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 undergraduates studying microeconomics and high-level executives. Let x be the number of articles that a user requests per year. The executives have an inverse demand function PE (x) = 100 ? x and the undergraduates have an inverse demand function PU (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 identify which users are executives and which are undergraduates. In this case, it simply offers two packages and lets the users self-select the one that is optimal for them. Suppose that it offers two packages: one that allows up to 80 articles per year the other that allows up to 100 articles per year.

(e) What is the maximum price that the Journal can charge for 100 articles per year if it offers 80 a year at the highest price the undergraduates are willing to pay?

the answer key says p=$34, but I can't understand. Please provide the solution of it.

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.

Now a total of 100 articles are sold and out of them a block pricing of $32 per 80 articles is for undergraduates. Hence the residual demand is P = 20 - x and on this demand CS = 0.5*(20 - 0)*2 = 200 cents or $2.

This implies that if it sets a package of $34 per 100 articles and $32 per 80 articles both buyers type will self-select themselves.