GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.199

Cost Efficiency and Scale Economies of Japanese Water Utilities

Theara Horn and Hitoshi Saito

May 2011

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Cost Efficiency and Scale Economies of Japanese Water Utilities
Theara Horn†

Hitoshi Saito§
Abstract

With the data of 831 Japanese water utilities from 1999 to 2008, we used the stochastic cost
frontier analysis with a true fixed-effect model in order to estimate the cost efficiency andscale economies. We found that cost inefficiency was approximately 37%. The economies
of water delivery volume were observed and found to be remarkably higher for small water
utilities than for large ones. Scale economies were also discovered in small water utilities;
however, scale diseconomies are likely to be incurred in larger water utilities. The optimal
supply population size of a water utility is estimated to be 85,658 consumers, with a water
delivery volume of 15.7 million m3 and a network length of 522 km.
Keywords: Cost Efficiency, Scale Economies, Optimal Size, Japanese Water Utilities
JEL: H11, L38, L95

The authors wish to thank Professor Nobuo Akai for his useful comments and suggestions. Theara

Horn gratefully acknowledges financial aid from Japanese Society for the Promotion of Science
Research Fellowships for Young Scientists.
†

Corresponding author, Osaka University, Graduate School of Economics, 1–7 Machikaneyama,

Toyonaka, Osaka, 560–0043, Japan; E-mail: hge016ht@mail2.econ.osaka-u.ac.jp§

Graduate School of Economics, Osaka University, 1–7, Machikaneyama, Toyonaka, Osaka 560–

0043, Japan; E-mail: jgp010sh@mail2.econ.osaka-u.ac.jp1

Cost Efficiency and Scale Economies of Japanese Water Utilities
1- Introduction
Several countries have adopted the characteristics of successful water utilities topromote performance efficiency, such as imposing incentive-enhancing regulations (e.g. aprice cap in the UK), merging together to form larger water utilities (e.g. the case of Dutch
water utilities), and permitting the private sector to participate in operating water supply
services (e.g. the case of French water utilities).
In Japan, water utilities are operating their services at the municipal level, and most ofthem are public entities, similar to French water utilities. However, their service operations
are independent from each other, and private participation remains low; therefore, it isdifficult to exploit private sector know-how. Unlike Japanese water utilities, French water
utilities operate their services by outsourcing a part of their operations to a few large private
water companies.

Since the operations are outsourced to only a few large privatecompanies, the water utilities are likely to operate their service on a large scale, as they canmake use of the know-how and experience of the contracted private companies.
With the recent municipal consolidation, the number of Japanese water utilities has
decreased gradually, although there were approximately 1,300 Japanese utilities still
operating in 2008 and approximately 65% of them provide water services to less than
50,000 consumers. As compared to some other countries, this number is rather high; forexample, there are only 21 firms in the UK and 10 in the Netherlands operating watersupply utilities.

Given that water services consist of various operations (e.g. water2

withdrawal from its source, water purification, water delivery, fee collection, andmaintenance), the operating costs in large-scale water utilities seem to be lower than insmall-scale utilities, considering the possible cost saving from scale economies. The higher
cost in small-scale water utilities is likely to be caused by their lower rate of capitalutilization or higher labour force requirements. An example of higher capital investment insmall water utilities is the load factor (the ratio of average water use to peak-time water
consumption).

Given a lower supply population, the deviation of peak-time water

consumption from the average in small-scale water utilities is likely to be higher than thatin large-scale water utilities.

Therefore, the load factor in small-scale water utilities

appears to be smaller than that in large-scale water utilities. This leads to a low facility
utilization rate in small-scale water utilities.
However, it is not always true that a larger utility is better. When water utilities becomelarger, it is possible that their service areas also expand. Water utilities have to bear somecosts, such as costs on facilities and water transmission pipeline, if a large number ofsupply customers do not reside in a specific part of their supply area. As shown in Figure 1,
such a region shows an inverted U-shaped relationship between facility utilization rate andtransmission pipeline’s effectiveness with respect to the supply population size. Moreover,Figure 2 a also indicates an U-shaped variation of total cost and annual employee number
and an inverted U-shaped variation of the load factor with respect to population size,
implying that there is an optimal water utility size for a specific water supply population.
This study aims to estimate the cost efficiency and scale economies of Japanese water
utilities by using data from 831 water utilities from 1999 to 2008 in order to estimate the3stochastic cost frontier with a true fixed-effect model. From the results, we also attempt toestimate the optimal size of the supply population in order to minimize cost.
No general conclusion has been drawn regarding the scale economies of Japanese water
utilities. Different results have been obtained previously, depending on the estimation
sample or method. Kuwahara (1998) used a translog cost function in order to estimate 154
water utilities supplying water to 50,000300,000 consumers, and the results showedeconomies of scale in their performance. A similar result was also found in Takada andShigeno’s (1998) study, who used the pooled data of 75 water utilities for the period 1981–
1995 in order to estimate the translog cost function by incorporating network length
expansion as another output. In contrast, Mizutani and Uragami (2001) used the crosssectional data of 112 water utilities in 1994 in order to estimate the log-linear and translog
functions and diseconomies of scale (i.e. the economy of scale is between 0.85 and 0.96).
They also estimated that the optimal size to minimize the average cost is approximately
766,000 consumers.
With respect to cost efficiency, there are some controversial points that need to becontrolled for, especially, certain characteristics that water utilities may have and that arelikely to affect the efficiency scores. In order to deal with this, several indicators have beenused in previous studies, such as quality index (Saal and Parker 2001, Saal et al. 2007),service quality (Lin 2005), and water purification (Horn 2011). However, with stochastic
frontier analysis using a true fixed-effect model, originally introduced by Greene (2005),
the effects of time-invariant heterogeneity of water utilities can be separated from theefficiency score. Using this method, Filippini, Hrovatin, and Zoric (2008) estimated the4cost efficiency of 52 Slovenian water distribution utilities during the 1997–2003 and foundthat the model is likely to perform better than conventional panel data models.
This study combines the two points, estimations of the scale economies and cost
efficiencies, with the newly proposed true fixed-effect models for the case study ofJapanese water utilities. There are also two different points from previous studies.
First, for estimating scale efficiencies, we use more recent and broader panel data ofJapanese water utilities from 1999 to 2008, whereas Mizutani and Uragami (2001) usedcross-sectional data of 1994. The panel dataset would give more information than crosssectional data since the variation through time of estimation is also considered. Second, asa method to estimate cost efficiency, we use stochastic cost frontier analysis with a true
fixed-effect model, originally proposed by Greene (2005). The merit of this method is thatit separates the effects of time-invariant heterogeneity of water utilities from the efficiency
score.

The effects of heterogeneity can be owing to location characteristics (flat or

mountainous area), availability of water source, raw water quality, etc. In the conventional
panel method, estimators assume that the cost inefficiency is time invariant; withconventional methods, therefore, heterogeneity, in addition to inefficiency, is possibly
captured in the efficiency measure. To the best of our knowledge, a true fixed-effectfrontier analysis has not been applied in previous studies to estimate cost efficiency inJapanese water utilities.
We find that the average cost inefficiency is more than 37%. Our results also show thatwater utilities enjoy increasing returns to water delivery volume. However, the effects are5likely to be higher in smaller utilities than in larger ones. Moreover, scale economies arealso found in small water utilities, whereas scale diseconomies are likely to be incurred inlarge water utilities. We also found that the optimal size of water utilities is 85,658
consumers for a water delivery quantity of 15.7 million m3 and a network length of 522 km.
This result has the following implication for a water policy: merging water utilities into alarger scale is not always suitable. Water utilities should be of an optimal size.
2- Methodology and Model Specification
In order to estimate the cost efficiencies and scale economies, this study uses stochastic
cost frontier analysis methodology. The cost used is the total cost (C), which is the sum oflabour costs, capital costs, and other material costs. The cost function comprises water
delivery volume (Q), network characteristics (N), labour price (PL), capital price (PK), andother control variables such as network density (NetDen) and time trend (T). Owing to thedifficulty in defining the prices of the other materials, which consist of a variety of items,
we assume that their prices are constant during the estimation period. Thus, the stochastic
cost function can be defined as follows:
Cit  C (Qit , Nit , PLit , PK it , NetDen, T ,  ) exp( uit  vit )The cost function can be transformed into logarithmic form and can be expressed infollowing manner:ln Cit   i  C ( Qit , N it , PLit , PK it , NetDen, T ,  )  uit  vit ,(1)

where vit is the noise term, which is assumed to be in normal distribution vit ~ N (0, u2 ) . The
notation uit is the non-negative cost inefficiency term. It is the distance from the observed

6cost to the minimum cost on the cost frontier. In this study, it is assumed to be in truncatednormal distribution1 uit ~ N (, u2 ) . The term  i denotes time-invariant fixed effect, and  isthe vector of the slope parameter.
The cost inefficiency score can be estimated as the ratio of observed cost Cit to frontieror minimum cost CF:

Inefficien cyit Cit exp(uit )
CitF

(2)

The cost inefficiency score can be measured on the basis of some conventional models.
However, owing to the ability to distinguish between unobserved time-invariant firmspecific heterogeneity and cost inefficiency, this paper uses a true fixed-effect model,
which was originally introduced by Green (2005), in order to calculate the cost inefficiency.
Separating the effect of firm-specific heterogeneity is likely to make the evaluation moreaccurate since, in water utilities’ performance, different characteristics, such as locationfrom the water source and quality of water, are difficult to control for in the evaluation
process owing to lack of information and data.
As the cost function can be specified in several forms, this study estimates two different
cost functions: first is the log-linear cost function, and second is the translog cost function,
as shown in equations (3) and (4), respectively.

However, because the translog costfunction is more flexible, we use it as the basic model for estimating cost efficiency andscale economies.

1

The term, distribution of inefficiency, can be assumed in other commonly used
distributions, such as half-normal, exponential, or gamma.
7Model 1: Log-linear cost function:
ln

Cit
PL
  i  Q ln Qit   N ln Nit   PL ln it   Net NetDen   T T  uit  vit (3)
PK it
PK it

Model 2: Translog cost function:
ln

Cit
PL
1
  i   Q ln Qit   N ln N it   PL ln it   Q ,Q ln Qit ln Qit 
PK it
PK it 2
PLPL
1
 N , N ln N it ln N it   Q , N ln Qit ln N it   PL , PL ln it ln it 2
PK it PK it  PL ,Q ln

(4)

PLit
PL
ln Qit   PL , N ln it ln N it   NetDen NetDen   T T  uit  vit
PK it
PK it

In addition to cost efficiency, we also estimate the output density and economies ofscale. The output density determines how the cost reacts to the increase in output Q byholding the network characteristics fixed. It can be calculated through E OD, as shown inequation (5). If EOD is more than 1, it indicates the existence of the economy of output
density, implying that the average cost decreases when the output increases. Moreover, theeconomies of scale measure the reaction of cost to the proportional increases of output Q
and network characteristics (N). It can be calculated through ES, as shown in equation (6).
If ES is more than 1, it indicates the existence of economies of scale, and if it is less than 1,
it indicates the existence of diseconomies of scale. Table 1 summarizes the calculations of
output density and economies of scale that are available from our estimation models.
Measurement of output density:  ln C EOD    ln Q 

1

(5)

8

Measurement of economies of scale:ES    ln C   ln C   ln Q  ln N 

1

(6)

3- Data Description
Most water utilities in Japan are under the public authority of towns, cities, prefectures,and cooperatives. Following the municipal consolidation in recent years, the number ofJapanese water utilities gradually decreased to approximately 1,300 in 2008. Out of these,
this study uses the observations of 831 utilities from 1999 to 2008 for the estimation,
excluding those of the cooperatives and other utilities that merged during the 1999–2008
period. The reason for this is that it is difficult to determine their cost structures, sincecooperatives operate their services in conjunction with the other utilities.

Moreover,complete data of the merged utilities for the entire 10-year period is not available forcreating a balanced panel. Total cost (TC) is the sum of the costs of capital, labour, andother materials and price of labour (PL) is the annual basic salary of an employee. The
price of capital (PK) is the capital cost divided by the length of transmission pipe extension,
which is a proxy of the capital stock. Output (Q) is the annual volume of water delivery,
and network (N) characteristics represent the annual length of the transmission pipe
extension. Besides the basic variables for cost function, we also control for other variables
that may influence cost, such as network density and time trend. Network density is theratio of transmission pipe length to supply population. Supply population refers to the total9

customers of each water utility. All data are available in the annual Yearbook of Local
Public Enterprises (Chiho koeh kigyo nenkan in Japanese). Table 2 presents the descriptive
statistics.

4- Estimating Results
The estimations were made using the stochastic cost function with a true fixed-effectmodel1. The cost function is in both log-linear form (Model 1) and translog form (Model 2).
Table 3 presents the results.
Initially, we obtain the statistically significant and positive effects of output coefficientsin both models, which hold the non-decreasing characteristics of output in cost function.
This is consistent with economic theory.

Subsequently, in Model 2, although thecoefficient of squared N is not significant, we determine that the coefficient of squared Q is
positive and significant, indicating that cost is a convex function of Q. Moreover, theslopes of labour price (PL) are positive and statistically significant for both models,
whereas the slope of the squared labour price is negative and significant in Model 2. Thisis consistent with the theoretical characteristic of a cost function that is non-decreasing anda concave function of the factor’s price. Network density, which is the ratio of network
length to number of consumers, is negative. This implies an increase in the cost of
supplying water for water utilities that supply water with short pipeline networks to a large
number of consumers.
1

This is likely to negate any possible cost saving on water

LIMDEP 9.0 Software is used for the estimation.

10

distribution. However, as argued by Torres and Morrison (2006), this may occur because,
although short pipelines may save distribution cost, more cost is possibly required for
multiple complex connections, pressure, or maintenance problems.

The time trend isnegative and significant, which means that the cost decreases over a period of time, forexample, through progress in technology.
Table 4 reports the descriptive statistics of cost inefficiency. We found that the average
cost inefficiencies for both models are almost equal: 40.4% for Model 1 and 37.9% forModel 2. These percentages are twice of those obtained by Nakayama (2007), that is,approximately 20%. Nakayama (2007) used the panel data for water utilities in Shiga,
Kyoto, and Osaka from 1991 to 2003 in order to estimate the Cobb-Douglas cost function
with some alternative conventional panel models, but without a true fixed-effect model. By
using a true fixed-effect model, this study gives a different inefficiency score because theeffects of heterogeneity of water utilities on the efficiency score are controlled. From theestimation result, we find that there is more room to improve the cost efficiency score byintroducing proper incentive-enhancing schemes.
Table 5 reports the average output density and scale economies. The output density
for both models are considerably high, that is, approximately 5.3, which means that for agiven network length, an increase of water delivery quantity can substantially reduce theaverage cost. In addition, when the water delivery volume increases, it is likely that the
network length also needs to be increased; the cost reaction to these proportional increases
can result in scale economies. The scale economies are slightly less than 1 (i.e. 0.99) for
Model 1 and more than 1 (i.e. 1.03) for Model 2, showing that, on an average, it is likely
11that the phenomenon of constant returns to scale is exploited. However, based on Figures 3
and 4, which represent the relationships of network length and water delivery volume withscale economies, we observe that scale economies decrease with network length (N) andwater delivery quantity (Q). A scale economy value of more than 1 covers a large share ofwater utilities (see Table 6), mostly in small utilities. This value turns out to be less than 1
after the size of N and Q crosses a specific threshold.
The threshold is the point that turns economies of scale to diseconomies of scale (i.e.
the point where scale economies become 1), and, theoretically, this is the optimal size forminimizing average cost. Thus, the optimal size of N and Q can also be determined at thethreshold. From the estimated parameters, we can calculate the scale economies for eachwater utility. We average the values of Q and N of the utilities whose scale economies
equal 1. We find that the optimum size to minimize cost is at the point where Q equals
15,718 thousand m3 and N equals 522 km. However, in practice, the water delivery
quantity and network length are difficult to adjust because they may mostly relate toconsumer water usage or density, rather than to management of water utilities.
Nevertheless, water utilities can adjust the supply population, for example, through utility
consolidation or fragmentation1. Thus, from the optimal N and Q, we estimate the optimal
population size in order to minimize the average cost with equation (7). Equation (7) is a1

In order to find the optimal size of the supply population, the number of consumers should be
included in estimation models, as was done in Torres and Morrison (2006) or Filippini, Hrovatin,
and Zoric (2008). However, due to the high correlation between water delivery volume andpopulation size, this study does not include population size in the estimation models.

12panel regression with a fixed-effect model, which determines the relationship of N and Q
with supply population size (POP).
lnPOP =

3.64
(0.0392)+ 0.26 lnN+ 0.63 lnQ(0.0044)(0.0058)(7)
Overall R2 = 0.96

We found that the optimal size of supply population is 85,658 consumers.

This isapproximately 9 times lower than the finding of Mizutani and Uragami (2001); according
to them, the optimal size was approximately 766,000 persons. However, because Mizutani
and Uragami (2001) used cross-sectional data of only 112 water utilities, our finding gives
a new optimal size based on a new, broader, and longer dataset. Moreover, we found that
our results are consistent with those of Filippini, Hrovatin, and Zoric (2008) for the case of
Slovenian water utilities, in terms of scale economies and optimal supply population size.
Owing to the similarity between Japanese and Slovenian water utilities’ performance (i.e.
public entity in form of natural monopoly), we found the following two common points forboth the case studies: increasing return to scale in small-scale water utilities and optimal
size for water utilities. From these results, we can intuitively say that public water utilities
should merge and become an appropriate size, rather than being too small or too big.
However, the problem is the manner in which the optimal size must be determined, sincefor water utilities, optimal size can be related to some factors such as geographicalcharacteristics and socio-economic status of water users. Moreover, although the optimal
size can be determined by the manager, it may be difficult to reach this optimal size without
a proper incentive scheme.

135- Conclusion
Most Japanese water utilities are public entities and operate at the municipal level,
independent from each other and in the form of a natural monopoly. There is a remarkable
price gap among these utilities. This gap results not only from the different characteristicsof the area but also, possibly, from performance efficiency. Moreover, the size of most of
the water utilities remains small.
This study used the panel data of 831 Japanese water utilities for the period between
1999 and 2008 in order to estimate the cost efficiency and scale economies with log-linear
and translog cost functions. By using stochastic cost frontier analysis with a true fixedeffect model, we separated the effects of heterogeneity of water utilities from the efficiency
score, as argued in some previous studies.
The results showed that the average cost inefficiency is rather high, that is,approximately 37%. Thus, it is crucial to have an incentive scheme for reducing cost andimproving performance in the future. Moreover, small utilities are found to have higher
output densities and scale economies than large ones. We also found that an optimal water
utility is one with approximately 85,658 consumers, an annual delivery volume of
approximately 15,718 thousand m3, and a network length of approximately 522 km. Since
most water utilities are still smaller than this optimal size, consolidation to create larger
water utilities must be encouraged.

14

References
Filippini M., N. Hrovatin and J. Zoric (2008), “Cost Efficiency of Slovenian Water
Distribution Utilities: an application of stochastic frontier methods,” Journal of
Productivity Analysis, Vol.29, p.169-182
Greene, William (2005), “Reconsidering Heterogeneity in Panel Data Estimators of the
Stochastic Frontier Model,” Journal of Econometrics, Vol. 126, p.269–303
Horn, Theara (2011) “Incorporating water purification in efficiency
evaluation: evidence from Japanese water utilities,” Applied Economics Letters,
forthcoming, DOI: 10.1080/13504851.2011.564119
Kuwahara H. (1998) “Industrial Organization of Water Utilities: The Estimation of
Economies of Scale and Efficiency,” Journal of public utility economics, Vol.50 (1),45-54 (in Japanese)
Lin, Chen (2005), “Service quality and prospects for benchmarking: Evidence fromthe Peru water sector,” Utilities Policy, Vol. 13, pp.230-239
Ministry of internal affairs and communications, Yearbook of local public enterprises,
Tokyo: Institute of local finance. CD-ROM 2000-2008
Mizutani F., and T. Urakami (2001), “Identifying network density and scale economies forJapanese water supply organizations” Papers in Regional Science, Vol.50 (2),p.211-230.
Nakayama N. (2007) “Cost Efficiency and Economies of Scale in Japanese Water Utilities:
stochastic frontier analysis with panel data” presented paper at 44th meeting ofJapan Section of the Regional Science Association, Kyushu University, October 8th,15

2007 (in Japanese)
http://jsrsai.envr.tsukuba.ac.jp/Annual_Meeting/M44/resume_c/rC07-1_nakayama.pdf
Saal D.S. and D. Parker (2001), “ Productivity and price performance in the Privatized
Water and Sewerage Companies of England and Wales,” Journal of Regulatory
Economics, Vol 20(1), p.61-90
Saal, D. S.; D. Parker and T. G. Weyman-Jones (2007), “Determining the Contribution ofTechnical Change, Efficiency Change and Scale Change to Productivity Growth in
the Privatized English and Welsh Water and Sewerage Industry: 1985 2000”,
Journal of Productivity Analysis,Vol.28, p.127-139.
Takada S., and R. Shigeno (1998), “Economies of scale and density in water utilities,”
Journal of public utility economics, Vol.50 (2), p.37-44 (in Japanese)
Torres, M. and P. C.J. Morrison (2006), “Driving forces for consolidation or fragmentationof the US water utility industry: a cost function approach with endogenous output,”
Journal of Urban Economics. Vol. 59(1), p.104–120

16

Table 1: Measurement of Output Density and Scale Economies
Model

Output Density

Log-linear

1 Q

Translog

1

Scale Economies

1 ( Q   N )  Q   Q ,Q (ln Q)   PL ,Q (ln PL )   Q , N ln N 

1







  Q   Q ,Q (ln Q)   PL ,Q (ln PL )   Q , N ln N    N   N , N (ln N )   PL , N (ln PL )   Q , N ln Q 

Table 2: Descriptive Statistics
Variable
TC
Q
N
PK
PL
NetDenPop

Definition

Mean

Standard
Deviation
5.483
31,813.1

Minimum

Maximum

Total cost (109 yen)
Water delivery volume(103 m3)
Transmission pipe length
extension (103 m)
Capital price (yen/m3)
Labour price (103 yen)
Network density(m/person)
Supply population(person)

1.883
11,852.3
8
416.2

0.025
75

89.8
528,833

680.6

12.1

9,197.4

1,804.1
4,586.7
7.9

1,088.3
3,228.1
4.9

98.6
145.1
1.01

23,107.6
58,57267.2

88,452

230,2431,600

3,684,645

17

Table 3: Estimating Results of Stochastic Cost Functions
Coefficient

Model 1Model 2

Q

0.186***(0.004)0.817***(0.009)0.201***(0.002)0.183***(0.024)

N
 PL
 Q,Q

0.645***(0.038)0.776***(0.021)0.017*(0.009)0.020(0.015)-0.006(0.012)-0.118***(0.004)-0.123***(0.004)0.115***(0.006)

 N ,N Q, N PL, PL PL,Q PL, N

-0.003***(0.0005)-0.001**(0.0006)-0.007***(0.0006)  ( u2   v2 )1/ 2

2.63***(0.027)

2.47***(0.026)  u v

26.93***(1.666)

Observation number

8310

 NetDenT-0.002***(0.0006)

26.34***(1.904)8310

Note: Standard errors are shown in parentheses. ***, **, and * denote p-values at significancelevels of 1%, 5%, and 10%, respectively

18

Table 4: Descriptive Statistics of Cost Inefficiency
MeanStandard Deviation

Minimum

Maximum

Model 1

1.404

0.163

1.192

4.051

Model 2

1.379

0.160

1.172

6.479

Table 5: Average Output Density and Scale Economies
Model 1Model 2

Output density

5.37

5.42

Scale economies

0.99

1.03

Table 6: Summary of Scale Economies
Number of Utilities(%)

Increasing returns to scale

6,573(79.0%)

Constant returns to scale754(9.0%)

Decreasing returns to scale

983(11.8%)

19

Figure 1: Variation of facility utilization rate and percentage of transmission pipe
utilization’s effectiveness (sample: 831 water utilities, year 1999-2008)
70
60
Facility Utilization Rate (%)
Percentage of transmission pipe utilization's effectiveness (%)

50
40
30
20
10
0
15<

15-30

30-50

50-100100-150 150-300 300-1000 >1000

Supply Population Size (thousands)

Figure 2: Variation of number of employees, load factor, and total cost with respect tothe supply population size (sample: 831 water utilities, year 19992008)
Load Factor ; Employee
Cost per 1m3 of supply water (yen)
100
250
90
80
200
70
Employee ( person/ 10 million m3)
60
150
Load
Factor(%)
50
Cost per 1m3 of supply water (yen)
40
100
30
20
50
10
0
0
15<
15-30
30-50 50-100 100-150 150-300 300-1000 >1000

Supply Population Size (thousands)

20Figure 3: Relationship between network characteristics and scale economies

Economies of Scale
1.2

1.1

1

0.9
0

500

1000

1500

2000

2500

3000

3500

Network Length (km)Figure 4: Relationship between water delivery volume and scale economies

Economies of Scale
1.2

1.1

1

0.9
0

20

40

60

Water Delivery Volume (million m3)

21

80

100