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 and vi is value or willingness-to-pay.  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 credit. (10 points)

(b) In this subpart, the network does not subsidize any consumers. Suppose that the network can charge each consumer a different price, and that it can arrange their entry order. Assume that marginal cost = 0 and fixed cost = 0. 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 are 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 credit. (10 points) [Note that because there is no production cost, revenue is the same as profits in this question. That is, maximizing profits is the same as maximizing revenue.]

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 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 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? [show 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? [Make 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.] 

Q3. (5 points) Johns Hopkins Carey Business School is organizing its inaugural conference in healthcare marketing. The main purpose of this conference is to share cutting-edge research topics and methodologies among academics. Another purpose is to show healthcare providers the latest research in marketing so that they can apply it to improve adoption of new treatments and patient experiences. The conference provides a platform for professional networking and exchange of ideas, learning and knowledge. Conference attendees will include both academicians and industry practitioners. If someone would like to present his/her research in the conference, he/she needs to submit a research paper to the conference by a deadline, and the conference committee will select a subset of the submissions for presentation. In order to attend the conference, attendees must register. The registration fees are: i. Presenters $0 ii. Academic participants $300 iii. Industry participants $600 Note that Industry participants are the people who work for companies. Explain your answers in detail based on network externality and two-sided market theory. (a) Why does the conference charge the industry participants more than academic participants? (2 points) (b) Why does the conference decide NOT to charge presenters anything? (3 points) Q4. (10 points) 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=5*n. For consumers 5, 6, 7, 8, their WTP is: vi=8*n. For consumers 9, 10, 11, 12, their WTP is: vi=4*n. 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 does not subsidize any consumers. Suppose that the network can charge each consumer a different price, and that it can arrange their entry order. Assume that marginal cost = 0 and fixed cost = 0. 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 profit 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 cost, revenue is the same as profits in this question. That is, maximizing profits is the same as maximizing revenue.]Q3. (5 points) Johns Hopkins Carey Business School is organizing its inaugural conference in healthcare marketing. The main purpose of this conference is to share cutting-edge research topics and methodologies among academics. Another purpose is to show healthcare providers the latest research in marketing so that they can apply it to improve adoption of new treatments and patient experiences. The conference provides a platform for professional networking and exchange of ideas, learning and knowledge. Conference attendees will include both academicians and industry practitioners. If someone would like to present his/her research in the conference, he/she needs to submit a research paper to the conference by a deadline, and the conference committee will select a subset of the submissions for presentation. In order to attend the conference, attendees must register. The registration fees are: i. Presenters $0 ii. Academic participants $300 iii. Industry participants $600 Note that Industry participants are the people who work for companies. Explain your answers in detail based on network externality and two-sided market theory. (a) Why does the conference charge the industry participants more than academic participants? (2 points) (b) Why does the conference decide NOT to charge presenters anything? (3 points) Q4. (10 points) 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=5*n. For consumers 5, 6, 7, 8, their WTP is: vi=8*n. For consumers 9, 10, 11, 12, their WTP is: vi=4*n. 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 does not subsidize any consumers. Suppose that the network can charge each consumer a different price, and that it can arrange their entry order. Assume that marginal cost = 0 and fixed cost = 0. 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 profit 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 cost, revenue is the same as profits in this question. That is, maximizing profits is the same as maximizing revenue.]