Natch is an internet dating site that helps people meet partners by showing them profiles of potential matches. When a person signs up, she or he fills out a profile, then pays money to view profiles of others. The company has hundreds of profiles in the computer system and it costs nothing to email profiles to customers (so MC = 0). Suppose that there are two types of customers: desperate customers have an inverse demand for profiles given by pd = 40 â 2qd 1 and not-desperate customers have inverse demand pn = 20 â 2qn. The company has exactly one of each type of customer.

Required:
a. If the profile that the customers fill out has enough information in it to allow Natch.com to perfectly price-discriminate, what will the companyâs profits be?
b. Suppose Natch.com canât identify the desperate customer. It knows, however, that the desperate customer demands more profiles and the company takes advantage of this by selling two kinds of packages of profiles, instead of a uniform price. It offers a large package of 20 profiles and a small package of 10. The small package is priced to capture all of the consumer surplus of the non-desperate customer. What price should Natch.com charge for the large package to maximize profits and guarantee that the desperate customer buys the large package and not the small one? And what are the companyâs profits?
c. What would the companyâs profits be if it engaged in uniform pricing (charged a single, per unit price)? How does this compare to your answer from part a?