An Engineering Editor for a Large Publishing Firm Is Trying

An engineering editor for a large publishing firm is trying to decide whether or not to publish a manuscript he
has received. In making a decision he feels that it is sufficient to imagine that there are just four states of nature
which are
• S1, the book will sell an average of 500 copies per year;
• S2, the average annual sales will be 1500 copies;
• S3, the average annual sales will be 3000 copies; and
• S4, the average annual sales will be 10,000 copies.
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The prior probabilities which he assigns to these states of nature are, respectively, 0.30, 0.40, 0.25, and 0.05. The
discounted profits if he publishes the book are projected to be, respectively, -$30,000, +$4,000, +$12,000, and
+$100,000. Of course, the discounted profit is $0 if he does not publish it.
To gain additional information, the publisher can send the manuscript to a reviewer who would say he likes the
manuscript. From previous experience with this reviewer, the publisher feels that the conditional probabilities
of the state of nature given this response from the reviewer are respectively 0.1, 0.3, 0.5, and 0.1. Should the
publisher publish the book? To answer this question, do the following:
(a) What is the prior optimal act? Draw your decision tree here.
(b) Calculate the EVPI before sending the manuscript out for review.
(c) What is the posterior optimal act? Draw the decision tree
(d) Calculate the EVSI.