Demand and Marginal Revenue

Q:

Is the MR curve always twice as steep as demand or is that specific to a particular question?

A:

Always twice as steep...but keep in mind that twice as steep as horizontal is still horizontal. Here's why:

Let's take the deamnd curve Qd = 40-2P...
so total revenue = P * Q
If we solve for P in demand we get P = 20 - Q/2
substitute in to get TR = (20-Q/2)*Q = 20Q - (Q^2)/2
now, marginal revenue is just the derivative of total revenue with respect to Q. (We don't explicitly talk about this since calculus is not a prerequisite to the course) So,
MR = D(TR)/D(q) = 20 - Q
Which is the same P intercept and twice as steep. Whee! :)