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244 Revising judgments in the light of new information
the contamination is present then it is virtually certain that other
workers would fall ill. This would leave the company open to legal
action by employees. The total cost of this, and the closure of the
plant for fumigation that would be imposed by the authorities,
would amount to an estimated $2 million.
The doctor has another option. A test for Flaubert’s disease has
just been developed by a Swiss pharmaceutical company but, as
yet, the test is not perfectly reliable and has only a 0.6 probability
of giving a correct indication. The price of the test would have to be
negotiated with the Swiss company, but it is likely to be expensive.
(a) Determine the expected value of the information from the test,
assuming that the food company’s objective is to minimize
expected costs.
(b) Discuss the effect on the expected value of the information from
the test of the following changes (you need not perform any
calculations here).
(i) The doctor’s estimate of the probability of contamination
moving closer to 50%;
(ii) The doctor changing her mind so that she is certain that
there is no contamination in the plant.
(c) If the test was perfectly reliable what would be the value of the
information it yielded (assume that the doctor’s original prior
probability applies)?
(12) A new road is to be built through the Himalayan mountains to the
ancient valley of Zarksa. The road will provide access to the valley
for tourists, who currently have to travel on mules in a journey that
can take up to five days. At some point the road will have to cross
the river Yeli and a bridge will be built for this purpose. However,
the road builders have yet to decide on the exact location where the
road will cross the river. Two options are being considered: Yeli
Gorge and Bana.
If the Yeli Gorge location is chosen it is provisionally estimated
that there is a 0.6 probability that the geological conditions will be
favorable to the bridge construction and the construction costs will
be $40 million. However, should the geological conditions prove
unfavorable, the construction costs will soar to $70 million. There is
no doubt about the geology at the Bana site and it can be assumed
that a bridge built here will be certain to cost $50 million.
Before making the decision on the bridge location, the road
builders hear that a specialist firm of geologists will carry out a
detailed survey of Yeli Gorge and report on whether the conditions