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Week 61.
To describe ship cost, or the cost of, for example, a warehouse, the following relation is sometimes
used: Cost = a*Sb, where S is ship size (measured in, for example, container slots), a and b are
parameters.
The 2/3 power law says b is (close to) 2/3. For convenience, let a = 1. So: Cost = a*S0.66666,
Interpret the relation between Cost an S (so interpret Cost = a*S0.66666), and give a reason why b may
be (close to) 2/3.
Interpretation:
Capacity is related to the volume of ship, while (construction and maintenance) costs are proportional
to surface area (“bigger ships just add more steel”). So: cost proportional to capacity2/3: elasticity of
cost wrt size is 2/3, meaning a 10% increase in ship size leads to a 6.7% increase in costs.
Source of "2/3": basic mathematical relation between surface and volume of a ball or cube. You don't
need to give the exact derivation , as long as you mention it follows from the relation between
surfaces and volumes of basic shapes.
2.
The handling capacity is: H=SE (a bit simpler than in the lecture)
The cost per day (in port) is: C= Se (again a bit simpler than in the lecture)
Are there economies of scale in handling if E=0.2 and e=0.3? Motivate your answer.
Cost per ton = Se / SE = Se-E
e-E=0.1, so if S increases, cost per ton increases. This means there are diseconomies of scale.
3.
Use a cost function characteristic to explain why the Container Terminal Amsterdam failed.
Competitors nearby, that could accomodate bigger ships. Big ships are used on long routes (e.g. China
to Europe) to exploit economies of scale at sea, but such ships do not vist "all ports" in Europe
(diseconomies in handling, so limit the number of port vists). If A'dam cannot accomodate the biggest
ships, they will co to competitors (Rotterdam, Antwerp, Hamburg), and Amsterdam can be a feeder (at
most), but will never be a big container port.
Note: during an exam more details on ports would be given. This question is not meant to ask about
your knowledge on specific ports, but to test if you can apply economies of scale and ship size.
Note: In this case "a cost function characteristic" is economies of scale. You have to argue if it is
neutral or positive, and how this influences the container terminal. If you can think of another cost
charateristic: perfect, if the argument is consistent. During the exam we can have different
formulations (cost function characteristic, economic argument, " a consultant estimated ...").
4.
Explain why feeder services and trunk services (in short: short and long distances) have different ship
sizes. Note: the level of demand is not an argument (big cities and/or big ports may be loctaed close to
each other).
Use economies of scale in nandling and hauling to make your point: long routes means you spend a
(relatively speaking) long time at sea, and have oppoortinty to exploit economies of scale in hauling,
so you want big ships. Short routes means you spend, relatively speaking, a lot of time in ports, where
you suffer from diseconomies of scale in handling, so you want small ships.
, 5.
Explain the concept of random utility maximization.
Consumers maximize utility. In this case, utility is composed of a systematic part (observed by the
researcher) and a random part (unobserved by the reseacherm but known the the consumer in
question, the so-called idosyncratic preferences).
If we have a specific distribution for the random utility, it is possible to derive a specific specification
for the probability a consumer chooses a specific alternative. This allows us to estimate the parameters
of the systematic utility.
Note: not necessary to derive any specification, as long as you understand the idea that part of utility
may be "random", and we need some assumption on random utility in order to be able to estimate
parameters of systematic utility.
6.
Explain the concept of value of time.
VOT is the amount of money (additional travel cost) that a person would be willing to pay for saving
one unit of travel time T to be just as well off as before; hence also called Value of travel time savings.
This means: we evaluate how much a consumer is willing to pay if travel time is reduced (or should
be compensated if travel time is increased), given utility remains the same and we have maximum
utility.
7.
A consultant has estimated a discrete choice model to determine the value of time for metro
passengers, using stated preference data. The estimated systematic utility function is:
Vjn = -0.00445*cjn -0.2*Tjn + rest
where cjn is travel cost, measured in euros, and Tjn is travel time, measured in hours.
Explain how the consultant collected the necessary data.
The consultant used stated preference data. So the consultant conducted a survey (or used survey
data), in which respondents were asked to indicated what travel alternative they would choose, given
the characteristics of the the travel alternative. In this case, the focus is on VOT, so the respondets had
to choose between alternatives which differed in travel time and travel cost, making sure there were
no dominant alternatives (alternatives that were better in both aspects (faster and cheaper).
8.
A consultant has estimated a discrete choice model to determine the value of time for metro
passengers, using stated preference data. The estimated systematic utility function is:
Vjn = -0.00445*cjn -0.2*Tjn + rest
where cjn is travel cost, measured in euros, and Tjn is travel time, measured in hours.
What is the VOT? And what does this mean?
VOT=-0.2/-0.00445 = 44.94
Consumers are willing to pay EUR 44.94 for an hour reduction in travel time.
9.
Explain a common problem with stated preference data.
Consumers are asked to indicate what alternative they would choose, without actually having to pay,
and without actually having to travel. So they may not be motivated to really think about time saved
and/or money they want to pay: the perceived travel time savings may be different than actual travel
time savings in a real setting.
Note: Survey design is critical here (clear description, clear questions, realistic setting etc.)
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