What price will the dominant firm charge, Business Management

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What price will the dominant firm charge

Problem

Harper Industries is the dominant firm in a six firm industry with a homogeneous product, which has a total market demand given by Q = 62 - P. Harper has competition from a fringe of five small firms that produce where their individual marginal costs equal the market price. The fringe firms each have total costs given by TC_i = 15 + 8Q_i + 2.5Q_i². If Harper's total costs are given by TC_H = 200 + 2Q_H+ 0.25Q_H², what price will the dominant firm charge?

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