An Intro to estimating travel demand

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


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?

0 20 40 60 80 100

Air

Rail

Bus

Auto

Cycle

Walk

Trav

el M

ode

Modal Share (Percentage)


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.

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Transportation Demand in the Classical Economics Context


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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.).


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).


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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)


p2

p1

V2

1

2

V = f(Trip Price)


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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!


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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)


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)



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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

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• 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 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.)


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Classification of Demand ModelsDisaggregate vs. aggregate demand modelsConsider the following situation:

We seek to estimate the travel demand between the Lahore and Rawalpindi


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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


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)



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. 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


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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


POP = 2.6M

AVG INC = 3.2K


POP = 2.8M

AVG INC = 3.3K


POP = 2.9M

AVG INC = 3.3K


POP = 3.0M

AVG INC = 3.5K


POP = 3.5M

AVG INC = 4K


So, how do we estimate demand in Year 2009?


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OR

2001

POP = 2.3M

AVG INC = 3.1K


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


POP = 2.6M

AVG INC = 3.2K


POP = 2.8M

AVG INC = 3.3K


POP = 2.9M

AVG INC = 3.3K


POP = 3.0M

AVG INC = 3.5K


POP = 3.5M

AVG INC = 4K


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)


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OR

2001

POP = 2.3M

AVG INC = 3.1K


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


POP = 2.6M

AVG INC = 3.2K


POP = 2.8M

AVG INC = 3.3K


POP = 2.9M

AVG INC = 3.3K


POP = 3.0M

AVG INC = 3.5K


POP = 3.5M

AVG INC = 4K


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)


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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 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

…


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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.

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


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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 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

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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


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

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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


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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


25.01.02.03.012

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

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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 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)


CE863?

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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?


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

XabcDemand


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.

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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

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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 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

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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



Shopping

Meetings

Etc.



DemandandSupplyEquilibration

FlowofTraffic

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 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


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

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Is there always only one instance of equilibration?

Demand-Supply Equilibration – Series of Instances


Going to/from work



Visiting restaurants

Shopping

Meetings

Etc.



DemandAnd SupplyEquilibration

Facility Supply

Change in TransportationDemand

Change in TransportationDemand



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


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


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


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

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, 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

72

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.

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1. Direct and Cross Elasticities



Demand for Auto Travel

Demand for Bus Transit Travel

Parking PriceTravel TimeFuel

Transit FareTravel TimeSafety

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Examples of Direct Elasticities







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Examples of Cross Elasticities







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Examples of Cross Elasticities







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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.

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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.

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Fare ($)1.0

0.8

0.4

0 2000 4000 6000 q (persons/hr)

Consumer Surplus

Solution

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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

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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,

An Intro to estimating travel demand

Engineering

Transcript of An Intro to estimating travel demand