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Marginal revenue, and maximizing revenue & average revenue

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Intros
Lessons
  1. Marginal Revenue, and Maximizing Revenue & Average Revenue Overview:
  2. Understanding and Maximizing Marginal Revenue
  3. Understanding and Maximizing Average Revenue
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Examples
Lessons
  1. Finding & Maximizing Revenue
    Given the following information, find the marginal revenue and the value of qq which maximizes the revenue:
    1. R(q)=−q3+4q+2 R(q)=-q^3+4q+2
    2. R(q)=−200q2−2q R(q)=-\frac{200}{q^2} -2q
    3. p=−120q+100 p=- \frac{1}{20} q+100
    4. q=50−p2 q= \frac{50-p}{2}
  2. Finding & Maximizing Average Revenue
    Given the following information, find the marginal average revenue and the value of qq which maximizes the average revenue:
    1. R(q)=−3q4+18q2+5q R(q)=-3q^4+18q^2+5q
    2. R(q)=−2q2−20 R(q)=-2q^2-20
    3. p=−110q+25p= - \frac{1}{10} q+25
    4. q=100−p5 q= \frac{100-p}{5}
Topic Notes
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Marginal Revenue (MR) is the additional revenue that is gained when you increase the unit by one. It is also the derivative of the revenue function. In other words,
MR=R′(q)MR=R'(q)

Average Revenue (AR) is the amount of revenue generated per unit. In other words,
AR(q)=R(q)qAR(q)=\frac{R(q)}{q}
In this section, we would want to find the quantity qq, which maximizes revenue and average revenue. To maximize revenue, we would want to solve for:

MR=0MR=0

To maximize average revenue, we would want to solve for:

AR′(q)=0AR'(q)=0
Basic Concepts
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Related Concepts
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