Downloadable - About University

228 Revising judgments in the light of new information
Plant potatoes
Plant alternative crop
Seek perfect
information
Expected return
= $72000
Test indicates
virus absent
0.7
Test indicates
virus present
0.3
Expected return
= $57000
Plant potatoes
Plant alternative crop
Figure 8.8 – Determining the expected value of perfect information
Virus absent
0.7
Virus present −$20000
0.3
Virus absent
1.0
$90000
$30000
$90000
$30000
decides initially to work on the assumption that the test is perfectly
accurate. If this is the case, what is the maximum amount that it would
be worth paying Ceres to carry out the test?
A decision tree for the farm manager’s problem is shown in Figure 8.8.
In the absence of information from the test, he should plant a full crop
of potatoes since his expected return if he follows this course of action
will be:
0.7 × $90 000 + 0.3 ×−$20 000 = $57 000
which exceeds the $30 000 return he will receive if he plants an alternative
crop.
Now we need to determine the expected value of the perfect information
which will be derived from the test. To do this, we need to consider
each of the possible indications the test can give, how probable these
indications are and how the manager should respond to each indication.
The calculations are summarized in Table 8.1. First, the test might
indicate that the virus is absent from the soil. The specialist has said
that there is a 70% chance that the virus is absent so, because the test is
assumed to be perfectly accurate, the manager can assume that there is
a probability of 0.7 that the test will give this indication. If the test does