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Given that Marginal Revenue is change in Total Revenue:

TR = P*Q 
P = f(Q)
TR = f(Q) * Q
MR = dTR/ dQ

Or

TR = P*Q 
Q = f(P)
TR = f(P) * P
MR = dTR/dP

Which of these approach is right? My end goal is to relate revenue to elasticity. Does it matter how I arrive to it?

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    $\begingroup$ It would be less ambiguous if you used different notations for different functions: $P=f(Q) \Leftrightarrow Q=f^{-1}(P) \Leftrightarrow Q=g(P)$ $\endgroup$
    – Bertrand
    Feb 17 '20 at 10:03
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Both of these approaches are correct and valid approaches, in the first approach you calculate the derivative of total revenue with respect to quantity in second with respect to price.

If you are interested in seeing how total revenue varies with quantity you can use the first one if you want to see how the total revenue varies with price then the second one.

Also, you can have multiple different elasticities. Elasticity for single variable function is just by definition $EL=\frac{f’(x)x}{f(x)}$. Depending on what types of elasticity you want to relate the total revenue and what exactly is your ultimate goal of your study either of the formulas could be used.

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  • $\begingroup$ The derivative dTR/dQ is MR. What is dTR/ dP? Are they both MR. My end goal is to relate this to PED but I have that part figured out. Since the textbook definition of MR is change in TR with respect to Q, I was curious if change in TR with respect to price is also MR or not? $\endgroup$
    – Rumi
    Feb 17 '20 at 4:01
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    $\begingroup$ "Both of these approaches are correct and valid approaches". Well yes, but it's worth adding that, unless the context specifies otherwise, marginal revenue normally means dTR/dQ. $\endgroup$ Feb 17 '20 at 13:08

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