Lecture 1

Question 1

Define congestion

Answer 1

The loss of speed when more cars (and trucks, buses…) use a given road, or network of roads

Question 2

How else do some economists define congestion?

Answer 2

Economists often measure congestion in terms of “travel delay”, i.e. the extra amount of time it takes to travel one mile (or km), compared to “free flow” conditions.

Question 2

What does travel time (h/km) =?

Answer 2

1/speed (km/h)

Question 3

How do you calculate average time cost (£/km)?

Answer 3

Value of time (£/h) / speed (km/h)

Question 4

How do we measure travel delay (due to congestion)?

Answer 4

(1/speed [km/h]) - (1/Free flow speed [km/h])

Question 5

Which tends to be the most congested kind of road?

Answer 5

“A” roads include major roads within urban areas and tend to be highly congested

Question 6

Give some examples of road pricing in the UK.

Answer 6

• London Congestion Charge
• Highway tolls, e.g. M6 toll

Question 7

When building a model, what do we let V represent?

Answer 7

Traffic volume, ie the number of vehicles per unit of time that travel on this road.

Question 8

When building a model, what do we assume when capturing congestion?

Answer 8

We assume a decreasing relationship between traffic volume and speed.

Question 8

When building a model, what does c(V) represent? What does this assume?

Answer 8

This stands for the user cost of travel and assumes the only cost the user faces is time costs, which increase in V due to congestion. Also assume that this function is linear for simplicity.

Question 9

How do we calculate the value to the user of going from origin to destination?

Answer 9

𝐵(𝑉) = v∫0 𝑏(𝑥)𝑑𝑥

Question 10

Is the marginal value for an additional trip increasing or decreasing in V?

Answer 10

Decreasing in V

Question 11

What is the social cost of an additional trip (Social Marginal
Cost)?

Answer 11

smc(V) = c(V) + V. 𝜕𝑐/𝜕V

Question 12

Why is the Social Marginal Cost different to the private marginal cost?

Answer 12

As when I use the road, it negatively impacts others as well.

Question 13

Do private users take into account social costs when deciding whether to travel?

Answer 13

No

Question 14

What is the Marginal External Cost (MEC)?

Answer 14

The vertical difference between smc(V) and c(V).

Question 14

How do we calculate social welfare?

Answer 14

Total benefit- Cost of travel

Question 14

How do we maximise social welfare?

Answer 14

Set 𝜕SW/𝜕V=0

Question 15

If 𝜕SW/𝜕V=0, what does V* satisfy?

Answer 15

b(V) = smc(V) = c(V) +V⋅𝜕𝑐/𝜕V

Question 16

What does V* represent?

Answer 16

V* is such that the willingness-to-pay for the marginal unit of V (i.e., that of the marginal user) equals the marginal social cost

Question 17

When we set a toll, what is the new equilibrium?

Answer 17

b(V) = gen. price = c(V) + τ

Question 18

What does the optimal toll =?

Answer 18

Optimal toll equals the marginal external cost

Question 19

Why is a toll useful?

Answer 19

As it makes users internalise the external cost of congestion.

Question 20

What is DWL from excessive congestion?

Answer 20

DWL is the difference between the social marginal cost of travel and the social benefit (user valuation), for all travel that exceeds the socially optimal volume
* It is a DWL because this excessive volume of travel is inefficient (cost higher than benefit for each trip), a pure loss to society: welfare increases by eliminating it

Question 21

Is the toll a cost to society?

Answer 21

No, it is just a transfer to the government.