Consider the library-pricing model analyzed in Section 7.2.3. Suppose that there are = 1200 potential readers

Consider the library-pricing model analyzed in Section 7.2.3. Suppose that there are η = 1200 potential readers and λ = 50 libraries. The utility function of eachpotential reader is given by U def =  β − pb if she buys and owns the book β − 2pr i if she borrows (rents) from library i 0 if she does not read the book. There is one publisher who can sell either to individual readers, or to libraries but not to both. Each copy of the book costs µ to produce. Answer the following questions.

(a) Calculate the publisher’s profit-maximizing price and her profit level, assuming that the publisher sells directly to individual readers.

(b) Calculate the publisher’s profit-maximizing library price and her profit level assuming that the publisher sells one copy to each library only.

(c) Calculate the minimal value of µ (unit production cost) for which selling to libraries only yields a higher profit level to the publisher than selling only to individual readers.