3. Suppose the value of a social media account is worth P = 200 - 20 but this is only after a subscriber has experienced the good. Before that, they discount the value of the good by tau = 0.75 . Say Facebook moves first, and then Google joins the market.

A) Suppose Facebook introduces the product at a price of $50. How many subscribers would they obtain?

B) Suppose after this introduction, the Facebook raises price as much as possible without losing any subscribers. What price would Google have to offer in order to convert the 25th subscriber from Facebook?

C) Suppose instead that P = 200 - 20sqrt(Q) If Facebook offered an introductory price of $15, and after consumers tried the product, Facebook raises its price as much as possible without losing any of them, what price would Google have to offer to convert the 15th subscriber from Facebook?

A) Facebook introduces the product at a price of $50. The value of the product for subscribers before experiencing it is discounted by a factor of 0.75. So, the effective value of the product for potential subscribers is: Peffective =7XxP=07x50=37.5 Since the effective price is less than the value of the product, subscribers will be willing to purchase. To find out how many subscribers Facebook would obtain, we need to find the number of subscribers such that the value for them equals or exceeds $50. We can set up the equation: 200 20/Q = 50 204/Q = 150 V=% =15 Q =17.52=56.25 5o, Facebook would obtain approximately 56 subscribers. B) After the introduction, Facebook raises its price as much as possible without losing any subscribers. So, the new price is the maximum price that subscribers are willing to pay, which is $375. Now, Google wants to convert the 25th subscriber from Facebook. This implies that the value of Google's offer should equal the value of Facebook's offer to the 25th subscriber. We can set up the equation: Pttective, Google = 37.5 = 200 20,/QGoogle 204/QGoogle = 162.5 v/ QGoogle = 1557 = 8.125 QGoogle (8125)2 = 66.016 Google would have to offer a value equivalent to $66.016 to convert the 25th subscriber from Facebook. C) In this scenario, the value of the product for subscribers before experiencing it is given by Pogetive = T X P = 0.75 x 15 = 11.25. After experiencing the product, Facebook raises its price as much as possible without losing any subscribers. So, the new price is the maximum price that subscribers are willing to pay, which is P = 200 204/15. Now, Google wants to convert the 15th subscriber from Facebook. This implies that the value of Google's offer should equal the value of Facebook's offer to the 15th subscriber. We can set up the equation: Prttective, Google = 11.25 = 200 20/QGoogle 20/ QGoogle = 188.75 v/ QGooge = 2515 = 9.4375 QGoogle = (9.4375)? = 89.0703 Google would have to offer a value equivalent to $89.0703 to convert the 15th subscriber from Facebook