Hierarchical central place system and agglomeration economies on households

Daisuke Nakamura, Department of International Liberal Arts, Fukuoka Women’s University

Executive summary
Central place theory shows that the shortage of distribution of goods and services in rural areas can besubstituted from upper hierarchically-ordered central places. However, this paper demonstrates thatspatial consumer exclusion may exist if transportation network is not well organized. Besides, income
level varies among households in general. Under these circumstances, the importance of agglomeration
economies in rural areas has been revealed even though these sizes are small. While these economies
may be replaced by the well-organized infrastructure on interregional transportation, it is observed that thereplacement should be done for specific goods and services. Those goods and services are namely luxury
types rather than normal types, since spatial consumer exclusion on essential goods and services are much
more problematic. However, rural areas may be difficult to satisfy above criteria, and the argument would
be concluded by suggesting mixed strategic policy regarding the availability of goods and services throughboth regional and interregional access under the minimum sufficient transportation system by utilizing thebenefit of agglomeration in a small unit at the lower hierarchically-ordered region.
1 Introduction
An overview- Spatial economics: producer and consumer surpluses vary among different regions- Higher hierarchically-ordered regions: Sufficient attractiveness to both producers and households –urbanization economies- Lower hierarchically-ordered regions: Disadvantages on them due to physically limited conditions;more concretely, limited scale, scope, and complexity- Hierarchical regional structure in central place theory: Lösch (1944 [1954]) in terms of market areas --How final goods are distributed across an economic space
Scale, scope, and complexity: Agglomeration economies, if these are spatially-constrained internal andexternal economies (Parr, 2002)
Problems: Central places or higher hierarchically-ordered regions typically remark severe spatialcongestions or urbanization diseconomies
Mulligan (2013): The future of rural areas or non-metropolitan areas -- there are regions which
continue to prosper and which continue to decline
Solutions: Spread population and economic activity across the county or country involving rural-regions
Rural areas have several limitations to achieve sufficient regional development unless lower-----hierarchically-ordered regions or rural areas own enough attractiveness on both producers andhouseholds
Such attractiveness can be typically referred to tax competition and other pecuniary policies, althoughthese tend to be more difficult under the background which the budget constraint on local governments
become more tightly limited in many cases
Attractiveness of region: Quality of life or amenity attainment
Importance of quality of life or amenity: Empirically demonstrated by various relevant series ofliterature (Rickman and Rickman, 2011; Olson and Munroe, 2012; Rodriguez-Pose and Ketterer,
2012; Brown and Scott, 2012; Desmet and Rossi-Hansberg, 2013)
How to increase attractiveness forces in lower hierarchically-ordered regions without relying on tax
competition and other pecuniary policies
Optimal scale, scope, and complexity of regional economic activity but not to specify these maximum
levelsc.f., Data envelope analysis by Suzuki et al. (2012) and Takeguchi and Suzuki (2012)
Spatial policy on sustainable regional growth across a country applying the framework of hierarchicalcentral place theory and a part of household economics
Central place theory: a shortage of distribution of goods and services in rural areas can be substituted
from upper hierarchically-ordered central places
However, spatial consumer exclusion may remain if transportation network is not well-organizedSpatial consumer exclusion (Nakamura, 2010): A situation where there are consumers who are notable to obtain some goods and services because of the presence of excess transportation costs together
with the profit maximization behavior of the firm; Income level varies among households in general
Mulligan (1991): Accessibility to goods and services in terms of equality
Nakamura (2014): Equity and social capital

Main focus of the paper- Trade-off between agglomeration economies on households and interregional transportation--

Compare and contrast the primary difference between different types of goods and services -- Possibly
related to the law of economic growth stage in national and regional level (Rostow, 1956 and Parr,2001); Mulligan (2010): Interindustry linkages of the employment in rural areas
Total surplus to evaluate the impact of transportation costs on the trade of goods and services in thespatial market
Spatial consumer exclusion and quality of life or well-being on local households
A mixed strategic regional policy on the availability of goods and services through both regional andinterregional access under the minimum sufficient transportation system
Forecasting regional economy by applications of Israilevich et al. (1997) and Sonis and Hewings(2003)

2 Location model- Simple location model: Regional economic agents are producers, households, and local governments- A region: Has producers whose primary locations are either at other regions or at that region, has local
residents who are consumers and also labors, and has the local government- A representative firm: Maximizes his profit under his given production function- A representative household: Maximizes her utility under her given budget constraint- The local government: Maximizes social welfare at that region- Two different types of region: Urban and rural areas- Local government solely pursues social welfare maximization at that region applying their part of---budget; Accessibility to goods and services may be kept at a minimum sufficient level, and actual
welfare depends on the optimal size of the market and scope as well as the optimal size of economic
activity
Conventional central place theory: Optimal structure of the market can be always found applying thehierarchical structure, even though there are a number of restrictions in economic activity; Namely, ashortage of goods and services would be supplied from upper hierarchical central places
However, the socially optimal hierarchically central place system works only if transportation network
is well-organized -- Otherwise, spatial consumer exclusion may occur, in particular, a situation whereincome level widely varies among local households
Transportation costs: closely related to market access or accessibility
Accessibility on households may affect the level of consumer surplus; Fig. 1

Fig. 1 Producer and consumer surpluses-In spatial term, further necessary to employ the notion of transportation costs
Producer and consumer surpluses at region r: Fig. 2
where s (s > 0) = unit transportation cost, and    0 = transportation cost burden to the firm
which does not charge from households

Fig. 2 Producer and consumer surpluses at region k-Better accessibility improves total surplus
Accessibility is related to a part of infrastructure development on transportation by the local
government
Two types of transportation network: Regional and interregional segments
Regional transportation: Internal element to the region
Interregional transportation: External element to the region: longer distance than regional segment ingeneral-3 Hypothetical analysis- What kind of goods and services needs to be locally available applying the notion of regional andinterregional transportation costs- Two types of goods and services: Essential and luxury types- Spatial consumer exclusion on essential goods and services are much more problematic- Unless interregional transportation network is perfectly organized, these types of goods and services
always have to be locally distributed- Regional and interregional transportation are sustainable as long as enough demand exists- Problems may occur more frequently in rural areas where local population and economic activity
constantly decline
Effect of agglomeration economies to the local economic activity
An agglomeration of the market in a rural area may not only increase sales revenue on producers butalso save regional transportation costs on households-  p  t  1  B: Consumer goes to the shopping to obtain one commodity per trip m t j  / m  Bpjj 1
 j 1 : Consumer goes to the shopping to obtain several items per trip

mj 1jjm m j 1  m  p  t 1   p    t  / m   mj 1-jj

where p j

 j 1jj: Extent of cost-saving opportunity by an agglomeration p  0  j  1,, m = mill price of commodity j , tjtransportation cost of commodity j , and Bj

t  0 = unitjM  0 = budget constraint

4 An extension- Sustainable regional growth and environmental concern: minimization behavior of energy-consumption -- community-level central place system
Safety and security concern: accessibility to vital commodities; visible qualities of goods and services
Possibility of mixed strategy on distribution of goods and services: an increase of Firms should set their market areas not only at the higher hierarchically-ordered regions but also atrural central places

5 Further avenues- Regional and interregional transportation system as private arrangement or public sector -Environmental concern: public transportation preferred -- Utilize efficient facilities on transportation-Specification of the type of local industry whether these are raw-material oriented or market oriented;
also important to forecast the change of industrial type in the long run
Forecasting: i.e., regional econometric input-output model, originally investigated by Israilevich et al.
(1997); Connection between input-output analysis and central place theory by Sonis and Hewings(2003)

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