Q2. (15 points): A group of 12 consumers are considering whether to connect to a new social network. Consumer 1 has an intrinsic value (k) of $1 for connecting to the network, consumer 2 has an intrinsic value (k) of $2, consumer 3 has an intrinsic value (k) of $3, and so on up to consumer 12. Each consumers 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 is willingness-to-pay to connect to the network is i times the total number of persons connected. For instance, consumer 2s WTP if five people are connected to the network, including consumer 2, is $10 (=2*5). 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. (3 points) 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. (2 points) 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. (5 points) 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? [Create a table similar to part (a) and use it to help you answer the question. To receive full credit, you need to show this table in your answer.] d. (5 points) 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? [Create a table similar to part (a) and use it to help you answer the question. To receive full credit, you need to show this table in your answer.]