089) lack robuitneu for the lame rea«on
every region benefits from trade.
In section 4
we consider the
and
industrial policy, tariffs,
governments pursue to
policy implications of our theory. In particular
encompasses those
antitrust. Industrial policy
imposing them. The reason
that the goods subject to the
is
externality are sometimes produced disproportionately in one region.
of transport costs implies that regions benefit
policies that
In our model, such policies can
affect the location of industries.
raise welfare in the region
we study
But, the presence
from having such goods produced
locally.
Therefore, policies that ensure local production of these goods can be desirable from the
region's point of view.
While
tsu-iffs
can be a tool of industrial
where they do not
from such
beacuse they improve the importer's terms of trade. However,
who
workers in the exporting region
incentive to
become
trained.
foresee that tariffs will be levied, have a smaller
So, the perception that
equilibrium price of the good in the exporting region.
tariflFs
will
We show
be imposed raises the
that, as a result, tariffs
which are foreseen when workers seek training unambiguously lower welfare
This strengthens Lapan (1988) 's argument against
1.
The
Partial Equilibrium
We assume that skilled
duction.
The
in
both regions.
tariffs.
Model
labor and entrepreneurial activities are the only factors of pro-
"entrepreneur"
,
who
is
also a skilled worker,
necessary to create the firm and enable
has disutility of effort
tztriff"
have become trained, importers
after workers in the other region
tariffs
in situations
The usual "optimum
affect the regional pattern of production.
argument implies that,
benefit
can also be imposed
policy, they
c for
it
to function.
performing those
must perform preparatory work
We
activities.
If
assume that the entrepreneur
he
is
successful in creating a
firm that actually operates, however, he derives utility of v from his success.
Thus v—e, which we assume
entrepreneur.
We focus
to be positive,
is
the net utility from becoming a successful
mainly on the case where u
—e
is
arbitrarily small.
below, the role of these assumptions on the costs and benefits of managing
As we
is
shall see
to eliminate
the indifference between producing and remaining idle that characterizes stjmdard zeroprofit competitive equilibria.
We
siispect that introducing even a
5
minimal
level of
market
power would have
The other
essentially the
same
factor of production
is
effect.
At the margin, each
skilled labor.
skilled
worker
can produce one unit of output. However, one of the central parameters in our analysis
is
minimum
the
efficient scale of
assuming that, to produce at
himself
he must hire
(i.e.,
capture the presence of
the entrepreneur must employ
all,
5—1
We
production.
additional skilled workers).
successful, so that he receives v in utility,
if
his firm has
An
S
S
skilled
more ihan S. These assumptions can be formalized
L{eS)
=
skilled workers.
L{es)
where L{Q)
S
is
when
is
thus deemed
5
is
a measure
the firm produces
as follows:
=S
if
e
= es
if
e>i
L{S)
workers including
entrepreneur
of Tnin imiim efficient scale, but there are constamt returns to scale
by
efficient scale
<1,
the amount of labor required to produce
and
(1)
(2)
Q
units.
determines the number of firms that the industry can accommodate.
If
S
zero
is
then production exhibits constjmt returns to scale globally and an arbitrarily large number
of firms can be present at the
accommodate
at
most a
same time. For very
single firm,
S
the indiistry can
a natural monopoly. In between, the number
i.e., it is
of firms that can operate in equilibrium
large values of
falls
as
S
increases.
In order to obtain the requisite skills to be useful in this industry a worker must obtain
training at a cost of h to himself.
ly in
If
the worker chooses not to obtain training, he can earn
an alternative occupation. Thus a worker
can earn
w+h
will only
be willing to become trained
if
he
in this industry.
The entrepreneur
is
the sole residual claimant of the firm: he collects revenues from
customers and pays the other workers. So, in addition to his net
utility
from performing
the entrepreneurial function, he earns whatever profits there are in equilibriimi. Despite
the fact that the "entrepreneur" receives both the profits and the net utility of success,
for clarity in
decision to
what
follows
we
shall refer to the entrepreneur as the agent
form a firm and enter the industry, and the firm
who makes
the
as the agent that, once created
by the entrepreneur, makes the operational decisions of the firm such as what wages to
off"er
workers.
6
The quantity
of this product that
What matters
for the
and minimum
efRcient scale 5.
demanded equals D{P) where
is
form of equilibrium outcomes
w + h, D{w + h). Then
In particular,
let:
is
the price.
the relationship between
is
In particular, consider the
marginal cost
P
demand when
the outcomes depend on the ratio of
demand
price equals
D{w + h)
to 5.
^.i„t(^(^)
where
"int" denotes "the integer part
oP Then we
.
will
(3)
show that the form
of the equilibria
depends on N.
Our
goal
is
to contrast the industry outcome
industry - and hence
it
is
when
there
is
only a single firm in the
a monopsony purchziser of skilled labor - with one in which
wage competition
firms compete for skilled workers. Since
to attract workers
is
a
critical
firms' strategies in bidding for workers.
By
contrast, strategic interzwrtions in the output market are unessential to our argument.
We
aspect of our theory,
we
explicitly
examine
more than one firm
therefore
assume that whenever there
fictitious
Walrasian auctioneer which clears the output market.
however, we
in the
make
the natural assumption that
output market
The timing
in
is
it is
in the indxistry there exists
If
there
able to exercise
its
is
a
only one firm,
monopoly power
in the \isual way.
our model
is
as follows:
N
First,
individuals decide to
become en-
trepreneurs and perform the prepjo-atory work necessary for creating their firms (incurring
disutility e in the process).
to obtain training.
We
Second, workers, including the entrepreneurs, decide whether
denote the number of workers
firms simultaneotisly announce wages
for. If
two or more firms
{tZ'i,
offer the highest
.
.
.
,
who
obtain training by L. Third, the
Fourth, workers decide
t^ i&}-
whom to work
wage, workers ase assumed to spread themselves
uniformly across those firms. Finally, production takes place and goods are sold at a price
P
which the Walrasian auctioneer
Our subgame
sets to clear the
goods market.
perfect equilibrium requires that:
Workers make optimal training decisions;
(iii)
(i)
Entrepreneurs are successful;
(ii)
Firms choose {u;i,...,u>j^} to maximize
* We could have com idcred another itage in which flrmi decide which of their worken they actually uk to produce goods.
Thii would not change the analysis: the firms woukj ask all their workers to produce. The reason is that labor is the only factor
of production and labor costs are sunk at the time the decision of how much to produce is made.
profits; ajid (iv)
We
workers make optimal employment decisions given {tuj,.. ,tD^}.
.
consider two cases separately.
while in the latter case
to produce at
minimum
Case
when
efficient scale
The
is
greater than or equal to 2
feasible for
it is
the "competitive" price
is
a natural monopoly.
that, for v sufficiently close to
c,
the equilibrium has
(i):
We show
smaller. In the former case
N
industry
latter case that
1.1.
it Ls
In the first case
is
not feasible:
two or more firms
w+h
prevails. In the
N >2
N firms and produces
the "competitive" outcome. In paxticulair, prices and wages equal marginal resource costs
(including training),
exactly the
do
w^
number required
we
this,
P=
=
tv
-\-
h,
and the number of workers who obtain training
to satisfy market
demand
at that price {L
begin by exogenously specifying the number of entrepreneurs
and examine
equilibria of the
To
that enter,
subgames that ensue.
We informally describe why the competitive outcome
A we
In Appendix
Consider
first
e
the entry decision of entrepreneurs.
by entering as long as TV
view, anticipating wages of
w+
h (and receiving a wage of
employment
at
en equilibrium of the subgame.
B we show
that
it is
the only
in equilibrium.
break even as long as they can produce at
—
is
provide a formal proof and in Appendix
one that can emerge
cost
N
h)).
2<N <N
{a)
gain v
— D{w +
is
h,
is
minimum
in the
h)
= w+
eflBcient scale.
h
=
w*, firms
Thus entrepreneurs
range specified. From the workers' point of
any worker
w+
With P*
is
indifferent
between getting trained at a
and not becoming trained and taking alternative
a wage w. Moreover, since
all
firms offer the
same wage
in equilibrium,
workers are happy to spread themselves uniformly across the firms. Thus workers have no
incentive to deviate.
attracts
w + h.
no workers,^
Finally, consider the firms: If a firm unilaterally lowers its
if it
raises its
wage
it
loses
money on each
sale since then
tD,-
wage
it
> P* =
So the firms have no incentive to deviate.
precise, the firm kttrmcta no worken vith the pouible exception of the •ntrcpreneur hmuelf. If 5 > 1 thi*
eniure that the firm doein't deviate by lowering the wage. If 5 = 1 the *flrm" can offer the "entrepreneur" (in hii role ai
•killed worker) «< + /t - (v - e) and itill attract him. Even in thia extreme ca«c, however, the amount by which the wage can
fall below tu -t- A vaniBhei as v - ( vaniihei.
*To be more
will
8
To understajid the motivations
of the agents, consider first the firms'
wage announce-
Any
ments. In equilibrium the firms correctly anticipate the market clearing price.
it
believes that
are offering wages below the equilibrium market price, will
its rivals
a tiny amount more than the highest wage being offered by a
offer
firm,
workers, and thereby maximize
itself
rival, attract all the
This logic drives the firms to bid the wage
its profits.
up to what they believe the market
if
That
clearing price will be.
to say, they behave
is
analogously to Bertrand rivals in homogeneous goods output mzu-kets.
The workers,
which
will
be set to clear the market given that
correctly anticipate that the
training
wage
at
understand that the wage
for their part,
xintil
the
number
which a worker
is
wage
will equal
L
will
be bid up to the price
workers are employed. They therefore
D~^{L). Therefore, additional workers obtain
trained workers drives the mzu'ket clearing price
willing to
become trained and work
Although the industry can accommodate up to
down
in this industry,
to the
w+
h.
N firms in the competitive equilibrium,
the competitive outcome can be sustained with just two firms in the industry and the entry
of additional firms doesn't affect the price or
is
wage that
results (as long as
because Bertrand competition drives the equilibrium wage to the
two firms
price with jxist
Firms make zero
in the
N
<
N). This
level of the final
goods
market.
profits in equilibrium.
However, entrepreneurs
not indifferent about producing. They derive
utility v
who have
entered are
from producing. Therefore, each
entrepreneur tries to attract suflBcient workers to produce at least S. So, trained workers
can
feel
sure that entrepreneurs
the wage to
{h)
w+
who have
h.
N> N
The only
possible equilibria have the
for V sufficiently close to e there
N > N.
entered will compete for their services and drive
To do
this
we suppose,
is
wage equal
and
'The proof
in
(ii)
fewer than
in contradiction, that
Appendix B
NS
workers do.
kppliei to thii ca*e
u
ly
+
h.
We
show, however, that
no equilibrium where the wage equals
seriatim, the possibility that an equilibrium exists
training,
to
well.
9
the wage equals
where
(i)
NS
or
w+h
w
-\-
h when
and consider,
more workers obtain
If
NS workers or more obtain training and all obtain employment in this industry the
market clearing price
is
equal to
D~^{NS) < w + h. But
then
the firms produce, the
if all
workers are spread evenly over the firms and the entrepreneurs earn v — e-\-D~*^{NS) — {w +
h).
For
If
sufficiently close to c, this expression
t;
NS
fewer than
be successful,
workers obtain training
is
D~^{NS) < w + h).^
negative (becaiise
not possible for
it is
all
N entrepreneurs to
there are insuCBcient trained workers for every entrepreneur
i.e.,
who
entered
to produce at minimimi efficient scale. But then the unsuccessful entrepreneurs could have
done better by not entering (and saving the
{c)
If
N=
disutility of effort c).
1
only one firm has entered amd some number of workers, L, has obtained training,
the firm will pay
them just
slightly
above their alternative wage
w
and charge a
price equal
to:
jmx{D~^{L),&igmaixD{z){z-w)}.
The
first
expression
is
relevant
and charges a price which
very
lairge
will
of course,
is
small so that the firm hires
clears the mao-ket.
The second expression
is
after the workers have obtained training, no-one has
work
for this firm because they
first place.
entrepreneur suffers in vain his disutility of effort
when L
is
an incentive to deviate:
compensated
result,
for their training costs,
This in turn means that the single
Entry
that entrepreneurs gain utility in equilibrium
N but lose utility otherwise.
of entrepreneurs
As
relevant
e.
We have discussed these outcomes by fixing the
and
is
the trained workers
do not have a viable alternative. The
that, anticipating that they will not be
workers do not obtain training in the
(d)
all
so that the firm can act in the usual monopoly fashion in the goods market.
Note that
Workers
when L
(4)
in other
who
We now
if
the
initial
nimiber of firms and have shown
number
of
them who
enter
is
between 2
turn our attention to the question of the number
will enter initially.
models of external economies, the entry decision of firms
is
subject to
*Thc remkininc c««e« here - thow where tome of the tntined worker* arc not employed in thii indiutiy, or where tome of the
who have entered do not produce - are unintereitinf the worken who end up unemployed and the entrepreneur!
who do not produce in equilibnum could have done better by not obtaining training or not entering retpectively.
entrepreneur!
10
a coordination problem.
enter, then
that
it
it
potential firm
If
won't enter either.
t
believes that
the only firm that enters, potential workers
If it is
would end up paying a wage of
u;
and
will
lose
e.
If,
know
on the other hand, firm
believes that another firm will enter, then workers will obtain the necessary training,
the entrepreneur will gain v
We
follow Farrell
whether to enter
—
will
Thus the firm
not become trained.
would not have a workforce and the entrepreneur would
»
no other potential entrants
and
e.
and Saloner (1985) and assume that potential entrants must decide
in sequence,
the second potential entrant decides whether to enter
i.e.,
only after he knows whether the
first
can communicate their intentions
potential entrant will enter. This ensures that firms
vis-a-vis entry
through their actions. In the case where
only a few firms will ever enter this seems more appealing than maJcing
all
firms decide
whether to enter simultaneously. That assumption forces firms to maJce their decision
in
the absence of any information about what other firms are planning.
sequential entry the Farrell and Saloner (1985) reasoning eliminates no-entry
With
N.
equilibria in this case. Indeed, the only equilibrium has ff equal to
All entrepreneurs
that can possibly receive positive utility in equilibrium enter. Since the JV'th entrant enjoys
positive utility v
in fact
—
e
by entering
been a prior entrant,
it
if
another entrepreneur has already entered,
enters too.
But then any
b
that the
first
N entrepreneurs enter.
firms enter because the JV
Case
1.2.
This
two firms
price
as
(ii):
is
I'st
For suflBciently small
t;
-
e too.
— e no more
entrant would be sure to suffer a loss in
the second major case, the natural monopoly case, where
minimum
hi this case the industry
above, there
a single firm.
t;
knowing
The
than
N
utility.
N <2
to both produce at
w -\-h.
we saw
+
there has
prior potential entrant,
that the JV'th entrepreneur will follow, enters and obtains net utility of
result
if
We
is
is
efficient scale
S and
in
impossible for
also sell at the competitive
not viable under laissez
no equilibrium
it is
faire.
The reason
is
that,
which workers become trained when there
also demonstrated that firms cannot break even
when
M
the
number
is
of
th«r« U an interval of time
*In fact, it U not necewary for the »«iuencing of movM to be exogenously (peeined. A* long
during which entry can take place, if flmu endogenou»ly aelect when to enter the lame outcome r«»ulti. Farrell and Saloner
(1985) also ihow that itraw polU can have et»entially the iame effect aa tequential entry in their model.
11
existing firms
N exceeds
N. Therefore,
equilibria with
more than one
active firm also
fail
to exist.
Discussion
1.3.
The
model
results of the
The
competitive outcome emerges.
when
competitive output
who become
trained
of entrepreneurs
competition
so that
b
is
price
be sunmiarized as follows.
caji
is
social mau-ginal resource costs are
equal to those costs
who can
wage up
drives the
to
w+h.
minimum
If,
firms operating at
minimum
is
become
h,
and the
of workers
and
D{w + h) < 2S
hauid,
efficient scale
No
when
price
firms enter
and hence they have no
trained.
training before they have
had
ziny
critically
on our assumption that workers choose their
formal relationship with the firm.
We
long term contract which guarantees the workers a wage of
out any
initial
become
trained. Similarly,
w
-\-
not produced. This outcome results because the fixm cannot commit not
This latter conclusion hinges
be
25, the
maximum number
not viable.
to exploit the workers once they have obtained their training,
at a cost of h to
>
efficient scale enter,
on the other
equal to margined costs (including training), the industry
incentive to
w
k)
D{w + h). The number
is
create firms that produce at
demand cannot support two
is
D{w +
exactly sufficient to produce that quantity, the
among them
&nd the good
If
itself.
we
are thus ruling
u;
+ /i
if
they do
are ruling out arrangements in which the firm trains workers
In the presence of such employer-provided training the
and the allocation would be the same
as
when
the worker
is
wage could
sure to be paid
w + h'd
he becomes trained.
Our assumption
nient simplification.
setting
when
that these alternative arrajigements are impossible
We
is
only a conve-
expect that similar conclusions would follow in the more
realistic
where such contracts are possible but Involve a variety of costs which are absent
(as in the case of multiple firms) the
Such costs
workers make their
arise because long-term contracts that specify future
of worker training are hard to enforce and because
it
is
own
training decisions.
payments
difficult for firms
as a function
themselves to
provide the appropriate training.
Consider
first
the "solution" where the firms assume responsibility for the training
12
of the workers,
i.e.,
they train their workers at a cost per worker of h to the firm.
immediate problem with
or
may need
this
may
that the workers
not
all
be equally suited for training
For instance, training
different types of training.
some workers but not that
skill
is
of others. If workers
know whether
may
improfve the
skill
of
training will improve their
ex ante while firms only discover this ex post, the equilibria with two firms considered
above induce the right workers to obtain training. By contrast,
w
The
ex post and simply pays for their training,
likely to
it is
if
the firm pays
workers
all
obtain a rather mixed group of
trainees.*
Similar problems arise
who
workers
if
obtain training. The
contractually implementable.
must be taken, then the
course
the firm signs a contract conmiitting
itself:
If
difficulty
here
it
pay
to
in defining "training" in
is
w+
h to
a way that
is
the contract only specifies that a specific training course
difficulty
is
same
the
as
when the
firm provides the training
adverse selection results in the "wrong" workers becoming trained. Instead,
skill.
The
skill itself
than
the firm might try to write a contraict that specifies a required level of acquired
problem here
is
that
the completion of
it is
some
much more
difficult for
a third party to verify
training course. So, the workers cannot be sure that the firm will
not attempt to exploit them ex post by claiming that they are insufficiently skilled and
do not
therefore
2.
qualify for a skilled wage.
General Equilibrium Models
In this section
we
consider general equilibrium models in which trade
arbes precisely because workers only obtain training
among
and who
We
regions
they can be sure of competition
firms located within the region in which they work.
entail the
We
show that equilibrium can
emergence of "developed" regions that trade high wage goods among themselves
also trade their high
build
We
wage goods
up to a model with three
ering two simpler models,
goods.
if
among
for the low
regions and
in Section 2.1
we
wage goods of "undeveloped"
two high wage goods, by
first
regions.
consid-
consider a model with two regions and two
derive conditions under which equilibrium entails one developed region which
'In practice tho«« volunteering to join a training progr&m could well end up being those leut suitable for training. They
who are unemployed precisely because they are not very suitable.
are likely to include thoae
13
produces a high wage good of the kind we analyzed above, and which exports
to the
it
undeveloped region which produces only a low wage good. In Section 2.2 we then consider
a model with two regions
each region specializes
in
jind
derive conditions under which
one of the high wage goods, exporting
we combine
in Section 2.3,
We
two high wage goods.
it
to the other. Finally,
these elements in considering a model with three regions but
only two high wage goods.
2.1.
A
Model with Two Regions and Two Goods
One
of the two goods, good Y,
who have
by workers
and there
is
also
One
is
a
of the kind analyzed above:
is
received training, each skilled worker can produce a single unit of Y,
minimum
efficient scale 5.
The other good, Z, which
produced with constant returns to scale but there
unskilled worker can produce
supplied good that
ensxires that, in
can only be produced
it
is
produced
some sense
Helpman and Krugman
in
good Z. Good
units of
it;
is
no minimum
Z
The presence
both regions.
at least, workers are paid the
acts as the nvuneraire,
efficient scale.
serves as a competitively
of such a
same
in
common good
both regions. As
in
(1989) the presence of this good achieves at least a limited form
of factor price equalization.
M workers
There are
in each region, eau:h of
We
region.
assume that
produce at minimum
Eaxh
M
> 2S
efficient scale in
individual's utility function
is
given by:
+ Cz- K^h -
the individual becomes trained. Kg
who
assume that v
Goods
is
each region.
Q represents the consumption of good
individual
spent
is
one
if
t.
KeC
The
+ K^v
ac's
(5)
are indicator variables;
he becomes an entrepreneur, Kv
has become an entrepreneur produces at least
—
own
in their
so that there are sufficient workers for two firms to
U{Cy)
if
supplies one unit of labor inelas-
These workers are geographically immobile, they can only produce
tically.
where
whom
S
is
/c/j
is
one
units. Hereafter
we
if
one
the
shall
e is arbitrarily small.
ase costly to tr2Lnsport between regions. In particular, an
when one
unit of good
Y
is
amount
t
of
good
Z
transported from one region to the other.® Thus a well
'For timpUcity «c ignore tr&raport coitt on good
Z.
14
.
social planner
meaning
would avoid interregional trade,
if
possible.
Assuming an
solution where both goods are produced, a Pareto Optimal allocation
is self
i.e.,
sufficient
would have Cy
=w+
where U'{Cy)
where marginal
set at a level
interior
where each region
marginal cost,
utility equals
Such a Pareto Optimum would therefore involve training L*
h.
individuals in each region where L* satisfies:
U'{^) =
since L*
utility
/M
rv
+
h,
(6)
the per capita consumption of good Y. Finally, since entrepreneurs derive
\s
from owning active
firms, this production should be spread across as
many
firms of
TniTiiTniim efficient scale as possible.
Note that our assumptions on preferences make
sentially identical to the partial equilibrium
=
=
or dy{p)
p,
aggregate amotmt of
Y
model of section
1.
If
we
es-
write dy{p) for the
individual as a function of the price, then utility maximization
amount demanded by each
implies U'{dy)
model
this general equilibrium
U'~^. Since there are
demzmded
in
M individuals
one region as a function of price
in
each region, the
b now
given by
D = Mdy = MU'-'^ = M{^) = L\
(7)
For both goods to actually be produced in positive quantities at the Pareto Optimal
allocation
it
must be possible
to satisfy the total domestic
demand for good
domestic workers. This requires that L* be no greater than
We now
Optimal
assume
The
and those under which equilibrium involves interregional
free entry into the production of
issue then
decisions are
>
2.1.1.
Case
M
analyze the conditions under which equilibria exist which result in the Pareto
allocation,
not L*
Y by employing
how majiy
is
made
first.
good
Z
so that the
firms enter industry Y.
As
wage
before
in
trade.
terms of
we assiime
Z
We
is ty.
that entry
There are two main cases to consider, depending on whether or
25.
When
(i):
L*
> 25
L* exceeds 25 there
efficient scale in
is
sufficient
both regions. There
is
demand
for
two
firnis
to produce at
minimum
then an autarkic equilibrium in which each region
'"Note th&t if V - c u large, tht P«r«to Optimum would involve cresting even more flmu »nd having them produce at Icm
than minimum efficient tcale in order to allow more individual! to experieiKe the joy of entrepreneur«hip.
15
has
N=
Once
'mi{L* /S) active firms.
N
firms have entered, L* workers are
obtain training and the firms have enough workers to produce at
The
Faxrell
this
is
and Saloner (1988) reasoning we employed
is
impossible.
between regions since there
obviously remains an equilibrium
It
no incentive to
is
eration;
one of the regions produces
is
all
is
thus an equilibriimi
when
trade
allowed
is
for interregional trade at this equilibrium.
Even though the Pareto Optimal outcome
another class of equilibria when there
efiicient scale.
in the previous section implies that
The Pareto Optimal outcome
the only autarkic equilibriima.
when trade
minimum
happy to
may
an equilibrium, there
is
also exist
free trade.
These equilibria have regional agglom-
Y
and the other produces only Z. These
of
good
are the only other equilibria. In particulzLT there do not exist equilibria in which one of the
regions both produces
some
of
Y
To
domestically and also imports some.
Y
to the contrary that there are two firms producing
in
one of the regions and that this
region also imports Y. Suppose workers in the exporting region earn
must equal
w+h+
t
in the
importing region. But that would
the importing region would obtain training. Similarly,
is
to
w+
h
it IB
than that
less
become trained
shortly.
M
w +
.
The
the importing region.
first
when
applies
The landed
ty
w + h\s
therefore given by:
The
in
the wage in the importing region
they exist, can be of two types depending on the
if
in the region that
w+h+
M
more workers
M
"lajge" in a sense to be
is
produces
Y
pay
their workers a
made
precise
wage of
w+h
Denote the producing region as the foreign region while home
h.
BO that
that
Then, wages
exporting region and workers do not have an incentive
in the
equilibria,
Then, the firms
and charge
mean
w + h.
there.
The agglomerated
magnitude of
if
see why, suppose
home demzmd
cost (including transportation) in the
is
MU'~^{w +
U'-Uw + h + t\+
^
+
r>-U... .
= MU'-\w
+
uu.
h){l
=
since
(1
+
A)L*,
U'-'^
^^
X),
h
(^ +
t).
region
b
Aggregate demaind at a price of
'^)]
,.,..,.
where
A/l/'-^(u;
+
home
is
+
._U'-'{-^ + h +
X=
/i)
=
t)
^,-i(^^^)%
(8)
L*.
pzu-ameter A represents the per capita consumption of the high wage good in the
16
argiiment, A
capita consumption of
+
in the
the agglomerated equilibrium.
type of equilibrium to exist
It is
number
therefore the
is
now
what
clear
h bo that per
-\-
minimum
M must exceed
+
(1
other type of agglomerated equilibria which arise
for
w + h.
when
M to be
large: For this
Otherwise, even
X)L*.
efficient scale
of entrepreneurs that enter in
means
it
workers seek training, the market clearing price exceeds
if
w
importing region above
of firms that can operate abroad at
X)L* /S]. This
agglomerated equilibria,
its
lower there.
it is
The maximum number
given by int[(l
decreasing in
is
merely a reflection of the fact that transportation
is
wage good
costs raise prices for the high
is
This
thzin one.
is less
producing region. Since U'
in the
importing region relative to that
M
Such
available
the situation in the
is
than
is less
if all
(1
+
X)L*. These
they exist, have higher wages and prices.
In order for an equilibriima with agglomeration of either type to exist the transportation cost,
t,
must not be "too
importing region
is
that,
if t is
high, the price of
w
case, the price exceeds
we
-\-
h
is
even higher when
in the
M
is less
than
(1
+ A)L*
thus focus on the case where
two entrepreneurs enter
in the
2S which, by assumption
M exceeds
importing region and produce
is less
thain L*.
forms depending on the sign of U'{2S)
between the prices
th£Ln
t.
Thus there
U'{2S) and that
is
greater than
t,
in
(1
is
pf
The equilibrium
- U'{L *
(1
+ A)) -t.
+
U'(L* (1
+ A)).
If,
there would be an incentive to trade
home
region imports
between U'{2S) and U'{L
each.
its
[C7'-1
(p/ +
<)
+
+ A)L*
Output
price can
If it is
(1
* (1
+
if
t/'-^
17
in that region
of two
negative, the difference
entire production
instead, U'{2S)
home
is less
region
- U'{L *
(1
is
+ A))
both regions consume their entire
some
of good
Y
A)) while that at
(P^)] =
and that
now have one
and the equilibrium
home
In this case:
M
since, in this
X)L*.
in this case; the price in the
no incentive to trade
in the foreign region is
is
S
two regions when each region consumes
production of Y. Therefore, the
price abroad
in the
exporting region as well. For purposes of illiistrating
Suppose, for argument's sake, that the exporting region produces
is
Y
high as well. Such high prices create an incentive for two firms to enter
and produce 2S. This incentive
these incentives
The reason b
large".
(1
+
A)L*
+
25.
equals
P^ + 1.
If t is
b
However, the larger
bigger than
t,
0,
the equilibrium
of this second type
is
w+
w
and P' exceeds
the more likely that the resulting equilibrium with trade has
w + h or that U'{2S)-U'{L*{l + X))-t
price exceeds
minimum
5 >
zero and
workers
w+
h.
P^ +t
negative. In either case the domestic
is
h so two entrepreneurs can enter
efficient scale, offer their
-\-
in the
importing region, produce at
and make nonnegative
h,
But
profits.
then the Farrell and Saloner reasoning implies that they will enter. There thus cannot be
y
agglomeration of the production of
Similarly, for a given
smaller than S{t),
P* +
t,
be smnmarized as follows:
one region
if f is
sufficiently big.^^
there always exists a sufficiently small S{t) such that for
thdJi
is Icirger
t
in
if
5
is
w+
h.
S
Thus, the findings of this subsection can
small relative to
t
the unique equilibrium
is
autarkic,
otherwise there are multiple equilibria: both the autarkic equilibrium and equilibria in
which one of the regions specializes
on gains from trade (and prove
in
in the
production of
Appendix C) that
decisions sequentially in each region, the Farrell
equilibria with agglomeration.
2.1.2.
Case
As long
(ii):
as
We
exist.
argue in our section
workers also make their training
and Saloner reasoning eliminates the
equilibria are
more robust when L* > 25.
L* < 25
L* exceeds 5, the Pareto Optimal allocation with no trade
However since L* < 25,
scale in each region
and
it Is
not possible for two firms to operate at
so, for the reasons
equilibrium in which the good
The only
Thus the autarkic
if
Y
explored in Section
produced by each region
is
possible equilibria where
good
Y
is
for its
1,
is still
feasible.
minimum
efficient
there
is
no
laissez-faire
own consumption.
supplied in positive quantities must
therefore have only one region supplying the good, as in the equilibrium with agglomeration
of the previous subsection. For such an equilibrium to exist here aggregate
price of
have
(1
tv
-I-
+ h must
A)L*
Compared
regions.
>
exceed the
minimum
to autarky, trade for these parameter values
Under autarky,
"A •imilu' arcument
+
of the firms'
efficient scales, i.e.,
at a
we must
25.
since L*
The change from autarky
{1
sum
demand
<
is clezu'ly
beneficial to
25, the regions do not get to consume good
to free trade keeps the
wages of workers the saane.
demoiutratei th&t luch agglomerstion U impossible (even for tcro
X)L'.
18
t) if
M
is
On
Y
both
at
all.
the other
subfts.ntiklly smaller
than
hand consumers gain the consumer
surplus:
\u'{a)-{w + h)\da
(9)
/o
producing region and
in the
XL'
-[w-^h +
\y'{a)
j
t]
da
of
numerous trained workers makes
(10)
in the other region.
Trade
it
is
possible for the two firms producing
among
assuraince of competition
the external returns
makes workers
Figure
aire
is
no trade
as long as
2/(1
+
A)
as
L*/5 >
1.
feasible
varies.
and
X*/5
if
positive production of
and does not involve trade. The reason
itself.
However we czm support the Pareto
is
greater than 2.
good
Y
in
The
and with only
When L* IS
not sufficient competition for skilled workers.
amd 2 the equilibrium has
this
The Pareto Optimal
active firms in each region,
region, the equilibrium has international trade even
is
L*/5
an equilibrium only
we cannot have two
that otherwise
is
However,
for workers.
where one firm cannot obtain workers by
describing the outcomes a£
1 is useful for
one firm there
to be viable in one region. Similarly, the
of another firms affects the competition for workers
Optimal allocation without trade
reason
Y
makes training worthwhile
firms
available to both firms
allocation involves
good
not the usual ones. They might rather be viewed as a pecunijiry
The presence
externality:
The presence
driven by external returns.
\s
between
one region. In this
though the Pareto Optimal allocation
for this
is
that
it is
necessary for a region
to produce a relatively large amount of the good for there to be effective competition for
workers.
For L* IS between
and 2/(1
1
+
A),
by contrast, the Pareto Optimal allocation has
production in both regions while the equilibrium involves production in neither.
region arises because A
strictly less
is
than one. Put
prices in the region that does not produce the
and makes
it
more
difficult for
both firms
in
''For
tufflciently large
L' /S
thit
i*
differently, the costs of trade raise
good above
w
->r
h.
This reduces sales of
the producing region to exceed their
efficient scale.
the only equilibrium.
19
This
Y
minimum
The Pareto Optimal
values of
L*/5 below
allocation continues to involve positive production for certain
Let
1.
S denote
involves positive production.
1/(1
+ A)
2.1.3.
and
there
1
is
the highest
Then L/S
S
for
which the Pareto Optimal allocation
smaller than 1/(1
is
+
A).
But
for
L/S between
no production without government intervention.
The Gains from Trade
When L*
is less
thaji
25 trade
with trade but not without trade.
beneficial in that the regions
is
When L*
is
can consume the good
greater than 25, the autarkic allocation
remains an equilibrium even with free trade. This does not establish that free trade
good as autarky
exist equilibria
region
is
worse
These
plored by
in this case because, for sufficiently low transportation costs, there also
off.
from trade as a
Graham
is
result of multiple equilibria are analogous to those ex-
(1923), Melvin (1969),
A slight difference with
Ethier (1982)
losses are analogous to those
is less
than
+
is
fully specialized in the
These
(1
A)L*. They
Markusen and Melvin (1981) and Ethier
(1982).
when
the ex-
that he obtains losses from trade only
production of the good subject to external returns.
we obtain
in the
come about because,
w+
we
when the exporting
obtain losses from trade even
equilibria in
hx our
h.
which trade leads to
absence of transport costs when
M
in this case, the price in the exporting
region exceeds the autzirky price
The
as
where only one region produces good Y. In these equilibria the importing
losses
porting region
is
model with transport
losses rely
region
is
costs,
by contrast,
not fully specialized.
on a coordination
failure.
Workers
in
the importing region do not believe that other workers will enter in sufficient numbers to
make
the industry viable. This leads
workers to get trained
of workers to
them not
in the other region.
communicate to each other
expect them not to be robust to chainges
to get trained
when they expect
A)L*
Because these equilibria rely on the inability
their willingness to
in
(1 -H
become trained one would
the informational structure. This
is
what we
argue next.
Following Farrell and Saloner (1985)
we capture
the possibility that workers can com-
municate to each other their intentions by assuming that they take the decision to become
trained in sequence. First one worker has the option of becoming trained, then another and
20
Once a worker becomes trained
so on.
To ensure
We show
in
in
location of
Appendix C that
when
V
in
the other region and so on.
if
training decisions take this form, the autarkic equilibria
>
2S. Thus, with this small modification in the game,
always beneficial.
is
A
other potential trainees.
we assume that the
one region has the option, then a worker
are the only equilibria
2.2.
all
has the option of becoming trained alternates between the two regions.
who
one worker
trade
becomes known to
that the two regions are treated symmetrically
the worker
First
this
Symmetric Two-Region Version
The outcome
produces good
We now
Y
involving trade
is
the previous subsection
is
asymmetric: only one region
and, because of the transport costs, ends up slightly better
ofi"
as a result.
present a symmetric version of the two-region model which has two high-wage
goods.
The technology
now
for
also a third good,
now two goods which
Y
producing goods
X, whose technology
Z
and
remains the same as before. There
identical to that of
is
are produced by a relatively small
number
is
good Y. Thus there are
of large firms employing
specialized labor.
The
preferences of the representative worker are
U{Cx)
A
given by:
+ U{Cy)+C^-Khh-Kee + K^v
(11)
benevolent central planner would avoid the transport costs on goods
having 2L* trained workers in each region, half of
half produce
good Y. Again, however,
where both goods are produced
Y
now
in
if
L*
is
whom
produce good
smaller than 25, there
X and Y by
X while the other
is
no equilibrium
both regions. The only equilibria where goods
X and
are produced involve regional specialization even though this specialization leads to the
expenditure of tr£uisport costs.
In this
model with two goods,
it is
much
less likely
that one region will produce
the goods requiring the input of trained workers.
The reason
region has enough workers to supply both goods
X and Y
is
that
if
2(1
+ X)L* >
all
M no
to the entire world. Then, the
only equilibrium where both goods are produced has two specialized regions which trade
21
One
with each other.
world's
demand
for
region produces the world's
good
in
developed region has lower
less
wages than the developed region. Moreover workers employed
developed region
eeirn
To derive these
Y
and
X
(or
y)
scale
((1
(i.e.,
+
Z
wages that are higher than the average
results
we
<
L*
>
w+
h
for the region as a whole.
consider a model in which there exist the
\s
Moreover, 2(1
demand from
+
all
three regions
2A)L*, the aggregate
is
demand
same three goods
any one region
in
too small for two firms to produce at
2S), but the overall
25).
export sector of the
in the
but where there are three identical regions. Demajid
at a price oi
2X)L*
that
which the "developed regions" export high wage goods to the
developed region, and also trade with each other. The
X,
we now show
each of the previous subsections,
in
capable of explaining the coexistence of multiple "developed" regions and
is
an "undeveloped" region
less
the other the
with Three Regions
Combining elements developed
our model
X and
good
for
Y
An Asymmetric Model
2.3.
demand
minimum
efficient
sufficient to
for
both
X
for
do so
and Y,
exceeds Af , so that no one region can produce both on a world scale.
Then the only equilibrium where
wage good and imports the other, and one
regions each of which exports one high
X
developed" region which imports both
what
follows
we
To develop
w
earn
Z
as
All three regions produce
X
[Y) as Region
that
some workers
X
"less
good Z. In
(y), and the region
Region Z.
implications for wages, note
while other earn
w+
h.
first
in the
developed region
This meztns that the average wage in the region exceeds
that in the undeveloped region where
employed
and Y.
produces
refer to the region that
that produces only
three goods get produced has two "developed"
all
all
workers earn
it;.
in the exporting region of the developed region
is
Moreover, the wage of those
it;
+
/i
so that
it
exceeds the
average wage in the region.
This
is
also
an implication of the symmetric model of the previous subsection. This
implication of these models
They
is
consistent with the evidence of Katz
find that, in industrialized countries, the average
industries exceeds the average
wage paid
in
and Summers
(1989).
wage paid by a country's exporting
that country's manufacturing sector as a whole.
22
Our model
have found
in the
it
also gives
difficult to
amount
some guidance
as to
why Katz
auid
Summers
account for inter-industry wage differences by looking at differences
of formal education the workers in different industries possess. In our model,
wages are determined by industry-spec'iBc
skill
which
is
often obtained in
through formal education. For example, workers often acquire those
This could explain
change
in
(1989) and others
why
the wages of workers
who move from one
ways that are related to the inter-industry wage
acquired some industry-specific
skill in
ways other
skills
on the job.^'
industry to another
differentials.
Workers who have
one industry and move to another where those
are not valued, will experience a reduction in their wages. Conversely, workers
acquired
skills
skills
who have
that are not valued in the industry in which they are currently employed
but which are valuable
S.
thcin
in the
one they move to
will raise their
wages by moving.
Industrial/Commercial Policy
some goods
In our models the production of
involves high wages while that of other
goods does not. In such contexts, protection has been viewed as beneficial by numerous
authors
We
e.g.
Hagen
(1958),
Bhagwati and Rcimciswami (1963), Katz and Summers
(1989).)
are thus led to explore whether a region can gain by unilaterally deviating from free
trade.
We
consider two types of deviations. In the
first,
which we
call industrial policy,
the
central authority attempts to encourage the emergence of a specifically targeted industry.
In the second, the central authority
is
not interested in changing the pattern of regional
specialization but nonetheless taxes imports
industrial policy often involves the use of
because the
first tries
whose production requires
tziriffs,
we
skilled labor.
distinguish between the two policies
to affect the composition of trade without trying to affect
while the second affects mainly the
While
its level
level.
S.l. Industrial Policy.
Industrial policy can be carried out using various tools.
subsidy to firms
who produce
One approach
the desired good. Suppose, for example, that
is
we
to give a
are in the
**Of cour»« one might attempt to control for that in part by including "y**" of expyerience* variablei in the regresiion,
However luch v&riablet do not identify time ipent on the job acquiring induftry- specific tkilli.
typically done.
23
af
ii
simple case of Section 2.1 where there are two regions but only a single high wage good.
The
is
wage good
central authority in one region, acting unilaterally, can ensure that the high
produced
suppose
it
by
locally
offering a subsidy to firms
announces that
u
Then, two &rms
will
in the
for this
b
that
domestic market
wage equal to
No
ly
such that
is
= w + h-MU'-'^{{l +
if
if
X)L*).
(12)
they do not in f&ct end up exporting at aW in equilibrium.
the foreign market
will entail
somehow
is
foreclosed to them, equilibrium
an equilibrium price of P*
= MU'~^({1 +
A)L*) and a
+ h}^
foreign finns will enter this mzirket
been offered this subsidy. They
is
know that the domestic
they
if
firms have
out of the market since they will be
will decide to stay
unable to export and their domestic market
eflBcient scaJe
In particular,
be willing to enter the domestic market and to produce enough output
to satisfy world demeind even
The reason
the good.
domestic firms face foreign competition
in the event that the
they will receive a per unit subsidy, u, which
who produce
not sufficiently large to support
production for two firms. Therefore,
if
minimum
the central authority annoimces
its
subsidy plan before any entry decisions are made, the outcome will be that the domestic
firms will be the sole world producers of the high
wage good. Moreover,
since the central
authority only had to conamit to paying the subsidy in the event that foreign competition
materialized, domestic dominance of the industry
is
achieved without any subsidy actually
being paid in equilibriiim.
This outcome
is
desirable from the perspective of domestic residents since the utility
of the region that produces the high
wage good
is
higher than the utility in the other
however, the subsidy to one good makes
region. In the
symmetric model of Section
no
There each region can only produce one high wage good and that
difference.
2.2,
is
the
equilibrium outcome with or without the offer of the subsidy on a single good. While the
•*To MC this note flr»t that domettie coniumert are willing to eoniume (1
per unit that the firms receive (including the subsidy) is
MU'-'(1 + X)L' + w + A Thus the flmu arc wiUing
to bid the
wage up
to
«;
+
fc
Afi;'-'(1
+ X)L'
at a price of
+ X)L' = w +
MU'~^{1 + X)L'. The
h.
and so workers arc prepared to obtain training.
24
revenue
subsidy
csin
determine which of the high wage goods the domestic industry produces by
"Hargeting" that good, the country
is
indifferent in that
model
which of the goods
as to
it
produces.
In a slightly richer model, however, the subsidy can be socially costly. Suppose, for
example, that foreign workers can more easily become trained
domestic workers. This
thaji
could arise for example where the high wage good involves a
new technology and where
the workers of the foreign country have built up some relevant industry-specific know-how
with the old technology.
In that case efficiency
may
foreign firms whereais the offer of a subsidy
may
call for
production to be done by
lead to the emergence (and domineince)
of a domestic industry. Not only would foreign consumers be hurt by this since they must
bear the transportation costs, but even domestic consumers
may be
imposing a prohibitive import
foreign firms
market
is
mi^e
tariff
The
While they save
now pay
the transportation cost they would otherwise have to pay, they
training costs of the domestic workers.
hurt.
industrial policy can also be
for the higher
implemented by
on the targeted good. By announcing the
tariff before
and thereby convincing them that the domestic
their entry decisions,
foreclosed to them, they can be deterred from entering.
The end
result, again,
be the emergence of domestic firms as the sole world producers of the good. This
will
is
a
simple case of "import protection leads to export promotion". ^^
8.2.
Nondiscriminatory Import Taxes
In this section
we study
tariffs
which reduce the volume of trade but do not
pattern of specialization. This analysis
tariffs
tariff
of such policies in the context of our
mind the symmetric model
free trade has
is
will continue to
import the good on
has been levied.
To make sense
Y
thus closer in spirit to traditional analyses of
which are conducted assuming that a country
which a
in
is
affect the
of section 2.2 with
one of the high wage goods,
X
M
less
**Se* Krugtnan (1984)
for the original
tao-iff
on good
»tatement of thit
X so that
potsibility.
25
it
than 2(1
might be best to have
-f-
A)L*. In that model
produced by one region while the other,
produced by the other. Suppose that, as described
region imposes a prohibitive
model
it is
in the previous subsection,
sure to export
X. The
one
analysis
of this subsection then corresponds to the analysis of relatively small tariffs on
by the other region. Such moderate
tariffs
on
Y
Y
levied
not affect the regional pattern of
will
specialization in this case.
We show
Lapan
that the benefits from tariffs depends critically, as in
whether the government that imposes the
by "surprbe". In our model
tariff taikes
on
(1988),
the agents in the other country
depends, in particular, on whether workers in the for-
this
eign country correctly predict the imposition of the tariffs
when they make
their training
decisions.
Suppose
the
tariffs.
rmpK)rts of
for
Y
Then
Y
less
w + h. As
exceeds
u;,
(1
-I-
X)L* of them become trained
lowers the
must be
below
that the foreign workers do not correctly anticipate the imposition of
first
than
demand
for
w + h and
long as the tariff
Y. Thus,
the
is
wage
for the
market to
on imports of
Y
tzo-iff
of foreign trained workers will therefore
Y
and
its
output
when they
reduction in
demand
h and the
number of workers
is
the standard optimal tariff argument.
mcike their training decisions. Since they correctly anticipate the
that will follow the imposition of the
tariff,
fewer of them obtain
price charged abroad equals
that obtain training
w+
h.
If
the ex post tariff
is
wages
r,
Since the price charged abroad
domestic residents lose from the
to the foreign firms
is
tariff.
(13)
thus independent of the anticipated
Domestic consumption
falls
tariff rate,
and the imit price paid
unchanged. Domestic residents would be better
could commit never to levy a
off
if
the country
tariff.
These conclusions are similar
when
is
the
is:
MU'-'^(w + h] + MU'-'^ ({1 + t){w + h + t)Y
that
will
lowers the price charged by the foreign firms, small tariffs
training. Indeed, the nimiber of foreigners that obtains training adjusts until their
w+
still
that workers in the foreign region do correctly anticipate the imposition
of the tariff
equal
on
ako be
not too large, so that the wage for trained workers
helps the domestic region. This
Now suppose
tariff
the equilibrium price
cleao"
the skilled workers will prefer to be employed producing
not change. Because the
A
production of Y.
for the
to,
though stronger,
thain
Lapan 's. Lapan
(1988) shows
the production of output occurs before a government can levy a
26
t£a-iff,
the
incentive to raise tariffs
larger ex post than ex ante.
is
where countries trade because they are
small tariff
is
However,
intrinsically different.
desirable even ex ante. Here, by contrast,
As a
all tariffs
his
framework
result, in his
one
is
model a
are imdesirable ex ante
BO countries are sure to gain by committing themselves never to levy a tariff in the future.
One
reaison to stress these results
that they differ radically from those of the standard
is
models that explain trade among similar countries. Standard models of
increasing returns and monopolistic competition as motives for trade
can be seen
in
What we have shown
4.
among
regions.
As
Gros (1987), Venables (1987) and Helpman and Krugman (1989), under
these assumptions tariffs are generally desirable even
in
this type stress
is
when they
are correctly anticipated.
that Lapan's (1988) case against tariffs applies even
more strongly
a model where identical countries trade with each other.
o
Antitrust Policy
In the models
we have
presented the perfectly competitive outcome emerges even
there are only two competing rivals. In practice, however, a paucity of competitors
endow the
if
may
firms in the industry with market power over their customers and suppliers.
In particular, the firms
may be
able to restrict their consumption of inputs and thereby
reduce the amount they pay to their input suppliers.
This can occur, for example, when firms interact repeatedly and implicitly collude.
Suppose
in particular that after entrepreneurs
training, prices are set
and demeind
That norm may be sustainable
will lead to
a breakdown
in
if
realized over
is
be able to implement a collusive norm
have entered
many
which wages are
aind
workers have obtained
periods.
Then the
firms
may
below the competitive
level.
firms fear that any unilateral deviation from the
norm
in
set
cooperation in which wages return to the competitive
Each firm would then weigh the short term gain from
offering a slightly higher
level.^
wage while
others keep their wages at the collusive level, with the future loss that results from the
elimination of the collusive gain.
The
result
too large, they obtain an outcome that
discussion manageable
we
will
is
is
that, as long as the n\miber of firms
similar to that of perfect collusion.
assume that as long as no more than
**S«c Friedman (1971) for a thecry along these Unei for colluiion in output
27
prices.
N firms
is
not
To keep the
are present
w
they achieve the fully collusive outcome; the pay their workers
by
(4).
We
By
contrast,
if
there are
N
more than
firms, the competitive
chairge a price given
outcome
are interested in examining the effect of a strong antitrxist policy.
peirticular
on the vigor with which merger
that, initially, there are
N
>
N
policy
an industry to
The more vigorous
firms.
^
/x.
competition will characterize the industry and
(1
collude perfectly
and
drive the
suppose that the
at eflBcient scale
enforcement
We
and enforced.^
focus in
We assume
the antitrust enforcement, the
or fewer. Let the probability that the ajititrust authorities will prevent
such an increase in concentration be given by
training they
established
is
obtains.
that a set of mergers will be tolerated which reduce the nimiber of firms in
less likely it is
We
and
when
initial
the price
must expect
is
lax,
wage down
number
is u;
to earn
they must earn
+
w+
w + h/n
as well
—A*)
of firms,
/i.
For
it
is
n denotes the probability that
the probability that the firms will
N,
\s
such that they csm
there
all
operate
to be worthwhile for workers to obtain
h on average. Since they earn
w + h/n when
when
is,
to w.
antitrust enforcement
when
the wage and price are equal in equilibriimi
the price equals
That
w when
is
antitrust
vigorous. Since
firms are competing, this implies that
effective competition.
is
In order for the trained workers to be fully employed in the event that antitrust policy
is
vigorous, the nimaber of workers that seek training must equal
the nimiber of workers
who
obtain training
policy enables the firms to collude, [l
—
fi):
fewer workers obtain training. In the limit,
h/fi). Therefore,
decreasing in the probability that antitnist
is
A
if
D{w +
higher probability of collusion means that
the probability of collusion
is
one
(so that
n
equals zero), no worker becomes trained.
When
sales equal
the firms collude they set a wage of
D{w +
w
and
hire all the trained workers.
h/n) and the price must again equal
w+
h/n.
Thus
So the potential
for
collusion raises the price whether collusion takes place or not.
We now
consider international trade.
Suppose that, as
in
the model of Section 2.1
there are two regions but only one high wage good. Suppose that in the domestic region
'^In the U.S., for «x&mplc, the Deputraent of Juiticc hu coniidersble latitude in deciding which mercen It will challenge
and bai set out 'Guidelinei* it uiei in reaching thote deciiioni. The guideline* are lubject to reviiion and thoee in effect at
any time leave lubetantial room for interpretation. Accordingly merger policy can fluctuate lubitantially from adminiitration
to adminiitration.
28
the probability of collusion
competition
is less
fi
zero.
is
than one
i.e.,
By
contrast, in the foreign region the probability of
weak
the foreign region has a
for a sufficiently small (but strictly positive) foreign
antitrust policy. Then,
the foreign region
fi
must become the
importer of good Y.
This can be seen as follows. Suppose
of y.
h/fi
Then the
+ t]
which
total
is
this
find
it
fi.
abroad
U
So, for sufficiently low
profitable to
become trained
two firms do enter and the foreign wage
foreign firms compete.
from obtaining
fi:
at
home
two firms enter here.
if
below
falls
w + h/n
even when
antitrust policy
tolerated. This simple
rules, particularly in industries
region, with
is
tough
wage good.
Thus the country with the vigorous
is
the only producer
M\U'~^{w + h/fi)-\-U'~^{w +
The only equilibrium has the domestic
training.
which collusion
is
is
But, this means that in this case foreign workers do not benefit
antitrust stance, exporting the high
in
that the foreign region
of trained workers
decreasing in
Then, 2S workers
Knowing
number
first
is
better off than the coimtry
example suggests that relaxation of antitrust
where human capital accumulation
important, can well
is
be detrimental to a region's welfare. Insofar as cooperation between firms allows them to
exploit workers
more ex
post, fewer workers will obtain training
This concern for a strong antitrust policy
in
and the region
will suflFer.
order to ensure vigorous competition between
purchasers of inputs echoes that of Porter (1989)
who makes
this
argument strongly
for
similar reasons.
may appear
This result
cooperation
among
firms
is
surprising because in the iisual models of extemzJ returns
beneficial.
When
the externality
is
technological, so that
increased output by one firm reduces the inputs needed by another, an agreement between
the firms
is
beneficial since
socially desirable
it
allows the firms to internalize the externality, leading to a
output expansion. Similarly, in the case of localized knowledge
research joint ventures
joint venture to benefit
may improve
social welfare.
By
enabling
from the research carried out by them
externality from research
is
mitigated.
Indeed, this
29
is
all
the
spillovers,
members
of the
in the joint venture, the
precisely the
argument used by
Jorde and Teece (1988).^* Our paper serves as a warning that the appearance of external
returns
is
not enough to justify cooperation among firms. In particular, although very
large research consortia might lead to greater sharing of the fruits of the research, they
may
also reduce the compensation of their employees,
acquire the knowledge and the
5.
and thus reduce
needed to conduct the research.
skills
Conclusions
We
have presented a model of regional agglomeration
in the
goods where the principal motor behind a region's exports
among many
if
their incentive to
is
production of
specific
the healthy competition
suppliers located there. Competition ensures that workers earn high wages
they acquire industry-specific
human
makes human
capital which, in turn,
capital accu-
mulation attractive and the industry viable.
The main message from
to obtain the
same
the model
is
that even where
it
technologically possible
is
allocation with trade as without trade, trade serves a useful role. It
allows industries to operate on a sufficiently large scale that
same goods
firms producing the
it is
possible to have several
one location and thereby reap the benefits that flow
in
from regional agglomeration.
While we have focused on the
of
monopsony power,
there
salutziry eff^ect of regional
may be
htiman capital accumulation. That
which having several
other reasons
is, it is
local firms creates
why
agglomeration on the abuse
regional agglomeration enhances
an open question whether the mechanism by
an incentive
for
human
capital accumulation
is
through the increased competition they generate.
For example, a
some assurance
change
diff"erent
advantage of regional agglomeration
may be
that
to workers that they will remain employable in the industry
in the future.
That
is,
workers
may
prefer
it if
there
in the sirea that use their industry specific skills in case
is
if
it
conditions
a diverse range of
demand
provides
activities
conditions or production
techniques change in a way that eliminates the activity they choose to be employed
This preference for diversity might exist even
if
in.
long-term wage contracts can be written
'* *[W]c point out thkt our uititruit policy ... impoaet unneoeuary reitrictioni on high technology ioduttri** ... In our view,
trict antitrust enforcement i« generaily not needed in the circumitance* we contemplkte, because international competition
and new and unexpected entry
it est>ecially
itrong.*
30
specifying the
power
is
wage that the worker
will receive in
a particular activity, so that monopsony
not an issue.
Consider just three specific examples. Workers employed in the production of midsized automobiles
case
may want
demand shifts
to be located near plants that produce small automobiles in
in the direction of
Or workers employed producing computers
the latter.
based on a proprietary operating system, but whose
system,
may
prefer
it if
skills
are not specific to that operating
plants producing computers bzised on alternative operating systems
are located nearby in case theirs becomes obsolete. Finally,
worker
is
concerned that he
know that
if
it
could simply be that the
not get on with his supervisor or co-workers, and
will
he becomes unhappy in his job that he can easily
shift to another.
While the existence of such diversity may be important to workers making
ing decisions,
it is
not
clezir
why
it
and
if
if
when
workers are concerned about the possibility of bankruptcy
rolled into one.
about the "corporate culture" and that
arate divisions within the
is,
divisions. Multiple
two firms somehow have a combined probability of bankruptcy that
those firms would have
their train-
cannot be achieved within a single enterprise. That
one firm could encompaiss a range of technologies, products, plants, and
firms might have an advantage
like to
it is
Or
it
lower than
might be that workers are concerned
difficult to
same company. Such
is
maintain several "cultures"
in sep-
rationales for regional agglomeration
must
be highly speculative for the moment. Sorting out which of them, or others not suggested
here, can survive the scrutiny of formal modeling
Another open area for research
is
with high wages, extensive industry
in practice,
is
it
b hard
to
is
a question that awaits future research.
the extent to which competition
specific training
gauge when am industry
b
is
actually associated
and exports. One problem
is
relatively competitive. Nonetheless
worth providing some anecdotal examples which appear to support the model.
centrally planned economies have
firms
and are notorious
little
that,
it
First,
actual competition for workers between the various
for their inability to export
high wage goods. Second, consider the
automobile industry. Japan, the most successful exporter of high quality mass-produced
cars,
has a relatively large number of firms in this industry. Similarly, Italy has several
producers of high performance cars which are very successful exporters. In contrast, Italy
31
manufacturer, FIAT, whose exports to the
has only one large mass-production auto
are minimal.
cars
performance Italian
Interpreted within the context of our model, the high
and the mass-produced Japanese cars can be thought
use relatively skilled workers while
who employs
US
less skilled
FIAT can be thought
of as high quality goods
of as a lower quality producer
workers. These anecdotes suggest that a
of the empirical validity of the
model
is
warranted.
32
which
more
careful exploration
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May
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Thomas M. and David
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UC
Berkeley,
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MIT
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as Export Promotion," in Henryk Kierkowski
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of Resources," Journa/ of International Economics, 10, May 1980, 237-47.
Melvin James R.: "Increasing Returns to Scale as a Determinzint of Trade," Canadian
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,
Shleifer and Robert W. Vishny: "Industrialization and the
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Murphy, Kevin M., Andrei
Porter, Michael E.:
The Competitive Advantage of Nations, The Free
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York, Forthcoming.
Romer, Paul M.: "Increasing Returns and Long Run Growth", Journal of
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Political
Venables, Anthony J.: "Trade and Trade Policy with Differentiated Products:
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A
Williamson, Oliver E.,: Mariets and Hierarchies: Analysis and Antitrust Imp/icafions,
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34
(D)
(C)
(B)
(A)
(F)
(E)
^ Bqm. exists without trade
Eqm. exists with trade but
is not robust
Eqm. exists with trade and
is robust
No eqm. exists with
positive production
P.O. involves production ar
->
no trade
P.O. involves production
and trade
P.O. involves no product! oi
L*
(I4A)
S
s
s
Figure 1; Eqiiilibriun and Pareto Optinality
KEY:
(A)
No production in Pareto Optimum or in equilibrium
(B)
P.O. involves production amd trade but there is no production in equilibrium
(C)
Aut-arky is the P.O., but there is no production in equilibrium
(D)
Autarky is the P.O.
(E)
Autarky is the P.O.
(F)
Autarky is the P.O. and the unique equilibrium outcome.
,
but equilibrixom requires regional agglomeration and trade
There are multiple equilibria: An agglomeration
equilibrixun (which is not robust) and an autarkic equilibrium
/ ..
Appendix
Existence of
we prove
In this appendix
when
exists
<
2
The subgame
wages that firms
finns sets
If
<
iV
offer are: (a) If
=
tZ^,-
=
£>"^(L).
is
D~^{L); and
L<5
all
and the others
h) there are
and the remaining firms
set Wi
the assertion in Section 1 that a competitive equilibrium
equilibrium strategies are as follows: L* workers obtain training.
25 < L < D[w +
the firms set
The Competitive Equilibrium
TV.
= D{L) + j
tD,
A
(ii)
set their
(e) If
firms set
set
tD,
=
tDj
= D{L) + y — c
two cases to consider:
N
> N':
D{w) < L
(i)
N'
Jn his case
wage equal
0; (b) If
to 0; (d) If
firms set
ty,-
=
N
5 < L < 25 one
< N' =
-i-
h)
int j: In this case
tli,
=
D-'^{L)
< L < D{w),
In case (e) a
ty.
of the
for c arbitrarily small; (c)
firms set
D{w
The
+
^
firms
all
minor modification
required for the rule that workers use in allocating themselves across firms since there
are too
many workers
L — D{w)
to be employed at
workers elect to work
wage
w
in other industries.
industry distribute themselves uniformly across the
We first
Case
(a):
Since here fewer than
(b): Since the
5
Thus they
that remain in this
N firms.
workers obtain training, no firm
is
able to operate at
refuse to hire workers (set w^
=
0).
all
nimiber of workers
only one firm can op>erate at
in being the
The D{w) workers
demonstrate that the firms' wage strategies are equilibrium strategies.
rnin iTTnim eflScient scale.
Case
Here we assume that
in this industry.
minimum
who
obtain training exceeds
efficient scale. Since
one who hires the worker derives
utility of v,
5 but
is less
the entreprenexir that succeeds
they are each prepared to bid v
to the workers, or
y
Lf
each, for the right to be their employer. (Note that since e
cost at this stage
it
is
winning firm
is
irrelevant).
willing to pay
than 25,
is
a simk
Since the mairket clearing price will be I>~^(L), the
D~^{L)
+y
to each worker to be the sole producer. Since
Lf
the losing firms will not attract any workers in equilibrixim, they are prepared to
tiny
amount
less
than the wage of the "Svinning firm"
.
(c(i)): If
w + h.
Since
the
all
a
Doing so keeps the winning firm
"honest" and eliminates an incentive for him to shave his wage
Case
offer
offer.
L workers are hired the market clearing price will be D[L)
which exceeds
N firms can produce at minimum efficient scale in this case, they will bid
the wage
Case
up
to
(c(ii)):
minimum
scale.
D{L).
Here there are
efficient scale. A^*
As
Case
in
insuflBcient trained
is
the
number
workers for
N
all
firms to operate at
of firms that can operate at
(b) the entrepreneurs are willing to
pay
t;
minimum
to be successful. Since there
are -j^ workers per successful firm, the firms are willing to pay a "preniium" of
worker to attract them to the firm and be successful. Once the workers are
the market clearing price will be D~^{L). Thus the successful firms bid
workers. Unsuccessful firms bid
Case
Here
(d):
all
N
efficient
per
employed
all
D~^{L)
^^
+ ^^
for
0.
firms can produce at minimima efficient scale.
Once the workers are
hired the market clearing price will be D~^{L). Firms therefore bid the
wage up
to this
level.
Case
(e): If
firms offer w, workers are indifferent between being employed in this industry
and being employed elsewhere. Therefore
D~^{w) workers
if
to take
employment
they are employed, will be
Thus the firms are
tv.
in
it is
consistent with optimizing behavior for only
thb industry. But then the market clearing
Thus firms bid the wage up to w.
any number of
willing to carry out the proposed strategies for
workers that become trained. Those strategies are therefore subgame perfect.
now
to the training strategy of workers.
workers to obtain training.
and the wage that
is
offered
If
that
is
price,
The proposed equilibrium
number obtains
D~^{L*)
= w + h.
training.
Case
We
turn
strategy calls for L*
(c(i)) is
the relevant one
Since they recoup their training expenses
the workers are prepzu-ed to obtain training.
No
additional workers are prepared to obtain training, however.
worker obtains training. Case
D~^{L* +
Similao-ly,
1)
< w + h,
(d)
one additional
becomes the relevant one. The wage that
BO that the deviating worker
is
is
h and earning
w+h
offered
is
unable to recoup his training costs.
none of the L* workers has an incentive to deviate by not obtaining
Each worker who obtains training
at a cost
If
in equilibrium in indifferent
training.
between obtaining training
and not obtaining training and earning w.
Appendix
B
Uniqueness of the Competitive Equilibrium
In this
equal
Appendix we show that the equilibrium
+ fc,
u;
is
unique.
The proof of this
and the highest wage that
{i)
w < w+
trained workers
is
is
charged in a candidate equilibrixmi by P*
is
offered in equilibrium by w.
There cannot be an equilibrium where the highest wage
h:
less
than w-\-h since at
least
w > w
-^
w
h and P* >
h: In
-\-
off.
an equilibrium
like this it
the entire pool of untrained workers becomes trained because
untrained workers
is
sufficient to satisfy
below w-\-h for the market to
can make himself better
(iii)
w
>w
-\-
off
clear.
demand when
But then
offered to
one of the workers would be able to deviate
by not obtaining training and make himself better
(ii)
where the price and wage
proposition proceeds by contradiction for a series
Denote the price that
of exhaxistive cases.
in Section 1,
for v
—e
must be the case that
w > w + h.
Since the pool of
+ /i,
the price must be
the price
is u;
very small at least one entrepreneur
by not entering.
h and P* <
tt;
+
workers lose money. But then for r
When
/i:
—e
the price
is
below the wage, firms that hire
very small at least one entreprenexir could do better
by not entering.
(iv) vj
w
•\-
h.
=w
•\-
The reason
> w+
h.
and P*
is
that a firm can raise the wage infinitesimally, attract
workers and increase
its profits.
h:
Here a firm
will deviate
and
offer
a wage above
all
the trained
Appendix C
Uniqueness of Equilibrium with Sequential Training Decisions
Appendix we consider the case where L* > 25 and workers get trained
In this
sequence.
We
show
that, in this case, the
one region while none get trained
in
outcome where L*{1
the other
is
+ A)
in
workers get trained in
The only
not an equilibrium.
equilibrium
the autarkic one where L* workers get trained in each region.
is
Workers
in each region are ordered
from
be given the option of becoming trained.
After that, the
first
worker at home
If
M. The
1 to
worker abroad and so on.^^ Let s^ denote the strategy
we
equal one
let 8
for the t'th
if
the
first
to
it
is
for the t'th
given to the second
worker at home while
These strategies can take only one of two
s- denotes the j'th foreign worker's strategy.
values;
is
he declines he cannot later become trained.
given the option, then
is
worker
first
the worker becomes trained and zero otherwise.
The
strategy
worker depends only on the number of workers that have decided to become
trained before him. Thus:
m=l
Suppose that at
trained at
Xf
b
home
least
X^
two firms enter
n=l
each region and that
in
there
b no
region.
t,
then the price at
trade. If
it
home
greater than
t,
is
showed
equilibriimi
is
+t
home and
as
Y
flows
would be undimnged
-
U'{Xf)
17' (X')
and
from the foreign to the domestic
if
the equilibrium
many
as (1
+
+ h) +
b
of the former type
if
when 2S
X)L* workers get trained abroad, the
U'~^{w
+
h
If
2S workers become
+ t)]-2S
become trained abroad. On the other hand, 25 workers are
anftlyiii
U'{X^)
bigger than U'{X^) while the equilibritmi price
unique. So, consider the latter equilibria.
home, then no more than M\U'~^{w
**The
If
and b smaller than U'{X^).
in section 2.1.1 that
workers get trained at
workers become
U'{X^) while the price abroad b
good
The equilibrium price abroad P^ b
home, P^ equals P^
We
b
X^
workers become trained abroad. Given our interest, assume that
exceeds X^. Then the equilibrium prices can be of two forms.
smaller than
at
while
m=l
n=l
trained at
workers are willing to
willing to
become trained
the flnt deciiicn on training were taken by the flnt worker at home.
at
home
h)
number
as long as the
+ U'~^{w + — f)] — 25,
/i
of foreign trained workers does not exceed
which
The discrepancy comes from
larger.
is
K^ = M\U'~^{w +
the existence of
transport costs whose presence ensures that the price abroad must be below
to equal
+
lo
We now
at least
K^
/i
that,
if
trained. Consider first
subgames
workers ever become trained abroad. Then, 25 workers or more
trained
25 —
if
will enter
see this note that the
25 — 2 workers
exactly
if
M'th domestic worker
is
if it is
M—
I'st
perfect,
which fewer than
become trained
will
By doing so
got trained before him.
in
strictly better off
workers got trained before him. Similarly, the
1
/i
subgame
the strategies followed by foreign workers are
25 domestic workers become
To
+
home.
at
show
at home.
ti;
by becoming
domestic worker
he, just like the last
worker, recoups his training cost and lowers the equilibrium price. This reasoning extends
M — 25'th worker
backwards so that the
sure to become trained
is
if
other workers did
not get trained before him.
We now
argue that
Suppose there
to
exists a
become trained
K^ =
M[U'-'^{w
U'~^{w
-\-
h
—
t)]
subgame where the
/i)
+
K
good
Y
of
Y
—
1
and recoups
»
—
there are only
So
—
far
K
K°'
—
+
/i
+
t
01
- (^^ -
home
if
= 25 + 1 + M\U'-'^{w
1)
worker
there were
-\-h-\-t)-
would
definitely
—
even
if
his decision to
Similarly, the
if
there
he does not become trained,
t
—
become trained
triggers further
2'th domestic worker will get trained
if
2 workers trained before him. This argument extends backwards so
I'th domestic
we
If
become trained
(By the definition of K^^. By entering, he lowers the price
his training cost
we have argued
entry of two firms
that the
+
I'th domestic worker
training of domestic workers.
t
/i
K'Wi
from acquiring training
domestic workers already trained before him.
will cost u;
that the
+
refrain
worker becomes the
domestic workers already trained. In equilibrium, such a number will
always be present. The
were
U'-'^{w
workers ever to become trained abroad.
I'th foreign
That worker would
there.
+
K^
impossible for
it is
worker becomes trained.
that the
initially
home
region produces at least
25 which
justifies
the
assumed. In fact the argument can be strengthened to show
region produces L* and the autarkic equilibrium prevails. Suppose that, on
the contrary, the foreign region produces L*
+x
which
is
less
than
K' where x
is
positive.
For X sufficiently
leirge
the
home
region will import Y.
implies that the domestic region will then produce
(L*
+
i)
= MU'~^{w +
h -
t)
- X which
But, then, the price and wage abroad equal
exceeds
h)
+
U'~^{w
25 because L*
+
x
M[U'~^{w
w+h—t
BuflBciently small that the foreign region does
The backwards induction argument
which
-\-
is
is
h—
+
less
t)]
~
than K^.
impossible. So x
must be
not export the good. But, then, x must be
zero for otherwise the foreign price and wage would again be below
w+
h.
q-^'^-'^o
C^OBO
0^ s^e^
SV3
Date Due
DEC
c
li^u
3-33li
Lib-26-67