The <math>N\;</math> firms set their component prices independently and non-cooperatively. That is the model assumes that each firm is a monopolist so it sets price (quantity) to maximize profits.
Subbing in <math>\sum_i p_i = p - \alpha\;</math>:
With a single firm, <math>N=1\;</math>, the Lerner index is <math>\frac{1}{\etaepsilon}\;</math>, so with <math>N\;</math> firms the mark-up is <math>N\;</math> times the standard monopoly mark-up.