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Subbing in <math>\sum_i p_i = p - \alpha\;</math>:
:<math>\frac{p - \underbraceoverbrace{\alpha - \sum_i c_i}{c}}{p} = \frac{N}{\eta}\;</math>
With a single firm, <math>N=1\;</math>, the Lerner index is <math>\frac{1}{\eta}\;</math>, so with <math>N\;</math> firms the mark-up is <math>N\;</math> times the standard monopoly mark-up.
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