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Regard the "move-up"s of the whole industry's demand curve as a "dynamic process" at different times. When it happens to intersect with supply curve under perfect competition, we get the equilibrium price and quantity. At this time, firms seem like find their best "time" in the "dynamic process". So during this "time", the price for firms is perfect elastic because neither consumers would buy the product at a higher price nor firms would sell the product at a lower price. To sum up, the difference is -- the firm has a horizontal demand curve while the industry has a down-slope one under perfect competition.

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