Energy Policy 61 (2013) 909–919

Contents lists available at ScienceDirect

Energy Policy
journal homepage: www.elsevier.com/locate/enpol

An analysis of the inﬂuence of urban form on energy consumption
by individual consumption behaviors from a microeconomic viewpoint
Yanhong Yin a, Shoshi Mizokami b,n, Takuya Maruyama caFaculty of Maritime and Transportation, Ningbo University, 818 Fenghua Road, Jiangbei District, Ningbo 315211, China
Department of Civil and Environmental Engineering, Kumamoto University, 2-39-1, Kurokami, Kumamoto 8608555, Japanc
Center for Policy Studies, Kumamoto University, 2-39-1, Kurokami, Kumamoto 8608555, Japanb

H I G H L I G H T S

 Energy consumption is estimated by demand of composite goods, mobility goods.
 52.84 GJ of energy is estimated to satisfy one person per year in Kumamoto.
 80% of energy is for composite goods and 20% for mobility goods.
 Land use diversity and distance to city center, affect energy consumption most.
 Employment density and transit fare are inﬂuential factors of energy efﬁciency.

art ic l e i nf o

a b s t r a c t

Article history:
Received 2 December 2011
Accepted 13 June 2013
Available online 19 July 2013

Using 1997 personal trip survey (PTS) data in the Kumamoto metropolitan area, this paper examined theinﬂuence of urban form on energy consumption through an energy estimation model from a
microeconomic perspective. As all goods and service are assumed to satisfy the need of people, weestimated the individual energy consumption based on the demand of goods, which is explained by autility maximization problem constrained by income. 52.84 GJ of energy is estimated for one person one
year in Kumamoto metropolitan area. 19.57% of energy is used for mobility goods. A spatial regression
was performed to analyze the relationship between energy efﬁciency and urban form characteristics interms of density, diversity, and accessibility. The results of regression analysis show that employment
density, ratio of employee in retail department, transit fare, and distance to city center are the mostinﬂuential factors of energy efﬁciency. Findings suggest compact development and integrated policies forincreasing employment density, especially, employment proportion of local residents are suggested.
Moreover, measures to improve the attractiveness of mass transit should be encouraged to increaseenergy efﬁciency in Kumamoto.
Crown Copyright & 2013 Published by Elsevier Ltd. All rights reserved.

Keywords:
Individual energy consumption
Urban form
Compact development

1. Introduction
Urbanization is occurring at an accelerating pace, accompaniedwith the creation of some megacities, which is currently deﬁned
by the United Nation as cities with more than 10 million population (Bugliarello, 2006). The magnitude and rate of urban growth
make urban sustainable development become a crucial matter ofglobal sustainability. Many studies have discussed that the urban
forms attribute to sustainable urban development, such as thecompact city (Frey, 1999; Williams et al., 2000; Jabareen, 2006).
Urban from is considered to be an important factor in addressingnCorresponding author. Tel.: +81 96 342 3541; fax: +81 96 342 3507.
E-mail addresses: yinyanhong@nbu.edu.cn (Y. Yin),smizo@gpo.kumamoto-u.ac.jp (S. Mizokami),
takumaru@kumamoto-u.ac.jp (T. Maruyama).

urban sustainable development and climate change. The spatial
conﬁguration of urban land use within a metropolitan area
resulted in diverse social, ecological, and environmental consequences (Camagni et al., 2002; Holden, 2004). These consequencesof urban form have been analyzed by energy consumption becauseof two reasons. First, from the physical standpoint, the urban
spatial conﬁguration and land use affect the total amount ofenergy consumption. Second, the density and intensity of activities, such as trafﬁc and industry, is a major factor inﬂuencing
energy consumption. Moreover, growing concerns about surging
oil prices and the greenhouse gas produced by burning fossil fuelsrequire that urban development not only minimizes resource use
and spatial displacement for ecosystems, but also improves energy
efﬁciency.
The debate regarding the relationship between energy
consumption and urban form have attracted lots of studies from0301-4215/$ - see front matter Crown Copyright & 2013 Published by Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.enpol.2013.06.054

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Y. Yin et al. / Energy Policy 61 (2013) 909–919

both theoretical and empirical aspects. Some literatures analyzed
the relationship between energy consumption and urban form
factors among cities. Aggregate studies examined the bivariate
relationship between urban form and energy consumption (Crane,
2000; Ewing and Cervero, 2010). Newman and Kenworthy (1999)
analyzed the relationship between population density and gasoline consumption in megacities worldwide, which suggested an
obvious negative relationship between population density andtransportation energy consumption per capita. Their analysis did
not consider socioeconomic variations among cities. Such ananalysis fails to emphasize the social and economic effects onenergy consumption.
Socioeconomic attributes are very inﬂuential to household
travel and energy consumption (Susilo and Stead, 2008; Mustiet al., 2010; Liu and Shen, 2011). Increasing the income leads to achange in consumer needs, which results in rising energy consumption due to growing numbers of household electrical appliances and shifting toward energy intensive transportation modes(Feng et al., 2010). Previous studies utilized disaggregate household data to investigate the differences of household energy
consumption in different urban living environment. Using thedata of 2001 National Household Travel Survey, Brownstone and
Golob (2009) analyzed the relationship of residential density,
vehicle use, and fuel consumption for California households. They
found the most inﬂuential variables were the number of household drivers, the number of workers, education and income. Basedon six case studies in the United Kingdom and the Netherlands,
Banister et al. (1997) found factors signiﬁcantly affecting urban
energy consumption were density, employment, and car ownership. This kind of disaggregate studies included a rich set ofsocioeconomic variables and clearly demonstrated the effects ofurban form on energy consumption. However, most studies
focused on household, and the data included only householdenergy consumption in Residential and Transportation sectors,
such as energy for space heating and cooling, appliances andlighting, domestic hot water and private cars. Energy consumption
for Commercial and public services, which shared largely inhousehold energy consumption, was not considered. According
to a statistic report from Agency for Natural Resources and Energy,
METI (Ministry of Economy, Trade and Industry), energy use inCommercial sector accounts for 25.07% of total energy consumption in all sectors in Kumamoto prefecture, 1997, compared to thatof 23.07% in Residential sector. A study in China demonstrated thedecreased absolute amount of energy consumption and CO2
emissions for making food, but growth for education, culturaland recreational services as income increased (Feng et al., 2010).
It is essential but difﬁcult to obtain household energy data of all
sectors. The way to solve this problem is to build models toestimate the household energy consumption. Models that describe
behaviors under a number of demographic conditions enable us toestimate energy consumption and assess the impact of urban formon energy use. One commonly applied model was to forecast
urban energy consumption in transportation sector over a range ofdriving conditions (Stone et al., 2007; Swana et al., 2011). We
previously developed a quantitative model for estimating energy
consumption based on individual consumption behaviors (Yin and
Mizokami, 2011). The model was applied to assess compact levelof cities based on individual energy consumption and utility.
Moreover, models that integrated land use, transportation andresidential location choice have been built to estimate energy
consumption, such as integrated land use and transport model
TRANUS (Bravo et al., 2010). TRANUS enables users to study theeffects of land use and transport policies, either singly or in
combination. The location and interaction of activities determine
the demand of energy consumption. Its effort to model the causal
mechanisms, which combines direct and indirect links throughintermediate variables of urban form to travel and energy consumption, making TRANUS a very attractive point. However, themodel requires extensive data for calibration which limits its
application.
Anderson et al. (1996) provided a good literature synthesis byreviewing the basic concepts of urban form, the relationships
among urban form, energy use, and the effects of using various
land use and transportation policy instruments to achieve energy
reduction. Although a growing body of literature support thenotion that urban form plays a role in energy consumption, theempirical ﬁndings on energy consumption and urban form
outcomes are less conclusive, and little is known about how urban
form inﬂuences resident consumption behaviors. They concluded
that the inﬂuence of urban form on energy consumption is still
unclear. This uncertainty therefore requires more empirical workand more comprehensive quantitative models that involved more
behavior analysis. So far, few researchers have empirically investigate the linkage between the urban form factors and individualenergy consumption by behavior data.
This paper studies the link between urban form and energy
consumption through individual consumption behaviors from a
microeconomic perspective. At micro level, the effect of urban
form on energy consumption is reﬂected by the individual consumption behaviors. A focus on behavior allows for considerationof inﬂuence of socioeconomic factors, such as income. Moreover,focusing on consumption behaviors promotes ways to estimate
individual energy use for daily living. It is expected that thisestimation approach based on consumption behaviors would be
more feasible and rational for a better understanding of the effects
of urban form on energy consumption, which will have positive
returns for both the environment and city policy making.
Section 2 presents the methodology, including a model forenergy estimation, an index of energy efﬁciency, and thelinear regression. Section 3 describes the context of the empiricalwork, the studied areas of Kumamoto, data set, and quantitative
process for energy estimation. Section 4 presents and discusses theenergy estimation results and relationship analysis of urban fromand energy consumption by a regression model. The main ﬁndings
and suggestions for policies in Kumamoto are summarized in
Section 5.

2. Methodology
2.1. Energy estimation model
The purpose of all urban activities is assumed to satisfy thedemand of residents, which need energy to support. Thus, theenergy consumption can be estimated based on the demand of
individuals. In microeconomics, the demand is represented by theneed of goods and service, which are explained by personal
consumption behaviors. In economics, utility is a representationof preferences over some set of goods and services. Although it is
impossible to measure the utility derived from a good or service, it
is usually possible to rank the alternatives in their order ofpreference to the consumer. Economists have theorized that autility function could be used to express the scale of preference todescribe consumer behaviors. Individual demand is mathematically modeled as the process of maximizing utility under given
constraints, such as income (Stigler, 1950).
This study focuses on the individual ﬁnal energy consumptionof some categories that closely relate to the daily living, including
energy use in Residential, Commercial, and Transportation sectors.
Energy in Industry sector is not considered in this study because it
has less direct inﬂuence on individual daily life compared to theother three sectors. Moreover, it is complex and not suitable toY. Yin et al. / Energy Policy 61 (2013) 909–919

include energy in Industry sector into the model which focuses on
individual consumption behaviors.
Goods are carefully selected to represent all consumption
behaviors in daily living. As transport is a major contributor toenergy consumption, all goods are classiﬁed into two types:
mobility goods and composite goods. Transportation services arecalled mobility goods, including car trips and mass transit trips.
Composite goods are all other goods except mobility goods. It
represents all goods in Residential and Commercial sectors, suchas heating, cooling, food and recreation.
The subject of this study is a “representative individual” in a
trafﬁc zone. To estimate the energy consumption of a “representative individual”, it is essential to estimate the demand of goods
consumed by the “representative individual”, which is explainedby a utility function. Following assumptions are vital to develop
the utility function: (a) The consumption preference of the“representative individual” in a “representative household” isapplied as a representation of all individuals’ behaviors in one
zone. (b) The “representative individual” in each zone is assumed
to consume two kinds of goods: composite goods and mobility
goods. The demands is expressed by variables x1i and x2i, respectively, in zone i. (c) The demand of mobility goods x2i is a functionof the numbers of car trips x2Ci and mass transit trips x2Mi.
(d) Composite goods are all other goods except mobility goods.
(e) Utility ui is a function of three kinds of goods consumption.
(f) The individual is assumed to maximize utility and mobility
under an income constraint. (g) All income is spent on consuming
without saving.
Based on these assumptions, a nested constant elasticity of
substitution (CES) function is chosen to express the utility function(Fig. 1). CES is a particular type of aggregator function thatcombines two or more types of consumption into an aggregate
quantity (Kanemoto et al., 2006). This aggregator function is used
to represent the constant elasticity of substitution between composite goods and mobility goods at the ﬁrst order (Eq. (1)), andbetween car trips and mass transit trips at the second order(Eq. (2)). Here, s1 and s2 are the elasticity of substitution between
two kinds of goods at the ﬁrst and the second order. α1 and α2 are
the share parameters of composite goods and mobility goods,
which means the spending share for composite goods and mobility goods in total income. α2C and α2M are share parameters of car
trips and mass transit trips, indicating the spending share of car
trips and mass transit trips in total transport budget.
We assume that people attempt to maximize both utility andmobility. The maximum utility is achieved by solving two maximization problems. The ﬁrst is mobility maximization problem
provided in Eq. (3). It determines the number of car trips and masstransit trips subject to the transportation budget. The second
maximization problem is to calculate the maximum utility basedon consumption of composite goods and maximum mobility under
the income constraint (Eq. (4)). p1i, p2i, p2Ci, p2Mi are prices ofcomposite goods, mobility goods, car trip, and mass transit trip inzone i, respectively. Ii is the individual income and I2i is theindividual transportation budget. The solution process of the maximum mobility and maximum utility was outlined in Appendix A.

911

The energy consumption is estimated based on the demand of
three kinds of goods on the maximum utility. Ei is the individualenergy consumption in zone i, which is determined by thedemand of goods and trip time (Eq. (5)). Trip time is introduced
into the estimation function considering the relationship between
energy consumption and trafﬁc congestion. e1, e2, e3 are energy
consumption unit of composite goods, car trip, and mass transitnnn, x2Ci, x2Miare the optimal demand oftrip, respectively. x1icomposite goods, car trips, and mass transit trips on the maximum
utility uin , respectively.
2.2. Energy efﬁciency
The concept of energy efﬁciency refers to reducing the amountof energy required for production and services. In general,
improvement in energy efﬁciency is achieved by adopting a highefﬁcient technology or production process. Similar concept ofenergy efﬁciency is also applied in energy economic ﬁeld. Energy
intensity is a measure of the energy efﬁciency of a nation's
economy. It is calculated as units of energy per unit of GDP. Highenergy intensities indicate a high price or cost of converting
energy into GDP. Many factors inﬂuence an economy's overall
energy intensity, such as the general standards of living andweather conditions in an economy. Different from energy per unitof GDP, this paper introduces the indicator of energy unit ofexpenditure to evaluate energy efﬁciency. It represents how muchenergy is needed for spending one unit of expenditure on goods
from viewpoint of consumption. The energy unit of expenditure is
calculated as the ratio of energy consumption to expenditure of
one kind of goods. Bigger energy unit of expenditure means lower
energy efﬁciency, indicating more energy is needed for spending
one yen for goods consumption.
This paper also introduces a synthetic indicator of energy
efﬁciency, which is called synthetic energy unit of expenditure.
It evaluates the energy unit of expenditure for all kinds of goods.
Energy unit of expenditure of car trips, mass transit trips andcomposite goods are aggregated into synthetic energy unit ofexpenditure, which is calculated as follows:
Synthetic energy unit of expenditure¼(energy unit of expenditure of composite goods  expenditure share of composite
goods)+(energy unit of expenditure of car trips  expenditure
share of car trips)+(energy unit of expenditure of mass transit
trips  expenditure share of mass transit trips).
2.3. Multilinear regression analysis
A multiple linear regression model is applied to analyze theeffect of urban form on energy consumption. The synthetic energy
unit of expenditure is chosen as dependent variable. Explanatory
variables are indicators of urban form characteristics.
Urban form is not simply the structure of land use, but also
involves population distribution, transport accessibility, andcommercial development. Characteristics of urban form are
represented by nine variables from density, diversity, and accessibility aspects. Density is highly correlated with almost all

Utility ui
First order

Composite goods x1i

σ1
α1

α2

Mobility goods x2i
Second order

Car trips x2Ci

α2C

σ2

α2M

Fig. 1. The structure of CES utility function.

Mass transit trips x2Mi

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Y. Yin et al. / Energy Policy 61 (2013) 909–919

Fig. 2. The Kumamoto metropolitan area. (a) The location of Kumamoto prefecture in Japan, (b) Urban structure of the Kumamoto metropolitan area.

measures of urban form and is a measure most frequently used
(Ewing and Cervero, 2010). It is interpreted as a density of
population, employment, and students in this paper. Population
density and employment density refers to the number of person
or employees in per square meters, respectively. Of note is thatlittle is known about how school commuting inﬂuences energy
consumption. With the data of student numbers, study density isalso included as a density indicator in this study. The number of
employees in retail department is chosen as the indicator ofdiversity of urban form by some study (Jenks and Jones, 2009),
because it captures the variety of attractions within a designatedarea. However, the number of employees in retail department is
not the perfect indicator of diversity for this study, which focuseson energy consumption. Even with same number of employees inretail department, the proportion of local employees who live
and work in the same zone affect the amount of energy
consumption. More residents live and work in the same place,less and shorter commute trips are expected, contributing to lessenergy consumption. Thus, we developed the indicator of “ratioof employees in retail department to population” as a variable ofland use diversity. It evaluates the ratio of employees in retaildepartment to population in each zone. Accessibility reﬂects
potential spatial interaction and is categorized as trip-based
and activity-based. Trip-based accessibility is expressed by car
trip accessibility and mass transit trip accessibility. Road density
is chosen to evaluate the accessibility to car trips which is deﬁned
as the length of expressways and highways per square kilometer.
Mass transit trip accessibility is represented by three variables:transit stop density, frequency of mass transit service, and themass transit fare. As services are mainly concentrated in city
center, distance to city center zone is used to evaluate theactivity-based accessibility. It is a simple geometric distancecomputed from a map.
Multicollinearity may exist among selected explanatory variables because the dataset employed are aggregated at the levelof trafﬁc zone. A variance inﬂation factor (VIF) analysis isperformed to examine the independence of the explanatory
variables before regression. If VIF is greater than 20, multicollinearity is assumed to exist. The condition number is also
investigated as a general measure of multicollinearity. If thecondition number is bigger than 15, multicollinearity is assumed
to exist.

Y. Yin et al. / Energy Policy 61 (2013) 909–919

3. Case study
3.1. Studied area
Kumamoto metropolitan area is chosen as the study area
because of data availability. Kumamoto metropolitan area is partof Kumamoto prefecture located in the center of the Kyushu Island(Fig. 2). Kumamoto city is the center of the prefecture, culturally
and economically. It takes ninety-ﬁve minutes to reach the cityfrom Tokyo by airplane (1072 km), but only eighty-ﬁve minutes
from Seoul in Korea (631 km). Kumamoto prefecture, the ﬁfteenthlargest area in Japan, covers approximately 7402 square
kilometers. Kumamoto metropolitan area covers roughly 1077
square kilometers, including two cities (Kumamoto and Uto),
fourteen towns, and one village. The west part reaches to the
Ariake and the Yatsushiro seas which link to the East China Sea.
The population of Kumamoto prefecture is 1812,255 in 2010,
which ranks 23rd in Japan. There is a decreasing and ageing trendof population since 1995. The phenomenon of aging has begun ten
years ahead of the rest of the country. Kumamoto prefecture is
blessed with rich greenery and abundant groundwater. It is anagriculture-based region, famous for the production of rice,vegetable and fruits. Electronics, vehicle manufacturing and foodprocessing are major secondary industries in Kumamoto. In
particular, the IC (integrated circuit) industry commands around
12% share of domestic production and it constitutes the major
production hub in Kyushu Silicon Island.
3.2. Data
3.2.1. 1997 Personal trip survey (PTS)
Personal trip survey (PTS) is a person-based travel survey
conducted every ten years by Ministry of Land, Infrastructure
and Transport (MLIT). Daily travel is collected using one-day trip
diaries for all household members in selected households. The
main part of PTS dataset is the personal trip ﬁles which provide
the information of trip purpose, trip distance, travel time, andtravel mode. Raw PTS data has been aggregated at the trafﬁc zone
level, which is available from reports provided by Kumamoto
Metropolitan Area Urban transport Planning and Consultation
Council. Data of car trips and mass transit trips in 1997 areaggregated at zone level. We only focus on trips for purposes ofcommuting, business, shopping, and returning home.

913

3.2.3. Trip time
By assigning car trips and mass transit trips on maximum
utility, trip time of all trips is obtained. We set average time of all
trips from zone i to other zones as the value of trip time in zone i.
3.2.4. Energy consumption unit
According to the statistical summary of energy use by Agency
for Natural Resources and Energy, METI, energy consumption unitof Residential and Commercial sector is 16.14 kJ/yen in Kumamoto
prefecture, 1997 (includes residential, water supply, sewage andwaste disposal, trade and ﬁnance service, public service, commercial service, retail servicers). Composite goods include all goods in
Residential and Commercial sector. The energy unit of composite
goods is assumed same as the energy consumption unit of
Residential and Commercial sector, that is 16.14 kJ/yen in thisstudy (Table 1). Referring to energy consumption unit of trip
distance (kcal/trip·km) in the report, the energy consumption unitof trips is calculated as follows:
Energy consumption unit of trip (kJ/trip min) ¼energy consumption unit of trip distance (kJ/trip min)  average speed (km/min).
3.2.5. Income
It is difﬁcult to obtain individual income data (yen/person·day)in each zone. Only the average individual income of each administrative district in 1997 is available from the homepage ofKumamoto prefecture government (http://www.pref.kumamoto.
jp/site/statistics/list1288-2370.html). The total income of a town isdistributed among zones according to personal income ratio andpopulation in 1997. Since a positive relationship between land
price and income is assumed, the personal income ratio is
calculated based on the zonal land price ratio in 1997. Land pricedata is from the Japanese National Tax Agency.
3.2.6. Urban form data
The 1997 PTS provides data related to number of population,
employees and students. Data of road length, number of masstransit stops, frequency of mass transit services in 1997 are from
Kumamoto prefecture government. The distance to city center isdetermined by measuring the distance from zone centroid to city
center in a GIS map of the Kumamoto metropolitan area.
3.3. Parameter estimation

3.2.2. Price of goods
The price of composite goods, p1i, is set to be as one. The priceof mobility goods, p2i, is determined by the price of car trip andmass transit trip (Eq. (6)). The price of a mass transit trip p2Mi (yen/trip) is calculated by the mass transit fare based on assignment
results. It is essential to decide the running fee unit before
determining the price of car trips. The running fee unit is deﬁned
as unit of yen/km·vehicle by MLIT. It measures the monetary costfor running per vehicle kilometer, including fees related to oil, tire,
tube, vehicle maintenance and vehicle depreciation. Without
access to running fee unit in 1997, we referred to a report titled“A method to calculate unit value of time and running fee unit in2003” from MLIT. Considering the economic slump in Japan, it
assumed that there is limited inﬂuence of inﬂation on the price.
Utilizing the running fee unit in 2003, the price of car trip is
calculated as follows:
p2Ci (yen/ trip) ¼(running fee unit (yen/km·vehicle)  minimum
distance from zone i to j (km/trip))/average number of passengers(trip/vehicle).
Here, the average number of passengers in a car is 1.21
suggested by the report from MLIT.

The elasticity of substitution between composite goods andmobility goods, s1, is estimated as 0.6577 (Table 2). The elasticity
of substitution between car trips and mass transit trips, s2, is
1.0787. Residents spend most of their income on composite goods,
Table 1
Energy consumption unit of goods in Kumamoto
metropolitan area.
Goods

Energy consumption unit

Composite goods e1 16.14 (kJ/yen)
Car trip e2825.40 (kJ/trip min)
Mass transit trip e3 76.02 (kJ/trip min)Table 2Estimation of parameters of utility function.
s1

s2

s1

s2

s2C

s2M

0.65771.07870.99950.00050.80400.1960

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Y. Yin et al. / Energy Policy 61 (2013) 909–919

represented as large value of α1. The estimated α2C is 0.8040,
indicating more than eighty percent of transport fare is spent forcar trips. Mass transit trips fare accounts for only 20%, shown as
the small value of α2M.

model share. The estimation result of a, coefﬁcient of zone dummy,shows different signs on car and mass transit trip share, suggesting
more mass transit trips instead of car trips are expected if the zone
is closer to the city center.

3.4. Procedure of energy consumption estimation
It is necessary to estimate the optimal number of car trips andcorresponding trip time before energy estimation. However, it is
difﬁcult to determine the right number of trips, because there is arelationship between trip number and trip time. Trip number
inﬂuences the trip time, and verse versa. Trip time and trip
number affect each other, and ﬁnally reach to a balance solution.
To search the solution, a loop is designed to estimate the energy
consumption on maximum utility by seven steps (Fig. 3). Step 1:
The primary value of trip time and trip price is set by 1997 PTS
data. Step 2: The optimal demands of goods are calculated basedon solutions of maximum utility problem. Step 3: Using adestination choice model, all car trips and mass transit trips ofeach zone x2Ci and x2Mi are distributed to all zones to build OD（Original-Destination） matrices by mode. OD matrix is a “triptable” that matches trip makers’ origins and destinations. It
displays the number of trips going from each origin to each
destination. The destination choice model is mentioned in thefollowing paragraph in detail. Step 4: Comparing the new built OD
matrix with OD data obtained from previous loop (or OD matrix
from survey for the ﬁrst time running), if the difference between
two OD matrix is within 5%, they are assumed be same. Then thewhole process stops. Energy consumption is calculated based on
the demand data in step 2. Otherwise turn to step 5. Step 5: Car
trips and mass transit trips are assigned to renew the trip priceand trip time. Step 6: Optimal demand of goods on the maximum
utility is renewed based on revised trip price and trip time, p2Ci,
p2Mi, t2Ci, t2Mi. Step 7: Return to step 2 again.
An aggregated logit type model is applied to distribute trips by
three variables (Eq. (7)): center zone dummy Dj (takes the value
1 for center zone and 0 in other cases), job population Zj andgeneralized cost G2mij (generalized cost from zone i to zone j via
car or mass transit). Tijm is the number of trips from zone i to zone j
via mode m, while Tim represents the all trips in zone i by mode m.
Coefﬁcients of Dj, Zj and G2mij are expressed by a, b, c, respectively.
All three variables show signiﬁcant inﬂuence on model share withstatistical signiﬁcance level less than 5%. Generalized cost is foundnegatively related, while job population is positively related with

Maximum utility solutions

Amount of composite goods, number of

4. Results and discussion
4.1. Energy consumption
Table 3 shows the result of main features of estimated energy
consumption, which is summarized to give a brief introduction by
Statistical Program for Social Science (SPSS) software 18.0. A totalof 52.84 GJ of energy consumption is estimated to be necessary foreach resident per year in Kumamoto. Energy for composite goods
is 42.50 GJ per person per year, accounting for 80.43% of the totalenergy consumption. The proportion of energy for private car
travelling is 19.13%, that is 10.11 GJ/person year. Only 0.44% ofenergy is used for mass transit trips. Each resident in Kumamoto is
estimated to use 0.23 GJ for mass transit trips. 16.14 kJ is needed
for consuming one unit of composite goods. Each car trip costs
4.08 kJ in Kumamoto. While resident spends 0.09 kJ for one masstransit trip.
According to a report from Agency of Natural Resources andEnergy, METI, energy consumption unit of Residential, Commercial
and Passenger car transportation is 19.01 kJ/yen in Kumamoto
prefecture, 1997. The average individual income is 7,438 yen/person day in 1997 from website of Kumamoto prefecture government (http://www.pref.kumamoto.jp/site/statistics/list1288-2370.
html). It means that one resident is estimated to consume
141.40 MJ of energy each day, equaling to 51.61 GJ/person year inthis area. The 95% conﬁdence interval for mean of estimatedenergy consumption by model is from 50.74 GJ to 54.92 GJ. The
government data (51.61 GJ/person year) falls into 95% conﬁdence
interval, suggesting that the model estimation result is acceptable.
Individual energy consumptions in and out of Kumamoto city
are different (Table 4). Compared with people who live outside ofKumamoto city, residents in the city consume more energy forcomposite goods and mass transit trips, and less energy for car
trips. This tendency is also shown in the result of energy share,
indicated as high energy share of composite goods and masstransit trips, low share of car trips in Kumamoto city. However, thedifference between total energy consumption in and out of city isinsigniﬁcant.
Table 3A descriptive report of energy consumption estimation result in Kumamoto
metropolitan area.

trips by car and mass transit

Mean

x1i, x2Ci, x2Mi

Renewed cost p2Ci, p2Mi,
and travel time t2Ci, t2Mi

Standard
error ofmean

95% Conﬁdence interval for
mean
Lower
bound

Upper
bound

MedianDestination choice model
Assignmentof car and mass transit trips
OD matrix by modeNo

Convergence
Yes
Energy consumption

Fig. 3. A loop for energy estimation.

Energy consumption (GJ)
Energy for composite
goods (GJ)
Energy for car trips (GJ)
Energy for masstransit trips (GJ)
Energy per composite
goods (kJ)
Energy per car trip (kJ)
Energy per mass transit
trip (kJ)

52.84
42.50
(80.43%)
10.11(19.13%)0.23(0.44%)
16.14

1.06
0.84

50.74
40.85

54.92
44.15

50.41
41.07

0.58

8.96

11.25

8.92

0.07

0.09

0.37

0.11

0.00

16.14

16.14

16.14

4.08
0.09

0.24
0.03

3.60
0.03

4.56
0.14

3.62
0.05

Y. Yin et al. / Energy Policy 61 (2013) 909–919

4.2. Energy unit of expenditure
Table 5 lists the result of energy unit of expenditure of eachkind of goods, and synthetic energy unit of expenditure. All listed
values are the medium values, because it is necessary to eliminate
the inﬂuence of some extreme values. Energy unit of expenditureof composite goods is 16.14 kJ/yen for all residents in and out ofKumamoto city. A total of 168.70 kJ is needed for spending on car
trips in Kumamoto metropolitan area per yen. Energy unit ofexpenditure of mass transit trips is estimated as 13.82 kJ/yen. The
aggregated indicator of three kinds of goods is calculated as
5.19 kJ/yen. Comparing values in and out of the city, energy unitof expenditure of car trip is higher in the city than out of city.
However, there is no signiﬁcant difference between values ofenergy unit of expenditure of mass transit trips in and out of thecity. The synthetic energy unit of expenditure in the city is a little
higher than the value out of city.
Fig. 4. (a) presents the synthetic energy unit of expenditure ofeach zone in Kumamoto metropolitan area with values from 0 to
37.44. Five levels are classiﬁed with 35 zones in each level. The
minimum value of synthetic energy unit of expenditure is zero due
to none-residence in four zones named Kumamoto trafﬁc center,
Kumamoto station, Kumamoto port, and Kumamoto airport.
Lighter color represents lower energy unit of expenditure, whichmeans higher energy efﬁciency. Comparing to the map of transport network and population density of the area (Fig. 4. (b)), it
clearly shows that low energy unit of expenditure mainly locatedin high population density area, such as the city center. Zones
along mass transit lines are also featured by low energy unit ofexpenditure.

4.3. Relationship between urban form and energy efﬁciency
4.3.1. Ordinary least squares (OLS) estimation
The effect of urban form on energy efﬁciency is analyzed by
OLS method for 173 zones in Kumamoto metropolitan area. A
statistical report of variables is presented in Table 6. The R-square
is 0.783, indicating the linear relationship between urban formand energy efﬁciency could not be rejected at the p o0.01 level.
Suggested by VIFs and the value of the condition number, there isno multicollinearity among variables. The mean of standardized
residual equals zero and Standard deviation is 0.973, indicating
normal distribution of residuals. However, data is spatially auto
correlated according to the map of residuals. Spatial regression isnecessary to eliminate the inﬂuence of spatial correlation of zones.
Table 4
Estimated energy in and out of Kumamoto city in 1997 (GJ /person year).

Total energy consumption (GJ)
Energy for composite goods (GJ)
Energy for car trips (GJ)
Energy for mass transit trips (GJ)

Kumamoto city

Out of Kumamoto city

53.28
43.76 (82.13%)
9.15 (17.17%)
0.37 (0.70%)

52.44
41.37 (78.89%)
10.96 (20.90%)
0.11 (0.21%)

Note: () indicates energy share of goods.

915

If the absolute value of residual is bigger than 3, it is assumed to
be an outlier. We found two outliers and an inﬂuential observation. Zone 78 and zone 169 are the two outliers. In both zones,
employees are mainly distributed into farming, and only a few
employees are in retail department. The situation causes low ratioof employee in retail department to population (less than 10% of
average value), leading to low synthetic energy unit of expenditurein both zones. Zone 2, which is located in the city center, has foundbe the inﬂuential point. The distance to the city center is zero
because zone 2 just locates in the city center. High ratio of
employee in retail department to population (43 times of theaverage value), together with zero travel distance to city center
contribute the highest synthetic energy unit of expenditure inzone 2. Due to the specialty of the three zones, we do not consider
outliers and inﬂuential observation into spatial regression analysis.
4.3.2. Primary ﬁndings of spatial regression modelA spatial regressive model is applied in order to eliminate theinﬂuence of spatial autocorrelation of zones. Spatial regression
analysis is performed by GeoDaSpace software. Table 7 lists theestimation results. The model shows strong explanatory powerwith Pseudo R-square of 0.783.
4.3.2.1. Density. A signiﬁcant effect of selected density variables onenergy efﬁciency was detected. The density of employee is thestrongest inﬂuential factor that negatively affects energy unit ofexpenditure. Our results indicate residents live in the employment
dense areas are more likely to use less energy consumption. It isreasonable, because services and goods are easily available andpeople are less auto-dependent. The estimated coefﬁcient ofdensity indicates that energy unit of expenditure decreases as
the population increases. Population density is also a strong
inﬂuential factor of energy efﬁciency, which is consistent withprevious study (Brownstone and Golob, 2009). Student density has
a negative diminishing marginal effect on energy efﬁciency withpositive coefﬁcient with energy unit of expenditure. The inﬂuenceof student density is relatively small compared to other two
density variables.
4.3.2.2. Diversity. Land use diversity has signiﬁcant impact onenergy efﬁciency. The ratio of employee in retail department topopulation is the most inﬂuential determinant that affects energy
unit of expenditure (with the p-value less than 1%). This variable ispositively related with energy unit of expenditure. High ratio of
employee in retail department to population suggests small
proportion of local employee in retail department. Low
percentage of local employees in retail sector results in morecommuting trips and long travel distance, contributing to moreenergy consumption.
4.3.2.3. Accessibility. Low mass transit trip fare attracts more
residents to use mass transit as a travel mode. Reducing masstransit fare leads to low energy unit of expenditure due to the
incentive of mass transit usage, which is in consistent with theprevious report that mass transit mode share increases as fare

Table 5
Energy unit of expenditure of goods in Kumamoto (kJ/yen).

Energy unit of expenditure of composite goods
Energy unit of expenditure of car trip
Energy unit of expenditure of mass transit trip
Synthetic energy unit of expenditure

Kumamoto area

Kumamoto city

Out of Kumamoto city

16.14
168.70
13.82
5.19

16.14
173.07
13.18
5.35

16.14
161.26
14.47
5.14

916

Y. Yin et al. / Energy Policy 61 (2013) 909–919

Fig. 4. Energy consumption efﬁciency, transport network and population density of zone in the Kumamoto metropolitan area. (a) Energy efﬁciency in the Kumamoto
metropolitan area, (b) Transport network, and population density in the Kumamoto metropolitan area.

Table 6
Descriptive statistics of variables in the linear regression model.
Variable
Dependent variable
Synthetic energy unit of expenditure
Independent variable
Population density
Employment density
Student density
Ratio of employee in retail department to population
Road density
Transit stop density
Frequency of transit service
Mass transit fare
Distance to city center zone

Unit

Mean

Standard deviation

Minimum

MaximumkJ/yen

19.46

2.02

16.13

37.44

1000 person per km2
1000 person per km2
1000 person per km2
Employees in retail department /population
10 km per km2
10 stops per km2
100 times per day
100 yen per trip
km

2.37
1.69
0.65
0.65
2.68
0.86
3.01
3.64
8.74

2.65
5.16
1.97
1.62
2.40
1.09
7.29
1.72
5.09

0.03
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00

10.00
58.02
17.90
19.94
16.68
5.97
49.05
12.14
22.28

Note: the number of samples is 173 for each variable.

reduces (Pucher et al., 1995). High road density increases theaccessibility of car trips, which induces individuals to have highpreference for private car trips. Energy unit of expenditure
increases as road density increases. Our result further supports
the previous report that higher road density leads to greaterhousehold gasoline consumption (Su, 2010). However, masstransit stop density is found to have negative effects on energy

unit of expenditure and the inﬂuence is less signiﬁcant than masstransit fare. The result indicates that reducing mass transit fare isbetter than increasing the density of mass transit stops for
improving the energy efﬁciency. Although positively related withenergy unit of expenditure, the inﬂuence of frequency of masstransit service is insigniﬁcant. Distance from zone centroid to city
center is found be another most inﬂuential factor, which shows a

Y. Yin et al. / Energy Policy 61 (2013) 909–919

917

Table 7
Estimation results of a spatial regression model in Kumamoto metropolitan area.
Variables

Coefﬁcients

Std. Error

z-Statistic

Probability

VIF

Constant
Population density
Employment density
Student density
Ratio of employee in retail department to population
Road density
Transit stops density
Frequency of transit service
Mass transit fare (yen/trip)
Distance to city center zone
Spatial Pseudo R-squared

17.730−0.092−0.113
0.015
1.366
0.015
−0.199
0.003
0.130
0.085
0.782

1.539
0.057
0.049
0.042
0.132
0.056
0.176
0.019
0.055
0.023

11.519−1.603−2.2830.367
10.3160.268−1.133
0.157
2.385
3.708

0.000
0.109
0.022nn
0.713
0.000nnn
0.789
0.257
0.875
0.017nn
0.000nnn

4.837
7.019
1.388
10.450
3.619
9.414
3.518
1.801
2.876

nnn
nn

Indicates that the coefﬁcient is statistically signiﬁcant at the 1% or less.
Indicates that the coefﬁcient is statistically signiﬁcant at the 5% or less.

signiﬁcantly positive relationship with energy unit of expenditurewith the p-value less than 1%.
4.3.3. Discussion of results
4.3.3.1. Population
density,
employment
density,
student
density. Density is shown to have a direct effect on energy
consumption. Some of socio-demographic factors, such as population density and employment density, have signiﬁcant impact onenergy consumption. The distribution of population in highactivity centers concentrates economic activities and transports
needs. Neighborhoods in dense areas have less and shorter trips
because of high facility availability. Moreover, residents are lessauto-dependent because of expanding mass transit infrastructure.
As a result, residents live in dense areas are more likely to haveless energy consumption. The employment density is the strongest
determinant that positively affects energy efﬁciency. The numberof employers reﬂects the amount of services that available in thearea. Residents live in dense employment have easy access toservices or goods. It induce to less and shorter trips. Moreemployment opportunities attract local residents, resulting lesscommuter trips. Student density is found inﬂuential to energy
efﬁciency, but with limited inﬂuence. Findings by Marique et al.
(2013) conﬁrm school mobility behaviors are dependent upon thelocation of residences and education infrastructure in the territory.
School commuting and children's mobility behavior are affected
not only by the number of student but also the location of schools,that is the school density. From the social-demographic viewpoint,
policy implication regarding changes in urban form characteristics
should consider the distribution of population and employment
simultaneously. Compact city will enable a comprehensive pictureof future sustainable development, due to the high population andemployment density in the region.
4.3.3.2. Ratio of employee in retail department to population. Landuse diversity signiﬁcantly affects travel behavior, and has direct
and positive effect on energy efﬁciency. Compact city is widelyadopted because it is believed to increase the land use diversity.
The indicator of land use diversity in this paper is expressed by theratio of employee in retail department to population. It has a direct
effect on energy consumption. High ratio of employee in retaildepartment to population indicates only a few employees workand live in the same area. For most employees who live far away,
long commuting trips are necessary. High ratio of employee inretail department to population introduces more trips and moreenergy consumption. In Kumamoto, employment of service sector
accounts for the big share with more than 60% of all employees

work in the sector (Census in 2005, Kumamoto). Employment inretail department, such as shopping centers and supermarkets, is amain contributor of employment in service sector. Therefore, it iseffective to reduce the energy consumption for commuting trips inretail department as a way to decrease the total energy
consumption of the city. Two suggestions have been put forward
based on the result. One way is to decrease the travel distance ofwork trips through changing residential locations. Concentrating
population in hot employment areas may increase the proportionof local employees in retail department. Compact development isrequired for adopting more residents in hot employment places.
Moreover, efforts should be made to increase the attractiveness of
hot employment places as residential locations.
For employees who live far from their working place, public
transportation tools should be encouraged. Big capacity and highspeed mass transit mode, such as Shinkansen, could be a good
choice for the commuters. Moreover， improving the mass transit
service is another important attractive point.
4.3.3.3. Road density. Road density has a direct effect on energy
consumption through trafﬁc choice behavior. Trafﬁc behavior is acomplex process which is inﬂuenced by a few factors, such as car
ownership, gender, income, and so on (Liu and Shen, 2011).
Accessibility of road is one of essential driving conditions, but
not the determining factor. The effect of road density on travel
behavior is limited.
4.3.3.4. Transit stop density, frequency of transit service, mass transit
fare. The attraction of mass transit service has the signiﬁcanteffect on individual trafﬁc behavior and energy consumption.
Residents are attracted to mass transit due to high accessibilityof service and lower trafﬁc fare. Transit stop density is moreinﬂuential to public transport usage than frequency of transit
service. Residents pay more attention to the location of transit
stops, rather than frequency. High density of transit stops ensureseasy access to service, such as short walking distance to stops,
which increases the possibility of choosing mass transit as a travel
mode. Importantly, low mass transit fare also makes mass transit acharming attractiveness, which increases the real welfare of masstransit users. It is helpful to emphasize and ﬁx the mass travel
behavior and the effect will be enlarged when residents use
once more.
4.3.3.5. Distance to city center zone. Distance to city center zone
has signiﬁcant and direct effects on travel distance, and impacts
energy consumption positively. In Kumamoto, facilities, such as918

Y. Yin et al. / Energy Policy 61 (2013) 909–919

restaurants, shops, hotels, and bureau of administration, aremainly located in city center. Activities are concentrated in thecity center. Residents are attracted to the city center forcommuting, recreation and shopping. If the resident lives far
away, long trips are needed. From this viewpoint, policy
implication regarding changes in urban form characteristics
should consider the distance between residential area and main
activity centers. A compact city will enable a short travel
distance due to limited urban space. Moreover, mixed land use
policy ensures the accessibility of facilities and activities inresidential area.

efﬁciency in Kumamoto. Our study gives a timely policy suggestion
for urban sustainable development in Kumamoto. Of note is that,some suggestions have been applied into the planning practice.
Kumamoto prefecture government is carrying out a planning forcompact development for the future ten years. Moreover, thebullet train, called Shinkansen in Japan, has been operated
between Kumamoto and Tokyo in 2012. It improves the mobilityof residents along the line and attracts more mass transit usage.
The operation of Shinkansen increases the attractiveness of areas
along the line of Shinkansen, especially the station in city
center area.

5. Conclusion

6. Equations that referred to explicitly in the text

As a region located in a mountainous basin, the development ofKumamoto is expected to be much denser and transport networks
to be more efﬁcient. Kumamoto city has been pointed as one oftwenty cities designated by government ordinance since April,2012. Now, it is undergoing a transition to new urbanization
development with vigor. This transition is bringing changes tothe urban spatial distribution of population, employment, land use
and travel patterns, resulting in different energy consumption.
Facing the conﬂict of land preserving and energy tense situation,
Kumamoto needs guide for the future development urgently.
Present study provides a quantitative analysis on the relationship between speciﬁc indicators of urban form and individualenergy consumption in Kumamoto metropolitan area. First, amodel is developed to estimate individual energy consumption
based on consumption behaviors. 52.84 GJ of energy is estimatedto be needed for one person per year in Kumamoto metropolitan
area. 19.13% is for car trips and 0.44% for the mass transit trips.
19.57% of energy is used for mobility goods. The synthetic energy
unit of expenditure of three kinds of goods in Kumamoto metropolitan area is 5.19 kJ/yen. The method of energy estimation in thispaper enables us to estimate all individual energy consumption indaily life, including energy use in Residential, Commercial andTransportation sectors.
Our research ﬁndings provide additional evidences on the relationship between urban form and energy consumption. Considering
the spatial autocorrelation of data, a spatial regression is performedby GeoDaSpace software. The results indicate that the urban form
has signiﬁcant effects on individual energy consumption. Employment density, ratio of employee in retail department to population,
mass transit fare, and distance to city center, are four most inﬂuential
factors. Ratio of employee in retail department to population anddistance to city center were statistically signiﬁcant with energy
efﬁciency both with the p-value less than 1%. Shorter distance tocity center attributed to higher energy efﬁciency. Low mass transit
fare improves energy efﬁciency due to more mass transit usage.
Results showed that high employment density leads to high energy
efﬁciency. However, high ratio of employee in retail department topopulation tends to decrease energy efﬁciency. Two opposite inﬂuence directions suggest that: although increasing employment density is effective to improve energy efﬁciency, it is much better toincrease proportion of local residents as employees in retaildepartment.
By examining the relationship between the urban form andenergy efﬁciency, present study suggests two policy implications
for urban development of Kumamoto. First, in the micro-level,measures that increase mass transit usage should be encouraged,such as reducing mass transit fare and increasing mass transit stop
density. Second, in the macro-level, policies for improving employment density, especially, employment proportion of local residents
are suggested. These two levels are correlated with each other as awhole and suggest compact city development for high energyui ðx1i ; x2i Þ ¼ ðα1 x1i1

ðs −1Þ=s1

ðs −1Þ=s1 s1 =ðs1 −1Þþ α2 x2i1

ðs −1Þ=s2

x2i ðx2Ci ; x2Mi Þ ¼ ðα2C x2Ci2

ðs −1Þ=s2

max : x2i ¼ ðα2C x2Ci2

x2Ci ;x2Mi

s:t:

ð1Þ

ðs −1Þ=s2 s2 =ðs2 −1Þ2þ α2M x2MiÞð2Þðs −1Þ=s2 s2 =ðs2 −1Þ2þ α2M x2Mi

Þ

p2Ci x2Ci þ p2Mi x2Mi ≤I 2i
ðs −1Þ=s1

max : ui ¼ ðα1 x1i1
x1i ;x2i

s:t:

Þ

ð3Þ

ðs −1Þ=s1 s1 =ðs1 −1Þþ α2 x2i1

Þ

p1i x1i þ p2i x2i ≤I i

ð4ÞEi ¼ e1 xn1i þ e2 t 2Ci ðxn2Ci ; xn2Mi Þxn2Ci þ e3 t 2Mi ðxn2Ci ; xn2Mi Þxn2Mi
ui ðxn1i ; xn2Ci ; xn2Mi Þ ¼ uni

ð5Þs2
1−s2 1=ð1−s2 Þ22
p2i ¼ ðαs2Ci
p1−s2Ci þ α2Mi p2Mi ÞmTm
ij ¼ T i nð6ÞexpðaDj þ bZ j þ cG2mij Þ∑j∈zones expðaDj þ bZ j þ cG2mij Þð7Þ

Acknowledgments
This work was supported by the K. C. Wong Magna Fund in
Ningbo University. The authors are grateful to the editor andreviewers for their insightful comments.

Appendix A
Maximum mobility problem:ðs −1Þ=s2

max : x2i ¼ ðα2C x2Ci2

x2Ci ;x2Mi

ðs −1Þ=s2 s2 =ðs2 −1Þ2þ α2M x2MiÞs:t: p2Ci x2Ci þ p2Mi x2Mi ≤ I 2i
Using Lagrangian method, the likelihood function y is built as
follows:
ðs −1Þ=s2

y ¼ ðα2C x2Ci2

ðs −1Þ=s2 s2 =ðs2 −1Þ2þ α2M x2MiÞ

−λðp2Ci x2Ci þ p2Mi x2Mi −I 2i Þ

The ratio of the ﬁrst-order partial derivatives equals to 0:ðs −1Þ=s2∂y=∂x2Ci ¼ ðλp2Ci =α2C Þ−s2 ðα2C x2Ci2

ðs −1Þ=s2 s2 =ðs2 −1Þ2þ α2M x2Mi

Þ

−λp2Ci¼0
ðs −1Þ=s2∂y=∂x2Mi ¼ ðλp2Mi =α2M Þ−s2 ðα2C x2Ci2

ðs −1Þ=s2 s2 =ðs2 −1Þ2þ α2M x2Mi

Þ

−λp2Mi¼0∂y=∂λ ¼ p2Ci x2Ci þ p2Mi x2Mi ¼ 0
Solving above three equations, optimal solutions of car trips x2Ci

Y. Yin et al. / Energy Policy 61 (2013) 909–919

and mass transit tripsx2Mi are obtained as Eqs. (A(1) and A2):
α2C s2I 2i
x2Ci ¼
ðA1Þ
2
2
2
p2Ci
αs2C2 p1−s
þ
αs2M
p1−s
2Ci
2Mi

x2Mi ¼

α2M
p2Mi

s2

I 2i

ðA2Þ

s2 1−s22
αs2C2 p1−s
2Ci þ α2M p2Mi

The maximum mobility is shown as Eq. (A3):s2 1−s2 ð1=s2 −1Þ
2⋅I 2i
x2i ¼ ðαs2C2 p1−s
2Ci þ α2M p2Mi ÞðA3Þ

The price of mobility goods is shown as Eq. (A4):s2 1−s2 1=ð1−s2 Þ2
p2i ¼ ðαs2C2 p1−s
2Ci þ α2M p2Mi Þ

ðA4Þ

Maximum utility problem based on maximum mobility:ðs −1Þ=s1

max : ui ¼ ðα1 x1i1
x1i ;x2i

ðs −1Þ=s1 s1 =ðs1 −1Þþ α2 x2i1

Þ

p1i x1i þ p2i x2i ≤I i

s:t:Using Lagrangian method, the optimal solutions of composite
goods xn1i and mobility goods xn2i are given by Eqs. (A(5) and A6):
 s1
α1
Ii
xn1i ¼ðA5Þ11p1i
αs11 p1−sþαs21 p1−s1i2i
xn2i ¼

α2
p2i

s1

Ii

ðA6Þ

1
1
αs11 p1−sþ αs21 p1−s1i2i

As individuals are assumed to maximize their mobility and utility
at the same time, the trafﬁc budget is calculated as Eq. (A7):
 
α2
Ii
ðA7Þ
I 2i ¼ p2i xn2i ¼ p2i
p2i αs1 p1−s1 þ αs1 p1−s1
1 1i
2 2i
According to Eqs. (A(1),A2),(A4) and (A7)), the optimal solutions of car trips xn2Ci and mass transit trips xn2Mi for maximum
utility are listed as Eqs. (A(8), and A9)),:
α2C s2 s1 s2 1−s2
2
2 s2 −s1 =1−s2
xn2Ci ¼α2 ðα2C p2Ci þ αs2M
p1−s
2Mi Þ
p2Ci
(

1−s1

s2 1−s2 1−s122αs11 p1−sþ αs21 ðαs2C2 p1−s
1i
2Ci þ α2M p2Mi Þ
xn2Mi ¼
n

α2M
p2Mi

s2

−1

ðA8Þ

Ii

s2 1−s2 s2 −s1 =1−s22αs21 ðαs2C2 p1−s
2Ci þ α2M p2Mi Þ

s2 1−s2 1−s1 =1−s2
12αs11 p1−sþ αs21 ðαs2C2 p1−s
1i
2Ci þ α2M p2Mi Þ

o−1

Ii

ðA9Þ

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