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Exercises 167
(b) Assuming that Westward’s objective is to maximize expected
profit, determine the policy that they should choose. (For
simplicity, you should ignore Westward’s preference for money
over time: for example, the fact that they would prefer to receive
a given cash inflow now rather than in the future.)
(c) In reality, Westward have little knowledge of the progress
which has been made by the rival. This means that the probabilities
given above for beating the rival (if the launch is, or
is not, brought forward) are very rough estimates. How sensitive
is the policy you identified in (b) to changes in these
probabilities?
(4) The risk of flooding in land adjacent to the River Nudd has recently
increased. This is because of a combination of high spring tides and
the development by farmers of more efficient drainage systems in
the nearby hills, which means that, after heavy rainfall, water enters
the river more quickly. A tidal barrier is being constructed at the
mouth of the river, but the Hartland River Authority has to decide
how to provide flood protection in the two years before the barrier
is completed. Flooding is only likely to occur during the spring
high-tide period and the height of the river at this time cannot be
predicted with any certainty. In the event of flooding occurring
in any one year the Authority will have to pay out compensation
of about $2 million. Currently, the Authority is considering
three options.
First, it could do nothing and hope that flooding will not occur
in either of the next two years. The river’s natural banks will stop
flooding as long as the height of the water is less than 9.5 feet. It is
estimated that there is a probability of 0.37 that the height of the
river will exceed this figure in any one year.
Alternatively, the Authority could erect a cheap temporary barrier
to a height of 11 feet. This barrier would cost $0.9 million to erect
and it is thought that there is a probability of only 0.09 that the
height of the river would exceed this barrier. However, if the water
did rise above the barrier in the first year, it is thought that there
is a 30% chance that the barrier would be damaged, rendering it
totally ineffective for the second year. The Authority would then
have to decide whether to effect repairs to the barrier at a cost
of $0.7 million or whether to leave the river unprotected for the
second year.
The third option would involve erecting a more expensive barrier.
The fixed cost of erecting this type of barrier would be $0.4 million