Transport Economics

Topics to be covered:

-Transport Economics

- Road Pricing

- Travel Demand Forecasting

- Project Appraisal

Contact details: brian.caulfield@tcd.ie

Office: Red brick building

Recommended texts for Transport Economics

Transport economics / Kenneth Button

Applied Transport Economics / Stuart Cole

http://www.tcd.ie/Civil_engineering/Staff/Brian.Caulfield/

Transport Economics

Transport economics is an applied area of economics that is concerned with the

efficient use of society’s scarce resources for the movement of people and goods

from an origin to a destination.

Transport Demand

The demand for transport is said to be a derived demand. People do not travel for

the joy of travelling, rather they travel as they need/want to engage in some activity.

Transport demand can be focused upon the following:

• The need for persons to travel to other locations to partake in an activity

• The need to move goods/freight from the point of manufacture to the point of

consumption

The demand for transport depends largely upon consumers income and the price of

a particular good.

Example 1: consider a choice between two modes of transport.

A Dublin Bus route and a Luas line. The demand for both depends upon the fare of

each mode relative to the other mode.

Individuals can also drive to their location, for this example we assume those on

higher incomes drive and those on lower incomes use public transport.

Mathematically, the demand for a transportation good or service can be written as

(Da) and this is influenced by price (Pa) and the prices of other goods and services

(P1, P2, P3……Pw) and the level of income (Y)

1 2( , , ,........, , )

a a wD f P P P P Y=

The prices can be 1) the fare or out-of-pocket costs, 2) other costs (level of

service): time costs, comfort, convenience, etc. They can be measured and

expressed in monetary terms. These terms are called generalised costs.

A demand function represents the willingness of consumers to purchase the

transportation good or service at alternative generalised prices.

Below is an example of a linear travel demand function:

q a pβ= −

Where q is the quantity of trips demanded and a, β are constant demand

parameters. P is the total generalised price of the trip.

• Assume a particular level and distribution of income, population, and

socioeconomic characteristics.

• Is an aggregated demand curve, representing the volume of trips demanded at

different prices by a group of travellers.

• is also for a given OD pair at a specific time of day for a particular purpose.

• the following figure shows a series of shifted demand curves, representing

changes in the quantity of travel due to variables other than the perceived price.

Generalised Cost

Cost may be considered in terms of distance, time, money or a combination of

these.

• The generalised cost is typically a linear function

• Includes weighted coefficients

• These coefficients attempt to present their relative importance as

perceived by the traveller

One typical representation of this could be for mode k

1 2 3 4 5 6

v w t

ij ij ij ij nij nij jC a t a t a t a t a F a φ δ= + + + + + +

Where: is the in-vehicle travel time between i and j

is the walking time for and from stop stations

is the wait time at stops

is the interchange time if any

is the fare charged between i and j

is the terminal cost (typically parking) associated with the journey

is the modal penalty, representing other attributes, comfort etc

v

ijtw

ijt

t

ijt

nijt

ijF

jφ

δ

This expression of generalised cost represents an interesting combination of

subjective and objective disutility of movement.

It aims to represent the perception of disutility of travel by the trip maker

D3: increase in (say Luas) demand for the same price, this may be due to one or

more of the following:

• increase in income

• increase in population

• increase in the price of substitutes (Dublin Bus vs Luas)

• decrease in the price of a complementary service (DART vs Luas)

D2: decrease in demand for the same price

Sensitivity of Travel Demand

The functional form of travel demand can be used to forecast changes in travel

volume caused by specific changes in price in the short run. The measurement of

these changes is called elasticity.

Elasticity of demand is the ratio of relative changes in demand to relative changes

in price.

/*

/p

Q Q q pe

P P p q

∆ ∆= =

∆ ∆

Where ∆q is the change in the quantity of trips demanded which accompanies

a 1% change in price.

Typically three elasticity ratios are used in transport.

1. The shrinkage ratio

2. The midpoint (or linear) are elasticity, computed as

3. Log-arc elasticity, calculated as

These three measures of elasticity yield approximately equal values for relatively

small price changes. For larger differences the shrinkage ratio begins to deviate

significantly.

Example:

An aggregated demand function is represented by the equation

q = 200 – 10p

Where q is the number of trips made and p is the price per-trip. Find the price

elasticity when

q = 0, q = 50, q = 100, q = 200 trips

Corresponds to

p = 20, p = 15, p = 10, p = 5, p = 0 cents

Solution:

When the elasticity is less than -1 (i.e. more negative than -1) the demand is

described as being elastic, meaning that the resulting percentage change in

quantity of trip making will be larger than the percentage change in price. Or

demand is relatively sensitive to price change.

Elasticity between 0 and -1 is described as inelastic or relatively insensitive.

Direct and cross elasticity

Direct elasticity:

• the effect of the change of price of a good on the demand for the same good

• must be negative

Cross elasticity:

• the effect of the demand to the price of another good

• positive when goods are substitutes

• e.g. when the price of oil increases, individuals tend to use more public transport

• negative when goods are complements (used together)

• e.g. the price of downtown parking goes up, the demand for driving a car

downtown goes down.

Demand – Supply Equilibrium

1. Economic Theory

In demand and a supply we have two intersecting groups: producers – supply

function and consumers the demand function.

The supply function: expresses the amount of goods that the suppliers produce

as a function of the price of the product. As the price increases, it becomes

more profitable to produce more products, and the quantity supplied will

increase.

Demand Function: describes the aggregate behaviour of consumers. The

amount of the product consumed is given as a function of its price. As the price

increases, the amount consumed will decrease.

E: is the equilibrium point. The price at this point is the equilibrium market price.

At this equilibrium market price, the entire quantity produced is equal to the

quantity consumed.

2. Extension to include level of service

- The transportation market can be analysed in the framework of supply/demand

equilibrium.

- Like demand for a transportation good and service, the supply is characterised

by the level of service offered in addition to the price charged

- The level of service is defined by several characteristics of the service such as;

travel time, headway, reliability etc. This is termed the generalised cost.

- The level of service is dependant upon the usage of the transportation system.

For example the Luas, the greater the demand the longer it takes to fill the tram,

and an increased likelihood that commuters boarding closer to the city centre

will not be able to board.

The performance function:

- Describes how the level of service will decrease with increasing volumes

- This performance function describes the delay as a function of arrival rate

- The dependency of the level of service on flow is a fundamental characteristic of

the transportation market.

Consumer Surplus

Consumer surplus is the amount that consumers benefit by being able to

purchase a product for a price that is less than they would be willing to pay.

For example, a passenger is willing to pay €1 to travel to work every morning,

but the public transport fare is €0.80. The consumer surplus is said to be €0.20.

In the diagram above the area ABC is the consumer surplus

The area AOQB is the total community benefit from transport. In other words the

benefits that are yielded from the transport good.

If the price of transport is higher than AO no one will travel. As the price is

reduced to the area between AO, individuals are assumed to find it beneficial to

make a trip. Consumers are assumed to be rational, in other words they will not

make a trip for any cost C unless the benefit B is greater than the cost.

The area BCOQ is the total value the community paid and ABC is the

consumers benefit, or net community benefit.

The benefit of a transportation improvement can be measured in terms of the

change in consumer surplus. The change in consumer surplus is measured

using the following formula.

1 2 1 2( )( )

2

P P Q Q− +

Example: A bus company with an existing fleet of 200 50-seater buses increases its

fleet size by 10% and reduces its fare by €1.20 to €1.05.

Calculate the consumer surplus, and the price elasticity of demand.

You can assume that the existing buses had a load factor of 80% and it is expected

that the increase in LOS will result in a load factor of 90%.

Does the company make a loss?

Assume that all buses in the fleet are being used during the peak hours.

Vehicle load factor is a measure of seat availability, and a load factor of 1.0 means

that every seat is occupied.

Solution:

Existing situation:

200 (buses) * 50 (seats) * 0.8 (load factor) = 8,000 persons per hour

Revenue: 8,000 * €1.20 = €9,600

New situation:

220 (buses) * 50 (seats) * 0.9 (load factor) = 9,900 persons per hour

Revenue: 9,900 * €1.05 = €10,395

The company gains = €10,395 - €9,600 = €795

Change in consumer surplus = (1.20 – 1.05)(8,000+9,900)/2

= €1,342 per hour

Price elasticity

1 0 1 2

1 0 1 0

( ) / 2

( ) / 2

Q Q P P

P P Q Q

− +

− +

1900 1.1251.59

0.15 8950

− = −

−

Costs:

- The total cost of owning a company is broken down between fixed and variable

costs.

- A fixed cost is unrelated to production or utilisation of equipment, it’s a cost

which is incurred no matter what. For example in transport trucks in a freight

company, planes for an airline etc.

- A variable cost, is a cost which changes with the level of production. For

example staffing or fuel costs. As the demand for e.g. freight increases so too

does the cost of labour and fuel.

- Total costs = fixed costs + variable costs

- Marginal costs, is the production cost associated with the production of one

extra unit of output.

Total cost =

Average cost =

Marginal cost =

( ) ( )TC x FC VC x= +

( ) ( )( )

TC x FC VC xAC x

x x x= = +

( ) ( ) ( 1)MC x TC x TC x= − −

Example

Example

Example

When the marginal cost is below the average total costs or the average variable

costs ,then the AC would be declining. When marginal cost is above the

average cost then the average cost would be increasing. Therefore the marginal

cost should intersect with the average cost at the lowest point in order to pull the

average cost upwards.