Suppose that fax machines are made newly available in NeverNeverLand. Companies are deciding whether or not to install a machine. This decision partly depends on how many other companies are expected to install fax machines. Think of a graph that describes how many companies will install fax machines as a function of how many companies are expected to install fax machines.

(a) If there are complementarities in the adoption of fax machines, describe the shape of this graph.

(b) Now suppose that even if no companies in NeverNeverLand are expected to install fax machines, A companies will indeed do so (because of communication to the outside world). If x companies are expected to install, then an additional (x²)/1000  companies (over and above the number A) will install machines. This occurs up to a maximum of one million companies (which is the total number of companies in NeverNeverLand). Plot this relationship as a graph.

(c) Think of A as the strength of contact with the outside world. Analyze the equilibrium adoption of fax machines in NeverNeverLand as A varies. Pay attention to the possibility of multiple equilibria. For which values of A does a unique equilibrium exist? Provide some intuition for your answer.