Remember: what is supply? It is the relation between the price and the quantity that people want to sell. For an individual firm, that is: the relation between the price and the quantity the firm wants to sell.
So we ask: at a given price, how much will a (profit- maximizing) firm want to sell? The answer: enough so that the price is equal to marginal cost. In other words, the marginal cost curve is the supply curve for the individual firm.
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