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# Why is the Marginal Revenue curve twice as steep as the Average Revenue curve?

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1. 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?
2. 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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