A firm in a perfectly competitive market invents a new method of production that lowers its marginal costs. What happens to its output?

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In such a case, the firm's output should increase.  The reason for this is that the firm should always produce the quantity at which the marginal revenue and marginal cost are equal.  When the firm invents the new method of production, its marginal costs fall.  This means that marginal costs are now lower than marginal revenue.  By definition, this means the firm is not making as much profit as it could be.  In order to maximize its profit, it will need to produce more goods so that it can return to the level where marginal cost equals marginal revenue. 

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