Firm is operating in perfectly competitive market

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Suppose a firm's produces computers and it's associated costs are only fuction is given by C(y) = y^3 - 8y^2 + 32y. find the long run market price that prevails if this firm is operating in perfectly competitive market. Derive the shut-down condition for the general case, wher profits are given by pi = py - C(y), and C(y) = C(y) + F. an aswer with just maths is not enough tell me the intution behind the condition.

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