# Marginal revenue, and maximizing revenue & average revenue

### Marginal revenue, and maximizing revenue & average revenue

#### Lessons

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,
$MR=R'(q)$

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

$MR=0$

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

$AR'(q)=0$
• Introduction
Marginal Revenue, and Maximizing Revenue & Average Revenue Overview:
a)
Understanding and Maximizing Marginal Revenue

b)
Understanding and Maximizing Average Revenue

• 1.
Finding & Maximizing Revenue
Given the following information, find the marginal revenue and the value of $q$ which maximizes the revenue:
a)
$R(q)=-q^3+4q+2$

b)
$R(q)=-\frac{200}{q^2} -2q$

c)
$p=- \frac{1}{20} q+100$

d)
$q= \frac{50-p}{2}$

• 2.
Finding & Maximizing Average Revenue
Given the following information, find the marginal average revenue and the value of $q$ which maximizes the average revenue:
a)
$R(q)=-3q^4+18q^2+5q$

b)
$R(q)=-2q^2-20$

c)
$p= - \frac{1}{10} q+25$

d)
$q= \frac{100-p}{5}$