A group of 12 consumers are considering whether to connect to a new social network. Index them as consumer 1, 2, 3, 4, ..., 12. Let n denote the size of the network.

For consumers 1, 2, 3, 4, their willingness-to-pay (WTP) is: vi=2*n. For consumers 5, 6, 7, 8, their WTP is: vi=5*n. For consumers 9, 10, 11, 12, their WTP is: vi=7*n.

For all subparts below, assume that a consumer will join the network if and only if his/her WTP after joining is higher than or equal to the price.

(a) The network subsidizes consumers 7, 8, 11, 12 to join for free. After that the price to join the network is $32. Which consumers will join the network? Describe the order in which these consumers decide to join the network. Assume that for any given number of people who are already in the social network, the potential participant with the highest WTP will join first. You need to show your calculation (you can construct a table similar to the one in class) to justify your answer in order to receive full credits. (10 points)

(b) In this subpart, the network does not subsidize any consumers. Suppose that the network can charge each consumer with a different price, and that it can arrange their entry order. Assume that marginal cost = 0 and fixed cost = 0 (i.e., there is no production cost). Explain how the network will arrange the entry order and set prices (different consumers may be charged at different prices) to maximize its profits. What is the maximum profits that the network can achieve? You need to show your calculation (you can construct a table similar to the one in class) to justify your answer in order to receive full credits. (10 points)

[Note that because there is no production costs, revenue is the same as profits in this question. That is, maximizing profits is the same as maximizing revenue.]