46(10) 2045–2059, September 2009
The Gap between Free Market and Social
Optimum in the Location Decision of
Economic Activity
Miki Malul and Raphael Bar-El
[Paper first received, August 2006; in final form, July 2008]
Abstract
This article presents a simplified model for comparison of the spatial distribution
(core–periphery) of economic activity resulting from free market conditions, with the
distribution that would lead to a social optimum. It further examines the public policy
measures required to lead the economy towards the optimal distribution. Simulations
are conducted to illustrate the mechanism of intervention of public policy and to test
the feasibility of various measures. An important conclusion is that public investment
in the creation of competitive ability in the periphery may provide the solution to
market failure and therefore lead to the achievement of a social optimum greater than
the free market optimum. Another preliminary conclusion is that public policy should
consider a combination of measures (such as improving both regional infrastructure
and the quality of the labour force), since focusing on a single measure may not be
sufficient to achieve a social optimum.
1. Introduction
The objective of this article is to elaborate a
simplified methodological tool for evaluation
of the social efficiency of core–periphery free
market behaviour and the need for public
intervention. Here we use the broad definition
of ‘core’ as a region with the greatest concentration of economic activity and generally
also of population (in terms of product or employment per area or density of population).
This is what would generally be referred to
as the ‘metropolitan’ area, while the periphery
is defined as regions beyond the metropolitan
area and its immediate surroundings. Free
market conditions may lead to a greater concentration of economic activity in core regions
and to an economic optimum for the private
investors. However, this ‘private optimum’, as it
will be referred to here, may be different from
a ‘social optimum’. In other words, we may
be experiencing a market failure. The social
Miki Malul and Raphael Bar-El are in the Department of Public Policy and Administration, Ben Gurion
University, Beer Sheva, 84000, Israel. E-mail: [email protected] and [email protected].
0042-0980 Print/1360-063X Online
© 2009 Urban Studies Journal Limited
DOI: 10.1177/0042098009339427
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MIKI MALUL AND RAPHAEL BAR-EL
optimum is defined as the optimum for
society as a whole and includes considerations of costs and benefits for society beyond
those perceived by the private investors, and
resulting from the concentration of economic
activity. These may include costs such as increasing public infrastructure expenses or
benefits such as external positive economies.
We also take into consideration the fact that
public intervention also involves costs.
The natural tendency of spatial concentration has been analysed and investigated by
many scholars, generally under the global
title of the ‘core–periphery’ issue. However,
most research is oriented towards understanding free market behaviour, sometimes
including the influence of the public sector
as one of the actors. In a recent article, Bar-El
and Schwartz (2006) summarised some of
this research. Krugman (1991) established a
significant starting-point with the development of a rather simplified model to explain
the geographical concentration of manufacturing. He explains, using a two-region/
two-sector model, how a concentration of
manufacturing activity may be found in
one region, depending on the interaction
among three main parameters: the share
of manufacturing in the economy, the existence of economies of scale and the level
of transport costs. This core–periphery (CP)
model implies that economic efficiency considerations lead to a heavy concentration of
the population around the manufacturing
activity in one region (core), while the second
region (periphery) will be less populated and
based on agricultural activity.
Further developments of Krugman’s model,
mainly changing some basic assumptions,
have led others to different conclusions.
Lanaspa et al. (2001a) found that assuming
the existence of congestion costs and abandoning the assumption of constant transport
costs led (using the same basis as Krugman’s
CP model) to the existence of various asymmetric stable equilibria, thereby providing a
“theoretical justification for economic landscapes in which large industrial belts co-exist
with smaller ones” (Lanaspa et al., 2001a,
p. 437). We can state that the theoretical structure established by Krugman may justify a
concentration of manufacturing activity, but,
under different assumptions and parameters,
may also explain simultaneous growth in
various regions. Krugman himself explains
in a later article (Krugman, 1999) the action of
‘centrifugal’ and ‘centripetal’ forces that may
lead to the concentration of economic activity
in more than one place. The co-existence of
multiple locations of economic growth has
been justified by other factors: physical capital
mobility (Forslid, 1999), the decreasing cost
of trading ideas (Baldwin and Forslid, 2000),
the differing qualities of land (Lanaspa and
Sanz, 1999), the influence of the public sector (Lanaspa et al., 2001b; Bar-El and Parr,
2003) and specifically tax differentials (Borck
and Pflüger, 2005). Challenging the core–
periphery model has led to the development
of alternative models (Copus, 2001; Fishman
and Simhon, 2002; Hu, 2002).
In Krugman’s model, as well as in research
that extended this model, no distinction is
made between the free market solution and
the social optimum. A model that enables the
identification of a social optimum would
naturally be much more complicated than a
model for the identification of a private optimum. Social optimum may be viewed in
terms of the total welfare of the population
as a whole. An exact measure would be difficult to achieve since it would require quantitative parameters, such as the influences of
externalities (both positive and negative), as
well as much more qualitative or ideologyoriented parameters, such as the value of
equality or marginal utilities of income. Efforts
to evaluate such a social optimum have therefore been quite restricted in the literature, or
have focused on specific issues.
Dohse (1998), Fujita and Abdel-Rahman
(1993) and Helsley and Strange (1990) refer to
FREE MARKET OR SOCIAL OPTIMUM?
the market failure that stems from firms’
failure to consider the positive externalities
(the marginal influence on the agglomeration
advantage) and the negative externalities (the
marginal influence on the free market prices),
yet these models do not refer to the extra
social costs. Ottaviano and Thisse (2001) relate
to the externalities created by the workers
through the price of the goods in each region
(pecuniary externalities). In another article
(Ottaviano and Thisse, 2002) they found, in
the context of the EU integration process, that
at given costs of factor mobility, free market
agglomeration would not lead to maximum
efficiency. This leads them to the conclusion
that it would be more efficient to impose restrictions on factor mobility (this would, for
example, prevent a ‘brain drain’ from poorer
regions).
Charlot et al. (2006) also address the welfare
properties of market allocations in new
economic geography models; they add the element of societal values and reach the general
conclusion that the market equilibrium may
not coincide with the social optimum. Still,
the existence of a gap between the free market
optimum and the social optimum does not
automatically justify government interference. For example, the cost of intervention
might be greater than the additional welfare
gained by the policy. Charlot et al. (2006)
found that interregional transfers may be
the better solution for correcting the discrepancies arising in a core–periphery structure,
since it seems problematic for the government to undertake a major reorganisation of
the spatial patterns of economic activities. The
same concern was raised by Knarvik (2004),
who also suggests taking into consideration
intraindustry and interindustry knowledge
spillovers, as well as trade costs.
Our intention in this article is to create a link
between the private considerations and social
consideration in one model, being aware of
the cost of having to consider only measurable elements of the social aspects. We intend
2047
to construct a general simplified model that
includes both the free market considerations
that lead to the distribution of economic
activity between regions and the social considerations (in terms of economic influences
on the society as a whole) that may lead to a
different distribution. We examine the spatial distribution of firms under free market
conditions, compare it with the distribution
that would lead to a social optimum and
examine the type of public policy required
to lead the economy towards the optimal
distribution. Further, we check the extent to
which the increase in social benefit justifies
the cost of public intervention.
2. The Model
The model elaborated here focuses on the
process of decision-making at the private
level, in terms of selecting a location for
investment in economic activity to achieve
maximum business benefits, and further
focuses on the implications such a process
may have for the social benefits or costs.
This is an oversimplified model in the sense
that it does not consider all factors that may
influence such decision-making, but rather
focuses on those that reflect the difference
between private business considerations and
public considerations.
2.1 The Basic Model
We assume that the objective of the public
sector is to maximise welfare—W. For the sake
of simplification, we assume the existence of
only two regions j: A is a core region (defined
as a region with a high level of economic
activity) and B is a peripheral region. We take
this situation as given, in the sense that we
do not initially refer to the reasons that led A
to be a core region.
The number of firms in region j is nj. Here, the
number of firms actually stands for the level
of economic activity. At the starting-point
nA > nB . The objective of the firm when making
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MIKI MALUL AND RAPHAEL BAR-EL
a decision to locate in region A or in region B
private
is
is to maximise the private NPV: NPVj
the net present value the firm sees under free
market conditions, taking into consideration
all private benefits versus all private costs.
For analytical purposes, let us make the
simplistic assumption that NPV can be disaggregated in two parts, one determined by
the technological specific factors of the firm
or the sector, and the other dependent on
location factors: NPVbasic is the part of NPV
that does not depend on the region in which
the firm locates and is determined by the
specific characteristics of the firm or the
sector, such as production technology and
production factors.
t
∑ NPV (X
j
ji
)
i =1
is the part of NPV that is attributable to
regional factors, where, Xji are variables that
affect the NPV and whose values are different in each region, such as distance, access to
markets and infrastructure, where i represents the index for each variable i = 1 ... t and
j represents the region index j = {A, B}.
Therefore
t
NPV jprivate = NPVbasic + ∑ NPV j (X ji ) (1)
i =1
To simplify, let us define Wi as the relative
weight of influence of variable Xji. The location
decision will be based on the following
equation
t
NPV jprivate = NPVbasic + ∑Wi X ji
i =1
Given that NPVbasic is identical for both regions, the firm will want to maximise the
following expression
t
ZPj = ∑Wi X ji
(2)
i =1
where, the ZPj is the private ‘score’ of region
j for a specific firm.
We normalise the value of each Xji in region
B to one, so that the value of the variable in
region A reflects the relative advantage of
region A for each of the variables.
The next step is to identify the main variables that influence the location of economic
activity. If we summarise the results of the
research studies conducted by Henderson
(1983, 1986), Roberts (1985), Bar-El and
Felsenstein (1990), Taylor (1993), Wong (1998),
Mano and Otsuka (2000) and Hodgkinson
and Pomfret (2001), we can see that most
location factors can be classified into five main
broad variables
(1) PE: agglomeration economies (expressing
factors such as proximity to other firms,
proximity to suppliers and services).
(2) PP: price of production factors (rent, cost
of labour force and other production
factors).
(3) LF: quality of regional labour force.
(4) INF: infrastructure quality (quality
of roads, quality of communication
networks).
(5) OTHER: other factors (such as the location in a central place providing higher
levels of accessibility to urban amenities
—COM, or proximity to the entrepreneur’s place of residence—HOME).
The five factors that define ZPi can be divided
into exogenous and endogenous factors, as
follows
(1) Exogenous factors: variables determined
by external forces, mostly government:
INF, LF, OTHER.
(2) Endogenous factors: variables determined
for each region as a function of the number of firms in the region: PE, PP.
It is clear that the classification of these three
factors as exogenous is almost arbitrary,
but is necessary for well-known technical
reasons. The level of infrastructure (INF) is
exogenously determined by the government,
FREE MARKET OR SOCIAL OPTIMUM?
but public decisions about this are certainly
influenced by the level of economic activity
in each region. The labour force variable
(LF) is also influenced by the level of economic activity in each region and this issue
is broadly covered in the extensive literature
on migration and labour force commuting.
However, for the sake of simplicity, here we
assume this variable to be exogenous. Its inclusion as an endogenous variable requires
another dimension in this model and justifies
a separate article (under preparation).
The endogenous variable PE. Agglomeration economies are defined by Isard (1956)
as scale economies that are external to the firm
and internal to the city or the region. They
include localisation and urbanisation economies, as analysed by Catin (1991). It has
been shown in the literature that an increase
in the number of firms in a region increases
agglomeration economies and therefore increases the productivity of each firm in the
region (Segal, 1976; Arnott, 1979; Henderson,
1983, 1986; Nakamura, 1985; Goldstein and
Gronberg, 1986; Ciccone and Hall, 1996;
Davis and Weinstein, 1999). We express the relationship between the number of firms and
agglomeration economies by the equation
PEj = f(nj)
and
MPEj = f'(nj) > 0
where, MPEj is the marginal productivity of
the positive agglomeration effect.
We further assume that there is an ‘agglomeration diseconomies’ effect. The existence
of such diseconomies after the achievement
of a certain level of agglomeration is quite
widely recognised. Illeris (1993), for example,
explains the limitations of the theory of polarisation between the centre and the periphery,
and suggests an inductive theory to explain
the development of various regions as a
2049
function of their specific characteristics. We
integrate this effect in our model by assuming
that the marginal productivity decreases
f''(nj) < 0
The normalised value of PE in region A (as
noted, region B values are set equal to one) is
PE An =
PE A
PEB
We can express the PE function as
PE j = λ(n j )α
α < 1, λ > 0
where, α is the elasticity of the agglomeration
advantage in relation to the number of firms;
and λ is a positive coefficient.
The relative ‘score’ of region A is therefore
PE An = (nA / nB )α
The endogenous variable PP. As the
number of firms in the region increases, the
prices of production factors are generally
expected to increase as a consequence of
increasing demand, the immobility of some
production factors, such as land, and the
assumed not-total mobility of other factors
such as labour (Mera, 1973; Conrad, 1997;
Mitra, 1999; Verhoef, 2000).
PPj = g(nj)
and
MPPj = g'(nj) > 0
where, MPPj is the increase in prices that
results from an increase in the number of
firms in the region. We assume that prices
increase at a growing rate
g''(nj) > 0
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MIKI MALUL AND RAPHAEL BAR-EL
The relative ‘score’ of region A is
PPAn =
PPA
PPB
The private ‘score’ of each region is defined as
Let us assume that the PP function is
PPj = ω(nj)β
constA > constB , y > 1
p
ZPB = const Bn + WPE 1α − WPP 1β
p
ω > 0, β > 1
where, β p is the elasticity of prices in relation to the number of firms, defined as the
percentage change in price in relation to the
change in the number of firms; and ω is a
positive coefficient.
The relative ‘score’ of Region A is therefore
PPAn = (nA / nB )β
ZPA = const An + WPE y α − WPP y β P (4)
p
The score of each region can be now formulated as
ZPj = const nj + WPE PE nj − WPP PPjn (3)
where, const jn is determined by all exogenous
variables, and can be expressed as
const nj = WLF LFjn + WINF INFjn
+WOTHEROTHERnj
where, all W parameters are the relative weights
of influence of the exogenous variables
(LF, INF, OTHER) and of the endogenous
variables.
P
Given the characteristics of α and β, these
functions would behave as in Figure 1, showing that until point R, the score for region
A rises, indicating a faster growth of the
advantage of agglomeration over the disadvantage of increasing prices. From point R
to point S, the relative advantage of region A
decreases, but still persists, so that it is beneficial for firms to locate in region A. In the
free market, the proportion of the number of
firms in regions A and B is determined by the
proportion yp. That ratio represents a stable
system equilibrium (every shift from it will
create an advantage for one of the regions so
the firms will change their location towards
equilibrium). The value of the ratio y p is
determined by the following factors
(1) The ratio between constA and constB: the
greater this ratio, the larger yP will be.
(2) WPE, the relative weight of PE, relative
to WPP, the relative weight of PP in the
objective function: the larger WPE is in
relation to WPP, the greater yP will be at
equilibrium.
2.2 Free Market Solution
Lemma 1. In a system with two regions, A
and B, the free market will lead to a finite
ratio y, where
y=
nA
nB
We assume a better starting-point for the core
region A: it enjoys more economic activity
and better values for its exogenous variables
(5)
Figure 1.
Equilibrium of the free market
2051
FREE MARKET OR SOCIAL OPTIMUM?
(3) The size of α and β P: the larger α is and
the smaller β P is, the higher the value of
the yP ratio at equilibrium.
2.3 The Social Optimum
Lemma 2. There is market failure in the location
of firms under free market conditions.
In other words, the ratio yp does not represent a social optimum when we consider
all of the benefits and costs of the national
economy. We therefore claim that such a
situation may exist
NPVAprivate > NPVBprivate
while
NPVAsocial < NPVBsocial
When a firm locates in a region, it increases
congestion, worsens air pollution and forces
the costs of public infrastructure upward,
among other things. These are external centrifugal forces that are not expressed in the
price mechanism as seen by the private investor. Consequently, the firm does not take
them into account.
We should note that functions PE, PP and
PS are cumulative and indicate the effects
created by all the firms already located in
the region. We assume that all of the positive
agglomeration effects created by the firms
already located in the region are taken into
consideration by any new firm in the process
of determining its location preference between
regions A and B. However, not all the negative externalities created by the firms that are
already located in the region are taken into
consideration by the new firm. Examples of
such negative externalities may be pollution
or congestion that diminish the utility of the
local population.
where, β S represents the social elasticity of
prices relative to the number of firms
β S > β P >1
PS reflects the total cost to the economy
based on the location of firms in a region,
in addition to PP (the cost reflected in the
market prices) that includes the cumulative
cost of externalities. Actually, from a social
point of view, the firm should consider the
full cost to the economy in its location decision, including the costs reflected in market prices such as rent and labour, but also
including the costs of the externalities not
necessarily reflected in the market prices, such
as congestion and pollution. Thus, to achieve
efficiency, the optimal location decision
should be based on PS and not PP.
Equation 4, modified for social scores, is
therefore
ZSA = const An + WPE y α − WPP y β (4a)
S
The addition of social costs (β S > β P) leads
to the result that at any given value of y
ZSA < ZPA, so that the social equilibrium yS is
lower than the private equilibrium yP as can
be seen in Figure 2. In practical terms, this
We define ZSj as the social score of region j. It
is influenced by the social prices PSj
PS j = ( y)β
S
Figure 2. Social equilibrium compared with
free market equilibrium
2052
MIKI MALUL AND RAPHAEL BAR-EL
means that total welfare at the national level
(the aggregation of the two regions) could be
greater if the share of economic activity in the
core region A was less than the one achieved
in free market conditions.
Existence of a significant market failure
is illustrated in Fig. 2: the fact that the free
private market does not assume social costs
leads to an equilibrium that discriminates
against the peripheral region.
2.4 Government Intervention
We assume that the government’s objective
is to direct the economy into an optimal spatial structure in terms of maximising total
welfare (reaching a social optimum). In
fact, the government should reject a strategy
of following the free market and adopt a
more active one where it directs the market
as required by the social optimum (Bar-El
and Benhayoun, 2000; Begg, 2002). The
government wants to achieve the equilibrium yS that results from the function ZSA,
while the market actually operates under
the function of ZPA. As we assume that all
location decisions are only made by private
entrepreneurs in the free market, the policy
measure leading to achievement of optimum
yS with the function ZPA is the introduction
of changes in the parameters of the function.
This can be done in two ways
(1) Changing the relative prices (either
through subsidies granted in region B
or by a tax assessed on locations in
region A, such as a congestion tax).
(2) Changing constj, for example by public
investments in the improvement of infrastructures and labour force quality in
region B.
We keep in mind that yP is a stable equilibrium state and, given the initial conditions,
any movement will immediately lead to
reconvergence to the same point. Therefore,
changing the relative prices will not lead to
a permanent change in the spatial distribution, but rather to a one-time change for
the point in time at which the relative prices
were changed. As soon as the change in relative prices by the government stops, equilibrium will immediately return to yP.
In contrast, if the government adopts a
strategy that changes constj, it will actually induce a permanent and fundamental change
in the equilibrium and bring the economy
to the optimal point, yS. In this case, governmental intervention in the market will not
be required on a regular basis, because it will
have created a permanent competitive advantage for region B, the periphery. This is in
line with the study conducted by Begg (2002),
who found that the local government needs
to subsidise certain projects in areas where it
wants to create economic conditions that will
provide the given region with a competitive
advantage and give the area ‘investability’.
The actual implementation of government
intervention requires further investigation
in another study. Increasing the ‘const’ term is
an oversimplified expression of government
intervention. At least two additional perspectives should be considered. First, government intervention has a cost in terms of
public expense needed for the increase of the
‘const’ term. Such expense may justify an optimum equilibrium level between yP and yS.
Secondly, the extent of government intervention is primarily evaluated as a function
of the values of elasticities α. and β. Higher
levels of α and lower levels of β imply greater
benefits of concentration at lower costs,
therefore decreasing the need for government
intervention.
3. Model Simulation
Before we go into the numeric simulation, we
will draw the lines for a comparative static
analysis in Table 1. All the changes are additive:
a change in one parameter does not induce a
change in the others.
FREE MARKET OR SOCIAL OPTIMUM?
2053
Table 1. Comparative static analysis
Parameter changed
Change of yP
Change of yS
α↑
βP ↑
βS ↑
LF/INF/OTHER ↑
↑
↑
↓
↓
Unchanged
↓
↑
↑
We now carry out a simplified simulation
of the model, based on Israeli data (the core
region of Tel-Aviv being defined as A, and the
peripheral region of the south being defined
as B), to illustrate how it may be implemented.
We first make a rapid estimation of the values
of the parameters of the model and of the
present values of the exogenous variables. In
a second phase, we simulate alternative policy
measures that would lead to a social optimum
and assess their feasibility.
Given the ZP equations (4) and (4a) above
ZPA = const An + WPE y α − WPP y β
ZSA = const An + WPE y α − WPP y β
P
S
and given
const An = WLF LFAn + WINF INFAn
+WOTHEROTHERAn
the simulation can be done after we evaluate
the various weights W, the values of the exogenous variables LF, INF and OTHER and the
parameters α, β P and β S.
In the first phase, we find the gap between
yP and yS at the prevailing conditions. In the
second phase, we evaluate the changes in
the exogenous variables that would lead yP to
be equal to yS.
The values used in the simulation process
for the various parameters are drawn primarily from rough evaluations, based on past
research, excluding the values of the weights
W that were estimated on the basis of a questionnaire (see sub-section). We do not intend
to elaborate any exact evaluations of the
values of the parameters, since our intention
is restricted to illustrate implementation of
the model. To keep the illustration as close as
possible to reality, we decided not to use arbitrary values as examples, but rather to adopt
some of the values that were estimated by
other researchers, in various other contexts.
3.1 Weights W
We use the analytical hierarchy process
(AHP) method (Saaty, 1980) to estimate
the weights of each variable in the location
decision. Using a questionnaire with 50 firms
that recently located in Israel, each firm
owner or manager was asked to estimate the
relative importance of each location variable,
compared with each of the other variables,
on a scale of 1–9. The average results are
presented in Table 2.
For example, the agglomeration advantage was evaluated by the respondents as 1.14
times more important than the level of prices
of production factors in the region, but only
0.58 times as important as the quality of the
regional labour force. The numbers under
the diagonal values of 1 are naturally the inverse values of the respective values above
the diagonal.
The consistency index (see Saaty, 1980) for
this matrix is 0.002375 < 0.1, meaning that
the answers of the participants are consistent (reflect transitivity). The relative weights
according to this method are added to 1 and
are presented in the right-hand column in
Table 2.
3.2 Relative Values of the Exogenous
Variables
We evaluate now the values of the three exogenous variables—labour force quality (LF),
2054
MIKI MALUL AND RAPHAEL BAR-EL
therefore evaluated as 1.221 (the ratio between the two elasticities).
infrastructures (INF) and other (OTHER), in
the core region in relation to the peripheral
region.
Other (OTHER). The last exogenous variable represents mainly the level of accessibility
of the entrepreneur to various services and
the proximity to place of residence. This is
naturally difficult to quantify. We approximated this variable to be 20 per cent greater
in the core region than in the periphery. Its
value is therefore set at 1.20.
Labour force quality (LF). Relative labour
force quality is measured by the distribution
of the population in each region by level of
education, weighted by the hourly income
of the population at each level. The raw data
are presented in Table 3. The quality of the
average worker in the core region is 1.176
times greater than that of the average worker
in the periphery.
3.3 Parameters α, β P and β S
Following the basic assumptions of the
model, the parameters α and β are expected
to be positive, α being less than 1 and β being
more than 1. We assume for these illustration
purposes:
α = 0.7
Infrastructure quality (INF). We use the
estimate found by Bar-El (2001) regarding
infrastructure elasticity between 1983 and
1998, with respect to labour force (in terms
of changes in infrastructure in the region
in relation to changes in labour force). The
elasticity found for the core region is 0.83,
compared with 0.68 in the peripheral region.
The relative advantage of the core region is
β P = 1.2
As for β S, we use the evaluation made by Pines
(1996) for the social costs induced by private
Table 2. Location variable weight and importance relative to the other variables
PE
PP
LF
INF
OTHER
PE
PP
LF
INF
OTHER
Weight
1
0.88
1.71
0.92
1.48
1.14
1
2.11
0.94
1.51
0.58
0.47
1
0.45
0.72
1.08
1.06
2.25
1
1.3
0.68
0.66
1.39
0.77
1
0.167
0.150
0.309
0.151
0.223
Table 3. Labour force distribution and level of income by years of education
Labour force (thousands)
Years of education
0–4
5–8
9–10
11–12
13–15
16+
Core
8.8
58.1
93.2
398.7
292.9
283.5
Source: Israel labour force surveys, 2000.
Periphery
5.4
15.1
29.5
121.2
86.7
58.8
Income per hour
NIS
22
23.6
25.2
31.2
39.6
57.9
FREE MARKET OR SOCIAL OPTIMUM?
investors,in relation to the costs covered in the
free market, and assume therefore that β S is
15 per cent more than β S
β S = 1.38
3.4 Equilibrium at Prevailing Conditions
Solving the equations with the estimated values
of the various weights, exogenous variables
and parameters, we find the following results for equilibrium
y p = 2.36 and y s = 1.98
The value of 2.36 means that the model
predicts a level of economic activity in the
core region that is 2.36 times that in the peripheral region. If we measure this level by the
number of jobs prevailing in each region, we
find that the actual relation is not far from
this number: 2.20. In practice, we can try to
calibrate this model by changing some of the
estimated variables or parameters, until we
reach the right figure. However, since at this
stage we are undertaking these simulations
solely for the sake of illustration and since
the level of economic activity is not defined
by a clear variable, we keep this result without
further elaboration.
The result for yS is naturally less and shows
that, for the achievement of a social optimum,
the gap between economic activity in the core
region and in the periphery should be less
(1.98 times greater in the core region than in
the periphery, instead of 2.36).
3.5 Policy Options
As explained earlier, the intervention of the
government is designed to create exogenous
conditions so that the free market is led to the
social optimum, a ratio of 1.98 in our case.
We test here two main alternative options of
policy measures and a combination of them.
Both are based on changes in the exogenous
variables that are naturally the responsibility
of the public sector: one is the improvement
2055
of infrastructure and the other is the improvement of the quality of labour force. We
focus on these two policy measures that are
generally considered highly important, for
purposes of illustration. Naturally, we do not
pretend that there are no other instruments:
various governments use other measures,
such as capital incentives, transfer payments,
tax regulations, direct public investments
in business ventures and the provision of
municipal services. Each of these measures
could be used for the evaluation of the model,
but we choose to focus our illustration on
measures of infrastructure and labour force
quality improvement.
Policy of infrastructure improvement. Let
us assume that the government tries to solve
the market failure by changing the infrastructure gap between the core and the
southern area. We try to find the infrastructure gap that leads to the optimal ratio (1.98)
under the free market process
ZPA ( y s , INFAr (required)) = ZSB ( y S )
The solution is
INFAr (required) = 0.92
Given that the prevailing infrastructure gap
was evaluated at 1.221, the required measure
is not only to reduce the gap, but also to create
a gap in favour of the periphery. This solution
may not be feasible: according to the National
Long Term Plan (NLTP), the prevailing gaps
between the core and the periphery could
only be decreased by 50 per cent over a period
of 20 years.
Policy of improvement of labour force
quality. Let us assume now that the government tries to solve the market failure
by changing the labour force gap between
the centre and the southern area, to lead
2056
MIKI MALUL AND RAPHAEL BAR-EL
to the optimal ratio under the free market
process
ZPA ( y s , LFAr (required)) = ZSB ( y S )
The solution is
LFAr (required) = 1.03
Given that the gap in labour force quality now
stands at 1.176, it follows that the government
should diminish the infrastructure gap almost
totally. This is also not feasible, especially given
the long-term plans as detailed in the NLTP.
We are aware of the fact that the results may
largely depend on the values of parameters α
and β. We tested the sensitivity of our results
to changes in the values of both parameters
within quite wide ranges: α (0.5–0.9) and β
(1.1–1.5). The results for the LFAr (required)
are between 0.68 and 1.04, and the results
for INFAr (required) are between 0.9 and 1.09,
which means that for all of that range of
values for α and β, the one instrument policy
is not feasible.
Mixed policy of improvement in infrastructure and labour force. We should
keep in mind that, when the government
tries to improve one of the exogenous variables (infrastructure and labour force) in the
southern region, it will face a diminishing
return to scale concurrent with increasing
marginal cost. Therefore, lacking any information about the exact behaviour of these
variables, it seems most reasonable to improve the infrastructure and the labour force
concurrently in the same proportion.
Let us assume that ϕ is the equal rate of
improvement of both parameters
ZPA ( y s , LFAr (required) = (1 + 0.176 * ϕ ),
INFAr (required) = (1 + 0.221 * ϕ )) = ZSB ( y S )
The result is: ϕ = 0.49. In other words, the gap
in infrastructure and labour force should be
reduced by 51 per cent. This solution fits the
one suggested by the NLTP. The gap between
the core region and the peripheral region
would therefore reach 1.09 for labour force
and 1.108 for infrastructure.
4. Conclusion
The location of economic activity has been
widely analysed in the literature and the addition of the core–periphery model by Krugman
and his followers in the new economic geography has contributed significantly to the
understanding of this issue. However, most
of literature on this subject has dealt with free
market considerations, trying to understand
the behaviour of firms, while the social optimum, taking into consideration the costs
and benefits to the nation as a whole, has not
generally been taken into consideration. As
noted in the introduction, there are articles,
such as those by Dohse (1998) and Charlot
et al. (2006), which also refer to the gap that
may occur between the free market equilibrium and the social optimum. Still, the
relationship between the processes that lead
to the social optimum and those that lead to
the private optimum have not been integrated
into one complete model. This is mainly a
result of the fact that many of the elements
that influence the social optimum are not
quantifiable or are not readily identifiable.
The modest contribution of this article is
in the effort to integrate both the free market and the social considerations into one
model. The cost of such an effort is in the
necessity to simplify the model, confining
the analysis to measurable elements of social considerations.
The theoretical simplified model elaborated here shows that free market forces lead
to a stable market equilibrium, where the proportion between economic activity in core
and peripheral regions reaches yP. We have
FREE MARKET OR SOCIAL OPTIMUM?
shown that the optimal equilibrium in social
terms is necessarily lower than the one to
which the free market leads, meaning that
a significant market failure exists in the distribution of firms between regions by the
free market.
The government role in this case is to lead
to the optimal spatial distribution of firms
by using the mechanism of the free market.
The government should lead firms to internalise the additional social cost. Given that the
free market leads to stable equilibrium in
the spatial distribution of firms, government
intervention is needed to change the equilibrium permanently by influencing the regional constants. Instead of the government
subsidising specific projects in a manner
that cannot change the equilibrium unless
the subsidy is permanent, it needs to create a
competitive advantage for the periphery and
thus achieve the social optimum (new stable
equilibrium) through the mechanism of the
free market.
The simulation exercise performed here
illustrates the implementation of this model
for the case of Israel. It also permits evaluation
of the feasibility of a policy of government
intervention into one of the exogenous policy
variables. In the case of Israel, it is shown that
the government cannot solve the regional
market failure by concentrating on policy
instruments and that a combined action for
the improvement of both infrastructure and
quality of labour force is required.
This article focused on the question of free
market versus social optimum, for the sake of
simplification leaving many issues still open
for further investigation and inclusion in the
model. Some of the most acute questions to
be solved are briefly suggested here.
One relates to the behavioural functions.
They are all presented in this model in an
extremely simplified manner and they may
require more detailed elaboration. As an
example, the function describing the influence of the agglomeration economies may
2057
be oversimplified. It is not clear if, in the peripheral region, agglomeration economies are
already in effect in the first steps of economic
growth, or only after a certain stage has been
reached. A more elaborated function would
therefore be needed.
Another factor that should be considered
and added to complement this model is the
element of labour mobility between regions.
The hidden (and unrealistic) assumption in
our model so far is a lack of labour mobility.
It would seem that reducing the cost of mobility between regions might in certain cases
widen the gap between the centre and the
periphery and increase the market failure.
At the same time, however, it may reduce
inequality in the distribution of income between the regions by allowing for a broader
employment market for the labour force in
the periphery. The reduction in mobility
cost, if done concurrently with changes of the
regional constants may, on the other hand,
increase the attraction of economic activity
to the periphery.
Another important factor needed to complement this model, as mentioned, is the cost
of government intervention. Governmental
intervention, even if it resolves the market
failure, is not necessarily worthwhile as long
as it is subject to cost–benefit considerations.
It seems that adding public cost–benefit
considerations would lead to a lower gap
between market and social optimum.
Acknowledgement
The authors wish to thank Walter Isard, of Cornell
University, for his helpful comments.
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