A group of 12 consumers are considering whether to connect to a new social network. Consumer 1 has an intrinsic value of $1 for connecting 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: consumer i's willingness-to-pay to connect to the network is i times the total number of persons connected. For instance, consumer 2's WTP is $10 (=2*5) if five people are connected to the network including consumer 2.

For all subparts below, assume that

• for any given number of people who are already in the social network, the potential participant with the highest WTP will sign up first;
• a consumer will join the network if and only if his/her WTP after joining is higher than or equal to the price

A. Use a table to show the relationship among the total number of people in the network, the intrinsic value of the consumer next in line (marginal consumer), and the willingness-to-pay for that consumer. The table should have three columns: (i) the intrinsic value of the marginal consumer, (ii) # participants in the network assuming the marginal consumer joins; (iii) WTP of the marginal consumer

B. Suppose we set the price of joining the network to be $35. What is the critical mass of this network given p=$35? Explain your answer.

C. Suppose the network has decided to subsidize consumers 1 and 2 (i.e., the consumers with intrinsic value = 1 and 2) to join the network for free, and then set the price at $35. What is the total number of consumers who will sign up the network?

D. Suppose the network has decided to subsidize consumers 7, 11 and 12 (i.e., the consumers with intrinsic value = 7, 11, and 12) to join the network for free, and then set the price at $40. What is the total number of consumers who will sign up the network?