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I presume it's because they're price makers, but this doesn't really answer much. Furethermore, in a monopoly is it Marginal Cost or Long run marginal cost that's horizontal?

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That is basically an assumption here. Often in monopoly problems we assume constant marginal costs (i.e. a linear cost function) to keep things simple. In that case the Marginal Cost Curve is horizontal in the graph.

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  • $\begingroup$ Is there a reference for the constant MC assumption in the literature? $\endgroup$
    – Paul
    Commented Oct 27, 2016 at 15:03
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    $\begingroup$ Well, a constant MC is usually assumed in teaching materials and not as much in the scientific literature. However, several papers sometimes do assume it. In the literature this assumption is not really defended or motivated, beyond ensuring simplicity. Also when making such an assumption it is not referenced to a source, as it is very natural. $\endgroup$
    – BB King
    Commented Oct 27, 2016 at 15:11
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    $\begingroup$ I also want to point out that linear costs amounts to zero returns to scale. $\endgroup$
    – user526463
    Commented May 26, 2018 at 20:18
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While principles level textbooks do usually assume that MC is constant for the monopolist for simplicity, by no means does it have to be constant. It may indeed be upward-sloping. Also, both the long-run and short-run marginal cost curves may be horizontal and/or curved, depending on the technology in use.

An upward-sloping MC curve will affect the distribution of Consumer Surplus, Producer Surplus and Dead-weight Loss.

The monopolist being a price-maker is sometimes due to the production technology (and hence the cost structure) it faces but always due to the lack of (real or the threat of) competition.

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  • $\begingroup$ This is incorrect. The cost structure can affect market structure. For instance, the existence of a large fixed cost and low MC creates a natural monopoly. $\endgroup$
    – Peutch
    Commented Feb 1, 2021 at 16:35
  • $\begingroup$ I have edited my answer based on your comment. However, your comment indicates my original answer was entirely incorrect whereas it was only the third paragraph of my answer that was originally incorrect. $\endgroup$
    – Mishal Ahmed
    Commented Feb 2, 2021 at 17:16

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