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Y3 Micro > Lecture 3- Public Transport > Flashcards

Lecture 3- Public Transport Flashcards

1
Q

If passenger fares cover about half of the total costs of bus operation, what is most of the rest covered by?

A

Subsidies

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2
Q

What are the main operator costs in the public transport sector?

A
  • Infrastructure: tracks, depots…
  • Rolling stock (vehicles)
  • Operating costs: personnel, energy, fuel, maintenance…
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3
Q

What are the main user costs of public transport?

A
  • 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)
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4
Q

What kind of economies of scale do public transport often exhibit do to large fixed infrastructure costs?

A

*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

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5
Q

What is one of the most important decision variables when designing public transport services?

A

Service frequency

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6
Q

What is the tradeoff regarding service frequency?

A

More frequent services increase operator cost but reduce user cost!

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7
Q

What did Mohring (1972) state?

A

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.

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8
Q

What letter do we use to denote passenger trips?

A

q

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9
Q

What 2 inputs do we use to get the output of q passenger trips per hour?

A
  • Number of buses per hour (V)
  • Waiting time per hour (W)
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10
Q

What is the value of time?

A

𝛼 (£/h)

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11
Q

What is V, and what is it produced at?

A
  • V is the operator’s intermediate output
  • V is produced at unit cost cB
    (in £ x h/veh)
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12
Q

Assuming buses travel at equal distance, what is the headway?

A

1/V

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13
Q

What does V denote?

A

Service frequency

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14
Q

What does headway mean?

A

The time interval between 2 buses

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15
Q

What does W/q = 1/(2V) mean?

A

Effectively if buses run every half an hour, the average waiting time of the user is 15 mins (ie half the headway)

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16
Q

What is each user’s waiting time cost?

A

𝛼/2V

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17
Q

So what is the total (aggregate) waiting cost for users?

A

𝛼q/2V

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18
Q

So what is the total (aggregate) cost for operators?

A

Cop = cBV

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19
Q

Do we ignore capacity constraints?

A

Yes, there is always room for one more user on the bus

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20
Q

What is interesting to note about operator costs?

A

It is linear- there are no economies of scale

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21
Q

What is the objective of public transport economics?

A

To find the desired frequency of public transport to minimise the sum, of the aggregate user and operator cost

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22
Q

How do we write the sum of aggregate user and operator costs, and how is this calculated?

A

𝐶𝑜𝑝 + 𝐶w = Cb𝑉 + 𝛼𝑞/2V

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23
Q

What is the optimal public transport frequency?

A

Cb= 𝛼𝑞/2V*^2

24
Q

What is important to note about the marginal cost of increasing the frequency when at optimal frequency?

A

The Marginal Cost should be equal to the Marginal Benefit of increasing the frequency (through reduced user waiting costs).

25
Q

What does the graph representing optimal bus frequency look like?

A

Downwards sloping. It shifts right with an increase in q, to reflect how there is an increase in the marginal benefit.

26
Q

When finding the optimal public transport frequency, when solving for V*, we get…

A

√𝛼𝑞/2𝑐B

27
Q

What is the “square root rule”?

A

Doubling passengers (q) implies about 40% higher optimal frequency, as √2 = approx 1.4

28
Q

Do optimal frequency and costs for users and operator increase proportionally with the quantity of passengers carried? What does this mean?

A

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

29
Q

When finding optimal frequency V* to equal √𝛼𝑞/2𝑐B, what do Cw* and Cop* =?

A

Cw* = √𝛼𝑞cB/2
Cop* = √𝛼cB𝑞/2

30
Q

At optimal frequency, what are the average costs for both user and operator, and what is the significance of this?

A

*√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

31
Q

What does the first rationale for public transport subsidies stem from?

A

The relation between economies of density, socially optimal pricing and the operator’s financial viability.

32
Q

In a nutshell, what do economies of scale mean?

A

Marginal Cost < Average Cost

33
Q

What is one reason to subsidise public transport?

A

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.

34
Q

What would happen if the fare was at least equal to the Average Operator Cost?

A

The fares would be inefficiently high and excessively restrict the volume of public transport trips.

35
Q

Why is there a positive externality from the users perspective, to an additional passenger choosing to get the bus?

A

↑ additional passengers →↑optimal frequency →↓ the user cost of trips through additional waiting time.

36
Q

Is this positive externality an external benefit? Why/why not?

A

This is an external benefit because the user taking the bus typically ignores the positive effects on user users.

37
Q

What is the second reason for public transport subsidies? What is the caveat?

A

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.

38
Q

What does qA denote? What about qP?

A

The number or trips by automobile, and the number of trips by public transport

39
Q

How is the aggregate cost of auto travel written?

A

CA= qA . cA(qA)
The user cost cA(qA) increasing in qA (congestion)

40
Q

What is the total cost of public transport travel? What does this assume?

A

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.

41
Q

Assuming that automobiles and public transport are perfect substitutes, how do we denote the total benefit of travel for users?

A

B(qA + qP)

42
Q

What is the marginal benefit for an additional trip by either mode? What is this also called? What principles are these very similar to?

A

b(qA + qP)
This is also called the inverse demand
This is similar to the second best pricing principles

43
Q

In equilibrium, what must hold?

A
  • 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)
44
Q

In equilibrium, how do we write the conditions which must hold?

A

𝑏(𝑞𝐴 + q𝑃) = C𝐴(𝑞𝐴) + 𝜏𝐴
𝑏(𝑞𝐴 + q𝑃) = C𝑢𝑠 + 𝜏P

45
Q

Does the user cost of car travel increase with congestion? What about public transport travel?

A

The user cost of car travel increases with congestion, but the user cost of public transport travel does not increase with congestion.

46
Q

Are tolls and fares costs to society?

A

No, they are just transfers of resources from consumers to the government.

47
Q

Assuming the government can optimally control both tolls and fares, what is the maximum net social benefit written as?

A

max𝑞𝐴,𝑞𝑅B(q𝐴 + 𝑞𝑃) − 𝑞𝐴 ⋅ 𝑐𝐴(𝑞𝐴) − 𝑞𝑃 ⋅ C𝑢𝑠 − 𝑞𝑃 ⋅ Cop

48
Q

What maximising the net social benefit expression with respect to 𝜏P, what is the first-best fare? What is this?

A

𝜏𝑃fb = Cop
This is the marginal cost of a public transport trip to the operator.

48
Q

What maximising the net social benefit expression with respect to 𝜏𝐴, what is the first-best toll? What is this?

A

𝜏𝐴fb = 𝑞𝐴C’a
This is the marginal external cost of congestion (MEC)

49
Q

Why should the first-best fare for public transport be the Cop?

A

Because this is the only part of the social marginal cost of a trip which users ignore.
𝜏𝑃 = 𝑆𝑀𝐶P − AC𝑢𝑠 = Cop

50
Q

What is the second-best optimal fare assuming no road toll?

A

𝜏𝑃𝑆𝐵 = C𝑜𝑝 − 𝑞𝐴C′𝐴 ∙ (−𝑏′/C’𝐴 − 𝑏′)

51
Q

What parts make up the second best fare?

A

Marginal operator cost - (MEC of a car trip*Share of removed PT Trips that switch to cars)

52
Q

Why is MEC of a car trip*Share of removed PT Trips that switch to cars relevant in the second-best fare model?

A

Raising the fare will deter some individuals from using public transport, and some may switch to automobile transport instead.

53
Q

What is the 3rd reason for government subsidies?

A

Unpriced road congestion, as public transport is a substitute for cars, hence more public transport usage should reduce the DWL of congestion.

54
Q

What happened in Los Angeles during a public transport strike?

A

There was a 47% increase in average delay due to the increased congestion following the public transport strike.

Y3 Micro (11 decks)

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