An Intro to estimating travel demand

CE-807 Traffic Engineering
(Fall 10)
Lecture # 10
Traffic Studies and Programs
(Statistical application in Traffic
Engg.)
Estimating Transportation Demand
National University of Science &Technology (NUST)

2
Importance of Transportation Demand in Systems Evaluation
(Why do we need to estimate demand?)
• Provides a basis for predicting the need for a proposed
transportation system, in terms of passenger, freight or vehicle
volumes expected to use the facility.
• Helps provide a basis for deciding to go ahead with a proposed
project or policy change.
• Demand estimation - forecasts are vital in evaluating alternative
actions at every stage of the transportation development process
• Influences the proposed size of the project or the scope of
proposed operational policies
• Provides a basis for quantifying the benefits (positive impacts) of
the proposed facility on the facility (e.g., total savings in travel time)
• Provides a basis for quantifying the costs (adverse impacts) of the
proposed facility on the environment (e.g., noise, air pollution, etc.)
• Knowing the expected demand at each future year helps in
developing agency cost streams for preserving facilities whose
deterioration or performance are influenced by usage.

3
What is Demand?
 Demand: The extent to which consumers seek a
product.
 Transportation Demand:
The number of trips that individuals/firms are prepared
to make under a
given set of conditions
(trip price, trip time, security, comfort, safety, etc.)
 is generated by the need of humans to carry out socio-
economic activities
 described as a derived demand because trips are
undertaken not for the sake of traveling but rather for an
expected activity at the end of a journey (reporting for
work, shopping, returning home, picking up or
delivering goods, etc.)
 The volumes of traffic observed or predicted at a system
is therefore the interaction of travel demand and system
supply

4
Types of Passenger Transportation Modes:
Air Water Rail Bus
Auto Bicycle Walk Other
Transportation Demand by Mode

5
Types of Freight Transportation Modes:
Air Water Rail Truck
Pipeline
Transportation Demand by Mode

6
What is a “modal share” of transportation demand?
Is the distribution of the overall amount of
travel demand among the various modes.
Example, modal share of travelers between two cities

7
How do We Measure Transportation Demand?
(Units of Transportation Demand)
• Number of vehicles
• Number of passengers
• Number of trips
• Number of vehicle-miles
• Number of passenger-miles
• Number of trip-miles
• Amount of freight (tons)
• Number of freight-miles
Point A Point C
Point B
Point D
8 mi.
5 mi.

Basic Concepts - Transportation Demand Estimation
• The demand for any specific transportation facility or service
depends on the characteristics of the activity system and the
transportation system.
• An activity system: The totality of social, economic, political,
and other transactions taking place over space and time in a
particular region
• Transportation system: A collection of physical facilities,
operational components, and institutional policies that enable
travel between various points in a transportation network.
• Service Attributes: The characteristics of a transportation
network that are relevant to travel choice (and hence demand
estimation) are termed as service attributes and include
travel time, travel cost (out of- pocket expenses), safety and
security, and comfort and convenience.

9
Transportation Demand in the
Classical Economics Context

10
Transportation Demand in Context of Classical
Economics
• Transportation Demand: The amount of trips that
travelers are willing to undertake
• Demand functions or demand models: quantify the
willingness of trip makers to “purchase” (i.e.,
undertake) a trip at various “prices” (i.e., levels of
service attributes associated with the trip) under
prevailing socioeconomic conditions.
Mathematical expressions that describe
transportation demand.
V = f(X1, X2, … Xn)

11
Transportation Demand in Context of Classical
Economics
• Transportation Demand: The amount of trips that travelers
are willing to undertake
• Demand functions or demand models: quantify the
willingness of trip makers to “purchase” (i.e., undertake) a trip
at various “prices” (i.e., levels of service attributes associated
with the trip) under prevailing socioeconomic conditions.
• Single Attribute: Simple formulation, a demand function is a
two-dimensional model such as the classic demand–price
curve. (trip price-only service attribute)
• Multi-attribute: Complex formulation, demand is a
multidimensional function of several explanatory variables
(often including price) that represent the service attributes
and trip-maker characteristics (trip price, trip time, security,
comfort, safety, etc.).

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Demand functions or demand models
• Mathematical expressions that describe transportation
demand.
V = f(X1, X2, … Xn)
• X1, X2, … Xn are the variables that affect transportation
demand.
• Of these variables, some are mode-specific (example,
trip price, trip comfort, trip time, etc.).
• Others are generic (example, trip-maker’s income).

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Demand functions or demand models
The most common variable is trip price.
Therefore, the most common demand function is as
follows:
V = f(Price)
Trip
Price (p)
V1
Quantity of trips
demanded, V
p2
p1
V2
1
2
V = f(Trip Price)

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• When trip price increases, the demand for trips decreases
• When trip price decreases, the demand for trips increases
• In Economics, this is known as The Law of Demand
• Any exceptions? Yes. For abnormal goods and services,
the Law of Demand does not apply.
Trip
Price (p)
V1
Quantity of trips
demanded, V
p2
p1
V2
1
2
V = f(Trip Price)

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Abnormal demand curves
Abnormal Goods
and Services
Giffen Goods
a. Inferior, but staple goods and services
b. Giffen goods exist when there is a lack of
cheaper substitutes
c. Maze, Wheat, Rice
Veblen Goods
a.a good made more fashionable by a higher price
b.Status symbol
c.Rolls-Royce - as the price rises wealthy people
may see it as more exclusive than other luxury cars
Price
(p)
Quantity of trips
demanded, V
Note: In this course, we are only interested in transportation demand as a normal good!

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Shifts in the Transportation Demand Function
• Is it possible to have a change in demand even when the
price is fixed?
• In other words, can we have a “shift” in the demand curve?
Trip
Price (p)
V1
Quantity of trips
demanded, V
p2
p1
V2
1
2
V = f(Trip Price)
• Recall the basic, single-attribute demand function
• V = f(Price)

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Example:
For auto travel,
- increased auto security,
safety;
-reduced transit comfort,
safety, and security, or
- higher transit prices
can cause an increase in
auto demand even when
auto trip price is constant
What Causes Shifts in the Demand Curve?
(a) A Shift in the Right Direction
Price (p)
Example,
Auto Trip
Price
Quantity demanded, v
Base Case (Example, Auto Demand)
VA VB
DA
A
DB
BA
p
Increased Transit Price;
Reduced Transit quality of service;
Increased Auto quality of service)
Cause: A competing good or service is made less attractive to the customer

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Example:
For auto travel,
- decreased auto security,
safety;
- increased transit comfort,
safety, and security, or
- reduced transit prices
can cause a decrease in
auto demand even when
auto trip price is constant
(b) A Shift in the Left Direction
Cause: A competing good or service is made more attractive to the customer
Price (p)
Example,
Auto Trip
Price
Quantity of Auto Trips
demanded, V
Base Case (Example, Auto Demand)
VC VA
DA
A
DB
BA
p
Reduced Transit Price;
Enhanced Transit quality of service;
Reduced Auto quality of service)

19
Major Causes of Shift in Transportation Demand Curve
• Sudden change in customer preference (season etc.)
• Change in the level of the attribute of interest (e.g., price
increase) of related good.
• Change in regional income
• Change in the number of potential consumers.
• Expectations of an impending change in the level of the
attribute of interest

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Classification of Demand Models

21
• Single attribute vs. Multiple attribute
• Aggregate vs. Disaggregate
• Deterministic vs. Stochastic
• Time series (trend) vs. Cross-sectional
• Further classification of Cross-sectional models:
- Demand estimation based on end point attributes vs.
- Demand estimation based on attributes of entire network.
• Classification by Functional Form

22
Single attribute vs. multiple attribute demand models
Single attribute: only one variable
Demand = f(X)
Examples: Demand = f(Trip Price)
Demand = f(Trip Time)
Multiple attribute: more than one variable
Demand = f(X1, X2, …, XN)
Examples: Demand = f(Trip Price, Time, Safety, Comfort, etc.)

23
Disaggregate vs. aggregate demand models
Consider the following situation:
We seek to estimate the travel demand between the Lahore and Rawalpindi

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Aggregate vs. disaggregate demand models
Consider the following situation:
We seek to estimate the travel demand between the Lahore and Rawalpindi
Lahore
Population = 10 M
Area = 410 sq. km
Number of Industries = 420
Nr. of Shopping centers = 134
Rwalpindi
Population = 5 M
Area = 265 sq. km
Number of Industries = 140
Nr. of Shopping centers = 84
Travelers between H and C
For each traveler:
- Income
- Occupation
- Etc.
Lahore
Rawalpindi
Overall Demand
= f(popH, popC, AreaH, AreaC, etc.)
Demand of each traveler i
= f(INCi, OCCi, etc.X)
Overall demand = sum of traveler demands

Aggregate vs. disaggregate demand models
 Aggregate demand models: the variables are combined for all
travelers and pertain to the areas (regions, cities, towns, etc.)
 Overall Demand = f (Characteristics of the demand-generating regions)
 Characteristics include population, regional area, number or total
area (sq. ft.) of industries, shops, schools, etc.),
 Disaggregate demand models: the variables are for each
individual traveler
 Demand = f (Characteristics of individual traveler)
 Characteristics include income, occupation, etc.
 f is often an econometric discrete choice model (logit, probit, etc.)
 Overall demand = sum of demand of individual travelers
 Based on the assumption that the trip makers seek to maximize their
utility.
 For sketch planning, the aggregate approach, (estimates overall demand
directly) more appropriate than the disaggregate approach (past research)

Scope of Analysis and Level of Planning
 expressions ‘macro’, ‘meso’, and ‘micro’ are sometimes used to describe
the level of detail or the size of an area used for an analysis
 Expressions ‘site specific’, ‘corridor’, and ‘areawide’ or ‘metropolitan’ are
used - describe variations in the scope of a problem
 Sketch Planning (macro)
 Deals with the planning of major corridor
 Requires minimal details
 Large number of alternatives can be considered
 Meso-level Planning
 Analysis is focused on facility
 Large data required, precision need not be great
 Micro level Planning or Site Specific
 Treats small portion of facility such as congested road intersection
 Large amount of precise data required

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Deterministic vs. stochastic
Deterministic demand models: the exact outcome (travel demand)
can be predicted with certainty.
- Makes the demand estimation process easy
- May not be realistic
Stochastic demand models: the exact outcome (travel demand) is
not known with certainty
- The estimated demand falls between a certain minimum and
maximum, and is governed by a probability distribution
- Each individual demand has a certain probability of occurring
- Makes the demand estimation process
relatively complicated
- More realistic in real world where there
are so many uncertainties
V1 V2 V3 V4 V5 V6 V7 V8 V9
P(Vi)
Travel Demand, Vi

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Time Series vs. Cross-sectional Models
t1
X1, t1
X2, t1
X3, t1
Y t1
t2
X1, t2
X2, t2
X3, t2
Y t2
t3
X1, t3
X2, t3
X3, 3
Y t3
t4
X1, t4
X2, t4
X3, t4
Y t4
tN
X1, tN
X2, tN
X3, tN
Y tN
…

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2001
POP = 2.3M
AVG INC = 3.1K
AREA_BUSINESS
= 4.1M
26,000
2002
34,000
2003
42,000
2004
53,000
2009
Y 2009 = ?
2005
61,000
2006
72,000
…
POP = 2.4M
AVG INC = 3.1K
AREA_BUSINESS
= 4.2M
POP = 2.6M
AVG INC = 3.2K
AREA_BUSINESS
= 4.4M
POP = 2.8M
AVG INC = 3.3K
AREA_BUSINESS
= 4.5M
POP = 2.9M
AVG INC = 3.3K
AREA_BUSINESS
= 4.7M
POP = 3.0M
AVG INC = 3.5K
AREA_BUSINESS
= 4.7M
POP = 3.5M
AVG INC = 4K
AREA_BUSINESS
= 5.3M
So, how do we estimate demand in Year 2009?

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OR
2001
POP = 2.3M
AVG INC = 3.1K
AREA_BUSINESS
= 4.1M
26,000
2002
34,000
2003
42,000
2004
53,000
2009
Y 2009 = ?
2005
61,000
2006
72,000
…
POP = 2.4M
AVG INC = 3.1K
AREA_BUSINESS
= 4.2M
POP = 2.6M
AVG INC = 3.2K
AREA_BUSINESS
= 4.4M
POP = 2.8M
AVG INC = 3.3K
AREA_BUSINESS
= 4.5M
POP = 2.9M
AVG INC = 3.3K
AREA_BUSINESS
= 4.7M
POP = 3.0M
AVG INC = 3.5K
AREA_BUSINESS
= 4.7M
POP = 3.5M
AVG INC = 4K
AREA_BUSINESS
= 5.3M
To estimate demand in Year 2009:
0
20000
40000
60000
80000
100000
120000
0 2 4 6 8 10
Year
Demand,VorY
Demand2009 = f(Y2001, Y2002, …. Y2006)

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OR
2001
POP = 2.3M
AVG INC = 3.1K
AREA_BUSINESS
= 4.1M
26,000
2002
34,000
2003
42,000
2004
53,000
2009
Y 2009 = ?
2005
61,000
2006
72,000
…
POP = 2.4M
AVG INC = 3.1K
AREA_BUSINESS
= 4.2M
POP = 2.6M
AVG INC = 3.2K
AREA_BUSINESS
= 4.4M
POP = 2.8M
AVG INC = 3.3K
AREA_BUSINESS
= 4.5M
POP = 2.9M
AVG INC = 3.3K
AREA_BUSINESS
= 4.7M
POP = 3.0M
AVG INC = 3.5K
AREA_BUSINESS
= 4.7M
POP = 3.5M
AVG INC = 4K
AREA_BUSINESS
= 5.3M
So, how do we estimate demand in Year 2009?
0
20000
40000
60000
80000
100000
120000
0 2 4 6 8 10
Year
Demand,VorY
Demand2009 = f(Y2001, Y2002, …. Y2006)
Demand in Year 2009
= f(POP2009, AVG_INC2009, AREA_BUSINESS2009)

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Time Series demand models: Here, we estimate demand on the basis of
historical demand for that specific system or for similar systems.
Cross-sectional demand models: Here, we estimate demand using the present
characteristics of the region that affect travel demand
Panel (or pooled) demand models
Use both time-series and cross sectional approaches. Econometric techniques often
used.
t1
X1, t1
X2, t1
X3, t1
Y t1
t2
X1, t2
X2, t2
X3, t2
Y t2
t3
X1, t3
X2, t3
X3, 3
Y t3
t4
X1, t4
X2, t4
X3, t4
Y t4
tN
X1, tN
X2, tN
X3, tN
Y tN
…

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Example of demand estimation using time series
The historical demand for a certain rail transit system is as follows:
Use the linear and exponential functional forms to predict the expected
demand at year 2008.
Solution
The expected demand in the year 2008 can be determined using the
mathematical functional forms of the linear and exponential curves as follows:
Linear form: V = 0.089(Year – 1990) – 1.1408 (R2
= 0.95)
Thus, the projected demand in Year 2008 on the basis of linear trends
= 0.089(2008 – 1990) – 1.1408 = 2.74
Exponential form: V = 1.2106e0.0499
(Year – 1990) (R2
= 0.98)
Thus, the projected demand in Year 2008 on the basis of exponential trends =
1.2106e 0.0499(2008 – 1990) = 2.75
Year 1990 1992 1994 1996 1998 2000 2002 2004
Demand 1.25 1.37 1.45 1.58 1.72 1.95 2.31 2.48

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Class Discussion
Why is the “Trend” approach not always
appropriate for demand estimation?

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Example
The total rail demand (passengers in thousands per day) between
City A and Town B, Vij, is:
Where INCij = average income for the two urban centers, in ten
thousands
POPij = average population of the two urban centers, in millions
Determine the rail demand ten years from now when the average
per capita income is $35,600, average population of the two
urban centers is 3 million.
Solution
Vij = 3.560.316
30.221
= 1,904 passengers per day.
221.0316.0
ijijij POPINCV ×=
Demand estimation using cross-sectional data

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• Further classification of Cross-
sectional demand models:
 Demand estimation based on end
point attributes only, vs.
 Demand estimation based on
attributes of entire network.
H C
H C

 Demand estimation based on the attributes of a
Corridor or Project or end point only
 Multimodal approach: that recognizes the relationships that
exist between modes and thus carries out the estimation in a
simultaneous fashion (Models structures similar to TPM)
 Mode-specific approach: Assumes that the modal demands
are independent and therefore estimates these demands
separately.
 Steps in Demand Estimation:
 Market Segmentation: Division into different segments
(flow units (freight vs. passenger); trip purpose; mode)
 Selection of Demand Function:
 Model selection
 Data collected for end points attributes such as population and
employment etc.
 Demand estimation
H C

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Demand Estimation Based only on Attributes of Corridor/Project
or its End Points
Examples
1. Air travel demand
2. Intercity passenger demand models
Kraft-SARC model, McLynn model, Baumol-Quandt model:
V12 = A*(P1P2)B
* C(I1I2)D
*E(tM1tM2)*G(cM1cM2)
P is population, I is income, t is the time taken by mode m, c is the
average passenger cost of taking mode m.
Q
e
Z
V /
1
12 2
1 β
β+
=
Z is a measure of socio-economic activity
Q is schedule frequency
Beta’s are model parameters
1 2

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Demand Estimation Based only on Attributes of Corridor/Project or its
End Points
Examples
3. Transit demand
V12 = transit ridership/hr between 1 and 2
T = transit travel time (hrs)
P = transit fare ($)
A = cost of auto trip ($)
I = average income ($)
1 2
25.01.02.03.0
12
−−−
= IApTV

Demand estimation based on Entire Network attributes
 The four-step transportation planning model (TPM) is the most widely used
model for estimating the link-by-link demand for an urban or regional
network demand
 Ability to estimate demand with respect to trip type, mode, and route.
 Can be used for statewide transportation planning involving passengers and
freight
 The TPM estimates expected demand on the basis of the attributes of the
activity system (e.g employment and population) that generates such
demand and the characteristics of the transportation system (that serves this
demand)
 The end product: is the demand on each link in a network at
“equilibrium” condition.
 A transportation network is considered at equilibrium when all traffic patterns
stabilize and no driver has any incentive to change its current route

Demand estimation based on Entire Network attributes
 Establish the market segmentation
 Establish traffic analysis zones (TAZ)
 Four step transportation planning model

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Demand Estimation based on Attributes of Entire Parent Network
1. Trip Generation:
What generates the trips? – Trip productions and attractions.
2. Trip Distribution:
For the trips generated, how are they distributed (shared) among the
various destination points?
3. Traffic Assignment
Which routes are taken by the travelers from any origin to any
destination?
4. Mode Choice or Mode Split
For a given set of travelers on each chosen route, what fraction takes
which mode (auto, bus, walk, rail, air, etc.)?
This is known as the Transportation Planning Model (TPM)
CE863?

44
Classification by the Functional Form of the Demand Model
Generally, V = f(X)
where X is:
- (for disaggregate demand), is a factor (or vector of factors) that
affects the individual travel demand, such as trip price, time, safety,
comfort, etc.
- (for aggregate demand), is a factor of vector of factors that affect
the overall travel demand, such as population, average income,
employment levels, etc.
- for a time series demand model (often aggregate), is simply the
time in years
The Big Question: What is the shape of f?

45
V
X
Linear Power
V
X
Common Functional Forms
V
X
Demand = a + bX
Demand = aXb
, b>1
Demand = aXb
, b<1

46
Demand = a*bX
Exponential Demand Models

47
Modified Exponential Demand Models
Demand = c + a*bX

48
Logistic Demand Models
)(
1
X
abc
Demand
+
=

49
Transportation Supply
• Transportation Supply
The quantity (or quality) of transportation facilities that
facility producers are willing to provide under a given set
of conditions.

50
Elements of Transportation Supply
Quantity Quality
• Amount of service
• Nr. of buses / rail
cars per hr
• Size of runway area,
harbor area, etc.
• Capacity of
transportation
facilities
• Level of Service
• Traveling comfort, safety,
convenience, etc.
• Non-physical systems and
operational features that
increase facility capacity (ITS
initiatives, ramp metering, HOV)
• Can help increase the flow of
traffic even when the physical
capacity is constant

51
How to Estimate Transportation Supply
• Supply functions or supply models :
• Mathematical expressions that describe transportation supply.
S = f(X1, X2, … Xn)
• When trip price increases, the supply of transportation services increases
• When trip price decreases, the supply of transportation service decreases
• In classical economics, this is known as The Law of Supply
Trip
Price
Quantity Supplied
p1
p2
S
V1 V2

52
Shifts in the Supply Curve
• A change in supply can occur even when the price is
constant
Trip
Price
Quantity Supplied
p
SA
V2V1
SC
Causes of shifts in supply curve
Number of competing transportation modes that are available
Changes in prices of using any alternative transportation modes
Changes in technology

53
Shifts in the Supply Curve
• A change in supply can occur even when the price is
constant
Trip
Price
Quantity Supplied
p
SA
V2 V1
SB
Causes of shifts in supply curve
Number of competing transportation modes that are available
Changes in prices of using any alternative transportation modes
Changes in technology

54
Equilibration of Transportation
Demand and Supply

55
Demand-Supply Equilibration
o Combination of demand and supply determines how much of a
good or service is produced and consumed in an economy and at
what price.
o Equilibrium is defined to be the price-quantity pair where the
quantity demanded is equal to the quantity supplied, represented
by the intersection of the demand and supply curves.
Going to/from work
Going to/from school
Leisure/Entertainment
Shopping
Meetings
Etc.
Socio-economic Activities
Transportation
Demand
Demand
and
Supply
Equilibration
Flow
of
Traffic
Facility
Supply

56
Demand-Supply Equilibration
In a competitive market, the unit price for a particular good will vary
until it settles at a point where the quantity demanded by consumers
(at current price) will equal the quantity supplied by producers (at
current price), resulting in an economic equilibrium for price and
quantity.
Going to/from work
Shopping
Meetings
Etc.
Socio-economic Activities
Transportation
Demand
Demand
and
Supply
Equilibration
Flow
of
Traffic
Facility
Supply

57
An Instance of Demand-Supply Equilibration – How it happens
Trip Price (p)
Quantity (V)
V*
p*
Demand function: fD(p, V)
Supply Function: fS(p, V)
At equilibrium, Demand = Supply
fD(p, V) = fS(p, V)
Solving simultaneously, we get:
p = p* (equilibrium trip price) and V = V* (equilibrium demand)

58
Demand-Supply Equilibration – Example 1 (Rail transit)
• Demand function
V = 5500 - 22p
• Supply function
p = 1.50 + 0.003 V
• Solving the above 2 equations simultaneously yields: the
demand/supply equilibrium conditions
V = 5,431 passengers daily
P = $3.13 fare (trip price) per passenger
Trip
Price (p)
Quantity (V)
V*
p*
VD = 5500 -22p
p = 1.50 + 0.003VS

59
Demand-Supply Equilibration – Example 2 (Air Travel)
Supply Function
price per seat = 200 + 0.02*(nr. of airline seats sold per day)
p = 200 + 0.02*q
Demand Function
Nr. of seats demanded per day = 5000 - 20 (price per seat)
q = 200 + 0.02*p
Solving simultaneously ….
Equilibrium price, p* = $214.28
Nr. of seats demanded and sold at equilibrium, q* = 714

60
Demand-Supply Equilibration – Example 3 (Freeway travel)
Supply Function
Travel time = 15 + 0.02*traffic volume
t = 15 + 0.02*q
Equilibrium conditions:
Travel time = 27.94 mins.
Traffic volume = 647 vehs/hr
Travel
Time
27.94
mins
Traffic Supply
Function
Traffic
Demand
Function
Traffic Flow647 vehs/hr
Demand Function
Traffic volume = 4,000 – 120* Travel time
q = 4000 - 120*t

61
Is there always only one instance
of equilibration?

Demand-Supply Equilibration – Series of Instances
Going to/from work
Visiting restaurants
Shopping
Meetings
Etc.
Socio-
economic
Activities
Transportation
Demand
Demand
And Supply
Equilibration
Facility
Supply
Change in
Transportation
Demand
Change in
Transportation
Demand
Demand
And Supply
Equilibration
Demand
And Supply
Equilibration
Change in Facility
Supply

Demand-Supply Equilibration – A Series of 3
Instances (Graphical Illustration)
Trip
Price (P)
Quantity V
DOLD
DNEW
SOLD
SNEW
V2
V1
P2
P1
V0
P0
A. Initial equilibrium point
B. Increased demand (New business, more employment)
C. Improvement in transportation supply (New lanes. ITS)
Equilibration occurs continually, because of the dynamic nature of socio-
economic activity and transportation decisions.
A
B
C

64
Elasticity of Transportation Demand

65
Elasticity of Demand
• Definition:
o % Change in demand in response to a 1 % change in a
demand factor or service (supply) attribute, X
o Elasticity is a term widely used in economics to denote the
responsiveness of one variable to changes in another
o Price elasticity of demand: is the % change in quantity
demanded with respect to the % change in price
• Demand factors and service attributes include:
o Price
o Total trip price
o Parking price
o Fuel price
o Congestion price (price for entering the CBD)
o Transit fare, etc.
o Travel Time
o Trip comfort, safety, convenience, etc.

Point Elasticity
Point Elasticity:
Point elasticity is used when the change in price is very small, i.e. the two
points between which elasticity is being measured essentially collapse on
each other.
Measure of price elasticity of demand at a point on demand curve
Calculation of the point elasticity requires detailed knowledge of the
functional relationship between variables
Factor or
Attribute, x
Quantity of trips
demanded, V
V=f(x)
V*=f(x*)
x*
xofvalueOriginal
xinChange
demandOriginal
demandinChange
e XV
___
__
_
__
, =
))((
/
/
,
x
V
V
x
xx
VV
e XV
∂
∂
=
∂
∂
=
XinChange
demandinChange
e XV
___%
___%
, =

Arc Elasticity
Arc Elasticity:
Arc elasticity measures elasticity at the mid point between the two selected
points
Arc elasticity measures the "average" elasticity between two points on the
demand curve
The arc elasticity is used when there is not a general function for the
relationship of two variables, but two points on the relationship are known
Factor or
Attribute, x
Quantity of
trips
demanded,
V
V=f(x)
V0
x0
x1
V1
( )( )
( )( ) 2/
2/
_
011
011
VVxx
xxVV
ElasticityArc
o
o
+−
+−
=
xofPoMid
xinChange
demandofPoMid
demandinChange
Arce
_int__
__
_int__
__
)( =

Point & Arc Elasticity
http://www.kevinhinde.com/elearning/pointarc/

69
Example of Arc Elasticity Calculation
Two years ago, the average air fare between two cities was $1,000 per
trip, 45,000 people made the trip per year. Last year, the average
fare was $1,200 and 40,000 people made the trip.
Assuming no change in other factors affecting trip-making (such as
security, economy, etc.), what is the elasticity of demand with
respect to price of travel?
Solution:
Arc price elasticity, ep =
647.0
2/)000,40000,45()200,1000,1(
2/)200,1000,1()000,40000,45(
2/)(
2/)(
21
21
−=
+×−
+×−
=
+×∆
+×∆
VVp
ppV
( )( )
( )( ) 2/
2/
_
011
011
VVxx
xxVV
ElasticityArc
o
o
+−
+−
=

70
Elasticity of Demand
• Why Elasticity is Important: Elasticity is important because it
describes the fundamental relationship between the price of a
good and the demand for that good
• Elastic goods: Elastic goods and services generally have plenty
of substitutes. As an elastic service/good's price increases, the
quantity demanded of that good can drop fast. Example of elastic
goods and services include furniture, motor vehicles, and
transportation services.
• InElastic goods:
Inelastic goods have fewer substitutes and price change doesn't
affect quantity demanded as much. Some inelastic goods include
petrol, electricity etc.

71
Interpretation of Elasticity Values
Inelastic Inelastic
0 1-1
+ ∞- ∞
Elastic, DirectElastic, Inverse
Perfectly Inversely
Elastic
Perfectly Directly
Elastic
Perfectly Inelastic
A unit
increase in x
results in a
very large
decrease in
demand, V A unit increase
in x results in a
very small
decrease in
demand, V A unit increase in
x results in NO
change in
decrease in
demand, V
A unit increase
in x results in a
very small
increase in
demand, V
A unit
increase in x
results in a
very large
increase in
demand, V

72
Interpretation of Demand Elasticity Values -
Example:
( )
( )
39.0
2/26002000
2/5.1
5.0
600
=
+
+
×=e
When the fare, p, on a bus route was $1, the daily ridership, q,
was 2000. By reducing the fare to $0.50, the ridership increased
by 600. What is the elasticity of demand with respect to trip
fare?
Solution:
( )( )
( )( ) 2/qqpp
2/ppqq
01o1
01o1
+−
+−
e =

73
Interpretation of Demand Elasticity Values -
Example:
( )
( )
39.0
2/26002000
2/5.1
5.0
600
−=
+
+
×
−
=e
When the fare, p, on a bus route was $1, the daily ridership, q,
was 2000. By reducing the fare to $0.50, the ridership increased
by 600. What is the elasticity of demand with respect to trip
fare?
Solution:
( )( )
( )( ) 2/qqpp
2/ppqq
01o1
01o1
+−
+−
e =
Because the resulting elasticity is less than 1.00, the demand is
considered inelastic.
Inelastic Inelastic
0 1-1
+ ∞- ∞
Elastic, DirectElastic, Inverse
Perfectly Inversely
Elastic
Perfectly Directly
Elastic
Perfectly Inelastic

74
Applications of the Concept of Elasticity
Prediction of expected demand in response to a change in trip
prices, out-of-pocket costs, fuel costs, etc. Thus helps in evaluating
policy decisions.
For transit agencies, elasticities help predict the expected change in
demand (and therefore, predict expected change in revenue) in
response to changes in transit service attributes (trip time, safety,
comfort, security, etc). Thus helps agencies examine the potential
impact of their transit investment (enhancements) or increases or
decreases in transit fare.
Elasticities therefore are generally useful for
evaluating the impact of changes in transportation
systems on travel demand.

75
Applications of the Concept of Elasticity (cont’d)
Prediction of revenue changes
How does demand elasticity affect revenues from fare-related
transportation systems?
Elasticity of transit demand with respect to price is given by:
% change in ridership
% change in price
If e > 1, demand is elastic
increase in price will reduce revenue decrease in
price will increase revenue
e < 1, opposite effect on revenue
e = 1, revenue will remain the same irrespective of the change in price
e =

76
Direct and Cross Elasticities
• Direct Elasticity – the effect of change in the price of
a good on the demand for the same good.
• Cross Elasticity – the effect on the demand for a
good due to a change in the price of another good.

77
1. Direct and Cross Elasticities
Demand for
Auto Travel
Demand for Bus
Transit Travel
Parking Price
Travel Time
Fuel
Transit Fare
Travel Time
Safety

78
Examples of Direct Elasticities
Demand for
Auto Travel
Demand for Bus
Transit Travel
Parking Price
Travel Time
Fuel
Transit Fare
Travel Time
Safety

79
Examples of Cross Elasticities
Demand for
Auto Travel
Demand for Bus
Transit Travel
Parking Price
Travel Time
Fuel
Transit Fare
Travel Time
Safety

80
Examples of Cross Elasticities
Demand for
Auto Travel
Demand for Bus
Transit Travel
Parking Price
Travel Time
Fuel
Transit Fare
Travel Time
Safety

81
Consumer Surplus and Latent
Demand

82
Consumer Surplus
• Analysis of the impact of changes in the market price of a
transportation service - consumer’s position (better or worse)
• Traditional analysis fails to quantify changes in consumer
satisfaction due to these price changes
• Consumer surplus. Compares the value of each unit of a
commodity consumed against its price
• Consumer surplus is the difference between what consumers are
willing to pay for a good or service and what they actually pay (the
market price)
• Willingness to pay

83
Consumer Surplus - Conceptual Illustration
• Consider you go to the mall and you see a flashy
new i-pod
• Display price is $75.00
• But you like it (or need it) so much that you are
even prepared to pay $200 for it
• Your individual consumer surplus = $125 (= 200-
75)
• Others may have a CS that is less or more than
yours.
• Let’s say the average consumer surplus of potential
buyers is $100.

84
Consumer Surplus – In the Context of
Transportation Demand
• Existing transit fare is p dollars.
• Some people are prepared to pay up to q dollars for the trip,
where q > p
• Then, maximum consumer surplus = q - p
minimum consumer surplus = 0
the average consumer surplus = ((q - p) + 0) / 2
= 0.5(q - p)
• For all the travelers that demand that trip at equilibrium conditions,
VP*, the total consumer surplus is
= VP* 0.5(q - p) = 0.5 VP* (q - p)×

85
Unit Trip
Price, p
Consumer
Surplus
Demand
Function
Supply
Function
p
0 Vp0
Quantity of Trips
demanded, VVp*
q
p - q
Consumer surplus = 0.5VP*(q - p)

86
Unit
price,
p
p1
p2
V2V10 V
S1 = Existing Supply Curve
S2 = Supply Curve after improvement
( ) ( )( )1221121
2
1
VVppVpp −−+−=
( )( ) 2/2121 VVpp +−=
The change in consumer surplus, which is a measure of
the beneficial impact of the improvement, is given by:
Change in Consumer Surplus
A change in transportation supply (e.g., increased quantity, increased
capacity, increased quality of service (comfort, safety, convenience,
etc.) can lead to a change in the consumer surplus.

87
Consumer Surplus - Example:
Urban Bus Service – Current Scenario
a.Total Buses = 100
b.# of seats per bus = 40 (bus capacity)
c.90% load factor
d.fare $1
Urban Bus Service – Proposed Scenario
a.20% increase in fleet size (120 buses)
b.fare $0.9
c.95% load factor
Calculate the change in consumer surplus.
Determine if there is a revenue gain.

88
Fare ($)
1.0
0.8
0.4
0 2000 4000 6000 q (persons/hr)
Consumer Surplus
Solution

89
Fare ($)
1.0
0.8
0.4
0 2000 4000 6000 q (persons/hr)
Consumer Surplus
Existing situation
q1 = 100 buses x 40 seats
x 0.9 (load factor)
= 3600 persons
Rev = 3600 x $1
= $3600
Solution
Proposed Situation
q2 = 120 buses x 40 seats x 0.95 (LF)
= 4560 persons
Rev = 4560 x 0.9
= $4140
Change in Consumer Surplus
= (1.0 – 0.9)(3600 + 4560)/2
= $408
Rev Gain = (4140 -3600) = $504

90
Unit Trip
Price, p
Latent demand
Demand
Function
Supply
Function
p*
0 VL
Quantity of Trips
demanded, VVp*
Latent demand = VL – VP*
Latent Demand
 Latent Demand: The difference between the maximum possible
number of trips and the number of trips that are actually made
 Application of the latent demand concept - travel demand
management, such as transit fare reduction for non–peak hour
travel

91
Latent Demand - Conceptual Illustration
• Again, consider you go to the mall and you see that flashy
new i-pod
• Display price is $75.00
• Assume the producer is willing to give it out free to anyone
who is interested.
• How many people would demand it?
• This is the latent demand.
• What does this tell the producer? Gives indication of
demand under pro-bono conditions.
– Useful for sales promotions of the good (example, free good
for limited period to help advertise)
– Useful for sales promotion of complementary goods (e.g., free
phone but you pay for the service.)

92
Latent Demand – In the Context of Transportation
Demand
• Existing transit fare is p dollars.
• On the average, VL people are prepared to use the transit
service if it were free-of-charge.
• Then the latent demand is VL – Vp*
where VP* is the demand at equilibrium conditions,

An Intro to estimating travel demand

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