In the fictitious land of Smuckersburg, there exists a single social networking platform, Face-back, and all 1,000 residents of Smuckersburg are members of Faceback. EACH resident derives the following net utility (i.e. surplus) from being a member of a social network: u(N, p) = (N/500) p where N is the number of participants on the platform, and p is the price charged for membership on the platform. In other words, the value of being on the platform for a single person is N/500 , and the price of being on the platform is p, such that the net surplus an individual consumer receives from platform membership is equal to (N/500) p, which I am referring to simply as net utility. The current membership price is p = 1. Recently, representatives of the Smuckersburg Department of Justice (the Smuckersburgian antitrust authority) have raised concerns about Faceback's monopoly power in the social networking market. They argue that Faceback's dominant position poses a significant barrier to entry in the industry. They have even suggested splitting the network into two competing networks, Faceback and Facefront.

The following questions will analyze this proposal.

(c) The barrier to entry is indeed significant. Assuming residents can join at most one platform, what price would a potential entrant to the industry (i.e. a competing network with zero participants) need to charge in order to entice residents to switch platforms?

(d) Compute the current consumer surplus in the social networking market.

(e) Suppose Faceback is successfully split into two competing social networks, each with half of the Smuckersburg population. Assume that residents can join at most one platform, and suppose price remains constant at p1 = p2 = 1. Compute the new consumer surplus.

(f) Suppose that the constant marginal cost of hosting a resident on any network is mc = 0, and suppose that the split results in price competition as in the standardized products Bertrand model. Compute the new consumer surplus in equilibrium.

(g) Finally, consider that the Smuckersburg Department of Justice values overall social welfare, not just consumer surplus. Would you advise the DOJ to follow through with its proposal to split Faceback? Why or why not? (Continue to assume Bertrand price competition, constant marginal cost of 0, an even network split, and non-overlapping networks.)