Total Revenue is given by TR=100Q-2Q². (a) Derive the Marginal Revenue function using the derivative. (b) Find

Worked Examples · Example 3

TR=100Q-2Q^{2}

(a) Derive the Marginal Revenue function using the derivative.

(b) Find MR at Q=10, and verify your answer using the central-difference method

\left[TR(11)-TR(9)\right]/2

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(a) Applying the power rule term by term to $TR=100Q-2Q^{2}$ :

Derivative of $100Q$ (i.e. $100Q^{1}$ ): $100\times1\times Q^{0}=100$ .
Derivative of $-2Q^{2}$ : $-2\times2\times Q^{1}=-4Q$ .

MR=\dfrac{d(TR)}{dQ}=100-4Q

(b) At $Q=10$ :

MR=100-4(10)=100-40=60

Verification by the central-difference method: compute TR at $Q=9$ and $Q=11$ and take the average change:

TR(9)=100(9)-2(9)^{2}=900-162=738

TR(11)=100(11)-2(11)^{2}=1100-242=858

$\dfrac{TR(11)-TR(9)}{2}=\dfrac{858-738}{2}=\dfrac{120}{2}=60$ …

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Q.Total Revenue is given by $TR=100Q-2Q^{2}$ .

Concept understanding — Derivatives and Marginal Concepts

Q.Total Revenue is given by TR=100Q−2Q2TR=100Q-2Q^{2}TR=100Q−2Q2.

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Q.Total Revenue is given by $TR=100Q-2Q^{2}$ .

Unlock everything free for 14 days