# Elasticity of demand

### Elasticity of demand

#### Lessons

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.

• Introduction
Elasticity of Demand Overview:
a)
Elasticity formula

b)
What does Elasticity tell you?

• 1.
Calculating and Determining Elasticity

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

a)
Find $\epsilon (p)$

b)
What is the price elasticity of demand when $p = 20$? What should the company do to increase revenue?

c)
What is the percent change of quantity if $p = 20$, and $p$ increases by $2\%$?

• 2.
The demand curve for computers is given by $p = 400 - q^{2}$.
a)
Find $\epsilon (p)$

b)
What is the price elasticity of demand when $q = 10$? What should the company do to increase revenue?

c)
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?

• 4.
The demand curve for glasses is given by $p = 600 - 2q^{2}$. For what value of $p$ maximizes revenue?

• 5.
The demand curve for shoes is given by $p^{2} + q^{2} = 1000$. What is the elasticity of demand if price is \$$25$?