# Elasticity of demand

#### Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

#### Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

#### Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

##### Intros
###### Lessons
1. Elasticity of Demand Overview:
2. Elasticity formula
3. What does Elasticity tell you?
##### Examples
###### Lessons
1. Calculating and Determining Elasticity

The demand curve for cakes is given by $q = 400 - 5p$.

1. Find $\epsilon (p)$
2. What is the price elasticity of demand when $p = 20$? What should the company do to increase revenue?
3. What is the percent change of quantity if $p = 20$, and $p$ increases by $2\%$?
2. The demand curve for computers is given by $p = 400 - q^{2}$.
1. Find $\epsilon (p)$
2. What is the price elasticity of demand when $q = 10$? What should the company do to increase revenue?
3. What is the percent change of price if $q = 10$, and $q$ decreases by $3\%$?
3. Maximizing Revenue using Unit Elasticity

The demand curve for glasses is given by $q = 600 - 3p$. For what value of $p$ maximizes revenue?

1. The demand curve for glasses is given by $p = 600 - 2q^{2}$. For what value of $p$ maximizes revenue?

The demand curve for shoes is given by $p^{2} + q^{2} = 1000$. What is the elasticity of demand if price is \$$25$?

###### Topic Notes

The Elasticity of Demand is the percentage change in quantity divided by the percentage change in price. In other words,

$\epsilon = \frac{\% \Delta q}{\% \Delta p} = \frac{p}{q}\frac{dq}{dp}$

Note that $\epsilon$ will always be negative because the slope of the demand curve $\frac{dq}{dp}$ is negative.

The Elasticity of Demand is very important because it tells us how to optimize our revenue.

1) When $|\epsilon|$ > 1, then the good is elastic. This means $\%\Delta q$ > $\%\Delta p$, thus decreasing price will increase revenue.

2) When $|\epsilon|$ < 1, then the good is inelastic. This means $\%\Delta q$ < $\%\Delta p$, thus increasing price will increase revenue.

3) When $|\epsilon|$ = 1, then the good is unit elastic. This means $\%\Delta q$ = $\%\Delta p$, so you are already at the optimal price which maximizes revenue

To maximize revenue, we set $|\epsilon|$ = -1 and solve for $p$ so that we know what price maximizes revenue.