Question

The Mall Street Journal is considering offering a new service which will send news articles to readers by email. Their market research indicates that there are two types of potential users, impecunious students and high-level executives. Let x be the number of articles that a user requests per year. The executives have an inverse demand function P E( x ) = 100 − x and the students have an inverse demand function P U( x ) = 80 − x . (Prices are measured in cents.) The Journal has a zero marginal cost of sending articles via email.

Suppose that the journal cannot observe which type any given user is. The journal continues to o§er two packages. Suppose that it offers one package which allows up to 80 articles (intended for students) and one package that allows up to 100 articles (intended for professors). What is the highest price that students will be willing to pay for the 80-article package? What is the highest price that the journal can charge for the 100-article package if it offers the 80-article packages at the highest price the students are willing to pay? In this situation, what is the consumer surplus obtained by a professor?

Assume that the number of executives in the population equals the number of students. Let (Xe,Te) be the profit maximizing "executive package", where Xe is the number of articles the executive can access at a Total charge of Te, and (Xu,Tu) be the profit maximizing "student package", where Xu is the number of articles the student can access at a total charge of Tu. Is Xe=100? Is Xu=80? Explain. Derive the values of Xe,Te,Xu,Tu.

Answer 1

This is the case of block pricing

The first block is 80 articles to be self-selected by undergraduates. The price to be charged by them is their maximum willingness to pay measured by consumer surplus. Since MC =0, we assume per article price = $0 and CS = 0.5*(80 - 0)*80 = 3200 cents or $32.