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    Hi guys,

    So at the moment i'm teaching myself A2 economics over the summer and i understand why MR is steeper than AR, but can anyone prove why MR is two times steeper than AR?
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    It's only true if we assume the demand curve is linear. (Which you do at A-level).

    A linear demand curve is written generally as P = a + bQ

    Total revenue is then PQ = aQ + bQ^2

    Marginal revenue is then MR = dP/dQ = a + 2bQ

    Now you can see that the gradient for AR is b and the gradient for MR is 2b, i.e. twice as steep.
 
 
 
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Updated: July 11, 2016

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