please show work

Q3. (19 points) Consider an online support group which tackles opioid addiction patients. This is an example of digital health social network (DHSN). Suppose that there are 2 potential influencers and 40 potential patients. Let n be the number of influencers who decide to join the network. Let n2 be the number of patients who decide to join the network. Assume that everyone is very conservative and will only join the network if the willingness-to-pay of joining is higher than or equal to his/her time cost. The time cost of joining the network is $20 and $5 for influencers and patients, respectively. Assume the willingness-to-pay functions described below are expressed in dollar value. Influencers (side 1) are content contributors, their willingness-to-pay function (u) of joining the network is: If n2 = 0, u' = 0. If n2 > 0, ut = 2*n2. . Patients (side 2), who seek help, have the following willingness-to-pay function (UP): . . . If ni = 0, up = 0. If ny = 1: up =10, for n 10. [Too many participants congestion!]? If n = 2: uP=10, for nz20. (a) Given the assumptions set above, if the company just starts this platform (i.e., it starts with 0 participants from both sides), how many participants will join on each side? Explain your answers. (4 points) (b) You need to come up with the most cost efficient way to have everyonejoin this online support group. This is an example of two-sided market. You need to subsidize some potential users in order to kick-start the network. (i) Which side of the market do you propose to subsidize and how much is the subsidy per person, and how many people would you give subsidy? (3 points) (ii) After your proposed subsidy in part (i), describe the order in which patients and/or influencer(s) will join the network in detail? (12 points) Q3. (19 points) Consider an online support group which tackles opioid addiction patients. This is an example of digital health social network (DHSN). Suppose that there are 2 potential influencers and 40 potential patients. Let n be the number of influencers who decide to join the network. Let n2 be the number of patients who decide to join the network. Assume that everyone is very conservative and will only join the network if the willingness-to-pay of joining is higher than or equal to his/her time cost. The time cost of joining the network is $20 and $5 for influencers and patients, respectively. Assume the willingness-to-pay functions described below are expressed in dollar value. Influencers (side 1) are content contributors, their willingness-to-pay function (u) of joining the network is: If n2 = 0, u' = 0. If n2 > 0, ut = 2*n2. . Patients (side 2), who seek help, have the following willingness-to-pay function (UP): . . . If ni = 0, up = 0. If ny = 1: up =10, for n 10. [Too many participants congestion!]? If n = 2: uP=10, for nz20. (a) Given the assumptions set above, if the company just starts this platform (i.e., it starts with 0 participants from both sides), how many participants will join on each side? Explain your answers. (4 points) (b) You need to come up with the most cost efficient way to have everyonejoin this online support group. This is an example of two-sided market. You need to subsidize some potential users in order to kick-start the network. (i) Which side of the market do you propose to subsidize and how much is the subsidy per person, and how many people would you give subsidy? (3 points) (ii) After your proposed subsidy in part (i), describe the order in which patients and/or influencer(s) will join the network in detail? (12 points)