Development Strategy for San-En-Nanshin Region in Japan-A Simplified Spatial Computable General Equilibrium Modeling Approach Ha Thi Thu Trang
Department of Environmental and Life Science Engineering, Toyohashi University of Technology
Yuzuru MIYATA
Department of Architecture and Civil Engineering, Toyohashi University of Technology
1. Introduction
A large scale San-En-Nanshin Expressway with 100 kilometers length starts from Iida city in Nagano Prefecture, runs through
Aichi Prefecture and ends at Hamamatsu city of Shizuoka Prefecture. This Expressway is taken into the National Comprehensive Development Plan of the Japanese Government under Regional Revitalization Project. It is expected that with the completion of the Expressway, San-En-Nanshin Region’s economy and living convenience will significantly be improved. In order tomaximize the economic benefit of the expressway, it is necessary to measure the investment scale in approximation with benefit
returns and interregional benefit returns. Therefore, in this research, first, we present a simplified spatial model of San-En-Nanshin
region and try to measure the economic impacts of San-En-Nanshin Expressway by applying the shortcut method developed in
the transportation economics. And then some recommendations for increasing the benefit are discussed in the concluding remarks.
2. Firms Behavior
This part explains the outline of the model for measuring the economic impact of San-En-Nanshin Expressway. There are nzones in the study region and the number of population is denoted by N. This model considers an aggregated single industry forsimplicity. A representative firm in zone s is defined for one worker, and aims at profit maximization.

max π s ≡ py s − tc s

tc s ≡ p cs pc s +(1)subject to pc s z s 
y s ≡ min ,  a0 a1 

(2)

σF


 rs    p + pTF µ TF  t   PTF rs z s ss 
r =1   t  


n

∑

(3)

n
 s s  s sp cs ≡  p va
va +  pTP + w
t sr PTPB sr δ b  z TP
 / pc
r =1

 


∑

[

]

p vas ≡ w ⋅ ld s + r ⋅ kd s + hFs ⋅ ad s / va s( ) (kd ) (ad )va s ≡ η 3 ld s

βl

s βk

s βa

(4)

( ) (z )pc s ≡ η 2 va s

(5)
(7)

PTF rs ≡

α

s 1−α
TP

(6)

[

rs
− (t rs / t ss ) σ F + 100
ξ TF

]

σs

∑ ξ [− (t / t )σ + 100]
n

rs
TF

rs

ss

F

(8)
σs

r =1

Where, πs: firm’s profit in zone s; p: price of commodity; ys: firm’s output in zone s; tcs: firm’s production cost in zone s; pcs:
firm’s production capacity in zone s; a0: firm’s production capacity rate; zs: intermediate input of commodity i in zone s; a1: intermediate input coefficient; pcs: price of production capacity; pTF: price of commodity transport service; µTFi: input of unit commodity transport service associate with input of commodity i; trs: time distance between zone r and zone s; PTFirs: probability of inputting zone r ’s commodity i in zone s; pvs: price of value added in zone s; vas: value added in zone s; pTP: passenger transport price;
w: wage rate; PTPBsr: choice probability of passenger transport destination r by a firm in zone s; δb: number of business trips per-1-

unit passenger transport service; zTPs: input of passenger transport service in zone s; η2, η3 and ξTFrs: parameters; lds: labor input inzone s; kds: capital input in zone s; ads: land input in zone s; βl, βk and βa: elasticity parameter ( βl + βk + βa = 1 ); σS, σF, and α: elasticity parameters
Solving this minimization problem, the conditional inputs of labor, capital and land associated with the value added vascan beobtained as follows:
βl

βl

βa

βk

1 β l  w   r   hFs sld =      va
η3 w  β l   β k   β a 
s

β

βk

βa

1 β k  w   r   hFs skd =      va
η3 r  β l   β k   β a 
s

(19)

(20)

βa

β

l
k
1 β a  w   r   hFs sad =  va
η3 hFs  β l   β k   β a 

s

(21)

Price index of value added pvas is obtained as follows:
βl

p

s
va

βk

1  w   r   hFs = η 3  β l   β k   β a 

βa

(22)

From the above, we can obtain the minimized cost tcsassociated with the firm’s output ysdetermining its profit.
3. Firms’ Location Choice Behavior
Each firm determines its location choice probability to maximize the following expected weighted profit based on the profit
which would be gained in each zone.
nmax SF ≡ ∑ PF rξ Fr π r −
r =1

1

n

∑ PF ln PF
θ
r

r

(23)

F r =1nsubject to ∑ PF r = 1

(24)

r =1

where, SF: firm’s expected profit with weight obtained by location choice; PFr: probability of choosing zone r; ξFr: weight for
firm’s profit in zone r; πr: firm’s profit which would be obtained in zone r; θj: Logit parameter
Solving this optimization problem, firm’s location choice probability for zone r and the maximum expected profit with weight isobtained as follows:
PF r =

exp θ F ξ Fr π r
n

∑

ξ π

exp θ F Fs

(25)

SF =

s

1

θF

n

ln

∑ exp θ ξ π
r
F F

r

(26)

r =1

s =1

4. Households Behavior
Each household is assumed to behave to maximize its utility function of the current consumption, future consumption, and land
under the budget constraint. The utility maximization is then specified as follows:
max u (G rs , H rs , a Hrs ) ≡ G rsα G H rsα G a Hrsα a(27)

subject to p Gr G rs + p Hr H rs + hHr a Hrs = w(T − n rs t rs ) + r ⋅ ks rs(28)

where, u : household utility function; Grs : current consumption by a household residing in zone r and working in zone s; Hrs :future consumption by a household residing in zone r and working in zone s; aHrs : land consumption by a household residing inzone r and working in zone s; αG, αH and αa : elasticity parameter ( αG + αH + αa = 1 ); pGr : price of current consumption in zoner; pHr: price of future consumption in zone r; hHr : residential land rent in zone r; w : wage rate; T : total available time endowed bya household; nrs : number of commuting trips from zone r to zone s; trs : commuting time between zone r and zone s; r : capital
return rate; ksrs : capital stock endowed by a household working in zone r working in zone s
Solving this utility maximization problem, we obtain the following demand functions:-2-

rs rsp Grrs

H rs =

(29)

αH
p Hr

[w(T − n t ) + r ⋅ ks ]
rs rs

(30)

rs

[w(T − n t ) + r ⋅ ks ]αaa Hrs =

[w(T − n t ) + r ⋅ ks ]αGG rs =

rs rs

hHr

(31)

rs

We further solve these three equations (29) to (31) hierarchically, and then we can know details of the household utility maximization behavior.
5. Households Residential Location Choice Behavior
The choice probability of household’s residential location in zone r and working in zone s can be derived from the following
maximization problem for the expected utility function with weight.
nn
1 n
subject to ∑ PH rs = 1(40)
max SH s ≡ ∑ PH rs ξ Hrs v rs − s ∑ PH rs ln PH rs (39)
θ H r =1r =1
r =1where, SHs: expected utility from choosing a residential place of a household working in zone s; PHrs: probability of residing inzone r of a household who works in zone s; ξHjrs: weight corresponding to indirect utility value in a household working in zone s
and residing in zone r; vrs: indirect utility value in a household working in zone s and residing in zone r; θHs: Logit parameter
Solving this optimization problem, household probability of residing in zone r and working in zone s is obtained as in equation(41) and the household maximum expected utility value with weight for working in zone s and residing in zone r is calculated as
equation (42):PH =exp θ Hs ξ Hrs v rs

rs

SH s =(41)n∑ exp θ ξ v

s ks ks
H H

1

θ

s
H

n

ln

∑ exp θ ξ v
s
H

(42)

rs rs
H

r =1

k =1

The number of firms in zone s, that is, the number of employees is expressed by E s = m E s . Thus N rs ≡

∑

j

j =1

PHrsEs expresses not only the number of households working zone s and residing in zone r, but also the number of commutingntrips. The number of households in zone r is expressed as N r = ∑ N rs
s =1

6. Behavior of Absentee Land Owner
The absentee land owner in zone s provides differentially the land for business use ASFs and residential use ASHs. The amount ofabsentee land owner’s services is assumed to be expressed as hFs·ASFs + hHs·ASHs by using the initial land rents by zone. The absentee land owner obtains its income from land rent earned in the entire study region, and consumes goods produced in the study
region.
7. Market Equilibrium Conditions
Market equilibrium conditions in the model are summarized as follows:
Commodity market
Supply of commodities in the entire study region = Demand for commodities in the entire study region(43)
Labor market
n

n

n

 n

n

 s =1k =1∑ ∑ T ⋅ N − ∑  ∑ ∑ t PTPF
rs

r =1

−

s =1

r =1

n

n

s =1

r =1

rk

 n
 n
rs
δ f 
xTP
N rs   −   s =1
  r =1

rsk 

∑

n

∑∑x N
rs
TP

s =1

rs

(44)

n

∑ ∑ δ t N = ∑ n ld
rs

rs

r

r

C

r =1

Capital marketnnn∑ ∑ ks N = ∑ n kd
rs

r=

s =1

rs

r

(45)

r

r =1

Land market for business use and Land market for residential use-3-

AS Fr = ad r E r(46)( r = 1,L, n)

AS Hr =

n

∑a N
rs
H

rs

(47)

(r = 1, L , n)s =1

According to the model, the volume of traffic distribution by business objective, private objective, and commuting objective canbe determined when (generalized) transport cost is given. Moreover adding a traffic assignment model to the current one, we canobtain simultaneous equilibrium of traffic, economy and location.
8. Economic Benefit of San-En-Nanshin Expressway(1) Shortcut Method
In this research, we tried to measure economic benefit of San-En-Nanshin Expressway by estimating parameters of above presented model. However, because of sensitive changes of location choice probability, the benefit estimation was not highly plausible. Thus, the shortcut method was adopted to estimate the economic benefit. Shortcut method is quite complicated, so here we
only explain the results of this method for page constraint.
When the transportation sector sets price equals to the marginal cost, transportation economic benefit is obtained as below:∑ EV = ∫A→ Be Ω (−D3 dq3 + D3 dp3 − NdI ) = ∫A→ BeΩ ( −D3 p 5 dt 3 − NdI )(48)

Where, A and B: indices before and after transportation investment; Integration : Integration of the change between the states before and after transportation investment; EV : equivalent variation.; D3 : transport demand function; w3 : wage rate; N : the number of regional population; I : transportation investment cost
From the formula (48), the economic benefit is obtained by subtracting transportation investment cost from the money
valuation of travel time saving due to wage rate. Study employs this formula to measure the economic benefit of San-EnNanshin Expressway.
(2) Study Region and Time benefit after San-En-Nanshin Expressway
The total length of San-En-Nanshin Expressway is 100 km with 4 lanes for motor vehicles. This expressway is expected to create a large transportation network beyond prefectural boundary in San-En-Nanshin region. Figure 3 illustrates a current situationof interregional commuting persons. Following these, we can see that the passenger intraregional flows in each zone are naturally
high. One can observe that the interregional commuting persons in Toyohashi city are much more extensive than in Hamamatsu
city.
Thousands pe ople
3000
Hamamatsu =>Hamamatsu

Toyohashi=>Toyohashi

2500

2000

1500

1000

Toyohashi=>Kosai

500
Chita peninsula
Mito

Nanshin
Maisaka
ShitaraTaharaToyokawa
AsukeWest Nagoya

TenryuHosoe
Horai
Toyohashi
MitoToyotaHamakita
MikabiTsukudeKozakai
Gamagouri
HekinanNanshinNanshinHamamatsu

Kosai

Hosoe

TaharaMikabiTsukudeMito

Ichinomiya

HekinanAtsumiOkazakiWest Nagoya

0

Hamamatsu
Inasa
Shinshiro
Ichinomiya
NukadaChita peninsula

Yutou
Kosai
Atsumi
Otawa
OkazakiNagoya area

Figure 3. Intercity Commuting Persons Distribution in San-En-Nanshin Region-4-Particularly, commuting person trips between Toyohashi and other sub-zones such as Nanshin region, Hamamatsu, Kosai, Shinshiro, Toyokawa, Gamagori and Toyota are quite higher than others left. In case of Nanshin region, there are a lot of commuting
persons departed from Nanshin, but terminating at this region is quite low.
Figure 4 shows the difference in travel time (by minutes) before and after San-En-Nanshin Expressway. Because of the existenceof Chuo Expressway, San-En-Nanshin Expressway gives little impact on West Aichi prefecture. However, impact of this new
Expressway on Inasa, Hamamatsu and Tenryu is quite large. Although it takes a little long time to travel from Toyohashi to Inasa,
economic benefit at certain level is still expected due to large transportation demand between Toyohashi and Nanshin region.
Minutes140

Inasa=>Nanshin

120

Tenryu =>Nanshin

100

Tsukude=>Nanshin
80

Atsumi=>Nanshin
60
40
20
ya
go
Na
st
We
e
uk
wa
As
ka
yo
To
ra
ha
Ta

Hamakita
Inasa
AtsumiToyokawa
Toyota

Na
ns
hi
n

Ma
is
ak
a

Sh
it
ar
a

Ta
ha
ra

As
uk
e

We
st

To
yo
ka
wa

TenryuMikabi
Shinshiro
Otawa
Asuke

a
ak
is
Ma
n
hi
ns
Na

Nanshin
Hosoe
TsukudeIchinomiya
OkazakiWest Nagoya

a
ar
it
Sh

Na
go
ya

0

Hamamatsu
Kosai
TaharaMito
Hekinan

Yutou
ShitaraToyohashi
Gamagouri
Chita peninsula

Figure 5. Time Difference after San-En-Nanshin Expressway

Maisaka
Horai
Kozakai
NukadaNagoya area

Figure 4. Distance in Time after San-En-Nanshin Expressway(4) Cost benefit Analysis after San-En-Nanshin Expressway
Economic benefit of San-En-Nanshin Expressway is calculated based on formula (48) called shortcut method as mentioned
above. When the shift in transportation demand is so small and the transportation demand function in inelastic as in Figure 7,
general equilibrium consumer’s surplus = decreasing in general transportation cost × current transportation demand. Withassumption of inelastic transportation demand, the total annual time benefit (in commuting persons) is estimated as 24.4 billion
yen.

Figure 7. Economic Impact with a Small Indirect Impact andInelastic Transportation Demand Function
Next, the total project cost of San-En-Nanshin Expressway will be examined from the viewpoint of annual cost. Here we assume
that the duration term of San-En-Nanshin Expressway is 50 years, the total project cost is estimated as 500 billion yen or 1 trillion-5-yen, and the social discount rate is 4% according to the manual of cost-benefit analysis issued by Ministry of National Land andTransportation, the Japan’s Government. Then the annual project cost of each case is calculated as follows:
annual project cost = 500 billion ×

annual project cost = 1 trillion ×

0.04 ⋅ (1 + 0.04)50= 23.3 billion yen(1 + 0.04)50 − 1

0.04 ⋅ (1 + 0.04)50= 46.6 billion yen(1 + 0.04)50 − 1

Thus if the annual benefit is under 23.3 billion yen, it means that the efficiency of the expressway investment will be questionable. According to above data of commodity flow and commuting person flow, we can see that the demand for San-En-Nanshin
Expressway is not so large. If the project cost is about 500 billion yen, the construction of San-En-Nanshin Expressway passes
the cost benefit criteria. In the case of the project cost over 500 billion yen, passing the cost-benefit criteria seem to be difficult.
9. Concluding Remarks
In this article, we have developed a spatial computable general equilibrium model to measure the economic impacts of San-EnNanshin Expressway. Combining this model and the short cut method for the evaluation of economic benefit of a transportation
project under the general equilibrium framework, we estimated economic benefit and the annual construction cost of San-EnNanshin Expressway.
The total annual benefit is estimated as 24.4 billion yen, and it has been clarified that the construction of the expressway can pass
the cost benefit criteria or not, depending on the scale of project cost. Besides, we also measured total benefit and benefits by zone
as well. The results obtained in this study could be the first attempt among researches about San-En-Nanshin Expressway in Japan. The induced demand caused by shortened time after road improvement and the development demand due to a change offirms’ and households’ location choice behaviors is not internalized at present yet. As a result, the benefit of this expressway may
be underestimated considering its potential. However, the current approach is safest to analyze cost benefit ratio from the construction investors’ view.
There is a great expectation for San-En-Nanshin Expressway for improving the convenience of community health, so there aresome additional benefits of shortening time after road construction that are not studied in this research yet. Therefore, the real economic impact of this expressway could be larger than our estimate. San-En-Nanshin Expressway is expected to give a significant
economic impact on San-En-Nanshin region, and moreover economic benefit maximization for San-En-Nanshin Expressway
has become an important issue to be studied with comprehensive observation of the regional economy and social infrastructures.
Although San-En-Nanshin Expressway is planned as a national project, a part of construction cost will be born by the prefectures that this expressway runs through. It is estimated that the total project cost reaches several hundred billion yen. Therefore aconsiderable financial burden hangs to Nagano Prefecture, Aichi Prefecture, and Shizuoka Prefecture, and how to consistently
solve the financial resource problem has been becoming important. This is a beneficiaries’ responsibility assignment problem in across prefectural border region, thus an appropriate committee for solution of this problem is necessary as well.
Industrial promotion in San-En-Nanshin region is considered as a key to make San-En-Nanshin Expressway more effective.
People want to live a place where living circumstances are convenient, and firms will invest in a place where those firms can gethigher returns. The estimation of economic impact should take into account such a market mechanism, thus the present study canbe regarded as a pioneering approach in economic analysis of transportation projects. Moreover the most important thing is toincrease the endowment of economic resources in San-En-Nanshin Region, but not re-distribution of existing resources. For
example, creation of businesses and/or project that enables coexisting of environmental conservation and economic growth. Following this idea, the establishment of large area management agency in the prefectural cross border region is necessary, thus the
expectation for currently existing San-En-Nanshin Agency could become higher.
This study has just started from the initial stage. In the near future, the computation of the full spatial general equilibrium model
will be completed although the shortcut method is employed in the present paper.

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