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Perfect Competition
This term refers to a market with a very large number of firms, producing identical products, with easy entry of new firms. Since each firm is producing exactly the same thing and the firm is such a small player in the overall market, the individual firm is a "price taker." Examples -- agricultural markets historically (75-100+ years ago), international currency markets, etc.. Typically, this market structure yields the "best" outcome for the society, because the price charged is the lowest and the quantity produced is the most, compared to the other structures.
Profit-Maximization Rule
Rule that states than in order to maximize profits, all firms should produce to the level where MR=MC. Proof -- If MR>MC for a unit, the revenues are growing faster than costs, and increasing production will increase the firm's profits. Conversely, if MR<MC for a unit, the costs are growing faster than the revenues. In this case, decreasing production will increase the firm's profits. The logical conclusion -- profits are maximized at the level of output where MR=MC.