Location decision-making of economic agents and social welfare for sustainable regional
economy
Daisuke Nakamura
Department of International Liberal Arts
Fukuoka Women’s University
Abstract: This paper investigates the relationship between regional economic growth and its
surrounding attractiveness of the local society.
can be measured by regional welfare level.
The attractiveness of the local society which
The analysis examines three types of economic
agent; namely, households, firms on basic industries, and firms on non-basic industries. First,
households are assumed to maximize their utilities and their location decision-making would
depend on the regional welfare level.
This part treats households not only as consumers of
final goods and services but also as labors and community members. Hence, their constraints
include time, space, and quality of work and of life in addition to budget constraint. Second,
firms on basic industries maximize their profit and they can choose locations of head office,
research unit, factories, and so on according to the availability of advantageous factors on
revenue and cost for their activity.
These are relevant to the economies of agglomeration
which are spatially constrained internal and external economies of scale, scope, and complexity.
Finally, firms on non-basic industries maximize their profit under the term of regional planning
policy based partly on the demand of the local community. An integrated framework shows
that there are some missing links to optimize regional system by combining maximization
objectives of each economic agent.
The investigation particularly indicates the role of local
authority, which connects each segment in a systematic way.
Keywords: household economics, welfare, firm location, agglomeration economies, selfsustaining regional growth
JEL classifications: D62, I31, O18, Q51, R11
Location decision-making of economic agents and social welfare for sustainable regional
economy
Daisuke Nakamura
Department of International Liberal Arts
Fukuoka Women’s University
Overview
The primary objective of this paper is to reveal the relationship between regional economic
growth and its surrounding attractiveness of the local society.
Regional economic growth is
closely related to the extent of export-base industries within the region (Tibout, 1956a;
Parr,1973; Mulligan and Vias, 1996).
In addition, local population is also an important factor.
Tibout (1956b) revealed that households choose their location where sufficient public services
are available. Public services are part of attractiveness of the region. The attractiveness of
region also includes society atmosphere such as better safety, security, and community
coordination, and non-human based factors such as beautiful scenery, clean air, water, and other
natural environmental elements (See Glaeser et al. (2001), Nakamura (2013; 2014)).
Hence,
it is important to explore surrounding attractiveness of the local society which can be measured
by regional welfare level.
Regional welfare is related to welfare economic which can return
to Pigou (1932), Hicks (1939) and other early studies.
As addressed by Arrow (1950) and his
followers, there are unavoidable problems to handle with welfare in economics (Arrow and
Scitovsky, 1969).
Availability of regional attractiveness varies with the type of region which
the type can be measured by hierarchical central place system.
The hierarchical central-place
system is a part of central place theory that is systematically investigated by Lösch (1944
[1954]).
Within the framework of central place theory, there is a problem called spatial
consumer exclusion.
Spatial consumer exclusion is a situation which consumers exist who
face difficulty to obtain goods and services due to the insufficient accessibility to the market
(Nakamura, 2010).
Such accessibility can be achieved under the condition where sufficient
population is present such as at the metropolitan area.
In location economies, metropolitan
areas are characterized as available places of urbanization economies.
economies are the economies of agglomeration.
Urbanization
These economies have other elements such
as localization economies, urbanization economies, and activity-complex economies (see
Weber (1909 [1928]), Marshall (1892), Hoover (1937), Isard (1956), Parr (2002; 2015), and
Nakamura (2015)). Externality can be divided into two parts according to the investigation
by Meade (1952) and Scitovsky (1954) which are pecuniary and technological types of
economies.
Location model
First, households maximize their utilities, which depend on market price and quantity of
consumption of various goods and services.
Here, additional elements exist such as qualities
of air, water, safety, security, community atmosphere, and so on. These elements are named
as regional welfare.
Households’ location decision-making would depend on the regional
welfare level.
U  U  x1 ,, xn ; z1 ,, zm 
max
(1)
As denoted in Equation (1), a representative household maximize his utility U which depends
on the quantity of consumption of n types goods and services.
represents m types of factor of regional welfare.
life.
In addition, z1 ,..., zm
Regional welfare can be a part of quality of
Households not only as consumers of final goods and services but also as labors and
community members -- Hence, their constraints include additional burden such as communityactivity time, commuting time and patience, accessibility for goods and services, space to live
and sleep (floor space, common area, etc) as well as typical budget constraint.
These elements
are expressed as the symbol  in equation (2). This also indicates the office atmosphere and
the extent of job match for each individual.
n
s.t. B   pi xi 
(2)
i 1
Second, firms on basic industries maximize their profit, and they can choose locations
of head office, research unit, factories, and so on according to the availability of advantageous
factors on revenue and cost for their activity.
 j  p j y j  wL L j  wK K j  
max
s.t.
(3)
y j  f L j , K j ,  
(4)
Hence, the notion of agglomeration economies is explicitly argued in the model framework as
shown symbols  and  in equations (3) and (4).
In equation (3), a representative firm
j’s profit  j is composed by market price p j , quantity supplied y j , unit wage wL , unit
price of capital wK , quantity of labor input L j , quantity of capital input K j , and pecuniary
externality  .
In equation (4), another symbol  represents technological term of
externality.
Finally, firms on non-basic industries also maximize their profit but under the term of
regional planning based on the demand of the local community.
max
s.t.
 k  pk y k  wk L  wk K  r
(5)
y k  f Lk , K k , r 
(6)
Here, the notion of agglomeration economies is included as the case of basic industries but they
do not relocate to other regions, since non-basic industries are engaged their activity within the
region.
If agglomeration economies are weaker to cover this firm’s profit, they do not
continue to supply goods and services.
In that case, regional goods and services are
substituted by interregional or international products.
The additional expression r in equations
(5) and (6) shows that the impact of changes in externality on firm’s profit is not stronger than
the case of basic industries.
The next concern should be given to examine the maximization of incentive of nonbasic industries to contribute to self-sustaining regional growth, since the solid availability of
goods and services within the region can be directly linked with self-sustaining regional growth.
Now the paper investigates how such firms continue to supply goods and services within the
region by means of consumer and producer surpluses.
for a particular product is illustrated in Fig. 1.
Regional aggregate consumer surplus
Regional aggregate value is the sum of all
individual consumer surplus of this particular product within the region.
In the figure,
potential regional demand and supply curves of this product meet at E * where price is p *
and quantity traded is X * .
If a firm on non-basic industries does not sufficiently supply
product to the region and it supply curve S ' stops at the quantity supplied X ' , the market
equilibrium is achieve at E ' where price increases up to the level p ' . On the open economy,
the gap between X * and X ' can be filled by import from other regions.
However, price
would not recover due to the presence of transportation costs, and the price may be fixed
somewhere between p * and p ' i.e., at p '' .
To sum up, consumer aggregate regional
consumer surplus of this product decreases from the triangle area aE * p* to aE '' p '' . If the
region is isolated from other regions, consumer surplus becomes much smaller as the triangle
area aE ' p ' .
Similarly, producer surplus also decreases from the triangle area bE * p* to the
area bHFp '' on the open economy and bHE ' p ' on the closed economy.
categorize region types according to central-place theory.
It is possible to
For reasons of simplicity, three
representative types are considered; namely, high, medium, and low hierarchically-ordered
level regions.
First, high hierarchically-ordered level regions have sufficient population and
the point E * is achieved.
Fig. 1 Regional aggregate consumer surplus
Second, medium hierarchically-ordered level regions may have the case E * if they have
sufficient population or E '' if insufficient.
Since their hierarchical level is intermediate,
interregional connectivity should be well established and no situation of E '' can be observed.
By contrast, low hierarchically-ordered level regions could cause the situation of the point E '
if the region is closed economy or E '' if the region is an open economy.
Hence, the problem
of self-sustaining regional growth should be more severe at this type of region.
Low hierarchically-ordered level regions face more serious situations of selfsustaining regional growth, and now the paper indicates spatial policy which may vary with
regional attributes. First, the primary concern should be given to accessibility of goods and
services.
There are two types of spatial policy which are external to the firm but internal to
the industry.
One is to expand external dimension of agglomeration economies.
In equation
(5) the symbol  shows the availability of regional pecuniary externality as well as the
symbol  as regional technological externality in equation (6).
If local authorities manage
to coordinate regional agglomeration economies, both indicators  and  or a parameter r
increase.
For instance, firms engage their production under risk and uncertainty.
In labor
market, if information of labor improves, firms receive merits to save searching time, cost, and
mismatched human resources.
These normally are available on localization economies which
are external to the firm and internal to the industry, but regional agglomeration economies,
which are external to the firm and industry but internal to the region, are also available.
Another is to reduce the price p '' in Fig. 1 which includes transportation costs to import the
product from other regions.
As spatial policy, this is feasible by means of the improvement of
interregional accessibility.
More development on interregional accessibility reduces
transportation costs to obtain goods and services.
down towards the level p * in Fig. 1.
spatial policies with each other.
Lower transportation costs push the price
It is now necessary to compare and contrast the above
The arrangement of regional agglomeration economies
expands regional job market which implies that more people increase the level of B that
encourages much higher utility.
For firms on base industries, both indicators  and 
include, therefore, regional tax revenue would increase by this development.
economic agents within the region achieve mutual growth.
Hence, whole
The arrangement of interregional
accessibility has the reduction effect of pi in equation (2) which should be the same direction
to improve individual’s utility in equation (1).
For firms on base industries, costs for regional
export decline which can reflect by increase of the value y j in equation (3) as transportation
costs are implicitly included in this specific variable in addition to indicators  and  as
highly-advanced network of transportation if the connectivity between interregional and
regional transportation systems are well-organized.
Remaining issues are cost and benefit balances to arrange these systems.
A simple
examination can be presented within the framework of this analysis reviewing Fig. 1 again.
Firms on non-basic industries which face the supply curve S ' have producer surplus bHFp ''
on the open economy and bHE ' p ' on the closed economy.
The better arrangement of
interregional transportation network increases the distance between p ' and p '' which
reduces profit of firms on non-basic industries, while consumer surplus increases.
Hence, it
may be better to maximize the opportunity of expansion on  ,  , and r which maximizes
both aggregate regional consumer and producer surpluses.
However, if some firms on non-
basic industries are not possible to keep positive profit after these developments, it is necessary
to organize minimal sufficient interregional accessibility.
Here, minimal means that
maximum is unfeasible unless there is no cost to develop these facilities.
The measurement
should be done by observing price elasticities of demand and supply for locally unavailable
goods and services, but be noted that types of goods and services (i.e., essential or luxury type),
are different from the impact analysis on price elasticities of demand and supply.
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