# Price elasticity of demand

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##### Intros
###### Lessons
1. Price Elasticity of Demand Overview:
2. Definition for Elasticity
• Analyze supply and demand with good precision
• How buyers and sellers respond to change
• Price Elasticity of Demand
• Why is it important
3. Formulas for Price Elasticity of Demand
• Two ways to calculate Elasticity of Demand
• Point Elasticity of Demand
• Arc Elasticity of Demand
• An Example of using both
4. Notes about Price Elasticity of Demand
• Why use average price and quantity?
• Percentages and Proportions
• Units-Free Measure
5. Types of Demand Curves
• Inelastic demand and elastic demand
• What each value of elasticity means
• Perfectly inelastic, perfectly elastic, unit elastic
6. Total Revenue and Price Elasticity of Demand
• How to calculate total revenue
• How revenue changes in an inelastic demand
• How revenue changes in an elastic demand
• How revenue changes in a unit elastic demand
##### Examples
###### Lessons
1. Understanding Price Elasticity of Demand
Suppose the price of oranges increases from $1 to$3 a box, and the quantity demanded decreases from 500 to 300 boxes a day. Calculate the point elasticity of demand and the arc elasticity of demand.
1. If the quantity of car services demanded increases by 30% when the price of car services decrease by 20%, is the demand for car service elastic, inelastic, or unit elastic?
1. The following graph shows the demand for books.
Calculate the arc elasticity of demand when the price increases from $2 to$4 a book. Over what price range is the demand for books inelastic?
1. Suppose the company decided to decrease the price of chocolate from $10 to$6. They expect that the price cut will boost the chocolate sales by 40%.
1. What is the arc elasticity of demand?
2. If you were making the pricing decisions at this company, would you increase or decrease the price? Why?
2. Suppose the company decided to decrease the quantity of phones from to 100 to 70. They expect that the quantity cut will boost the price sales by 22.2%.
1. If you were making the pricing decisions at this company, would you increase or decrease the price? Why?
###### Topic Notes

Definition for Elasticity

Elasticity helps us analyze supply and demand with great precision and shows us how buyers and sellers respond to change.

Price Elasticity of Demand = $\frac{\% \;change \;in \;quantity \;of \;demand}{\% \;change \;in \;price}$

The elasticity of demand measures the responsiveness of the quantity demanded to a change in the good.

Formulas for Price Elasticity of Demand

Using the formula above, there are two ways to calculate price elasticity of demand.

First Way: Point Elasticity of Demand

Point Elasticity of Demand = $\frac{(Q_{2}-Q_{1})/Q_{1}}{(P_{2}-P_{1})/P_{1}}$

Second Way: Arc Elasticity of Demand

Arc Elasticity of Demand = $\frac{(Q_{2}-Q_{1})/Q_{avg}}{(P_{2}-P_{1})/P_{avg}}$

Where $Q_{avg}$ = $\frac{Q_{1}+ Q_2 } {2}$ and $P_{avg}$ = $\frac{P_{1}+ P_2 } {2}$

Ignore the negative sign when calculating the elasticity, it is unimportant.

Notes about Price Elasticity of Demand

Average Price and Quantity: We use average price and quantity when applying the arc elasticity of demand formula because we get the same elasticity value regardless of whether the price rises or falls. It is also more accurate.

Percentages and Proportions: The ratio of two proportionate changes is the same as the ratio of two percentage changes.

$\frac{\%\triangle Q}{\%\triangle P}= \frac{\triangle Q}{\triangle P}$

Units-Free Measure: Since Elasticity uses percentages, the change in the units of measurement of price and quantity does not matter.

Types of Elasticities

Inelastic Demand: Quantity demanded does not respond strongly to price changes.
Elastic Demand: Quantity demanded responds strongly to price changes.
Unit Elastic Demand: Quantity demanded responds equally to price changes.

Mathematically, if:
1. $\in_{p}$ > 1, then it is elastic, and 1% Change in P results in greater than 1% Change in Q
2. $\in_{p}$ < 1, then it is inelastic, and 1% Change in P results in less than 1% Change in Q
3. $\in_{p}$ = 1, then it is unit elastic, and 1% Change in P = 1% Change in Q

Two Unique Cases of Demand Curves

Case 1: If a demand curve is perfectly inelastic, then the quantity demanded does not respond to price changes.

Case 2: If a demand curve is perfectly elastic, then the quantity demanded changes infinitely with any price changes.

Total Revenue and Price Elasticity of Demand

Total Revenue = Quantity × Price
1. If demand is elastic, then 1% price cut increases the quantity sold by more than 1%. This causes revenues to increase.

2. If demand is inelastic, then 1% price cut increases the quantity sold by less than 1%. This causes the revenue to decrease.

3. If demand is unit elastic, then 1% price cut increase the quantity sold by 1%. This does not change the revenue.

4. The goal is to always have unit elastic demand.