A Computable General Equilibrium Analysis ofElectric Vehicle Society in Toyohashi City, Japan
Yuzuru Miyata
Graduate School of Architecture and Civil Engineering, Toyohashi University of Technology
Hiroyuki Shibusawa
Graduate School of Architecture and Civil Engineering, Toyohashi University of Technology
andShamsunnahar Khanam
Graduate School of Environmental and Life Sciences, Toyohashi University of Technology
1. Introduction
This article aims to apply a computable general equilibrium (CGE) model extending authors’ previous study
concerning this field [1] to evaluate the economic impacts of an electric vehicle society (EVS) taking Toyohashi
City, Japan as a study region. More concretely, this paper emphasizes a CGE-modelling approach to evaluate thefollowing contents: economic impacts of subsidies for promotion of an EVS, the possibility of prices reduction,
modal shift towards an EVS and industrial structure change towards an EVS. In constructing the model, the authors referred to the literature of Miyata and Shibusawa [2], Shoven and Whally [3], and Shibusawa and Sugawara [4].
The rest of the paper is organized as follows. Section 2 explains the assumptions of the model and behaviours of
the economic agents. Section 3 summarizes the simulation results and concluding remarks.
2. The Model
2-1 Main Assumptions
The main assumptions made in our model are as follows:(1)The 2005 Toyohashi city’s economy is examined. The economic agents are households, the firms in 38 industries, the government and the external sector.
(2)40 markets are considered. They are 38 commodity markets, one labor market and one capital market. These
are assumed to be perfectly competitive and in equilibrium in 2005.
2-2 Behaviour of industries
In industries, intermediate goods, labor and capital are inputted to produce goods. Industries have the CobbDouglas technology with respect to labour and capital inputs, and Leontief technology with respect to intermediate inputs and value added input. Constant returns to scale are assumed in the technology. The cost minimization
problem can be written as follows: (see Figures 1 and 2 for the industrial classification.)38(1)

min ∑ pi xij + (1 + tp j )( wL j + rK j )( j = 1,...,38)
i =1with respect to xij, Lj and Kj
subject to
X j = min [
α

x
x'
x
1
f j ( L j , K j ), 1 j ,..., ij' ,..., 38 j ]
a10 j
a1 j
aij
a38 j
α

x18' j = x1818j j x1919j j(2)(α 18 j+α 19 j= 1)

(3)

1

α

α

α

α

α

(α 27 j+α 28 j+α 29 j= 1)

(5)

α

α

α

(α 34 j+α 35 j+α 36 j= 1)(6)(α 25 j+α 26 j= 1)

'
25 j
26 j
x25
j = x25 j x26 j

'
27 j
28 j
29 j
x27
j = x27 j x28 j x29 j
'
34 j
35 j
36 j
x34
j = x34 j x35 j x36 j(4)(1− a j )f j ( L j , K j ) ≡ A1 j L j K j
aj

(7)

where
pi : price of commodity I, xij : intermediate input of industry i's product in industry j, tpj : net indirect tax rate imposed on industry j’s product (indirect tax rate - subsidy rate), w : wage rate, r : capital return rate, Lj : labor input
in industry j, Kj : capital input in industry j, Xj : output in industry j, a0j : value added rate in industry j, aij : input
coefficient, Aij and αij : technical parameters in industry j
Conditional demands for intermediate goods, labor and capital in production process are as follows:

xij = aij X jα ⎡p ⎤
x19 j = 19 j ⎢ 18 ⎥p19 ⎢⎣α18 j ⎥⎦α ⎡p ⎤
x18 j = 18 j ⎢ 18 ⎥p18 ⎢⎣α18 j ⎥⎦(8)
α 18 j⎡ p19 ⎤⎢⎥⎢⎣α19 j ⎥⎦α ⎡p ⎤
x25 j = 25 j ⎢ 25 ⎥p 25 ⎣⎢ α 25 j ⎦⎥α 25 jα ⎡p ⎤
x26 j = 26 j ⎢ 25 ⎥p 26 ⎢⎣ α 25 j ⎥⎦α 25 jα ⎡p ⎤
x27 j = 27 j ⎢ 27 ⎥p 27 ⎣⎢ α 27 j ⎦⎥α 27 jα ⎡p ⎤
x28 j = 28 j ⎢ 27 ⎥p 28 ⎢⎣α 27 j ⎥⎦α 27 jα ⎡p ⎤
x29 j = 29 j ⎢ 27 ⎥p 29 ⎢⎣α 27 j ⎥⎦α 27 jα ⎡p ⎤
x34 j = 34 j ⎢ 34 ⎥p 34 ⎣⎢α 34 j ⎦⎥α 34 jα ⎡p ⎤
x35 j = 35 j ⎢ 34 ⎥p 35 ⎢⎣α 34 j ⎥⎦α 34 jα ⎡p ⎤
x36 j = 36 j ⎢ 34 ⎥p 36 ⎣⎢α 34 j ⎦⎥α 34 jα 18 j⎡ p19 ⎤⎢⎥⎢⎣α19 j ⎥⎦α 19 ja18' j X j(9)

α 19 ja18' j X j⎡ p 26 ⎤⎢⎥⎣⎢α 26 j ⎦⎥α 26 j⎡ p 26 ⎤⎢⎥⎢⎣α 26 j ⎥⎦α 26 j⎡ p 28 ⎤⎢⎥⎣⎢ α 28 j ⎦⎥α 28 j⎡ p 28 ⎤⎢⎥⎢⎣ α 28 j ⎥⎦α 28 j⎡ p 28 ⎤⎢⎥⎢⎣ α 28 j ⎥⎦α 28 j⎡ p 35 ⎤⎢⎥⎣⎢ α 35 j ⎦⎥α 35 j⎡ p 35 ⎤⎢⎥⎢⎣ α 35 j ⎥⎦α 35 j⎡ p 35 ⎤⎢⎥⎣⎢ α 35 j ⎦⎥α 35 j

(10)

'
a25
jX j

(11)

'
a25
jX j

(12)

⎡ p 29 ⎤⎢⎥⎣⎢α 29 j ⎦⎥α 29 j⎡ p 29 ⎤⎢⎥⎢⎣α 29 j ⎥⎦α 29 j⎡ p 29 ⎤⎢⎥⎢⎣α 29 j ⎥⎦α 29 j⎡ p 36 ⎤⎢⎥⎣⎢α 36 j ⎦⎥α 35 j⎡ p 36 ⎤⎢⎥⎢⎣ α 36 j ⎥⎦α 35 j⎡ p 36 ⎤⎢⎥⎣⎢α 36 j ⎦⎥α 35 j

'
a27
jX j

(13)

'
a27
jX j

(14)

'
a27
jX j

(15)

'
a34
jX j

(16)

'
a34
jX j

(17)

'
a34
jX j

(18)

2

αj

⎡(1−α j )r ⎤ a0 j X j
LDj = ⎢⎥⎢⎣ α j w ⎥⎦ Aj(1−a j )⎡ aw ⎤
KDj = ⎢ j ⎥⎢⎣(1− aj )r ⎥⎦(19)

a0 j X j(20)

Aj

where LDj: conditional demand for labor in industry j and KDj: conditional capital demand in industry j
Zero profit condition is realized in the industries under the perfect competition.
38

profit = p j X j − ∑ pi xij − (1 + tp j )[ w ⋅ LD j + r ⋅ KD j ] = 0

(21)

i =1

2-3 Behaviour of households
The households in Toyohashi City are assumed to be homogeneous with the fixed number of households.
Thus, one can consider that the households share an aggregate single utility function. To explain the householdbehaviour, first, derivation of future good is described here. The future good implies the future consumption
which is derived from the household saving, however, the saving formulates capital investment. Therefore, capital good can be regarded as saving good. Investment is made by using produced goods, and let their portions in38

investment be denoted by bi. Then the price of investment good is expressed as pI = ∑bi pi . This can be rei =1

garded as the price of saving good ps. The expected net return rate of household saving rs is written as follows:

rs = (1 − ty )(1 − k o )(1 − k r ) rδ / p s(22)where ty: direct tax rate imposed on households, ko: rate of transfer of property income to the external sector
kr: capital depreciation rate, δ: ratio of capital stock measured by physical commodity unit to that by capital service unit.
Then, the derivation of demands for composite consumption and leisure time from the current good G is described. The current good G is a composite of consumption and leisure time, and G is obtained from the following optimization problem:
max G ≡ {β 1/ v C ( v −1) / v + (1 − β )1/ v F }
2

2

1

1

(23)

v2 /( v2 −1)

C ,F

subjected to(24)

p ⋅ C + (1 − ty)(1 − lo )w ⋅ F = (1 − ty)FI − TrHO− SH

By solving this utility maximization problem, the demand functions for composite consumption, leisure timeand labor supply are obtained.
β [(1 − ty ) FI − TrHO − SH ](25)
C=
pv ⋅ Ω
2F =(1 − β )[(1 − ty ) FI − TrHO − SH ][(1 − ty )(1 − l o ) w ] v ⋅ Ω

(26)

2

LS = E − F(27)Ω ≡ βp(1−v2 ) + (1 − β )[(1 − ty)(1 − lo )w](1−v2 )(28)

where LS: household labor supply, β: share parameter, v2: elasticity of substitution between composite consumption and leisure time, C: composite consumption, F: leisure time, p: price of composite consumption good, SH :household nominal saving (＝PS･S )3

By substituting the composite consumption (25) and leisure time (26) into (23), the price index of the present
good is derived as follows:

pG = {β p 1−v + (1 − β )[(1 − ty )(1 − lo ) w]1−v }1 /( v −1)
2

2

(29)

2

Moreover, composite consumption good is disaggregated into produced goods through the maximization of a
Cobb-Douglas sub-utility function given the household income and leisure time.
38

max C ≡ ∏ C iγ
i =1

38

i

(30)

( ∑ γ i = 1)i =1subject to
38

(31)

∑ p ⋅ C = (1 − ty )Y − TrHO − SH
i

i =1

i

where Ci: household consumption good produced by industry i, pi: price of good i,Y: household income(=(1-lo)w･LS+LI+(1-ko)(1-kr)r･KS+KI+TrGH+TrOH )From this optimization problem, consumption good i is derived as follows:
γi
Ci =

pi

[(1 − ty )Y − TrHO − SH ] ( i = 1,⋅ ⋅ ⋅,38 )(32)

The price of composite consumption is calculated as follows:
38 ⎡p ⎤p = ∏ ⎢ i⎥i =1 ⎣ γ i ⎦

γi

(33)

2-4 The Government
The government sector in this study consists of the national and local governmental activities in Toyohashicity. Thus, the concept of the government corresponds to the definition of SNA framework. The government
income and expenditures are expressed as the following balance of payments.
3838∑ p ⋅ CG + TrGH + TrGO + SG = ty ⋅ Y + ∑tp (w ⋅ LD + r ⋅ KD ) + TrOG
i

i =1

i

i =1

i

i

i

(34)

where CGi: government consumption expenditures on commodity i, TrGH: current transfers to households,
TrGO: current transfers to the external sector, SG: government savings, TrOG: current transfers from the external
sector
2-5 The External Sector
The external sector’s income and expenditures are described as the following balance of payment as well.
3838∑ p ⋅ EX + TrOH + TrOG+ KI + LI + SO = ∑ p ⋅ EM + TrHO+ TrGO+ KIO + LIO
i

i =1

i

i =1

i

(35)

i

where EXi: export of commodity I, EMi: import of commodity I, SO: savings of the external sector (= national
current surplus), LIO: labour income transfers to the external sector (= lｏ· w ·LS ), KIO: property income transfers to the external sector (= k0 · r · KS)
2-6 Balance of investment and savings
Household, government, the external sector’s savings and the total capital depreciation determine the total
investment.
38

38∑ p ⋅ I = SH + SG + SO + ∑ DR
i =1

i

i

i =1

(36)

i

4

where Ii : demand for commodity i by investment and DRi: capital depreciation in industry i
2-7 Prices of commodities
Due to the zero profit condition, the following equation is obtained. Figure 1. Change Rate of Industrial Output
38

(37)

p j X j = ∑ pi xij + (1+ tpj )[w⋅ LDj + r ⋅ KDj ]i =1Given a wage and a capital return rate, we can formally calculate the commodity prices as follows:(38)

P = ( I − A′) −1[(1 + tp j )(w.ld j + r ⋅ kd j )]where P: vector of commodity prices, A': transposed matrix of industries' input coefficients, [・]：column vector
whose elements are in parentheses ldj≡LDj / Xj and kdj≡KDj / Xj
2-8 Derivation of equilibrium
The equilibrium conditions in the model can be summarized as follows:
Commodity Market(39)⎡ a11 L a131 ⎤ ⎡ X 1 ⎤ ⎡C1 ⎤ ⎡CG 1 ⎤ ⎡ I 1 ⎤ ⎡ EX 1 ⎤ ⎡ EM 1 ⎤⎡X1 ⎤⎢ M ⎥ = ⎢ M O M ⎥⎢ M ⎥ + ⎢ M ⎥ + ⎢ M ⎥ + ⎢ M ⎥ + ⎢ M ⎥ − ⎢ M ⎥
⎢
⎥⎢
⎥
⎥ ⎢
⎥ ⎢ ⎥ ⎢⎥ ⎢ ⎥ ⎢⎥⎢⎣⎢ X 31 ⎦⎥⎣⎢ a 311 L a 3131 ⎦⎥ ⎣⎢ X 31 ⎦⎥ ⎣⎢C 31 ⎦⎥ ⎣⎢CG 31 ⎦⎥ ⎣⎢ I 31 ⎦⎥ ⎣⎢ EX 31 ⎦⎥ ⎣⎢ EM 31 ⎦⎥38

Lobor Market LS = ∑ LD
j =1

(40)

j

38

Capital Market KS = ∑ KD
j =1

(41)

j

3. Simulation Results and Concluding Remarks
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
-0.4

1.42%

total
agriculture,forestry &…
miningfood processing
textile productpulp, paper & wooden…
chemicalcoal & petroleum productplastic productceramics
stone & clay productiron & steel productnon-ferrous metal
metal productgeneral machinery
electrical machinery
information &…
electronic component
gasoline vehicles (GVs)electric vehicles (EVs)aircraftother transportation…
precision equipment
other manufactured
construction
electric power
solar powergas supply
heatcogenerationwater supply & sanitary…
commerce
financial & insuance service
reale state
GVs transhipment
EVs transhipment
other transhipment
telecommunication &…
service

0.85%

servicetelecommunication &…

EVs transhipment

other transhipment

reale state

GVs transhipment

commerce

financial & insuance…

water supply & sanitary…

heat

cogeneration

gas supply

solar power

construction

electric powerother manufactured

precision equipment

aircraftother transportation…

electric vehicles (EVs)gasoline vehicles (GVs)

information &…

electrical machinery

metal productgeneral machinery

non-ferrous metaliron & steel productceramics

plastic productchemicaltextile productminingelectronic component-0.8

stone & clay product-0.6

pulp, paper & wooden…

-0.4

food processing

0-0.2

agriculture,forestry &…

Figure 1 Change Rates of Industrial Outputs-1-1.08%-1.2-1.4-1.53%-1.6

Figure 2 Change Rates of Commodity Prices5

In this article we have applied a CGE model to evaluate the possibility and economic impacts of an EVS taking
Toyohashi City, Japan as a study region. By employing the CGE model, the two numerical simulations have been
implemented. (1) Case one (business as usual). The simulation of this part has done by simply calculating the
input- output (I-O) table of Toyohashi City, Japan. (2) Case two (introduces 20% subsidies to the industries including EV manufacturing, EV transport, solar power, cogeneration, and other transport). From the simulation
results, some interesting conclusions have been obtained.
The results demonstrate that after introducing subsidies, total industrial output increases 0.07%. A large increase
rate is found in industries like solar (1.42%), cogeneration (0.85%), EV manufacturing (0.46%), EV transport and(0.80%), other transport (0.73%), and non-ferrous metal (0.54%). Conversely a decreasing tendency is seen in oil,coal product (-0.30%), mining (-0.06%), heat supply (-0.39%), and the GV transport (-0.10%). The reason behind the large decrease of oil and coal products is due to an increase in the share of EV, solar power, and cogeneration, and a decrease in mining is relates to a decline of oil and the coal product. Moreover, a decreasing trend in
the heat supply industry is found because of an increase in the cogeneration.
The total industrial output increases by 0.07%, as the city GDP depends on industrial output, thus the total real
GDP also grows by 0.8% in Toyohashi city. Besides, the total labor demand increases a few (0.08%), however alarge increasing trend in labor demand is found in solar energy (5.84%), cogeneration (4.50%), other transport(2.44%), and EV manufacturing (1.74%) and EV transport (1.08%) respectively. Taking into account the current
serious situation of job opportunity an increase in labour demand may be interpreted as a positive fact.
Moreover, all the commodity prices decrease though in industries where subsidies are presented prices shrink
appreciably. For example, solar energy (-1.53%), other transportation (-1.09%), EV manufacturing (-0.42%) and
EV transportation (-1.00%), cogeneration (-0.32%) decreases largely.
Hence Toyohashi city’s economy shows a direction where the demand for conventional vehicles and energy are
decreased, conversely, the demand for EVs and renewable energy are increased, illustrating a different lifestyle
from the current one. In this study therefore it is clear that the society changes to EVS. By all reasons mentioned
above, as a conclusion of the study, it is authors’ opinion that giving 20% subsidies to EV manufacturing and EVtransport, solar power, cogeneration and other transport can really represent a realistic alternative society to EVS,
both in terms of economic development and CO2 emissions reduction. Thus we have suggested a promotion of
new industrial structure to introduce an EVS in Toyohashi city, Japan. The proposed model can be expanded tothe other cities in Japan and other countries in the world which are similar to this area.
References[1] Y. Miyata and S. Khanam (accepted), New Industrial Structure Coping with the Economic Impacts of Shifting
Production to Battery –based Electric vehicle in Toyohashi City in Japan-A CGE Modeling Approach-, Regional
Science Inquiry, Vol IV, No 3, Special Issue, December, 2012.
[2] Y. Miyata and H. Shibusawa, Does a Decrease in the Population Prevent a Sustainable Growth of an Environmentally Friendly City?-A Comparison of Cases of Decreasing and Increasing Populations of Obihiro Metropolitan Area, Japan by an Intertemporal CGE Modeling Approach, Interdisciplinary Information sciences, Vol.
14. No.1, pp. 1-24.
[3] J. B. Shoven and J. Whalley, Applying general equilibrium, Cambridge Survey of Economic Literature, 2007,
Cambridge University Press.
[4] H. Shibusawa and T. Sugawara, Evaluation the Economic Impacts of the Production of New Generation
Automobiles with Technological Innovations. Studies in Regional Science, Vol 41, No.1, 2011, pp. 127-146.

6