let's assume that consumers are named using real numbers between 0 and 1. Individual x has the reservation price r(x) = 1 - n before
we consider the network e?ect. The network e?ect is given by f (z ) = z for m ≤ 1/4 and by f (z ) = (1/2) - z for z ≥ 1/4. So the network bene?t to being a user is maximized when the fraction of the population using the product is z = 1/4, once the fraction is beyond 1/4 the bene?t declines, and it becomes negative if more than 1/2 of the population is using it. Suppose that the price of this good is p where 0 < p < 1/16.

(a) How many equilibria are there? Why? [You do not need to solve for the number(s) of users; a graph and explanation is ?ne.]

(b) Which equilibria are stable? Why?

(c) Consider an equilibrium in which someone is using the good. Is social welfare maxi- mized at this number of users, or would it go up if there were more users, or would it go up if there were fewer users? Explain.