Problem:

Eileen O'Donnell is trying to choose between two publishing companies that are competing for the marketing rights to her new novel. Company A has offered $10,000 plus $2 per book sold. Company B has offered $2,000 plus $4 per book sold. The author believes that five levels of demand (states of nature) for the book are possible: 1,000, 2,000, 5,000, 10,000 and 50,000 books sold.

(a) Compute the payoffs for each company's offer at each level of demand.

(b) Set up a payoff table indicating decision alternatives and states of nature, together with the amount the author would earn under each possible combination.

(c) Set up a decision tree. Here are probabilities associated with the demand levels:

Demand     Probability
 1,000             0.45
 2.000             0.20
 5,000             0.15
10.000            0.10
50,000            0.10

(d) Determine the expected value and standard deviation of Eileen's earnings from signing with each of the two companies.

(e) Compute and explain the expected value of perfect information.

The Bodnar Croup, a literary review organization, has an outstanding reputation for predicting the success of original works of fiction, based on its famous "thumbs up" or "thumbs down" evaluations. In the past, for novels that have eventually sold 1,000 copies, only 1% had received "thumbs up" from Bodnar prior to publication. Of novels that eventually sold 2,000 copies, 5% had received "thumbs up" from Bodnar prior to publication. Similarly, 25% of novels that sold 5,000 copies had received "thumbs up", 60% of novels that sold 10,000 copies had received "thumbs up", and 99% of novels that sold 50,000 copies had received "thumbs up".

(f) Eileen submits the novel to Bodnar and receives a "thumbs down". What is the implication of this evaluation for Eileen's choice of publishers?

(g) What is the expected value and the efficiency of a Bodnar review in this problem?

Summary

This question is basically Finance as well as it is about computing the pay off to an author in the form of fixed amount plus royalty upon each book sold. The author requires help in computing the probability of anticipating the demand for the books.