Many social customs exhibit network effects. To this end, consider a party given by a group of individuals at a small university. The group is called the Outcasts and has twenty members. It holds a big party on campus each year. These parties are good, but are especially good the more people are in attendance. As a result, the number of people who actually come to the Outcasts party depends on how many people are expected to attend. The more people that are expected to attend, the more fun it will be for each attendee and, hence, the more people who actually will come. These effects are captured by the following equation: A = 20 + 0.95Ae. Here, A is the number of people actually attending the party. This is equal to the 20 Outcast members plus 0.95 times the number of partygoers Ae that are expected to go.

a. If potential party attendees are sophisticated and understand the equation describing actual party attendance, how many people are likely to attend the Outcasts party?

b. Suppose that each party attendee costs the Outcasts $2 in refreshments so that the Outcasts need to charge a fee p for attending the party. Suppose as well that when going to the party requires paying a fee, the equation for attendance is: A = 20 + 0.95Ae − p. What value of p should the Outcasts set if they want to maximize their profit from the party? How many people will come to the party at that price?