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Perfect Competition: sample question

A representative firm with long-run total cost given by TC = 20 + 20q + 5q2 operates in a competitive industry where the short-run market demand and supply curves are given by QD = 1,602 - 40P and QS = - 400 + 20P. If it continues to operate in the long run, its profit-maximizing level of output is

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First we determine the market equilibrium price.

At equilibrium, Qs = Qd, ...