Q2. (30 points) 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: 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. (7 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. (3 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