CJW
April 25, 2022, 9:13am
#1
Hi, I’m reading Marginal Revenue and have a question about the equation.

The textbook says : change in total revenue(△TR) can be written as (P)(△Q)+(Q)(△P).

But if I understood the concept correctly, △TR = (P+△P)(Q+△Q)-PQ = PQ+(P)(△Q)+(△P)(Q)+(△P)(△Q)-PQ = (P)(△Q)+(△P)(Q)+(△P)(△Q).

Where the term (△P)(△Q) is gone…?

\Delta TR = P(\Delta Q) + (\Delta P)(Q) + (\Delta P)(\Delta Q)
\Delta TR = P(\Delta Q) + (\Delta P)(Q + \Delta Q)
\dfrac{\Delta TR}{\Delta Q} = P(\dfrac{\Delta Q}{\Delta Q}) + \dfrac{\Delta P}{\Delta Q}(Q + \Delta Q)
\dfrac{\Delta TR}{\Delta Q} = P + \dfrac{\Delta P}{\Delta Q}(Q + \Delta Q)

As \Delta Q \rightarrow 0,

\dfrac{d(TR)}{dQ} = MR = P + \dfrac{dP}{dQ}(Q)

3 Likes

CJW
April 25, 2022, 11:42am
#3
The textbook is not introducing the concept of differential yet, so I tried to understand without considering it.

I think I need to read further and will refer to your reply…

I appreciate your reply, anyway!

If \Delta P is small and \Delta Q is small, then \Delta P\Delta Q is really , really small, so they ignore it.

2 Likes

There’s really not much calculus anywhere in the entire CFA syllabus. If anything, I would recommend reviewing compound interest math, 'cuz you’re gonna see lots of that!!