MR is twice as steep as DD curve, as a geometric assumption?

Question

my lecturer once said something like the maths part are not always proved true, but just assumed to be so. is MR the same? i could never plot out a graph with my own hypothetical data that says MR is twice as steep as DD, unless i manipulate my data to suit it. that said, is the teaching of MR twice as steep as DD, a maths thing, or an assumed thing?

Answer 1

Only when the demand curve is linear is the slope of the marginal revenue curve twice as steep. It is taught for simplicity.

Answer 2

This is only true if the price is linearly dependent on q and the cost per unit is constant.
In this case the revenue depends on the slope of DD*q^2 + other terms that are linear in q, so the MR = 2 slope of DD*q +constant terms.
(From calculus the derivative of x^2= 2 x and of x=1)

Answer 3

The slopes of the demand and marginal revenue curves are calculus results.