Samenvatting Transport Economics
VALUE OF TIME, SCHEDULING AND RELIABILITY
Wardrop: choose the cheapest routes, in terms of monetary costs (real expenditure) and
the time span of travelling, in the network.
Compensating variation: amount money needed to reach the same utility level following
a price/quality change.
Value of Time (VOT): the amount of money a person would be willing to pay for saving
one unit of travel time to be just as well of as before (also called value of travel time
savings). If the travel time is changed, by how much should the price be changed so that
the utility level remains the same. The VOT can be measured by stated (hypothetical bias)
and revealed preferences (lack of variation, correlation time-money), and by discrete
choice analysis (binary). The VOT is around 50% of the gross wage rate. It rises with
income, but less than proportionally. The VOT differ by the travel condition and travel
mode. It is endogenous, it depends on the policy.
𝑑𝐶$% 𝜕𝑉$% /𝜕𝑇$%
𝑉𝑂𝑇$% = 𝑀𝑅𝑆*+, -+, = − =
𝑑𝑇$% 𝜕𝑉$% /𝜕𝐶$%
If V is linear: 𝛽4$56 /𝛽7894
Random Utility Modeling:
Utility of alternative j: 𝑈;% = 𝑉<𝑧;% , 𝑠% ; 𝛽A + 𝜀;%
V: systematic (indirect) utility
Z: attributes of alternative j for person n (airline type)
S: attributes of decision maker n (passenger type)
𝛽: parameters
𝜀: random utility (reflects idiosyncratic preferences)
The random utility represents personal preferences, unobservable. If V is small, the
choices become random. No information about how the choices are made. Travel time
and costs are important.
Change in utility must be 0, this can be changed by travel time and costs.
Value of Reliability (VOR): the valuation of travel time reliability (costs associated with
travel time variability). Perspective of operator: robustness (external shock), reliability.
Planning costs: stress and anxiety due to not knowing the exact travel time (uncertainty).
Risk aversion: reserve time to plan ahead to be on time, lower the risk of being too late.
Scheduling costs: not arriving at the preferred arrival time (PAT). Expected schedule delay
cost: actual travel time is much higher than the scheduled. The VOR can be estimated by
using stated preference and revealed preference data:
- Mean-dispersion (mean-variance) approach: uses a measure of dispersion in the
utility function. à variation = standard error. Reliability ratio = 𝛽9D /𝛽4$56 sd =
standard deviation, mostly 0.7.
- Scheduling approach:
, Horizontal axes: time
t* = preferred arrival time
𝛼 = VOT
𝛽 = effect/cost of being too early, lose time (shadow price). Value of being early.
𝛾 = cost/stress of being too late (shadow price). Value of being late.
Value deviations of the most desired arrival time, t*=0. Being too early/late costs
time, time is lost.
What is the distribution of the data set, influenced by many factors: year, month, week,
weekdays, road-works, weather conditions, holidays. There is a strong correlation
between travel time and travel time variability.
It is obligatory to have a cost-benefit analysis (CBA) if there will be an invest in
infrastructure. The lower the travel times, the higher the reliability benefits. The VOT and
VOR account for 80% of total benefits.
COST FUNCTIONS
A cost function gives the minimum cost of producing a given output, given the
production. In the long run all inputs are variable, in the short run at least one component
(capital) is fixed.
Long run: 𝑚𝑖𝑛J,K = 𝑤 ∗ 𝐿 + 𝑟 ∗ 𝐾 subject to 𝑌 = 𝛾 ∗ 𝐿R ∗ 𝐾S
To solve this, use the Lagrangian: ℒ = 𝑤 ∗ 𝐿 + 𝑟 ∗ 𝐾 − 𝜆 (𝛾 ∗ 𝐿R ∗ 𝐾S − 𝑌)
\
In the short run, K is fixed: 𝑌 = 𝛾 ∗ 𝐿R ∗ 𝐾S ⟺ 𝐿 = (𝑌 ∗ 𝛾 Z[ ∗ 𝐾 ZS )]
\
𝐶 = 𝑤 ∗ <𝑌 ∗ 𝛾 Z[ ∗ 𝐾 ZS A] + 𝑟 ∗ 𝐾
Scale economies
^- -
𝑠= = bc ; s>1 economies of scale (mc<ac, extra production: ac decreases)
_- `×
bd
Sshort run>Slong run because there are fixed costs in the short run (independent of output, ac
would relatively high à economies of scale).
VALUE OF TIME, SCHEDULING AND RELIABILITY
Wardrop: choose the cheapest routes, in terms of monetary costs (real expenditure) and
the time span of travelling, in the network.
Compensating variation: amount money needed to reach the same utility level following
a price/quality change.
Value of Time (VOT): the amount of money a person would be willing to pay for saving
one unit of travel time to be just as well of as before (also called value of travel time
savings). If the travel time is changed, by how much should the price be changed so that
the utility level remains the same. The VOT can be measured by stated (hypothetical bias)
and revealed preferences (lack of variation, correlation time-money), and by discrete
choice analysis (binary). The VOT is around 50% of the gross wage rate. It rises with
income, but less than proportionally. The VOT differ by the travel condition and travel
mode. It is endogenous, it depends on the policy.
𝑑𝐶$% 𝜕𝑉$% /𝜕𝑇$%
𝑉𝑂𝑇$% = 𝑀𝑅𝑆*+, -+, = − =
𝑑𝑇$% 𝜕𝑉$% /𝜕𝐶$%
If V is linear: 𝛽4$56 /𝛽7894
Random Utility Modeling:
Utility of alternative j: 𝑈;% = 𝑉<𝑧;% , 𝑠% ; 𝛽A + 𝜀;%
V: systematic (indirect) utility
Z: attributes of alternative j for person n (airline type)
S: attributes of decision maker n (passenger type)
𝛽: parameters
𝜀: random utility (reflects idiosyncratic preferences)
The random utility represents personal preferences, unobservable. If V is small, the
choices become random. No information about how the choices are made. Travel time
and costs are important.
Change in utility must be 0, this can be changed by travel time and costs.
Value of Reliability (VOR): the valuation of travel time reliability (costs associated with
travel time variability). Perspective of operator: robustness (external shock), reliability.
Planning costs: stress and anxiety due to not knowing the exact travel time (uncertainty).
Risk aversion: reserve time to plan ahead to be on time, lower the risk of being too late.
Scheduling costs: not arriving at the preferred arrival time (PAT). Expected schedule delay
cost: actual travel time is much higher than the scheduled. The VOR can be estimated by
using stated preference and revealed preference data:
- Mean-dispersion (mean-variance) approach: uses a measure of dispersion in the
utility function. à variation = standard error. Reliability ratio = 𝛽9D /𝛽4$56 sd =
standard deviation, mostly 0.7.
- Scheduling approach:
, Horizontal axes: time
t* = preferred arrival time
𝛼 = VOT
𝛽 = effect/cost of being too early, lose time (shadow price). Value of being early.
𝛾 = cost/stress of being too late (shadow price). Value of being late.
Value deviations of the most desired arrival time, t*=0. Being too early/late costs
time, time is lost.
What is the distribution of the data set, influenced by many factors: year, month, week,
weekdays, road-works, weather conditions, holidays. There is a strong correlation
between travel time and travel time variability.
It is obligatory to have a cost-benefit analysis (CBA) if there will be an invest in
infrastructure. The lower the travel times, the higher the reliability benefits. The VOT and
VOR account for 80% of total benefits.
COST FUNCTIONS
A cost function gives the minimum cost of producing a given output, given the
production. In the long run all inputs are variable, in the short run at least one component
(capital) is fixed.
Long run: 𝑚𝑖𝑛J,K = 𝑤 ∗ 𝐿 + 𝑟 ∗ 𝐾 subject to 𝑌 = 𝛾 ∗ 𝐿R ∗ 𝐾S
To solve this, use the Lagrangian: ℒ = 𝑤 ∗ 𝐿 + 𝑟 ∗ 𝐾 − 𝜆 (𝛾 ∗ 𝐿R ∗ 𝐾S − 𝑌)
\
In the short run, K is fixed: 𝑌 = 𝛾 ∗ 𝐿R ∗ 𝐾S ⟺ 𝐿 = (𝑌 ∗ 𝛾 Z[ ∗ 𝐾 ZS )]
\
𝐶 = 𝑤 ∗ <𝑌 ∗ 𝛾 Z[ ∗ 𝐾 ZS A] + 𝑟 ∗ 𝐾
Scale economies
^- -
𝑠= = bc ; s>1 economies of scale (mc<ac, extra production: ac decreases)
_- `×
bd
Sshort run>Slong run because there are fixed costs in the short run (independent of output, ac
would relatively high à economies of scale).
