Discussion
Derive the marginal revenue function for the demand function q = 400 − 0.1p.
Answer: A
The marginal revenue function is 4000 − 20q.
First express price in terms of quantity, then find total revenue and differentiate:
\[ \begin{aligned} q &= 400 - 0.1p \Rightarrow p = 4000 - 10q \\ TR &= pq = 4000q - 10q^{2} \\ MR &= \frac{d(TR)}{dq} = 4000 - 20q \end{aligned} \]
For a straight-line demand curve, MR has the same intercept and twice the slope. Marginal revenue is a function of quantity, so the options in terms of \(p\) are wrong, and \(+20q\) would make MR rise with output.
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