Network Goods

Suppose that consumer utility is given by Ui = vi − p + an where vi ∼ U[0, 1] – a uniformly distributed consumer valuation, a – common sensitivity to network effects and 0 ≤ n ≤ 1 is the number of consumers joining the platform. Suppose that platform has zero costs of serving consumers. Assume that consumers’ outside option is 0. Now consumers simultaneously decide whether to join the platform… 1. Show that both full participation and zero participation equilibria can co-exist only if a > p > 1. 2. Show that interior, i.e. partial participation, equilibrium can only exist if a < 1. What is the price in this equilibrium?