public transport part 2

Question 1

How is pricing of public transport modelled?

Answer 1

• Individual can travel by public transport or automobile
• Assume public transport doesn’t face congestion e.g. train doesn’t have issues of congestion
• Cost function for car users is TC=q*c, AC is increasing as q increases

Question 2

What is the cost function of public transport?

Answer 2

• Cr=Q(OC+UC)

- Ignore economies of density, which showed that cost of a operator and user are linked

Question 3

How is the benefit function derived for Public transport and car travel

Answer 3

• Denote benfit: B(Qa+Qr)
• Where we assume that, P.transport and car are substitutes
• A = automobile, R = rail
• You later derive this function

Question 4

What will be the equilibrium of public transport and car travel? Draw the diagram as well?

Answer 4

• D(qa+qr) = Ca(Qa) + ta: marginal trip by a car is = to the GP
• D(qa+qr) = Cus + tr: benefit of a public transport is = to the Gp

Question 5

How do you find the quantities that maximise welfare?

Answer 5

• Take derivates of welfare and equate them to 0
• Optimal car trips: MB of trip= SMC
• Optimal rail trip: MC trip = SMC
• So user must internalize the external cost
• Toll = MEC

Question 6

What are the first best road toll and fare? Why are they set

Answer 6

• T = MEC: toll = qa*c’a
• T = Cop
• 1ST Tolls controls congestion  the lost in speed due to a user entering a given road segment
• 2nd tolls ensure that generalized price of a PT trip with SC  users ignore the operator cost

Question 7

what would happen if there was no toll on the road

Answer 7

• T = 0
• 2nd best optimal toll = OC – MEC*(share of removed PT trips that switch to car)
• Reduce the spillover effect, the correction term is there to ensure there isn’t extra congestion on the no toll road.

Question 8

Draw the effect of raising public transport on deadweight loss of congestion (road)

Answer 8

refer to the notes

Question 9

What is the rationale of increasing the toll of PT?

Answer 9

• Raising the toll will deter individuals using PT
• This is undesirable when road congestion isn’t priced properly
• This would lead to a further increase in car congestion

Question 10

How could 2nd best pricing promotes the use of subsidies?

Answer 10

• PT is a direct substitute for cars
• If roads are not priced optimally: it would mean PT would cause greater deadweight loss
• PT subsidies hell reduced the deadweight loss of congestion

Question 11

the absence of road tolls implies that

Answer 11

• Subsidies to public transport are desirable because they reduce the demand for cars and hence deadweight loss

Question 12

What is the real-life evidence for congestion-relief?

Answer 12

• Effect on traffic congestion of public transport strikes
• 98% if daily passenger miles by car
• 52% on freeways
• Reg.Congestion: 0.34 minutes per mile of delay
• Delay increasing by roughly ~47%
• Total monetary loss is 2.1 bn dollar per year if public transit didn’t cease to operate