Applied Energy 168 (2016) 291–302

Contents lists available at ScienceDirect

Applied Energy
journal homepage: www.elsevier.com/locate/apenergy

Effect of housing relocation subsidy policy on energy consumption:
A simulation case study
Yanhong Yin a,b,⇑, Kohei Aikawa c, Shoshi Mizokami d,⇑aFaculty of Maritime and Transportation, Ningbo University, 818 Fenghua Road, Jiangbei District, Ningbo 315211, China
National Traffic Management Engineering & Technology Research Centre Ningbo University Sub-center in China, 818 Fenghua Road, Jiangbei District, Ningbo 315211, Chinac
Obayashi Corporation, Konan 2-15-2, Minato-ku, Tokyo 107-0062, Japand
Department of Civil and Environmental Engineering, Kumamoto University, 2-39-1, Kurokami, Kumamoto 8608555, Japanbh i g h l i g h t s
 Household consumption behaviors are simulated in housing relocation policies.
 Relocation subsidy policy contributes to more demand of general goods and land.
 Energy increases in most scenarios with the subsidy policy.
 Suburban residence taxation policy alone reduces energy.
 Less car trips and land, and shorter trip time contributes to less energy use.

a r t i c l e

i n f oArticle history:
Received 22 July 2015
Received in revised form 24 December 2015
Accepted 22 January 2016

Keywords:
Energy consumption
Housing relocation choice
Consumption behavior
Subsidy policy
Taxation policya b s t r a c t
This study investigates the effect of housing relocation policies on energy consumption by simulatinghousehold relocation choice behaviors and consumption behaviors. Energy consumption is estimatedbased on consumption behaviors. Three types of policy are analyzed: the relocation subsidy policy, thesuburban residence taxation policy, and the combination of subsidy and taxation policy. The results showthat all policies have influence on housing relocation choice and consumption behaviors. The number ofhouseholds in a given area would increase by two percent under the relocation subsidy policy. However,this type of policy contributes to greater demand of general goods, land, and more energy consumption.
A suburban residence taxation policy shows very limited effect on housing relocation choice behaviors,with only a 0.1% increase of households in the designated area. However, this policy shows strong effecton energy reduction due to shorter trip time and less demand of car trips and land. A combination of subsidy policy and suburban residence taxation policy attracts 2.2% of households move to the city centerarea. Energy consumption increases as consumption of general goods increases.
Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction
The magnitude and speed of urban growth have made urban
development a crucial element affecting the long-term outlook ofcivilization. Along with climate change and energy security, issues
such as the growth of cities in developing countries and the depopulation of central areas in cities have become serious concerns.
⇑ Corresponding authors at: Faculty of Maritime and Transportation, Ningbo
University, 818 Fenghua Road, Jiangbei District, Ningbo 315211, China. Tel.: +86
574 8760 9546 (Y. Yin). Department of Civil and Environmental Engineering,
Kumamoto University, 2-39-1, Kurokami, Kumamoto 8608555, Japan. Tel.: +81 96
342 3541 (S. Mizokami).
E-mail addresses: yinyanhong@nbu.edu.cn (Y. Yin), smizo@gpo.kumamoto-u.ac.
jp (S. Mizokami).
http://dx.doi.org/10.1016/j.apenergy.2016.01.068
0306-2619/Ó 2016 Elsevier Ltd. All rights reserved.

Significant shifts of land use and travel behaviors in cities havebeen noticed in recent decades. Increasing income and vehicle
ownership have made it possible for many families to find housing
in suburban areas and travel longer distances, resulting in lesstransit usage and the decentralization of metropolitan areas [1].
A global urban renovation process of radically transforming
low-density urban zones has been started because there is anargument that efficient land use and land preservation are environmentally sensitive strategies. The pattern of lower-density development has been gradually substituted by compact development,
which reduces costs through more efficient use of land and infrastructure. Strategies that lead to compact development have generated considerable research interest. Because one of the widely
discussed aspects of compact development in the context of urban

292

Y. Yin et al. / Applied Energy 168 (2016) 291–302

sustainability relates to urban structure, or urban form [2,3], manystudies recommend a compact urban structure [4–6]. The structure
encourages high density, mixed land use, efficient public transportsystems, and dimensions that encourage walking and cycling [4]. It
is believed that less private car dependency and the preservation ofgreen fields and arable land are two major benefits of a compact
urban structure. Lower residential energy requirements could be
expected in the more compact urban structures, as densely settled
areas have more shared walls, smaller living space per capita and,potentially, more efficient heating technology, such as district
heating or natural gas [7,8].
The term ‘urban structure’ covers aspects of density, geometricshape, land use (residential, industrial), and infrastructure (road,rail, waterway), with implications for indicators such as density,
fragmentation and accessibility [9]. Researchers search for theproper index to represent the compact urban structure. Althoughmore complex land use index would be desirable, they are very
complicated to build. Land use index is mostly feasible for intracity research and is rarely used in comparative studies. Population
density can serve as a useful indicator of urban structure [8]. As theinfluence of land use and economic activities could be reflected by
the population distribution, literature focuses on the analysis of
population distribution to address the problem of compact development. The link between population density and householdenergy consumption has been supported by various urban energy
studies, which have highlighted the importance of high population
density as a factor to reduce transport energy consumption [10].
There is a wide spectrum of research which analyzes the strategies for population distribution toward compact development.
Broadly speaking, two major streams of studies are identified.
The first stream of literature estimates the initiative movementof populations by exploring effects of policies or projects on population distribution by housing location modeling. Factors that
influence housing location choice have been verified and models
have been built to forecast housing locations. Modeling behaviorsof residential location choice is a primary population distribution
concern for urban planners, policymakers, and researchers. Residential location modeling can be traced back to the land use modeling by Von Thunen [11]. He explained the effect of transport costson activity locations and the land market in an agricultural region.
Alonso applied this model in a monocentric city and found thathouseholds choose their residential location by maximizing a utility function depending on their goods expenditures, land lot size,and distance to the city center [12]. Studies afterward described
residential location choice by introducing the discrete modelingframework [13,14]. This framework quantifies the impact of different residential location characteristics and their interactions withhousehold characteristics. The preferences toward residential locations are sensitive to socioeconomic characteristics such as educational attainment, income, household tenure (rent or own),
important life events (particularly childbirth), attitudes and environmental awareness [15,16]. With detailed specification of location characteristics and housing units, households make thedecision to choose the alternative that provides highest utility
from a set of mutually exclusive alternatives.
The second stream of studies analyzes population movement
directions by investigating household housing location history. Literature pays more attention on surveys to investigate residents’attitudes toward housing location [17,18]. By analyzing the behaviors of residents who moved into high-density residential environments in the central area of Dublin, Howley found that mostresidents prefer lower-density locations, which call for more efforts
toward the long-term success of urban intensification [19]. Using alarge-scale household survey and aggregated census data from
Beijing, Wu et al. developed a framework to empirically measure
the relative impact of location characteristics versus individual

characteristics in determining households’ residential location
choices. The accessibility of local public goods was found to be significant in determining households’ location choices [20]. Torres
et al. designed a stated-choice (SC) experiment to investigate thelocational preferences of residents in Central Business District(CBD) in Santiago de Chile. Higher willingness to pay for accessibility and cleanliness of the neighborhood, and a lower valuation for
attributes related to recreation (i.e., gym and pool or cultural services) were found [21]. Drawing upon a stated-preference survey
in the Wasatch Front region in Utah, Liao et al. identified significant
heterogeneity in residential location preferences over compact,
walkable and transit-friendly neighborhoods. Compact development is highly accepted among families with fewer school-age children, low-income and renter-occupied households, and those who
appreciate social heterogeneity and have less desire for privacy [22].
Previous studies performed deep investigations of residents’housing location behaviors. Initial attempts to estimate population
relocation focus on identifying the factors of housing relocation andpopulation movement. The methodology and findings are useful forforecasting the population distribution under various policies.
However, most work payed attention only to residential location
behaviors, without considering the environmental outcome of
behaviors. The effect of compact development policy on consumption behaviors of residents and energy consumption is often
neglected or considered individually in previous literatures. Aiming
for compact and sustainable development, it is important to analyze not only the housing location but also the environmental outcome, such as energy consumption and greenhouse gas emission[23–25]. Because the goal of compact development is to preserve
arable land and to reduce energy consumption and thus pollution,
there remains a need for an efficient method to analyze not only
residential location choice but also energy consumption behaviors.
Increasing attention has been focused on analyzing the choiceof household location in certain zones and estimating energy consumption [26–30]. Despite efforts have been made to analyze theenergy consumption in housing sector, few researchers haveaddressed the effect of housing location choice behavior on household energy consumption from a microeconomic viewpoint. Raising awareness of these concepts in academic studies at the microlevel is crucial for providing advice to successful policy making
to encourage compact development and reduction of energy consumption of the city.
This paper aims to investigate households0 reactions to compact
development policy by simulating housing location choice andconsumption behaviors of residents. A scheme is introduced toforecast household energy use based on consumption behaviors.
Using a modeling approach, the paper simulates the influence of
three types of relocation policies on residential location choiceand consumption behaviors. Subsidy policy is introduced as a positive strategy for giving subsidy to households who relocate in certain zones. Taxation policy is introduced as a negative strategy forhouseholds who live outside of designed zones. Additionally, ajoint policy that combines subsidy and taxation is also analyzed.
A comparative analysis is conducted for comparing the energy
results of three types of policy scenarios to give suggestions forenergy saving toward compact development in Kumamoto.

2. Methods and data sources
Facing environmental problems, the Kumamoto municipal government plans for compact development. Decreasing and ageing
population and urban sprawl are main challenges. Kumamoto city
will lose more than ten thousand people every five years after2020. The ratio of elders (older than 65) will increase from 18.7%
in 2005 to 29.7% in 2030. Meanwhile, Kumamoto is experiencing

Y. Yin et al. / Applied Energy 168 (2016) 291–302

a process of urban sprawl. Considering the above challenges,
Kumamoto city tries to promote compact development throughrelocation subsidy policies, which aim to attracting citizens moving from suburban area to the central urban area. This type ofpolices has been implemented in Japanese cities such as Toyama,Gifu, Kanazawa, and Takayama. A maximum of 10,000 yen of rent
subsidy will be given to households who move to the designatedzones for three years in Toyama, compared to a maximum of
20,000 yen per month in Gifu. In Kanazawa and Takaoka, households who buy houses located in the designated zones will receive
a grant subsidy of up to 2,000,000 yen and 1,000,000 yen, respectively. As in other cities in Japan, the Kumamoto local government
would like to be involved in residential housing to internalize theexternal effect of compact city policies.
To investigate the effect of relocation subsidy policies on
residential location choice behaviors and consumption behaviors
in Kumamoto, three key points must be addressed in this study:(1) the influence on residential location choice; (2) the influence
on consumption behaviors; and (3) the influence on energy
consumption. Based on these points, the content in this section isorganized as five parts: (1) to introduce relocation policy scenarios
in Kumamoto, (2) to build a residential relocation choice model, (3)to construct a model to estimate consumption behaviors anddemand for goods, (4) to build a function for calculating energy
consumption, and (5) to explain the data and data sources.
2.1. Relocation policy scenarios in Kumamoto

293

included. The combination of policy P1-A-10000 and suburban residence taxation policy is called P3-A-10000, while the combinationof P1-A-5000 and the suburban residence taxation policy is called
P3-A-5000. P3-B-10000 indicates the P1-B-10000 policy combinedwith the suburban residence taxation policy. P3-B-5000 indicates
the P1-B-5000 policy combined with the suburban residence taxation policy.
2.2. Residential relocation choice modelHouseholds are assumed to make their home relocation decisions based on the utility level in different zones. A logit modelis used to forecast the possibility of home relocation based on
the utility (Eq. (1)).

expðui þ pi Þhji ¼ hj  P
k expðuk þ pk Þð1Þ

h⁄ji indicates the number of households which move from zone j tozone i. hj is the number of households in zone j. ui is the individual
utility level in zone i, which is determined by the consumption of
goods. pi is an index variable that reflect the accessibility of thezone. It is determined by the number of clinics per unit area (number/km2), number of shops (number/km2), number of supermarkets(number/km2), and central commercial district dummy value (take1 if the zone is within central commercial district, otherwise take 0).
The relocation cost of moving from zone i to zone j is assumed to be
the same regardless of the distance between zones.

Three types of relocation policies are analyzed, naming
relocation subsidy policy, suburban residence taxation policy,
and relocation subsidy plus suburban residence taxation policy.

2.3. Model to estimate consumption behaviors and demand for goods

2.1.1. Relocation subsidy policy
Relocation subsidy policy is a type of policy that government
provides subsidy to the household who relocate their home inthe designated area. The subsidy is paid only for the households
who relocate to the target zones from other zones. Two strategies
are considered for household relocation. The first strategy is called
P1-A, in which the households are encouraged to move into zones
located around transit centers or living centers with dense populations and high public service accessibility. The second strategy iscalled P1-B, in which the households are supposed to relocate toa circle with a radius of 4 km from the city center. Two subsidy
levels are set at 10,000 yen/month (333 yen/day) and 5000 yen/month (166 yen/day). Based on the relocation place strategies
and subsidy amounts, four scenarios are established: P1-A-10000,
P1-A-5000, P1-B-10000, and P1-B-5000. In scenario of P1-A10000, one household receive 10,000 yen per month as the subsidy
if they move into zones indicated in P1-A. The policy of P1-A-5000
indicates that one household receives subsidy of 5000 yen/monthwhen they relocate to the zones in the P1-A case. P1-B-10000 suggests that 10,000 yen is given to a household each month if they
relocate to a home in designated zones of P1-B. In the case of P1B-5000, 5000 yen is provided if one household relocates the hometo the zones for P1-B.

2.3.1. Assumptions
The model used in this study is supposed be a ‘‘closed-city”
model, which is characterized by a fixed population of urban residents who maximize the utility by consuming goods subject to abudget constraint. There is no import and export with outside
world. Utility is closely related to consumption behaviors, which
is a representation of preferences for goods and services. People
are assumed to make consumption decisions based on their preferences for different goods, the cost of goods, and their budget constraints (income) to maximize the utility. The following
assumptions are vital to developing the model to estimate consumption behaviors based on utility: (1) the ‘‘representative
household” in each zone is assumed to consume two types ofgoods: composite goods and general goods. General goods are all
goods except transport goods and land. (2) Composite goods
include transport goods and land. The demand for composite goods
is a function of demand of transport goods and land. (3) It is
assumed that transport goods include not only commuter trips
by car and public transport but also car and pedestrian trips foreveryday life, such as shopping, going to hospitals, and recreation.
(4) The demand for land is reflected by the living space of residential households. (5) Utility is a function of the demand for composite goods and general goods. (6) The ‘‘representative household”
spends all of its income on the consumption of goods. No saving
is assumed. (7) The demand for goods in reality equals the demand
for goods at maximum utility.

2.1.2. Suburban residence taxation policy
This type of policy influences the location decision in a negative
way. Tax is collected from households who live in the withdrawal
area, which is designated by the government. Suggested by the tax
policy in the existing literature by Ujihara et al. [31], 10% of theland rent is taxed as an extra cost of staying.
2.1.3. Relocation subsidy plus suburban residence taxation policy
This policy considers both a positive relocation subsidy and thenegative taxation of suburban residence. Four types of polices are

2.3.2. Constant Elasticity of Substitution functions based on
consumption behaviors
A four-stage CES (Constant Elasticity of Substitution) function isused to express utility. The nested structure is shown in Fig. 1. FiveCES functions are developed to reflect the relationship between
goods at four stages (Eqs. (2–6)). At the first stage, the household
utility level at zone i indicated as ui is determined by the consumption of composite goods and general goods (Eq. (2)). All variables in294

Y. Yin et al. / Applied Energy 168 (2016) 291–302

Utility(Ui)αAComposite goods (xAi)
αT
Transport goods (xTi)

3rd stageαO

1st stage

αG
General goods (xGi)αLLand (xLi)

2nd stage

Commuter trips purposed forworking, schooling, returning
home, and business (xOi)

4th stage

αP

αM

Trips by public transport (xMi)

αC2

Trips by car (xC2i)

Everyday life trips purposed for
shopping, go to hospital
hospital, andshopping
recreation (xPi)

4th stageαW

Trips by walking (xWi)

αC1

Trips by car (xC1i)

Fig. 1. The nested structure of the utility function.

this paragraph explain the household demand per day in zone i.
The demand of composite goods and general goods are express
by variables of xAi and xGi, respectively. At the second stage, composite goods include land and transport goods (Eq. (3)). xLi is thedemand of land and xTi is the demand of transport goods. At third
stage, transport goods are classified as everyday life trips and commuter trips according to the purpose of the trips (Eq. (4)). Everyday
life trips include car trips and pedestrian trips for shopping andrecreation. Commuter trips are trips for working, schooling, returning home, and business. The demand of everyday life trips andcommuter trips are indicated by variables of xPi and xOi, respectively. At the fourth stage, different traffic mode share is shown.
Eq. (5) shows the share relationship between the demand of car
trips (xC1i) and walking trips (xWi) for everyday life trips. Eq. (6)shows the share relationship between the demand of car trips(xC2i) and public transport trips (xMi) for commuter trips.

nor1 =ðr1 1Þ
ðr 1Þ=r1
ðr 1Þ=r1
ui ðxGi ; xai Þ ¼ aG xGi 1
þ aA xAi 1ð2Þnor2 =ðr2 1Þ
ðr 1Þ=r2
ðr 1Þ=r2
þ aT xTi 2
xAi ðxLi ; xTi Þ ¼ aL xLi 2ð3Þnor3 =ðr3 1Þ
ðr 1Þ=r3
ðr 1Þ=r3
xTi ðxPi ; xOi Þ ¼ aP xPi 3
þ aO xOi 3

ð4Þnðr 1Þ=r4p

xPi ðxC1i ; xWi Þ ¼ aC1 xC1i4pðr 1Þ=r4p

þ aW xWi4p

or4p =ðr4p 1Þ

nor4O =ðr4O 1Þ
ðr 1Þ=r4O
ðr 1Þ=r4O
þ aM xMi4O
xOi ðxC2i ; xMi Þ ¼ aC2 xC2i4O

and aO are the expenditures share of everyday trips and commuter
trips to the total expenditure of transport goods. aC1 and aW are theexpenditure share of car trips and walking trips to the expenditureof everyday trips. aC2 and aM are the parameters that explain the
expenditure share of car trips and public transport trips to the total
expenditure of commuter trips.
2.3.3. Demand for goods
Five maximization problems should be solved at four stages toforecast the demand of goods at maximum utility. At the fourthstage, the demand of everyday trips and commuter trips is determined by solving two maximization problems (Eqs. (7) and (8))
under the constraint of transport budgets for commuter and everyday trips. At the third stage, the demand of total trips is determined by the solutions to the maximization problem of Eq. (9)under the transport goods budget constraint. At the second stage,
the demand of composite goods is determined by the optimal solutions of the maximization problem as Eq. (10) for transport goods
and land under the composite goods budget constraint. At the firststage, the utility is determined by the optimal solutions of the
maximization problem as Eq. (11) for composite goods and general
goods under the income constraint. The detailed information forsolving five maximization problems is shown in Appendix A.

max

ð5Þ
ð6Þ

r1, r2, r3, r4P, and r4O are the elasticity of substitution between
two types of goods at the first, second, third, and fourth stages,
respectively. aG and aA are the share parameters, indicating thecomposite goods and general goods expenditures as a share of total
income. aL and aT are the expenditure share of land and transport
goods to the total expenditure of composite goods respectively. aP

fxC2i ;xMi gnor4O =ðr4O 1Þ
ðr 1Þ=r4O
ðr 1Þ=r4O
xOi ¼ aC2 xC2i4O
þ aM xMi4O

ð7Þ

s:t: pC2i xC2i þ pMi xMi 6 I4Oi
max

fxC1i ;xWi gnor4P =ðr4P 1Þ
ðr 1Þ=r4P
ðr 1Þ=r4P
xPi ¼ aC1 xC1i4P
þ aW xWi4P

ð8Þ

s:t: pC1i xC1i þ pWi xWi 6 I4Pi
max

fxPi ;xOi gnor3 =ðr3 1Þ
ðr 1Þ=r3
ðr 1Þ=r3
xTi ¼ aP xPi 3
þ aO xOi 3

s:t: pPi xPi þ pOi xOi 6 I3i

ð9ÞY. Yin et al. / Applied Energy 168 (2016) 291–302

nor2 =ðr2 1Þ
ðr 1Þ=r2
ðr 1Þ=r2
max xAi ¼ aL xLi 2
þ aT xTi 2

ð10Þ

fxLi ;xTi gs:t: pLi xLi þ pTi xTi 6 I2i

ð11Þ

pC1i and pWi are the prices of car trip and walking trips for everyday
life, respectively. pC2i and pMi are the prices of commuter trips by car
and public transport (yen/trip), respectively. pPi and pOi are theprices of everyday life and commuter trips, respectively. pTi andpLi are the prices of transport goods and land, respectively. pGi andpAi are the prices of general goods and composite goods, respectively. I4Pi and I4Oi are the traffic budget for everyday life trips andcommuter trips (yen/household day). I3i is the transport goods budget (yen/ household day). I2i is the budget of composite goods (yen/household day). Ii is the income (yen/household day).
By integrating the solutions of five maximization problems, theoptimal demands of general goods (x⁄Gi), demand of land (x⁄Li), anddemand of car trips, the demand of public transport trips, and thedemand of walking trips (x⁄mi) at maximum utility are shown as
Eqs. (12), (13), and (14).



aL

r2



Ii

r2
r2
arL 2 p1þ arT 2 p1
Li
Ti

pLi

X mi ¼

Ii

ð12Þ

r1
r1
arG1 p1
þ arA 1 p1
Gi
Ai

pGi


xLi ¼

r1

aG

r4k

am

pmi

p
1  r 1r Gi r 1raG1 pGi 1 þ aA 1 pAi 1
r4k r31r4k 1r4k
ni

r4k
r
ark 3 arT 2 arA 1 ðarm4k p1
þ ani4k p
miÞ

r4P 1r3
r4O
r4O
Þþ arO3 ðarM4O p1
þ arC24o p1Þþ arC14P p1
C1i
Mi
C2i

n

!
ð13Þ

r4P
arP 3 ðarw4P p1
wi

1r3

3 r2 n
or1
r
3

r2
arL 2 p1
L1

1r3

r4P
r4P
r4O
þ arC14P p1Þþ arO3 ðarM4O p1
þ arT 2 ðarP 3 ðarW4P p1
Wi
C1i
Mi
(

or2 r1
r4O 1r3 1r2 1r2
r1 1r1
r1
r2
þ arC24O p1
Þ
Þ
a
p
þ
a
arL 2 p1
G
G
L1
A
C2i

þ arT 2nr4P
r4P
arP 3 ðarW4P p1
þ arC14P p1
Þ
Wi
C1i

r4O 1r3
þ arC24O p1
Þ
C2i

91
r1
o1r2 11r2 =;

1r3

r4O
þ arO3 ðarM4O p1
Mi

Ii m ¼ C1; W; k ¼ P;n ¼ C2; M;

k ¼ O or m ¼ C2; M;k ¼ O; n ¼ C1;W;k ¼ P

Ei  PiX

ðeG xGi þ eL xLi þ eC t Ci xC1i þ eW t Wi xWi þ eC tCi xC2iis:t: pGi xGi þ pAi xAi 6 Ii

xGi ¼

295

i

¼

n
or1 =ðr1 1Þ
ðr 1Þ=r1
ðr 1Þ=r1
ui ¼ aG xGi 1
þ aA xAi 1

max

fxGi ;xAi g

E¼

X

ð14Þ

2.4. Energy estimation function
Energy consumption is estimated based on the demand forgoods. As shown in Eq. (15), E is the total energy consumption of
the region, which is a function of Ei. Ei is defined as the energy consumption of one household per day in zone i. Pi denotes the number of households in zone i. eG, eL, eC, eW, and eM are the energy
units of general goods, land, car trips, walking trips, and public
transport trips, respectively. Energy units are used to evaluate
the energy needed to consume one unit of goods. tCi, tWi, and tMi
are the trip times for car trips, walking trips, and public transport
trips, respectively. Trip time variables are introduced into the estimation function to reflect the relationship between energy consumption and traffic congestion. xGi, xLi, xCi, xWi, and xMi indicate
the demand for general goods, land, car trips, walking trips, andpublic transport trips, respectively.

þ eM t Mi xMi Þ  Pi

ð15Þ2.5. Data and data sources
2.5.1. Primary number of trips (xC1i, xWi, xC2i, xMi)
The primary number of trips for different purposes in zone i is
obtained from the Personal Trip Survey (PTS) in 2010. The PTS isa person-based travel survey conducted every ten years by the
Ministry of Land, Infrastructure and Transport (MLIT) in Kumamoto. The data are aggregated by traffic zone. The number of trips
by car, foot, and public transport for commuting and everyday purposes is calculated as the total number of trips divided by the number of households.
2.5.2. Trip time of car trips, walking trips, and public transport trips(tCi, tWi, tMi)
Trip time of car and public transport trips is determined by theassignment results of car trips and mass transit trips on the Kumamoto transport network. Trip time in zone i is the average time forall trips from zone i to other zones. Trip time of walking trips is calculated by dividing the distance between zones by the walking
speed (5 km/hour). Trip time of walking trips is the average timeof all trips from zone i to other zones.
2.5.3. Price of goods
The price of general goods, pGi, is set to one as a numeraire unit.
The price of composite goods, pAi, is determined by the price oftransport goods and land according to CES functions. The price oftransport goods is influenced by the prices of car trips, walking
trips, and public transport trips. We used the same method to estimate the price of a car trip in both cases of everyday life trips andcommuter trips. The price of a car trip is determined by following
equation: pC1i = [(running fee unit (yen/km vehicle)  minimum
distance from zone i to j (km/trip))]/average number of passengers(trip/vehicle), pC2i = [(running fee unit (yen/km vehicle)  minimum distance from zone i to j (km/trip))]/average number of passengers (trip/vehicle). The running fee unit is available from thedata from MLIT, which measures the monetary running cost per
vehicle-kilometer, including fees related to oil, tires, tubes, vehicle
maintenance and vehicle depreciation. The number of passengers
in a car is 1.21 according to MLIT. The price of a mass transit trip
is determined by the public transport fare resulting from trip
assignment. The price of walking trips is set at 1 yen/trip.
2.5.4. The demand of land and price of land
The primary demand of land for each household per day is estimated by dividing the total area of residential land by the numberof households in each zone. The land price of the zone is obtainedby dividing the aggregated land price of the district by the priceratio of land along main roads in zones. The daily land price pLi(yen/m2 day) is the result of dividing the land price of the zone
by 12,775 (35 years). It is assumed that households need to pay amortgage for the land for 35 years.
2.5.5. Income Ii
It is difficult to obtain income data of households in each zone.
Because a positive relationship between land price and income isassumed [32–34], the zone’s income ratio is assumed to be equal
to the zonal land price ratio of the main roads. We distribute thetotal income for each administrative district among zones

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Y. Yin et al. / Applied Energy 168 (2016) 291–302

according to the land price ratio of the main roads in 2010. The land
price data are available from the Japanese National Tax Agency.
2.5.6. Energy consumption units
The energy consumption unit of general goods, eG (kcal/yen), is
calculated by dividing the energy use in the residential sector by
the general goods expenditure of one household. Except the expenditure of transport goods and land, the remaining income isassumed be spent on general goods. The energy consumption ofland is assumed to be equal to the energy required for constructing
new houses in the zone. The energy consumption unit of land, eL(kcal/m2), is determined by the demand for new houses and theoperational life of houses. Therefore, eL (kcal/m2) is estimated by
the total energy required for the construction of new houses and35 years (12,775 days).
The energy consumption units of car and public transport trips
are determined by the running fee unit and trip speed. The runningfee unit (yen/km vehicle) is obtained from MLIT. Energy units for
car and public transport trips are estimated as follows: eC (or eM)= energy unit of trip distance (kcal/trip min)  average speed(km/min). According to the study by Matsuo [35], the energy consumption unit for walking trips, eW (kcal/trip min), is set as0.0556 kcal per trip per minute. All results for the estimated energy
consumption units of goods are shown in Table 1.
3. Results
3.1. Parameter estimation

Table 2Estimation results of parameters in the residential relocation choice model.

Constant
Utility
Number of clinics
Number of shops
Number of supermarkets
Central commercial district (dummy)
Correlation coefficient R

Estimatet value

3.19
1.75  1045.61  1022.70  1030.0871
5.57
0.60

8.61
3.32
4.13
0.622
1.32
7.23

Table 3
Estimation results of parameters in the utility function.

r1

r2

r3

r4P

r4O

aG

aA

aL

0.903

0.942

0.828

1.930

2.150

0.925

0.075

0.793

aT

aP

aO

aG

aW

aC2

aM

0.207

0.182

0.818

0.992

0.008

0.426

0.574

budget is used for commuter trips, compared to eighteen percent
for everyday life trips. The value of aC1 is 0.992, indicating that mostof the trip expenditure for everyday trips is for car trips. However,the share of car trips decreases to 0.426 for commuter trips. The
expenditure for walking trips is as small as 0.008 because of lesscostly and small mode share. For commuter trips, the share of car
trips decreases to 0.426. More than fifty percent of the budget isspent on public transport trips, shown as the value of aM as 0.574.
3.2. Residential relocation choice and population distribution

3.1.1. Parameters in the residential relocation choice model
The parameters in the residential relocation choice model were
estimated based on 2010 PTS data for 177 zones in Kumamoto. The
data were aggregated by traffic zone. Except the number of shops,
all variables show significant influence on the residential relocation choice (Table 2). The possibility of relocating increases as
the utility level and accessibility of services improve.
3.1.2. Parameters in the utility function
As shown in Table 3, the substitution elasticity between composite goods and general goods, r1, is less than one. The value of
r2 indicates a relatively weak substitution relationship between
land and transport goods. The substitution elasticity between car
trips and public transport trips and between car trips and walking
trips is larger than the substitution elasticity between commuter
trips and everyday life trips. The price strongly influences the traffic mode choice, as suggested by the larger substitution elasticity
values of r4P and r4O.
The share parameter of a indicates the expenditure of goods tothe budget. The value of expenditure share parameter aG is 0.925,
indicating that households spend most of their income on general
goods. Only a small portion of income is used for composite goods,
as shown by the value of 0.075 for aA. Around eighty percent of thebudget for composite goods is used for land, with a value of 0.793
for aL. Comparably, twenty percent of the budget is spent on transport goods, suggested by the value of aT as 0.207. The estimation
result of aO suggests that more than eighty percent of the transport
Table 1
Energy consumption units of goods.
Goods

Energy consumption unit

General goods eG (kcal/yen)Land eL (kcal/m2)
Car trip eC (kcal/trip min)Public transport trip eM (kcal/trip min)Walking trip eW (kcal/trip min)

3.044
10.22
137.653
14.4980.0556The change rates of population in P1-A-10000 and P1-A-5000
are shown in Fig. 2a and Fig. 2b. 1.8% of residents move to designated zones in the P1-A-10000 policy scenario, compared to
1.01% in P1-A-5000. As shown by Fig. 3a and Fig. 3b, more than
1.61 percent of households move into the central urban area in
P1-B-10000 policy scenario. Meanwhile, 1% of households would
like to relocate to the central urban area under P1-B-5000 policy
scenario. The population distribution result of P2 suggests a wide
spread, but not expected strong effect on housing relocation choice(Fig. 4). The number of households is estimated to increase by 0.1
percent in the designated area in the scenario of P2. P3, which integrates the relocation subsidy policy and suburban residence taxation policy, is much more effective on attracting households to acertain area, with increment rate of 2.2 and 1.1 percent for subsidies of 10,000 and 5000, respectively. Fig. 5a and Fig. 5b illustrate
the population change rate in P3-A-10000 and P3-A-5000. Compared to the result of P3-B-10000, P3-A-5000 shows a limited
effect on the rate of population change (Fig. 6a and Fig. 6b).
3.3. Demand for goods
Table 4 presents the estimated demand of goods. The demand
for goods in each policy scenario is compared to the data of thebase year in 2010 by the demand ratio. It is the rate between
demand of goods in scenarios and the demand in the base year.
As shown in Table 4, averaged 6937 units of general goods are consumed by one household in one day. Except the policy scenario of
P2, a slight increasing trend is found for the demand of general
goods in the P1-A, P1-B, P3-B, and P3-A scenarios. Although thedemand of land increases in P1-A and P1-B scenarios, decreased
values are shown in the results of P2, P3-B, and P3-A. The scenarios
also show different effects on demand of trips. Both P3-A and P3-B
show effects on decreasing the number of trips for commuting andeveryday life. However, public transport and walking trips increasein these two kinds of policy scenarios.

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Y. Yin et al. / Applied Energy 168 (2016) 291–302

abFig. 2. (a) Population change rate of P1-A-10000 and (b) population change rate of P1-A-5000.

baFig. 3. (a) Population change rate of P1-B-10,000 and (b) population change rate of P1-B-5000.

3.4. Energy consumption
The estimated results of energy consumption are shown in
Table 5. A ratio is also used to compare the energy consumptionof scenarios to the energy demand in the base year of 2010. One
household requires 32,800 kcal of energy for one day. Increased
energy consumption is shown in the results of P1-A-10000,
P1-A-5000, P1-B-10000, P1-B-5000, P3-A-10000, and P3-B-5000.
However, P2 shows decreased energy consumption compared tothe data of the base year. This means that taxation policy is helpful
in reducing energy consumption. An average of 25,240 kcal ofenergy is estimated for general goods in the base year. There is aslight increasing trend in the energy consumption for general
goods in all scenarios. The energy for land is estimated to increasein P1-A-10000, P1-A-5000, P1-B-10000, and P1-B-5000 scenarios.
Conversely, the results of P2, P3-A-10000, P3-A-5000, P3-B10000, and P3-B-5000 show decreasing energy for land. Most of
the energy for car trips is for commuter trips. 3755 kcal of energy

is used for commuter trips, compared to 1442 kcal for everyday
trips. The policies of P1-A-10000, P1-B-10000, and P1-B-5000 show
effect on increasing the energy consumption by car trips. However,
the results of P1-A-5000, P2, P3-A, and P3-B suggest a decreasing
trend in energy use for car trips. All scenarios indicate increased
energy for walking trips and public transport trips. Except for
P1-A-5000, an increasing trend of energy consumption for all typesof mode trips is shown in P1-A, P1-B, and P2. All scenarios show apositive effect on the travel time for car trips, walking trips, andpublic transport trips. Except P1-B-10000 and P1-B-5000, trip timedecreases in the results of all scenarios.
4. Discussion
4.1. Residential relocation choice
Three types of policies show effect on residential relocation
choice and population distribution. The subsidy policy influences

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Y. Yin et al. / Applied Energy 168 (2016) 291–302

Fig. 4. Population change rate of P2.

abFig. 5. (a) Population change rate of P3-A-10000 and (b) population change rate of P3-A-5000.

the relocation choice in a positive way by providing subsidy tohouseholds who move to the designated area. The results showthat the subsidy policy has a relatively strong effect on household
relocation choices. Of course, different levels of subsidy show different expected effect on households’ relocation choices. An average of one percent of the population moves into the area if thesubsidy of 5000 yen per month is provided. While the subsidy policy of 10,000 would increases two percent of residents who relocate to the designated area. However, tax policy in this study
indicates very limited influence on the rate of population change.
One reason may be the intensity of tax policy is not strong as subsidy policy. One household needs to pay 50 yen per day for living inzones which locate outside of the designed area. The amount of tax
is much lower than the subsidy, which is 333 yen/day and
166 yen/day. The other reason could be the high income groups

would like to sacrifice the tax and refuse to move into more compact living environment. Although the rate of population change
under the integrated policy is higher than the rate in the subsidy
policy, a lower possibility of relocation is shown in some zones
under the integrated policy, such as urban zones far from the urban
central area. Households in sub-center of the city have low willingness to relocate in the urban central area since the utility level andaccessibility to service in sub-center is not low enough to make therelocation decision.
4.2. Demand for goods
Households tend to increase their consumption of goods withthe support of subsidy. Moreover, higher subsidy leads to moreconsumption. The relocation subsidy policy of P1 shows an299

Y. Yin et al. / Applied Energy 168 (2016) 291–302

abFig. 6. (a) Population change rate of P3-B-10000 and (b) population change rate of P3-B-5000.

Table 4
Estimated demand for goods and trip time.

Total expenditure(yen/day household)Traffic expenditure(yen/day household)General goods(yen/day household)Land (m2/day household)Car trips for everyday life
(trip/day household)Car trips for commuting(trip/day household)Walking trips(trip/day household)Public transport trips(trip/day household)

Base
year

P1-A-10000
ratio

P1-A-500
ratio

P1-B-10000
ratio

P1-B-5000
ratio

P2
ratio

P3-A-10000
ratio

P3-A-5,000
ratio

P3-B-10000
ratio

P3-B-5000
ratio

8178

1.010

1.005

1.013

1.006

0.997

1.010

1.005

1.013

1.006

187.1

1.005

0.993

1.011

1.004

1.000

1.002

0.988

1.000

1.006

6937

1.010

1.005

1.013

1.006

0.999

1.010

1.005

1.013

1.006

229.2
0.341

1.007
1.003

1.004
0.996

1.003
1.008

1.001
1.002

0.975
1.000

0.983
0.998

0.979
0.986

0.979
0.994

0.977
1.004

0.895

1.001

0.994

1.006

1.001

0.999

0.994

0.979

0.988

1.002

0.395

1.012

1.007

1.017

1.009

1.003

1.016

1.012

1.023

1.012

0.120

1.017

1.012

1.026

1.013

1.003

1.024

1.022

1.038

1.017

Table 5
Estimated energy consumption.

Total energy consumption(kcal/day household)Energy for general goods(kcal/day household)Energy for land (kcal/day household)Energy for car trips for everyday life
(kcal/day household)Energy for car trips for commuter(kcal/day household)Energy for walking trips(kcal/day household)Energy for public transport trips(kcal/day household)Time for car trips (min/day household)Time for walking trips(min/day household)Time for public transport(min/day household)

Base
year

P1-A10000
ratio

P1-A5000 ratio

P1-B10000
ratio

P1-B5000 ratio

P2
ratio

P3-A10000
ratio

P3-A5000 ratio

P3-B10000
ratio

P3-B5000 ratio

32,800

1.009

0.998

1.013

1.006

0.997

1.005

0.995

1.006

1.003

25,240

1.010

1.005

1.013

1.006

1.000

1.01

1.005

1.013

1.006

2343
1442

1.008
1.006

1.004
0.963

1.003
1.021

1.002
1.005

0.978
0.992

0.983
0.993

0.979
0.959

0.979
0.992

0.977
1.002

3775

1.005

0.961

1.02

1.004

0.992

0.989

0.953

0.986

1.001

1.346

1.010

1.006

1.011

1.006

1.004

1.015

1.012

1.019

1.009

160.7

1.016

1.011

1.022

1.012

1.004

1.024

1.024

1.036

1.015

31.09
59.08

0.996
0.999

0.973
0.999

1.011
0.998

1.002
0.999

0.993
0.999

0.995
0.998

0.978
0.999

0.994
0.997

0.994
0.998

102.9

0.998

0.999

0.998

0.999

0.999

0.998

0.998

0.997

0.998

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Y. Yin et al. / Applied Energy 168 (2016) 291–302

increasing trend of the consumption of general goods, land, andtrips. Of note is that the number of car trips decrease even withthe subsidy of 5000. It indicates that residents would like to spend
extra money on goods rather than on car trips. Households also
adjust the traffic mode choice to maintain the mobility level andminimize the transport budget. The total traffic expenditure
decreases because part of car trips is substituted by walking andpublic transport trips. The suburban residence taxation policy of
P2 shows a negative effect on the expenditure because of lower
income. There is no subsidy for households who relocate to thedesignated area. But there is tax for households who refuse to
move. Thus the average income decreases relatively. Households
need to reduce expenditures in case of less income. However, not
all consumption of goods decreases. The consumption of general
goods and car trips for everyday life remains stable even income
decreases. Households who relocate to the dense city center area
need less land for housing. Meanwhile, residents tend to walk
more and use public transport as traffic mode rather than car forcommuter trips. The influence of P3 on demand for goods is complex because of a combination of subsidy policy and tax policy. On
one hand, the demand of general goods increases due to the subsidy. On the other hand, P3 shows an effect of reducing the demand
for land due to the effect of the suburban residence taxation policy.
P3 also has influence on the traffic mode share. The demand of car
trips decreases. However, the demand for public transport andwalking trips increases. The possibility of choosing walking andpublic transport as transport modes increases in a compact living
environment as more households locate in the dense designatedarea.
4.3. Energy consumption
Subsidy policy has a positive effect on energy consumption.
With the support of the subsidy, households could spend moremoney on goods, contributing to more energy consumption.
Although trip time of walking and public transport decreases inall subsidy policy scenarios of P1, the energy use of walking trips
and public transport trips increase because of increased demandof such trips. Therefore, total energy consumption in P1 scenarios
increased except P1-A-5000. Although dense living environmentis helpful for decreasing trip distance and reducing trip time, theeffect on energy saving is offset by more consumption of general
goods and land. Low level of subsidy encourages consumption of
goods, but the effect on energy consumption is limited. Energy savings by shorter trip time outweigh the increased energy use formore consumption of goods. This may explain the lower totalenergy consumption of P1-A-5000. However, the outcome is different in the case of P1-B-5000 scenario, in which the population is
supposed to be concentrated in a circle with a radius of 4 km fromthe city center. With more and more residents concentrated in thecity center, more and severe traffic congestions are expected insuch an urban structure. Trip time of car trips increases by 1.1%
and 0.2% in P1-B-10000 and P1-B-5000, respectively.
Suburban residence taxation policy shows a relatively strong
effect on energy reduction. This could be explained by the following reasons. First, the average income decreases due to the tax.
Therefore, residents reduce the expenditure thus consumption of
goods. Secondly, residents adjust the expenditure share of goods
to maximize the utility, which is helpful to decrease energy consumption. The energy used for general goods remains stable. The
consumption of energy-intensive goods, such as land and car trips,
decreases. Increased walking trips and public transport trips attribute to less energy consumption. Lastly, reduced trip timedecreases the energy consumption. Some households would relocate their homes to a dense designated area, which encourages
shorter trip distance and less trip time.

With a combination of relocation subsidy and suburban residence taxation policy, P3 shows a medium effect on energy consumption, neither as high as P1, nor low as P2. Except P3-A5000, energy consumption increases in all scenarios of P3. On
one hand, the relocation subsidy increases the consumption of
goods. On the other hand, the suburban residence taxation policy
means that households who refuse to move to a certain area haveto sacrifice part of their consumption because of the tax. The two
opposite influence directions lead to a medium increase in energy
consumption. Of note is that the energy for land is reduced in all
scenarios of P3. Households tend to choose a dense living environment, which leads to less land consumption at average. Moreover,traffic conditions are much more convenient because there arefewer trips. This leads to shorter trip times, resulting in less energy
consumption for car trips.

5. Conclusion
To investigate the effect of housing relocation policy on energy
consumption, this study simulated the consumption behaviors ofhouseholds under scenarios of subsidy policy and taxation policyin Kumamoto. Residential relocation choice behavior and consumption behaviors were estimated through modeling. A function
was also introduced to calculate the energy consumption based on
estimated behaviors and demand of goods. The simulation resultsin the Kumamoto metropolitan region show four major findings.
First, both subsidy policy and suburban residence taxation policy
influence household consumption behaviors and energy consumption. Second, subsidy policies show effects on household relocation
choice, attracting households to the designated area. However,more general goods and more energy consumption were found in
most subsidy scenarios. Third, suburban residence taxation policy
showed a relatively strong effect on energy reduction due to lessconsumption of car trips and land, and shorter trip time. But itshows a very limited effect on housing relocation choice. Finally,
compared to subsidy policy alone, the integrated policy of subsidy
and suburban residence taxation showed less effect on energy consumption. The incensement rate was lower.
The study provides deep insights into consumption behaviors
and energy use of households at the zone scale, and included aholistic perspective on the impact of relocation policies. It extends
the concept of compact development analysis to a very small
aggregated level and then compares the effect of three types of
housing relocation policies in Kumamoto. To the authors’ knowledge, there are no other models that attempted to quantify consumption of goods and energy use for a household at the zone
scale as this work. The methodology of this paper evaluates theeffect of urban relocation polices on energy consumption throughpersonal consumption behaviors from a new viewpoint. Unlike
previous studies which have taken a limited view of housing relocation choice behaviors, this study focuses not only on housing
relocation choice behaviors but also on consumption behaviors
from a microeconomic viewpoint. Energy consumption is also estimated to give a clear idea of the environmental outcome of policies. The study provides a context for evaluating the impacts ofhousing relocation policies on relocation choice behaviors and consumption behaviors. And it also allows a more quantitative comparison of energy use across different relocation policy scenarios.
Analysis results could not only give suggestions for urban planners
in Kumamoto, but also expand the field of analysis tool of policy
making for governments aiming for dense housing relocation.
Most planning policies in advanced countries aim to develop a
more sustainable urban development pattern of compact cities.
However, the reality of declining populations in the city centerand an increasing share of household in lower-density locations

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Y. Yin et al. / Applied Energy 168 (2016) 291–302

outside the central areas of cities makes achieving compact development challenging. Despite the general trend toward urban
sprawl, in recent times, many cities have made policies which
aim to attract households back into the central area by subsidies
or tax. Although this is a good starting point for compact development, questions that related to the environmental outcome andbehavior implications of such policies still remain. Policymakers
need to consider not just the attraction of high density policies
but also the environmental impacts of the residential communities
they choose. Our paper provided deeper understanding of consumption behaviors and energy use in the context of Kumamotoat a micro level, and give suggestions for the successful implementation of housing relocation policies toward compact development
at Kumamoto.
Based on the findings of this study, there are three implications
for the future policy making for compact development. First, residents would benefit from the subsidy policy through more goods
and a better social life. However, the amount of subsidy should
be carefully considered. Different subsidy levels show different
effects on energy consumption. Change of consumption behaviors
could save energy in a dense environment. But meanwhile theamount of consumption would increase due to the subsidy. Theenergy consumption of the whole city may increase because of
more goods consumption. Moreover, the government should havea clear idea of the origin of subsidy and distribution of subsidy
since they are important issues of the society. Second, it needs tothink twice when make suburban residence taxation policy.
Although it is found to be effective on reducing energy consumption, it is such a kind of punishment policy that could not be
accepted easily by households. Finally, beyond money incentives
such as a subsidy or tax, there is a significant role for urban planners to improve the design of the dwelling unit to provide residential environments that are suitable throughout all stages of anindividual’s life. This could increase the attractiveness of the dense
living areas in the city center because it could improve the stability
and quality of life experienced in these areas. All three points
would benefit future academic study by deeply investigating on
the relationship between consumption behaviors, energy use,
and relocation choice behaviors. Useful findings could be driven
form to give suggestions for urban planners, transport planner,and energy saving policy making that toward to compact
development.

nor4O =ðr4O 1Þ
ðr 1Þ=r4O
ðr 1Þ=r4O
xOi ¼ aC2 xC2i4O
þ aM xMi4O

max

fxC2i ;xMi gðA2Þ

s:t: pC2i xC2i þ pMi xMi 6 I4Oi
Using Lagrangian method, the solutions of Eqs. (A1) and (A2) are
shown as Eqs. (A3) and (A4):


xmi ¼

am

r4P


xni ¼

an

I4Pi

r4P
r4P
arC14P p1
þ arW4P p1
C1i
Wi

pmi
r4O

r4O 1r4O

I4Oi

aC2 pC2ipni

r4O
þ arM4O p1
Mi

ðm ¼ C1; WÞðA3Þ

ðn ¼ C2; MÞðA4Þ

The maximum demand of everyday life trips (x⁄Pi) and maximum
demand of commuter trips (x⁄Oi) are shown as Eqs. (A5) and (A6):
r4P
r4P
xPi ¼ ðarC14P p1
þ arW4P p1
Þ
C1i
Wi

1=ðr4P 1Þ

r4O
r4O
þ arM4O p1Þ
xOi ¼ ðarC24O p1
C2i
Mi I4Pi1=ðr4O 1Þ I4OiðA5ÞðA6Þ

Thus the price of everyday life trips (pPi) and the price commuter trips (pOi) are shown as Eqs. (A7) and (A8):1=ð1r4P Þ

r4P
r4P
pPi ¼ ðarC14P p1
þ arW4P p1
Þ
C1i
Wi

r4O
r4O
þ arM4O p1
Þ
pOi ¼ ðarC24O p1
C2i
Mi1=ð1r4O Þ

ðA7Þ
ðA8Þ

At the second stage, the maximum problem for the demand oftransport goods is solved (Eq. (A9)).

nor3 =ðr3 1Þ
ðr 1Þ=r3
ðr 1Þ=r3
xTi ¼ aP xPi 3
þ aO xOi 3

max

fxPi ;xOi gðA9Þ

s:t: pPi xPi þ pOi xOi 6 I3i
The solution of Eq. (A9) is shown as Eq. (A10)xai ¼

aa

r3

I3i

r3
r3
arP 3 p1þ arO3 p1
Pi
Oi

pai

ða ¼ O; PÞðA10Þ

The maximum demand of transport goods (x⁄Ti) is shown as Eq.
(A11).
r3
r3
xTi ¼ ðarP 3 p1
þ arO3 p1
ÞPiOi

1=ðr3 1Þ

 I3i

ðA11Þ

Thus the price of transport goods (pTi) is shown as Eq. (A12).
1=ð1r3 Þ

Acknowledgments

r3
r3
pTi ¼ ðarP 3 p1
þ arO3 p1
ÞPi
Oi

The project is sponsored by the Scientific Research Foundation
for the Returned Overseas Chinese Scholars, State Education
Ministry. The work described in this paper was also supported by
the National Science Foundation of China (NSFC) (41301171). This
work was supported by the K.C. Wong Magna Fund and the‘‘Subsidy stimulation mechanism and the influence on the operation of bus companies” project (XKl15D234), sponsored by the
key discipline of ‘‘Transportation planning and management” ofNingbo city.

At the third stage, the maximum problem for the demand ofcomposite goods is solved (Eq. (A13)).

Appendix A
Four steps are included in the solution process. At first, themaximum problem of everyday life trips for car trips and public
transport trips is shown as Eq. (A1), and the maximum problem
of commuter trips for car trips and walking trips is shown as
Eq. (A2):

max

fxC1i ;xWi gn

ðr4P 1Þ=r4P
þ
C1 xC1ixPi ¼ as:t: pC1i xC1i þ pWi xWi 6 I4Pia

ðr4P 1Þ=r4P
W xWi

or4P =ðr4P 1Þ
ðA1Þ

ðA12Þ

n
or2 =ðr2 1Þ
ðr 1Þ=r2
ðr 1Þ=r2
xAi ¼ aL xLi 2
þ aT xTi 2

max

fxLi ;xTi g

ðA13Þ

s:t: pLi xLi þ pTi xTi 6 I2i
The solution of Eq. (A13) is shown as Eq. (A14).


xhi ¼

ah

phi

r2

I2i

r2
r2
arL 2 p1þ arT 2 p1
LiTiðh ¼ L; TÞðA14Þ

The maximum demand of composite goods (x⁄Ai) is shown as Eq.
(A15).
r2
r2
xAi ¼ ðarL 2 p1
þ arT 2 p1ÞLiTi

1=ðr2 1Þ

 I2i

ðA15Þ

Thus the price of composite goods (pAi) is shown as Eq. (A16).
r2
r2
pAi ¼ ðarL 2 p1
þ arT 2 p1ÞLiTi

1=ð1r2 Þ

ðA16Þ

At the fourth stage, the maximum problem for the utility issolved (Eq. (A17)).

Y. Yin et al. / Applied Energy 168 (2016) 291–302

302nor1 =ðr1 1Þ
ðr 1Þ=r1
ðr 1Þ=r1
ui ¼ aG xG 1
þ aA xAi 1

max

fxGi ;xAi gðA17Þ

s:t: pGi xGi þ pAi xAi 6 Ii
The solution of Eq. (A17) is shown as Eq. (A18).

 r1

al

xli ¼

Ii

r1
r1
arG1 p1
þ arA 1 p1
Gi
Ai

pli

ðl ¼ A; GÞ

ðA18Þ

The maximum utility (u⁄i ) is shown as Eq. (A19).
1=ðr1 1Þr1
r1
ui ¼ ðarG1 p1
þ arA 1 p1
Þ
Gi
Ai

 Ii

ðA19Þ

By integrating the solutions of five maximization problems atfour stages, the final optimal demands of general goods (x⁄Gi), optimal demand of land (x⁄Li), and optimal demand of car trips, public
transport trips, and walking trips (x⁄mi) at maximum utility are
shown as Eqs. (A20), (A21) and (A22).

xGi ¼

Ii



¼

aL
pLi

aL

r2
r2



am

I2i

r2
r2
arL 2 p1þ arT 2 p1
Li
Ti

Ii

r2
r2
arL 2 p1þ arT 2 p1
Li
Ti

pLi

r4k

pmi

ðA20Þ

r1
r1
arG1 p1
þ arA 1 p1
Gi
Ai

pGi

xLi ¼

X mi ¼

r1

aGp
1  r 1r Gi r 1raG1 pGi 1 þ aA 1 pAi 1
r4k r3

!
ðA21Þ

n

r4k
r
1r
r4P
ark 3 arT 2 arA 1 ðarm4k p1
þ ani4k pni 4k Þ 1r4k arP 3 ðarW4P p1
mi
Wi
1r3

r4P 1r3
r4O
r4O
Þþ arO3 ðarM4O p1
þ arC24O p1Þþ arC14P p1
C1i
Mi
C2i

3 r2 n
or1
r
3

r2
arL 2 p1
L1

1r3

r4P
r4P
r4O
þ arT 2 ðarP 3 ðarW4P p1
þ arC14P p1Þþ aro 3 ðarM4O p1
Wi
C1i
Mi
(
or1
2 r1
n
r2
r4O 1r3 1r2
r1
r2
þ arC24O p1
ÞÞ
arG1 p1
þ arA 1 arL 2 p1
G
L1
C2i

n
r4P
r4P 1r3
þ arT 2 arP 3 ðarW4P p1
þ arC14P p1
Þ
Wi
C1i
r3

r4O 1r4O

þ aO ðaM pMi

r4O 1r4O 1r3

þ aC2 pC2i

Þ

91
1r
o1r2 1r12 =;Ii

m ¼ C 1 ;W;k ¼ P; n ¼ C 2 ;M; k ¼ O or m ¼ C 2 ;M;k ¼ O;n ¼ C 1 ; W;k ¼ P
ðA22Þ

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