Intro Econ: Monopoly Table and MR=MC

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I use a table with a demand schedule and production costs to motivate the MR=MC rule for a profit maximizing single price monopolist firm. Similar reasoning can apply to competitive firms as well.
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Thanks for the video! If MR=MC=P, doesn't that mean a monopolist firm is being competitive? Another part of my textbook by Halvarian says that P>MC for an inefficient monopoly. So should we assume that monopolies are competitive or inefficient when making calculations concerning monopolies?

suminoh