Does a monopolist achieve efficiency in its production? 

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No, a monopolist does not achieve efficiency in its production.  Instead, it produces too little of its product and sells it at too high of a price.  This means that a market that is controlled by a monopolist can never be efficient.

Like any firm, a monopolist produces at the quantity where marginal revenue equals marginal cost.  However, in a monopoly, this is not the same as the quantity where price equals marginal cost.  Instead, it is a lower quantity because the marginal revenue curve is downward sloping.  With the lower quantity, the price is also higher than it should be.  

Therefore, a monopolist does not achieve efficiency because it produces too little and charges too much for what it sells.

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