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 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, if five people are connected to the network including consumer 2, consumer 2s WTP 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.

(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.

(2 points) Suppose we set the price of joining the network to be $37. What is the critical mass of this network given p=$37? Explain your answer.

(5 points) Suppose the network has decided to subsidize consumers 1 and 2 (i.e., 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 explain you answer the question. To receive full credits, you need to show this table and explanation in your answer. **

(6 points) Suppose the network has decided to subsidize consumers 6, 9 and 11 (i.e., consumers with intrinsic value = 6, 9, and 11) to join the network for free, and then set the price at $48. What is the total number of consumers who will sign up the network? Which consumers decide not to join the network?

** Create a table similar to part (a), and use it to explain you answer the question. To receive full credits, you need to show this table and explanation in your answer. **