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# Elasticity of demand

- Intro Lesson: a4:13
- Intro Lesson: b6:26
- Lesson: 1a2:52
- Lesson: 1b3:36
- Lesson: 1c3:22
- Lesson: 2a6:39
- Lesson: 2b4:22
- Lesson: 2c3:31
- Lesson: 33:43
- Lesson: 48:33
- Lesson: 56:26

### Elasticity of demand

#### Lessons

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

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.

- IntroductionElasticity of Demand Overview:a)Elasticity formulab)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.
**Advanced Problems With Elasticity**The demand curve for shoes is given by $p^{2} + q^{2} = 1000$. What is the elasticity of demand if price is $$25$?