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CE-807 Traffic Engineering(Fall 10)
Lecture # 10Traffic 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.
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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
Estimating Transportation Demand
4
Types of Passenger Transportation Modes:
Air Water Rail Bus
Auto Bicycle Walk Other
Transportation Demand by Mode
Estimating Transportation Demand
5
Types of Freight Transportation Modes:
Air Water Rail Truck
Pipeline
Transportation Demand by Mode
Estimating Transportation Demand
6
What is a “modal share” of transportation demand?
0 20 40 60 80 100
Air
Rail
Bus
Auto
Cycle
Walk
Trav
el M
ode
Modal Share (Percentage)
Estimating Transportation Demand
Is the distribution of the overall amount of travel demand among the various modes.
Example, modal share of travelers between two cities
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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.
Estimating Transportation Demand
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.
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Transportation Demand in the Classical Economics Context
Estimating Transportation Demand
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)
Estimating Transportation Demand
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.).
Estimating Transportation Demand
12
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).
Estimating Transportation Demand
13
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)
Estimating Transportation Demand
14
• 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)
Estimating Transportation Demand
15
Abnormal demand curves
Abnormal Goods and Services
Giffen Goodsa. Inferior, but staple goods and servicesb. Giffen goods exist when there is a lack of cheaper substitutes c. Maze, Wheat, Rice
Veblen Goodsa.a good made more fashionable by a higher priceb.Status symbolc.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!
Estimating Transportation Demand
16
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)
Estimating Transportation Demand
17
Shifts in the Transportation Demand Function
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
Estimating Transportation Demand
18
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)
Estimating Transportation Demand
Shifts in the Transportation Demand Function
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
Estimating Transportation Demand
20
Classification of Demand Models
21
Classification of Demand Models
• 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
Estimating Transportation Demand
22
Classification of Demand Models
Single attribute vs. multiple attribute demand models
Single attribute: only one variableDemand = 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.)
Estimating Transportation Demand
23
Classification of Demand ModelsDisaggregate vs. aggregate demand modelsConsider the following situation:
We seek to estimate the travel demand between the Lahore and Rawalpindi
Estimating Transportation Demand
24
Classification of Demand ModelsAggregate vs. disaggregate demand modelsConsider the following situation:
We seek to estimate the travel demand between the Lahore and Rawalpindi
LahorePopulation = 10 MArea = 410 sq. kmNumber of Industries = 420Nr. of Shopping centers = 134
RwalpindiPopulation = 5 MArea = 265 sq. kmNumber of Industries = 140Nr. of Shopping centers = 84
Travelers between H and CFor 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
Estimating Transportation Demand
Classification of Demand ModelsAggregate 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)
Estimating Transportation Demand
Classification of Demand Models
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
Estimating Transportation Demand
27
Classification of Demand Models
Deterministic vs. stochasticDeterministic 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
Estimating Transportation Demand
28
Classification of Demand Models
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
…
Estimating Transportation Demand
29
Classification of Demand Models
Time Series vs. Cross-sectional Models
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?
Estimating Transportation Demand
30
Classification of Demand Models
Time Series vs. Cross-sectional Models
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 10Year
Dema
nd, V
or Y
Demand2009 = f(Y2001, Y2002, …. Y2006)
Estimating Transportation Demand
31
Classification of Demand Models
Time Series vs. Cross-sectional Models
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 10Year
Dema
nd, V
or Y
Demand2009 = f(Y2001, Y2002, …. Y2006)
Demand in Year 2009
= f(POP2009, AVG_INC2009, AREA_BUSINESS2009)
Estimating Transportation Demand
32
Classification of Demand Models
Time Series vs. Cross-sectional Models
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 modelsUse 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
…
Estimating Transportation Demand
33
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.
SolutionThe 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
Estimating Transportation Demand
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Class Discussion
Why is the “Trend” approach not always
appropriate for demand estimation?
Estimating Transportation Demand
35
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 thousandsPOPij = average population of the two urban centers, in millions
Determine the rail demand ten years from now when the average per capita income is $35,600, average population of the two urban centers is 3 million.
SolutionVij = 3.560.316 30.221 = 1,904 passengers per day.
221.0316.0ijijij POPINCV
Demand estimation using cross-sectional dataEstimating Transportation Demand
36
Classification of Demand Models
• Further classification of Cross-sectional demand models: Demand estimation based on end
point attributes only, vs.
Demand estimation based on attributes of entire network.
H C
H C
Estimating Transportation Demand
Classification of Demand Models Demand estimation based on the attributes of a
Corridor or Project or end point only Multimodal approach: that recognizes the relationships that
exist between modes and thus carries out the estimation in a simultaneous fashion (Models structures similar to TPM)
Mode-specific approach: Assumes that the modal demands are independent and therefore estimates these demands separately.
Steps in Demand Estimation: Market Segmentation: Division into different segments (flow
units (freight vs. passenger); trip purpose; mode) Selection of Demand Function:
Model selection Data collected for end points attributes such as population and
employment etc. Demand estimation
H C
38
Demand Estimation Based only on Attributes of Corridor/Project or its End Points
Examples1. Air travel demand
2. Intercity passenger demand modelsKraft-SARC model, McLynn model, Baumol-Quandt model:
V12 = A*(P1P2)B * C(I1I2)D *E(tM1tM2) *G(cM1cM2)
P is population, I is income, t is the time taken by mode m, c is the average passenger cost of taking mode m.
QeZV /1
12 21 Z is a measure of socio-economic activity
Q is schedule frequencyBeta’s are model parameters
1 2
Estimating Transportation Demand
39
Demand Estimation Based only on Attributes of Corridor/Project or its End Points
Examples
3. Transit demand
V12 = transit ridership/hr between 1 and 2
T = transit travel time (hrs)P = transit fare ($)A = cost of auto trip ($)
I = average income ($)
1 2
Estimating Transportation Demand
25.01.02.03.012
IApTV
Classification of Demand ModelsDemand 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
Classification of Demand ModelsDemand estimation based on Entire Network attributes
Establish the market segmentation Establish traffic analysis zones (TAZ) Four step transportation planning model
42
43
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 AssignmentWhich routes are taken by the travelers from any origin to any destination?
4. Mode Choice or Mode SplitFor 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)
Estimating Transportation Demand
CE863?
44
Classification of Demand ModelsClassification 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?
Estimating Transportation Demand
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
Common Functional Forms
47
Modified Exponential Demand Models
Demand = c + a*bX
Common Functional Forms
48
Logistic Demand Models
)(1
XabcDemand
Common Functional Forms
49
Transportation Supply
Estimating Transportation Demand
• 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 Estimating Transportation Demand
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
Estimating Transportation Demand
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 curveNumber 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 curveNumber of competing transportation modes that are available
Changes in prices of using any alternative transportation modes
Changes in technology
54
Estimating Transportation Demand
Equilibration of Transportation Demand and Supply
55
Demand-Supply EquilibrationEstimating Transportation Demand
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
TransportationDemand
DemandandSupplyEquilibration
FlowofTraffic
Facility Supply
56
Demand-Supply EquilibrationEstimating Transportation Demand
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
Going to/from school
Leisure/Entertainment
Shopping
Meetings
Etc.
Socio-economic Activities
TransportationDemand
DemandandSupplyEquilibration
FlowofTraffic
Facility Supply
57
An Instance of Demand-Supply Equilibration – How it happens
Estimating Transportation Demand
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 functionV = 5500 - 22p
• Supply functionp = 1.50 + 0.003 V
• Solving the above 2 equations simultaneously yields: the demand/supply equilibrium conditions
V = 5,431 passengers dailyP = $3.13 fare (trip price) per passenger
Estimating Transportation Demand
TripPrice
(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
Estimating Transportation Demand
Going to/from work
Going to/from school
Leisure/Entertainment
Visiting restaurants
Shopping
Meetings
Etc.
Socio-economic Activities
TransportationDemand
DemandAnd SupplyEquilibration
Facility Supply
Change in TransportationDemand
Change in TransportationDemand
DemandAnd SupplyEquilibration
DemandAnd SupplyEquilibration
Change in Facility Supply
Demand-Supply Equilibration – A Series of 3
Instances (Graphical Illustration)
TripPrice (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
Estimating Transportation Demand
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 priceo Parking priceo Fuel priceo Congestion price (price for entering the CBD)o Transit fare, etc.
o Travel Timeo Trip comfort, safety, convenience, etc.
Point ElasticityPoint 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 curveCalculation 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*xofvalueOriginalxinChange
demandOriginaldemandinChange
e XV
_____
___
,
))((//
, xV
Vx
xxVVe XV
XinChangedemandinChangee XV ___%
___%,
Arc ElasticityArc Elasticity:Arc elasticity measures elasticity at the mid point between the two selected pointsArc elasticity measures the "average" elasticity between two points on the demand curveThe 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
VVxxxxVV
ElasticityArco
o
xofPoMidxinChange
demandofPoMiddemandinChange
Arce
_int____
_int____
)(
Point & Arc Elasticity
http://www.kevinhinde.com/elearning/pointarc/
69
Example of Arc Elasticity CalculationTwo 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 =
647.02/)000,40000,45()200,1000,1(2/)200,1000,1()000,40000,45(
2/)(2/)(
21
21
VVpppV
2/
2/_
011
011
VVxxxxVV
ElasticityArco
o
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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.
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Interpretation of Elasticity Values
Inelastic Inelastic
0 1 -1 + ∞ - ∞
Elastic, Direct Elastic, 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
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Interpretation of Demand Elasticity Values - Example:
39.0
2/260020002/5.1
5.0600
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 =
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Interpretation of Demand Elasticity Values - Example:
39.0
2/260020002/5.1
5.0600
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, Direct Elastic, Inverse
Perfectly Inversely Elastic
Perfectly Directly Elastic
Perfectly Inelastic
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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.
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Applications of the Concept of Elasticity (cont’d)
Prediction of revenue changesHow 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 elasticincrease 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 =
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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
• 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.
Demand for Auto Travel
Demand for Bus Transit Travel
Parking PriceTravel TimeFuel
Transit FareTravel TimeSafety
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Examples of Direct 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.
Demand for Auto Travel
Demand for Bus Transit Travel
Parking PriceTravel TimeFuel
Transit FareTravel TimeSafety
79
Examples of 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.
Demand for Auto Travel
Demand for Bus Transit Travel
Parking PriceTravel TimeFuel
Transit FareTravel TimeSafety
80
Examples of 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.
Demand for Auto Travel
Demand for Bus Transit Travel
Parking PriceTravel TimeFuel
Transit FareTravel TimeSafety
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Consumer Surplus and Latent Demand
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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
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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.
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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)
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Unit Trip Price, p
Consumer Surplus
Demand Function
Supply Function
p
0 Vp0Quantity of Trips demanded, VVp*
q
p - q
Consumer surplus = 0.5VP*(q - p)
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Unit price, p
p1
p2
V2V10 V
S1 = Existing Supply Curve
S2 = Supply Curve after improvement
1221121 21 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 SurplusA 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 VLQuantity 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
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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.)
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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,