Reference no: EM132404703

A group of 12 consumers are considering whether to connect to a new social network. Consumer 1 has an intrinsic value of $1 for hooking up to the network, consumer 2 has an intrinsic value of $2, consumer 3 has an intrinsic value of $3, and so on up to consumer 12. Each consumer's willingness-to-pay (WTP) to connect to the network depends on the total number of persons who are connected to it. The exact relationship is described as follows: for each i, consumer i's willingness-to-pay to connect to the network is i times the total number of persons connected. Thus if 5 people are connected to the network, consumer 1's willingness-to-pay is $5, consumer 2's willingness-to-pay is $10 and so on.

Suppose the network has decided to subsidize consumers 1 and 2 (i.e., the consumer with intrinsic value = 1, and consumer with intrinsic value = 2) to join the network for free, and then set the price at $35. Assume that a consumer will not sign up for the network unless his/her willingness-to-pay will be higher than the price he/she pays, as soon as he/she signs up. What will be the total number of consumers who will sign up the network?