By many small firms, we mean that each firm is so small that it cannot affect prices by the amount of output it generates. By homogeneous products we mean that products are identical. Since the products are identical, firms can never increase price above market prices without having sales fall to zero. Because they are very small they can sell all they produce at the market price, thus they effectively face a horizontal demand curve at the market price. This is equivalent to ``price taking'' behavior, which simply means that firms in this industry have to take the market price a given and beyond their control. They can only react to the price, not alter it.

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