There are two types of regional development elements those are namely economic and social terms. While both developing and developed countries initially need to establish regional economic infrastructure, the next concern should be given to the social infrastructure. In local regions, the presence of sufficient social infrastructure may hold the number of populations which is the essential condition for a self-sustained regional structure system. In this paper, a consideration is given to the roles played by public sector for coordinating wider-regional sharing of the social infrastructure element. The analysis reveals the fundamental relationship between the wider-regional sharing and the economies of scale. The outcome also addresses potential issues on consumer accessibility by the integration of economic activity among different neighbour regions.

Daisuke Nakamura

English

Research Papers in Economics

1 
 
The structure of wider-regional sharing of the social infrastructure element
1 
 
Daisuke Nakamura   
The International Centre for the Study of East Asian Development, Kitakyushu (ICSEAD),   
11-4 Otemachi, Kokurakita, Kitakyushu, 803-0814, Japan, +81 93 583 6202, fax +81 93 
583 4202   
 
Email: nakamura@icsead.or.jp 
 
Abstract    There  are  two  types  of  regional  development  elements  those  are  namely 
economic and social terms.    While both developed and developing countries initially need 
to establish regional economic infrastructure, the next concern should be given to the social 
infrastructure.    In  local  areas,  the  presence  of  sufficient  social  infrastructure  may  hold 
regional population which is the essential condition for a self-sustained regional economic 
system.    In this paper, a consideration is given to the roles played by public sector for 
coordinating  wider-regional  sharing  of  the  social  infrastructure  element.    The  analysis 
limits the scope to reveal the fundamental relationship between the wider-regional sharing 
and the economies of scale.    The outcome also addresses potential issues on consumer 
accessibility by the integration of economic activity among different neighbour regions.   
 
JEL Classification: D62, H71, O18, R58 
Key  Words:  Regional  infrastructure  development,  economies  of  scale;  self-sustained 
regional policy   
 
1 INTRODUCTION 
For regional development policy, there are two types of infrastructure elements and these 
                                                   
1  This paper is presented at the 51th European Congress of the Regional Science Association International 
(ERSA) at Barcelona, Spain in August 2011. The preliminary research has been conducted under the ICSEAD 
Research Project 2011/12.     2 
 
are namely economic and social infrastructure elements (Nakamura, 2011).    The former is 
directly  related  to  productions  or  producers,  while  the  latter  can  be  relevant  to 
consumptions or households.    As investigated by Rostow (1956), economic growth in a 
country has several stages of development.    During the process of economic growth, the 
principal  objective  of  the  central  government  is  to  coordinate  economic  infrastructure 
development  across  the  nation.    When  the  economic  development  reaches  at  a  mature 
stage, the impact of effects in economic infrastructure investment on the national economic 
growth gradually declines.     
  Also, the heavy consideration to the economic infrastructure brings an insufficient 
social infrastructure development.    An enhancement of the social infrastructure element 
can  be  mandatory  for  sustainable  regional  economy,  since  this  type  of  infrastructure 
development directly reflects the convenience of living within that region.    Such elements 
include, for instance, availabilities of better educational, medical, cultural and landscape 
attainments.    Without these arrangements, local consumers as residents would prefer to 
move away from that region in the long run.    The decay of local population may cause 
centrifugal force of the regional economic activity through insufficient opportunities of the 
economies of scale.    As revealed by Glaeser et al. (2001), it is important not only to be 
convenient for the producer but also to be attractive for households for sustainable regional 
development  and  growth.    The  latter  case  is  referred  to  consumption  amenities  which 
include lower transportation costs in cities according to their investigations.     
  The main purpose of this paper is to examine a situation where local population 
level  is  not  enough  to  maintain  the  economies  of  scale  with  respect  to  the  social 3 
 
infrastructure element.    The outcome shows that interregional cooperative behaviour may 
be able to solve such problems.    In the following section, a hypothetical spatial model is 
built within the framework of central-place theory.    A case study is then given to the case 
of  population  declining  developed  countries,  and  finally,  policy  implication  is  provided 
with the description of the  limitation of  scope of the analysis  in terms of the trade-off 
interaction between efficiency and equity in spatial terms.     
 
2 THE MODEL 
Three  types  of  economic  agents  are  considered  in  this  analysis;  namely,  producers, 
households  and  public  sectors.    First,  producers  engage  processes  of  goods  or  provide 
services which are consumed within the region.    Secondly, households consume regional 
goods and services as well as supply labour force to the local producer.    Finally, public 
sectors provide necessary services which are not available within the market mechanism.   
The principal objective of the region is assumed to sustain the long-run regional economic 
development and growth.     
As  revealed  by  Nakamura  (2011),  the  elements  of  economic  and  social 
infrastructure are respectively related to producers and households within a region.    Also, 
these are arranged by public sectors whenever it is necessary as illustrated in Fig. 1.     
 
 
Fig. 1 Economic and social infrastructure elements with public sectors 4 
 
 
The economic and social infrastructure elements need to be invested in a well-balanced 
proportion  so  that the  much  securer  long-run  sustainable  regional  economy  is  attained.   
However, social infrastructure element tends to be unable to absorb costs in small-scale 
regions due to insufficient economies of scale.    The situation is illustrated in Fig. 2 where 
a representative region has a population  level at  N .    Here, the constant cost level  C  
exceeds the revenue curve  R .     
 
 
Fig. 2 Social infrastructure and the economies of scale 
 
A small size of the region implies that there is no huge distance to the neighbour regions.   
If the same situation is faced at these neighbour regions, it may be possible to establish a 
sharable social infrastructure element in a single region within that area.     
  The  shared  behaviour  can  utilize  the  economies  of  scale  as  expressed  in  the 
following equations.     
   
b n
C R n
C R 

  1 max                 (1) 5 
 
  s.t.  0  TrC m                 (2) 
where  R = revenue,  C = cost,  n= the number of regions,  b   1 0  b   = the extent of 
economies  of  scale,  m=  constraint  and  TrC=  interregional  transportation  costs.    The 
equations imply that regional revenue increases as the wider-regional cooperation works 
through  the  improvement  of  the  economies  of  scale.    As  the  index  b   increases,  the 
economies of scale approach to the optimal level.     
  However,  there  is  also  a  trade-off  relationship  between  the  wider-regional 
cooperation and the interregional accessibility.    This can be referred to the conventional 
location  theory  term  in  Weber  (1909  [1928])  as  the  trade-off  interaction  between 
agglomeration  economies  and  transportation  costs.    Isard  (1956:  176-182)  explained  a 
negotiation  behaviour  between  three  neighbour  producers  to  agglomerate  in  a  single 
location  using  the  critical  isodapanes  methods.    If  the  negotiation  is  for  social 
infrastructure  elements,  the  subject  is  replaced  by  the  regional  government  instead  of 
representative private firms.     
 
3 HYPOTHERICAL ANALYSIS 
There is a little concern to the interregional economic growth on the discussion of public 
policy.    This may be caused by the reason that each region is assumed to provide sufficient 
services such as public libraries, higher-education facilities and advanced medical centres.   
However, such arrangement cannot be fully-utilized in local regions, while the core region 
owns various highly-qualified services.    One of the main differences between the core and 
local regions is the density of demand.    There are two ways for enhancing local regions; 6 
 
namely,  either  normalising  national  population  distribution  or  forming  wider-regional 
cooperative  structures.    In  this  paper,  the  focus  is  solely  limited  to  the  wider-regional 
cooperative perspective for sustainable regional economic growth, and a concern is given to 
specify the required elements to achieve such alternative interregional structures.     
  Applying  the  fundamental  model  framework  that  is  provided  in  the  previous 
section, the following square spatial configuration is considered in Fig. 3.     
 
 
Fig. 3 Independent regional management 
 
This situation reflects the left-hand side of equation (1) where 9 regions own individual 
social infrastructure element and each region faces diseconomies of scale due to insufficient 
intraregional demand level.    The alternative situation as the right-hand side of the equation 
can be illustrated in Fig. 4.     
 
 
Fig. 4 An integrated centre 7 
 
 
  The single-centre form provides sufficient economies of scale and the index  b  
may  be  closer  to  1.    However,  this  configuration  also needs  an  improvement  of 
interregional accessibility improvement as stated by expression (2).    The dashed lines in 
the  figure  imply  that  interregional  transportation  network  is  enhanced  in  order  to  ease 
access to the central region from different neighbour regions.     
 
4 POLICY IMPLICATIONS 
In  the  previous  sections,  the  social  infrastructure  development  as  a  wider-regional 
coordination is examined in terms of economies of scale and interregional accessibility.    It 
can  be  particularly  important  to  consider  the  wider-regional  social  infrastructure 
coordination  for  developed  nations  those  which  observe  constant  national  population 
declines with aging  issues.    If the national population decrease  is predicted, the spatial 
integration  of  economic  activities  may  be  unavoidable  to  consider  for  efficiency  and 
cost-reduction  purposes.    However,  there  is  a  potential  issue  with  respect  to  equity  in 
spatial economy.     
  It can be argued that the improvement of interregional transportation network may 
solve the problem of accessibility  for  integrated services.    However, there should  be  a 
certain number of consumers those who have difficulty to travel long distance.    If a clinic 
is only located at the central region as a result of efficiency evaluation, older people those 
who live at non-central regions have to attempt frequent day-return trip to the central region 
for  the  convenience  of  consumers.    Under  such  circumstance,  the  clinic  should  situate 8 
 
every region.    By contrast, if a large concert hall is constructed in every small region, it 
may be unrealistic to sustain under the condition where the economies of scale do not work 
enough.     
  While conventional central-place theory, particularly market-area analysis, solely 
takes into account of mill price, distance and the demand conditions, the structure of market 
area also varies depend on the bulkiness of travel.    Since market-area analysis uses f.o.b. 
transportation costs as a measurement of distance, transportation costs should be put certain 
weight  of  bulkiness.    Hence,  the  conventional  expression  of  f.o.b.  price    t t p f     in 
Lösch (1944 [1954]: 107) should be replaced by    tk t p f   .    Here,  p = mill price,  t = 
transportation cost,  k     1 0   k = bulkiness of transportation.     
 
5 AN EXTENSION 
The bulkiness of interregional transportation has discussed in the precious section.    The 
related examination was attempted by Nakamura (2010) as the term of spatial consumer 
exclusion.    In order to reduce spatial  consumer exclusion with  sustaining efficiency of 
operation  in social  infrastructure elements, it can be suggested to employ the notion of 
hierarchical spatial structure in the central-place system.    Namely, the following scenario 
may  be  considered.    There  are  two types  of  group of  goods  and  services;  normal  and 
luxury goods and services.    First, normal goods and services are such as supermarket, day 
care service, clinic, general hospital, community centre and park.    Others may be a large 
concert hall, specialized medical centre, international museum, science park and airport, 
which are categorized as the luxury goods and services.     9 
 
  This partition enables the spatial configuration to form two layer systems.    For 
normal goods and services, an arrangement of lower-central hierarchy is required in order 
to maintain space-filling community-based structures.    For luxury goods and services, by 
contrast,  the  central  integrated  system  can  be  preferred  to  organize  for  the  purpose  of 
regional sustainability enhancing interregional coordination and cooperation.    In this way, 
two-layer system  may  increase the efficiency  as well  as reduce the  inequity to provide 
goods and services in local areas.     
 
6 CONCLUDING COMMENTS 
This  paper  has  examined  an  alternative  spatial  formation  for  the  sustainable  regional 
economic sustainability in local small-scale areas, examining the following three criteria.   
First,  social  infrastructure  elements  as  mandatory  facilities  for  local  population 
sustainability need to be shared among several different neighbour regions, if each region 
has  insufficient  economies  of  scale  in  population  term.    Secondly,  there  is  a  trade-off 
relationship between the wider-regional cooperation and the interregional accessibility as 
an  interpretation  of  agglomeration  economies  and  transportation  costs.    Finally,  an 
efficient spatial rearrangement may cause spatial consumer exclusion due to the necessity 
of  additional  interregional  access.    Under  these  situations,  two-layer  structure  of  the 
central-place system is considered as an extensional discussion.    While these are beyond 
the  scope  of  this  paper,  it  should  be  left  as  further  avenues  of  research  to  solve 
social-welfare issues in spatial terms.     
 10 
 
References   
 
Glaeser,  E.  L.,  Kolko,  J.,  and  Saiz,  A.  (2001)  “Consumer  city”,  Journal  of  Economic 
Geography, 1:27-50 
 
Isard, W. (1956) Location and Space-Economy, M.I.T. Press, Cambridge, Massachusetts 
 
Lösch, A. (1944 [1954]) Die raümliche Ordnung der Wirtschaft, Jena, Germany: Fischer, 
1944 (2
nd edn). English translation by W. H. Woglom and W. F. Stolper, The Economics of 
Location, Yale University Press, New Haven 
 
Nakamura,  D.  (2010)  “Spatial  competition  and  consumer  exclusion:  social  welfare 
perspectives  in  central-place  system”,  Letters  in  Spatial  and  Resource  Sciences,  3/3: 
101-110 
 
Nakamura,  D.  (2011)  “Sustainable  issues  of  economic  growth  in  developed  countries: 
regional  infrastructure  and  social  welfare”,  Conference  Proceedings  of  the  50
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Meeting of Western Regional Science Association 
 
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Consumer city”,

The structure of wider-regional sharing of the social infrastructure element

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