3. Background
• Mass transit railway services
– Safe, improve mobility, avoid congestion, etc.
– Ideal if financially sustainable, with affordable fares
and expedient quality
– The case of Hong Kong: all rail services are provided
under prudent commercial principles, renowned for
high quality and profitability, often considered as a
benchmark for urban rail transit projects
Public Transport in Hong Kong
• Public Transport in HK involves a multi‐modal
network
– Railways (MTR, LRT)
– Franchised Buses (over 600 routes)
– Red and green Minibuses (hundreds of routes)
– Taxi, ferries, tram, peak Tram
• All modes are financially sustainable without
direct government subsidy
6
6. Supply of transit services
Hong Kong London Singapore
Rail car-km (million) 255 414 89
Bus vehicle-km (million) 513 450 299
Population (million) 6.9 7.4 4.2
Rail car-km per capita 37.0 56.3 21.0
Bus vehicle-km per capita 74.4 61.2 70.5
Combined rail car and bus vehicle-km per capita 111.4 117.5 91.5
% total passenger-km on mass public transit 82% 30% 47%
Source: Lo, H., S. Tang and D. Z.W. Wang. 2008. Managing the Accessibility on Mass
Public Transit: the Case of Hong Kong. Journal of Transport and Land Use, 1:2, 23-49.
Land‐use and Transport Policy in Hong Kong
1. The policy on land development
2. The Policy of Limiting Private Car Ownership and Usage
3. The Policy of Transit Service Coordination and
Protection (1980’s)
4. The Policy of Service Proliferation and Competition
(1990’s)
5. The Policy of Service Rationalization and Consolidation
(2000’s)
12
Source: Tang, S. and H. Lo. 2008. The Impact of Public Transport Policy on the Viability
and Sustainability of Mass Railway Transit – The Hong Kong Experience. Transportation
Research Part A, 42, 563- 576.
8. 15
Example: TKO new town
The total
development area
of TKO is about
10.05 km², with a
population of
around 350,000.
The average
density is 35,000
per km²
Policy of Limiting Private Car Ownership
and Usage
• Passenger car ownership: 56 per 1000 people; US: 439;
Singapore: 121; Chile: 118 (World Bank Data 2009)
• New private cars are subject to the first registration tax
from 35% to 100% of the vehicle cost
• High fuel tax: Unleaded gas in Hong Kong is ~ HK$15/liter
or RMB 6/liter
• Private car trips constitute 10% of total daily passenger
trips, as compared with 95% in the US.
16
9. Transit service coordination and protection
(1980s)
• Higher priority given to off‐street public transit
• Rapid development of rail transit services, with protection
against direct competition from other modes
• Allowed the creation of a win‐win situation; the Govt could
rely on the private sector to provide for services based on the
user‐pay principle without subsidy
• But later criticized as protecting the existing sizeable operators
and unable to motivate their service improvement
Service proliferation and competition
(1990s)
• Encourage “healthy” competition between modes
– Remove the protection policy for the rail mode
– Massive expansions of both rail and bus services
• This policy was initially welcome, but at the expense of:
– Congestion externality – oversupply of buses on profitable
corridors
– Financial difficulties for operators – the demand was spread
too thin due to oversupply of services
11. Rail transit development model in Hong Kong
Property
Developer
Fund, build and operate the
railway, and pay back dividend
Define legal framework, derive
policies, drive and monitor railway
development, and grant land for
property development
Share property
development profit
Form joint venture to develop
property
Contribute to
economic
growth
Regulate
land use
and town
planning
Railway
Company
Government
Costs and revenues of MTR
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
year
million
Total Operating Cost after depreciation
Total Operating Cost before depreciation
Total Income including property profit
Fare Revenue
Turnover
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
year
million
Total Operating Cost after depreciation
Total Operating Cost before depreciation
Total Income including property profit
Fare Revenue
Turnover
Fare Rev
Op cost aft
depreciation
Op cost bef
depreciation
Total inc
14. …modeled by an analytical framework
A general equilibrium Residents’ location and
travel choices
System optimization
Residential location
Workplaces
Travel modes
Travel routes
Government/Planners
(Planning perspective)
TS-DM strategies:
Network expansion and/or
Road pricing, etc.
To be decided…To achieve… Stakeholders
Housing provision Developers’ decision( )r
S
r
s
m
p
( ) ( )
( , )
a ay ρ
A general equilibrium framework
– Bid‐rent Process (who to rent to and the resultant rent)
• Based on residents’ willingness to pay
• Auction process
• Bid‐rent at different locations (expected maximum rent)
– Residential location Choice (which location to rent from)
• Location choice: location accessibility, attractiveness
• Travel choice: transportation cost
• Utility maximization
– Developer housing supply problem
• Bid‐rent at different locations
• Cost of housing supply
• Profit maximization
28
Sources:
• Ma, X. and H. Lo. 2013. On Joint Railway and Housing Development Strategy. 20th International
Symposium on Traffic and Transportation Theory (ISTTT) and Transportation Research Part B,
57, 451-467.
• Ma, X., Lo, H.K., 2012. Modeling transport management and land use over time. Transportation
Research Part B, 46 (6), 687-709.
15. Combined Residential Location
Choice and the Bid‐rent Process
29
High
Lowr1
rr
s1
ss
High
Low
WP
WP
WP
WP
High
Lowr1
rr
s1
ss
High
Low
CS
CS
Residents’
perspective
r: location r: locations: working place s: working place
Landowners’
perspective
Resident
Demand
Housing
Supply
• The two choice processes are proven to be consistent and
produce identical allocations
Bid-rent
Process
Residence
choice
Bid‐Rent Process
30
High
Lowr1
rr
s1
ss
High
Low
WP
WP
WP
WP
r: location
/
∙
∑ ∑ ∙
∙ /
Willingness-to-Pay (WP): for a location r
is expressed as:
s: working place
Landowners’
perspective
: utility index by setting
: Income of class k
: Utility level (Non-housing spending)
: Attractiveness of Housing Units,
e.g. lot Size, Age, etc.
: Generalized Travel Cost
/Accessibility
The number of resident occupied in
location r:
Housing
Supply
Resultant housing rent: is expressed as the
log-sum term, adjusted by the housing supply
at that location
1
∙ /
1
Expected Maximum
Willingness-to-pay
Supply Effect
17. Developer housing supply choice
• Developers’ decision on housing provision
– Under the principle of profit maximization
( )r
S
22
22
( )
( )
2'( )
'
exp( )
Pr , 0, 1
exp( )
r nn
r
r nn
r R
n
2 2 2r n r n r n
Hb
(0)
2( )
( ) ( )
2
, 0
Pr ,
r
r
r
S n
S
S n
Following a quasi dynamic structure
Profit
Benefit distribution among stakeholders
• The impact of transport supply and demand
management on the benefit of
– heterogeneous income groups of residents
– housing developers
• General conditions
– Single time period
– One OD pair
– Fixed housing supply
18. • Proposition – transportation supply
– Under conditions
• (H0): One OD pair r and s, households with multiple income groups k
• (H1): One travel route p, travel time reduced by ∆t<0 with investment cost BT
• (H2): Homogenous value of time, votk=vot>0
– Any travel cost reduction due to transport infrastructure
improvement, either in time‐based or money‐based formulation,
will lead to an equivalent increase in land or rental value
– Consumer surplus (household)
– Housing supplier surplus
Benefit distribution among stakeholders
• Proposition – transportation supply
– Under conditions
• (H0)‐ (H1)
• (H3): Heterogeneous value of time, vot1<vot2<…<votk
• (H4): Money‐based travel cost formulation
– Residents with higher incomes/higher values of time benefit
more from transport improvement as compared with residents
with lower incomes/ lower values of time
– Consumer surplus (household) Lowest Highest
– Housing supplier surplus
Benefit distribution among stakeholders
19. Benefit distribution among stakeholders
• Proposition – demand management
– Under conditions
• (H0)‐ (H1)
• (H3): Heterogeneous value of time, vot1<vot2<…<votk
• (H5): Time‐based travel cost formulation
– Residents with higher incomes/higher values of time benefit more
from demand management, e.g. increasing link toll, as compared
with residents with lower incomes/lower values of time
– Consumer surplus (households’) Lowest Highest
– Housing supplier’s surplus
• A quasi dynamic structure
– Different time adaptabilities of sub‐systems
• Residents’ travel behavior
• Residents’ location choice
• Housing investment
• Transport/rail infrastructure investment
– Implying that given a time period τ, residents’ location and travel
choices are made under a fixed land use and transport system
Shorter
Longer
General equilibrium formulation over time
20. The problem is formulated as an equivalent Nonlinear
Complementarity Problem (NCP)
i.e. to find such that and
where,
*
0Ζ *
( ) F Ζ 0 *T *
( ) Ζ F Ζ 0
( )
,
( )
2
( )
, , , , , ,
= , ,
, ,
rsk
p m
r
k
f r s m p k
S r n
b k
Ζ
( ) ( ) ( )
, ,
( ) ( ) ( )
2
( ) / ( ) ( )
Pr , , , , , ,
( )= Pr , ,
Pr , ,
rsk rsk rsk
p m p m
r r
r k r k
r
f q r s m p k
S S r n
S H k
F Ζ
General equilibrium formulation over time
( ) ( ) ( ) ( ) ( ) ( )
( , ) ( ) ( , ) ( ) ( , ) ( ) 0T H T H T HNPV dr R R dr B B dr M M
Maximize social welfare (consumer and producer surpluses)
Optimal transport management strategies
Transport Supply and Demand Management,
e.g. Rail link expansion and fare pricing
Under a time‐dependent network following a quasi dynamic structure
With cost recovery conditions
Producer surplus
System optimization
(τ) (τ)
a a
( ) ( )
ρ ,
Maximize SW ( , ) +rsk rsk
y
rs k
dr q CS NPV
22. • Overall system performance I
– Transport management strategies increase overall social welfare
– TS‐DM is generally better than DM alone
– (* transport investment includes both construction cost for new expansions and
maintenance cost for all highway links)
0.0%
20.0%
40.0%
60.0%
80.0%
100.0%
120.0%
140.0%
Scenario 0 100.0% 100.0% 100.0% 0 100.0% 100.0% 100.0%
Scenario I 83.5% 107.1% 97.2% 100% 100.9% 107.8% 104.8%
Scenario II 97.4% 122.4% 98.4% 89% 96.1% 103.6% 102.2%
Travel time Travel cost
Consumers'
Surplus
Transport
investors'
profit*
Housing
developers'
profit
Producers'
surplus
Welfare
Results
0.0%
20.0%
40.0%
60.0%
80.0%
100.0%
120.0%
140.0%
Scenario 0 100.0% 100.0% 100.0% 0 100.0% 100.0% 100.0%
Scenario I 83.5% 107.1% 97.2% 100% 100.9% 107.8% 104.8%
Scenario II 97.4% 122.4% 98.4% 89% 96.1% 103.6% 102.2%
Travel time Travel cost
Consumers'
Surplus
Transport
investors'
profit*
Housing
developers'
profit
Producers'
surplus
Welfare
• Overall system performance II
– Travel time reduced through both transport strategies
– TS‐DM is better than DM alone in congestion relief
– DM alone introduces higher travel costs
– Consumer surplus reduced
Results
23. • Overall system performance III
– The overall producers’ surplus increased
– (Producer’s surplus = Transport investors’ + Housing developers’)
0.0%
20.0%
40.0%
60.0%
80.0%
100.0%
120.0%
140.0%
Scenario 0 100.0% 100.0% 100.0% 0 100.0% 100.0% 100.0%
Scenario I 83.5% 107.1% 97.2% 100% 100.9% 107.8% 104.8%
Scenario II 97.4% 122.4% 98.4% 89% 96.1% 103.6% 102.2%
Travel time Travel cost
Consumers'
Surplus
Transport
investors'
profit*
Housing
developers'
profit
Producers'
surplus
Welfare
Results
• Transport investment and Housing market
– Developer surplus increases monotonically with transportation
supply due to increasing housing rents
– Consumers may benefit or suffer from transportation supply
depending on the tradeoff between travel cost reduction and
increased housing rents
95%
100%
105%
110%
115%
120%
125%
0% 10% 20% 30% 40% 50% 60% 70% 80% 90%
Level of transport improvement
Performance
Housing revenue
Consumers' Surplus
Producers' surplus
Social welfare
Housing rev - Trans invest
Developer's surplus
Sensitivity analysis of transport supply
24. What about joint rail and property
development?
–To what extent one can exploit the synergy
between rail and property developments?
• Property development brings in rail patronage, hence
higher fare revenue
• Improved accessibility due to rail increases values of
properties
• To what extent property value increases can be used
to cross‐subsidize rail infrastructure development
47
Source: Ma, X. and H. Lo. 2013. On Joint Railway and Housing Development Strategy.
Transportation Research Part B, 57, 451-467. Presented at 20th International
Symposium on Traffic and Transportation Theory (ISTTT).
Joint railway and housing development
Profit function
1.2
rail( ) ( ) ( )Pr Pr
H HT T
rv rv rs v rv
H TC TO
v r rs
rv rs rv
v r
cp h
R R B B
q b B st b w
- The housing location
- The housing type
- The proportion of investing housing type in location
- The number of housing type invested in location ,
Pr
rv rv
rv
r
v
v r
v r (Pr )
- The railway fare between
- The operational headway
- The number of trains, ( )
r
r
v
s
cp
h
rs
st st hw
w
Housing revenue Rail revenue Housing cost Rail cost
25. Mathematical Program with Equilibrium
Constraints (MPEC)
1.2
Pr , ,
Maximizerv rs rs H HT T
hw cp
R R B B
( ) 0G Z
1Pr
r v
rv
, ,hw h rw wh s
, ,rs
cp c rp pc s
s.t. Gap function for the combined
equilibrium
Joint railway and housing development
• Proposition – Effects on Residents
– The travel costs of residents monotonically increase
with headway and fare
– Changes in railway investment, e.g. headway or fare,
do not change residents’ consumer surplus because
any decrease (increase) in transport cost is absorbed
by corresponding rent increase (decrease)
– A regressive effect also prevails, high income groups
gain more from transport service improvements
2
50
Joint railway and housing development
26. • Proposition – Effects on Rail + Property Developer
– Housing rents monotonically decrease with transport cost increases
(e.g. headway and fare)
– If rail is the only transport mode, the combined producer surplus
does not change with fare changes, due to the internal transfer
between property and fare revenue.
– In the presence of a multi‐modal network, the combined producer
surplus (housing and rail) monotonically decreases with fare.
Therefore, the joint developer has incentive to keep fare at a
reasonably low level to maintain producer surplus at a high level,
since gain from housing revenue offsets reduction in fare revenue
2
51
Joint railway and housing development
What about optimal housing supply: the
perspective of developer vs residents?
Assumptions:
• (H0): A linear network with two residential locations r connected in series to one
central CBD. Links 1 and 2 have fixed travel time. Homogeneous housing types are
to be developed in origin 1 and/or origin 2
• (H1): Homogeneous income class, e.g. votk = vot > 0
• (H2): Heterogeneous income class, e.g. two income class, votk1 > votk2
• Total Supply is fixed
– 1000
52
Fig. 1 Two Residential locations Network
Source: Ng, K.F. and H. Lo. 2015. Optimal Housing Supply in a Bid-Rent Equilibrium
Framework. Transportation Research Part B, 74, 62-78.
27. • Under (H0) and (H1)
• Instead of placing all 1000 units in origin 1, which is closer to CBD, the
developer places 200 units in origin 2. Although origin 2 has a higher
transport cost and therefore lower rent, doing so the rent in origin 1 will be
higher as the supply there is reduced from 1000 to 800. Revenue is
maximized when the marginal effects of the two are equal.
• The exact optimal allocation depends on the difference in travel cost, or beta
• At any optimal solution, more housing should be in origin 1 than in origin 2
• Create some housing shortage in origin 1
Developer optimal housing supply strategy
• Proposition: The optimal housing supply for developer:
∗
∙
exp ∙
exp ∙ exp ∙
∗
→
53
Transport
Cost Effect
Supply
Effect
No. of housing
units
Residents optimal housing supply strategy
• Proposition: The optimal housing supply for residents:
• Under (H0) and (H1)
• Concentrated Development (all development in origin 1 or 2)
• Concentrated development pulls down the rent dramatically
• Consumer surplus is then maximized
54
No. of housing
units
∗
→ 0
28. To analyze the performance of housing revenue and total consumer surplus when
housing supply in different locations change.
Assumptions:
• (H2): Two income classes: High and Low income, e.g. different vot’s and incomes
• The BPR congestion function is used to model links 1 and 2
Results:
• Vary with beta, scaling parameter, and the relative proportions of income groups
– Case 1: small beta. Choice becomes more random
– Case 2: large beta. Choice becomes more deterministic
55
Fig. 1 Two Residential locations Network
Residents optimal housing supply strategy:
sensitivity analysis
56
645000
647500
647500
650000
650000
650000
652500
652500
652500
655000
655000
655000
657500
657500
657500
657500
660000
660000
660000
660000
662500
662500
662500
665000
665000
667500
667500
670000
672500
The proportion of Supply in Origin 1
TheproportionofHighIncomeClassDemand
Total Housing Revenue (Large beta)
100 200 300 400 500 600 700 800 900
100
200
300
400
500
600
700
800
900
Maximum, less than 45 line
Housing Revenue
• When the number of high income
residents is high, say 700, the
optimal housing supply is to
provide housing which is slightly
less than the number of high
income resident, create shortage
for high income residents
• When the number of high income
resident is low, say 300, increasing
the housing supply will result in a
higher revenue
• Result is consistent with
Proposition 1
• It is not always good to put all
housing units in a convenient
locations, e.g. origin 1
Developer perspective (large beta)