Lecture 3- Public Transport Flashcards
If passenger fares cover about half of the total costs of bus operation, what is most of the rest covered by?
Subsidies
What are the main operator costs in the public transport sector?
- Infrastructure: tracks, depots…
- Rolling stock (vehicles)
- Operating costs: personnel, energy, fuel, maintenance…
What are the main user costs of public transport?
- Access time, (ie how to get to station etc)
- Waiting time at stops
- In-vehicle travel time (this could be crowding, as well as congestion)
What kind of economies of scale do public transport often exhibit do to large fixed infrastructure costs?
*Economies of density: economies of scale realized by expanding the density of output (more vehicle-kms for a given network size)
*Economies of size: economies of scale related to size of network (adding routes or links). This is usually not as important as economies of density
What is one of the most important decision variables when designing public transport services?
Service frequency
What is the tradeoff regarding service frequency?
More frequent services increase operator cost but reduce user cost!
What did Mohring (1972) state?
When time cost of users is taken into account,
there are economies of scale (density) in public transport operation, even if the operator’s cost structure does not exhibit
such economies.
What letter do we use to denote passenger trips?
q
What 2 inputs do we use to get the output of q passenger trips per hour?
- Number of buses per hour (V)
- Waiting time per hour (W)
What is the value of time?
𝛼 (£/h)
What is V, and what is it produced at?
- V is the operator’s intermediate output
- V is produced at unit cost cB
(in £ x h/veh)
Assuming buses travel at equal distance, what is the headway?
1/V
What does V denote?
Service frequency
What does headway mean?
The time interval between 2 buses
What does W/q = 1/(2V) mean?
Effectively if buses run every half an hour, the average waiting time of the user is 15 mins (ie half the headway)
What is each user’s waiting time cost?
𝛼/2V
So what is the total (aggregate) waiting cost for users?
𝛼q/2V
So what is the total (aggregate) cost for operators?
Cop = cBV
Do we ignore capacity constraints?
Yes, there is always room for one more user on the bus
What is interesting to note about operator costs?
It is linear- there are no economies of scale
What is the objective of public transport economics?
To find the desired frequency of public transport to minimise the sum, of the aggregate user and operator cost
How do we write the sum of aggregate user and operator costs, and how is this calculated?
𝐶𝑜𝑝 + 𝐶w = Cb𝑉 + 𝛼𝑞/2V
What is the optimal public transport frequency?
Cb= 𝛼𝑞/2V*^2
What is important to note about the marginal cost of increasing the frequency when at optimal frequency?
The Marginal Cost should be equal to the Marginal Benefit of increasing the frequency (through reduced user waiting costs).
What does the graph representing optimal bus frequency look like?
Downwards sloping. It shifts right with an increase in q, to reflect how there is an increase in the marginal benefit.
When finding the optimal public transport frequency, when solving for V*, we get…
√𝛼𝑞/2𝑐B
What is the “square root rule”?
Doubling passengers (q) implies about 40% higher optimal frequency, as √2 = approx 1.4
Do optimal frequency and costs for users and operator increase proportionally with the quantity of passengers carried? What does this mean?
No, optimal frequency and costs for users and operator increase less than proportionally with the quantity of passengers carried. It means there is economies of scale
When finding optimal frequency V* to equal √𝛼𝑞/2𝑐B, what do Cw* and Cop* =?
Cw* = √𝛼𝑞cB/2
Cop* = √𝛼cB𝑞/2
At optimal frequency, what are the average costs for both user and operator, and what is the significance of this?
*√𝛼𝑐𝐵/2𝑞
* We have economies of density: the average user cost and the average operator cost of public transport decrease with the quantity of users
What does the first rationale for public transport subsidies stem from?
The relation between economies of density, socially optimal pricing and the operator’s financial viability.
In a nutshell, what do economies of scale mean?
Marginal Cost < Average Cost
What is one reason to subsidise public transport?
Because the optimal price is when demand = marginal cost, yet if the MC<AC, this means that at this quantity, the low fare means that the operator will go bankrupt. Therefore subsidies are needed to ensure the financial viability of the operator.
What would happen if the fare was at least equal to the Average Operator Cost?
The fares would be inefficiently high and excessively restrict the volume of public transport trips.
Why is there a positive externality from the users perspective, to an additional passenger choosing to get the bus?
↑ additional passengers →↑optimal frequency →↓ the user cost of trips through additional waiting time.
Is this positive externality an external benefit? Why/why not?
This is an external benefit because the user taking the bus typically ignores the positive effects on user users.
What is the second reason for public transport subsidies? What is the caveat?
The fare should be set below marginal operator cost to internalise the external benefit of the positive externalities of getting a bus. Subsidies enable this to occur whilst keeping operations financially viable. The caveat is that we have ignored crowding.
What does qA denote? What about qP?
The number or trips by automobile, and the number of trips by public transport
How is the aggregate cost of auto travel written?
CA= qA . cA(qA)
The user cost cA(qA) increasing in qA (congestion)
What is the total cost of public transport travel? What does this assume?
CP= qP. (Cop+ Cu)
This assumes that the costs are independent of the quantity of users, so no economies of density or effects of frequency on waiting times.
Assuming that automobiles and public transport are perfect substitutes, how do we denote the total benefit of travel for users?
B(qA + qP)
What is the marginal benefit for an additional trip by either mode? What is this also called? What principles are these very similar to?
b(qA + qP)
This is also called the inverse demand
This is similar to the second best pricing principles
In equilibrium, what must hold?
- The benefit (value) of the marginal trip by auto is equal to the generalized price (user cost plus the road toll)
- The benefit of the marginal trip by public transport is equal to the generalized price (user cost plus the fare)
In equilibrium, how do we write the conditions which must hold?
𝑏(𝑞𝐴 + q𝑃) = C𝐴(𝑞𝐴) + 𝜏𝐴
𝑏(𝑞𝐴 + q𝑃) = C𝑢𝑠 + 𝜏P
Does the user cost of car travel increase with congestion? What about public transport travel?
The user cost of car travel increases with congestion, but the user cost of public transport travel does not increase with congestion.
Are tolls and fares costs to society?
No, they are just transfers of resources from consumers to the government.
Assuming the government can optimally control both tolls and fares, what is the maximum net social benefit written as?
max𝑞𝐴,𝑞𝑅B(q𝐴 + 𝑞𝑃) − 𝑞𝐴 ⋅ 𝑐𝐴(𝑞𝐴) − 𝑞𝑃 ⋅ C𝑢𝑠 − 𝑞𝑃 ⋅ Cop
What maximising the net social benefit expression with respect to 𝜏P, what is the first-best fare? What is this?
𝜏𝑃fb = Cop
This is the marginal cost of a public transport trip to the operator.
What maximising the net social benefit expression with respect to 𝜏𝐴, what is the first-best toll? What is this?
𝜏𝐴fb = 𝑞𝐴C’a
This is the marginal external cost of congestion (MEC)
Why should the first-best fare for public transport be the Cop?
Because this is the only part of the social marginal cost of a trip which users ignore.
𝜏𝑃 = 𝑆𝑀𝐶P − AC𝑢𝑠 = Cop
What is the second-best optimal fare assuming no road toll?
𝜏𝑃𝑆𝐵 = C𝑜𝑝 − 𝑞𝐴C′𝐴 ∙ (−𝑏′/C’𝐴 − 𝑏′)
What parts make up the second best fare?
Marginal operator cost - (MEC of a car trip*Share of removed PT Trips that switch to cars)
Why is MEC of a car trip*Share of removed PT Trips that switch to cars relevant in the second-best fare model?
Raising the fare will deter some individuals from using public transport, and some may switch to automobile transport instead.
What is the 3rd reason for government subsidies?
Unpriced road congestion, as public transport is a substitute for cars, hence more public transport usage should reduce the DWL of congestion.
What happened in Los Angeles during a public transport strike?
There was a 47% increase in average delay due to the increased congestion following the public transport strike.
