Elasticity and Its Application

class: center, middle, inverse, title-slide

.title[
# Elasticity and Its Application
]
.subtitle[
## Chapter 5
]
.author[
### Hussain Hadah
]
.date[
### University of Houston | 18 July 2022
]

---

# Table of contents

1. [Introduction](#intro)

2. [The Elasticity of Demand](#sec1)

3. [Computing the Price Elasticity of Demand](#sec2)

4. [Other Demand Elasticities](#sec3)

5. [The Elasticity of Supply](#sec4)

6. [Three Applications of Supply, Demand and Elasticity](#sec5)

7. [Problems and Applications](#sec6)

---
class: inverse, center, middle
name: intro

# Introduction

---
# Why does elasticity matter?

## Consider the following scenario

- There is a wildfire in Oregon and Washington (two states that produce wheat)
- Wheat supply will be affected

--
- Supply will decrease, causing the price of wheat to increase
- Wheat is an input in the production of bread (the supply of bread will be affected)
- Higher wheat prices will cause the price of bread to increase

--
### What will happen to the demand for bread in this scenario?

--
- An obvious answer will be: people will buy less bread.

--
- By how much would bread purchases fall in response to the higher prices?

--
- To answer the previous question, we need to learn about <span style="color:red;">elasticity </span>

---
# What is <span style="color:red;">elasticity </span>?

## <span style="color:red;">Elasticity </span> is a measure of how buyers and sellers respond to changes in market conidtions.

---
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name: sec1

# The Elasticity of Demand

---
# Price elasticity of demand

### - The <span style="color:red;"> _price elasticity of demand_</span> measures how much the quantity demanded responds to a change in price

### - Demand for a good is <span style="color:red;"> _elastic_</span> if the quantity demanded responds substantially to changes in the price

### - Demand for a good is <span style="color:red;"> _inelastic_</span> if the quantity demanded responds only slightly to changes in the price

---
# Availability of close substitutes

- A good with similar substitutes has more elastic demand
- People can switch from one more expensive good to another heaper good
- Pepsi and Coke are close substitutes

--
- A good with no substitutes has more inelastic demand
- People can't switch to another alternative
- Eggs don't have close substitutes

---
# Necessities vs luxuries

- Necessities have inelastic demands

--
- Luxuries have elastic demands

--
### Examples:

- If the price of water increases, people will not adjust their consumption dramatically

--
- If the price of sailboats rises, the number of sailboats sold will fall dramatically

---
# Definition of the market

- The elasticity of demand in any market depends on how we define said market

- Markets that are narrowly defined often have more elastic demand (ice cream)

- Markets that broadly define often have more inelastic demand (food)

---
# Time horizon

- Good tends to have more elastic demand over the longer time horizons

--
- If the price of gasoline rises, the quantity of purchased gasoline falls slightly

--
- Over the long run, more efficient cars will be invented
- More efficient cars reduces the amount of gasoline consumed
- The quantity of gasoline will fall more substantially

---
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name: sec2

# Computing the Price Elasticity of Demand

---
# Calculating Demand Elasticity

- Elasticity of demand is the percentage change in the quantity demanded over the percentage change in the price

$$
`\begin{equation}
\text{Price elasticity of demand} = \frac{\% \Delta \text{in quantity demanded}}{\% \Delta \text{price}}
\end{equation}`
$$

--
- Example: in response to a 10% increase in the price of ice cream, the quantity of ice cream demanded fell by 20%. Calculate the price elasticity of demand.

--
$$
`\begin{equation}
\text{Ice cream's price elasticity of demand} = \frac{20\%}{10\%} = 2
\end{equation}`
$$
- We can interpret this elasticity as the quantity of ice cream demanded response twice as large to change in the price of ice cream

--
- Quantities and prices have a negative relationship
- The numerator will always have the opposite sign of the denominator
- The convention in economics is to drop the negative sign when calculating the price elasticity of demand
- Price elasticity of demand is always interpreted as a negative number

---
# The midpoint method
### The midpoint method is a better way to calculate percentage changes and elasticities

Example:
$$
`\begin{align}
\text{Point A: } \text{ Price} &= $4,   \text{ Quantity} = 120 \\
\text{Point B: } \text{ Price} &= $6,   \text{ Quantity} = 80 
\end{align}`
$$

- If you calculate elasticity using the previous equation, elasticity from point A to B will seem different from the elasticity from point B to A

--
- Elasticity from A to B is 0.66

- Elasticity from B to A is 1.5

--
- You can avoid this problem by using the _midpoint method_

$$
`\begin{equation}
\text{Price elasticity of demand} = \frac{\frac{Q_{2} - Q_{1}}{0.5 \cdot (Q_{2} + Q_{1})}}{\frac{P_{2} - P_{1}}{0.5 \cdot (P_{2} + P_{1})}}
\end{equation}`
$$

---
# Variety of demand curves
<img src="images/image1.png" width="80%" height="80%" style="display: block; margin: auto;" />

---
<h1 style="font-size:32px">Total revenue and price elasticity of demand</h1>

</br>

- Total revenue is an important variable to look at when there are changes to supply and demand

- <span style="color:red;"> _Total revenue_</span> is the amount paid by buyers and received by sellers of a good

- `$R = P \times Q$`

--
<img src="images/image2.png" width="60%" height="60%" style="display: block; margin: auto;" />

---
<h1 style="font-size:28px">How does total revenue change as we move along the demand curve?</h1>

</br>

### It depends on the elasticity of the demand curve

--
<img src="images/image3.png" width="60%" height="60%" style="display: block; margin: auto;" />

---
# General rules on elasticity

- When demand is inelastic (a price elasticity less than one), price and total revenue move in the same direction: If the price increases, total revenue also increases.

- When demand is elastic (a price elasticity greater than one), price and total revenue move in opposite directions: If the price increases, total revenue decreases.

- If demand is unit elastic (a price elasticity exactly equal to one), total revenue remains constant when the price changes.

---
<h1 style="font-size:32px">Elasticity and total revenue along a linear demand curve</h1>

</br>

--
##### Even though the slope of a linear curve is constant, elasticity is not. The slope is the ratio of changes in two variables, whereas elasticity is the ratio of percentage changes in the two variables

--
<img src="images/image4.png" width="50%" height="50%" style="display: block; margin: auto;" />

---
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# Other Demand Elasticities

---
# Income elasticity of demand

- <span style="color:red;"> Income elasticity of demand</span> is a measure of how the quantity demanded changes as consumer income changes.

$$
`\begin{equation}
\text{Income elasticity of demand} = \frac{\% \Delta \text{in quantity demanded}}{\% \Delta \text{income}}
\end{equation}`
$$

---
# Cross-price elasticity of demand

- <span style="color:red;"> Cross-price elasticity of demand</span> is a measure of how the quantity demanded of one good response to a change in the price of another good

$$
`\begin{equation}
\text{Cross-price elasticity of demand} = \frac{\% \Delta \text{in quantity demanded of good one}}{\% \Delta \text{price of good two}}
\end{equation}`
$$

---
class: inverse, center, middle
name: sec4

# The Elasticity of Supply

---
# Price elasticity of supply

- <span style="color:red;"> Price elasticity of supply</span> measures how much the quanitity supplied responds to changes in the price

- The supply of a good is _elastic_ if the quantity supplied response substantially to a change in price

- The supply of a good is _inelastic_ if the quantity supplied response slightly to a change in price

---
# Calculating Supply Elasticity

$$
`\begin{equation}
\text{Price elasticity of supply} = \frac{\% \Delta \text{in quantity supplied}}{\% \Delta \text{price}}
\end{equation}`
$$

---
# The different supply curves

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# Three Applications of Supply, Demand and Elasticity

---
# Wheat farmers
<img src="images/image6.png" width="100%" height="100%" style="display: block; margin: auto;" />

---
# OPEC
<img src="images/image7.png" width="100%" height="100%" style="display: block; margin: auto;" />

---
# Drug policies
<img src="images/image8.png" width="100%" height="100%" style="display: block; margin: auto;" />

---
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name: sec6

# Problems and Applications

---
# Question 1

#### For each of the following pairs of goods, which good would you expect to have more elastic demand and why?

--
#### Required textbooks or mystery novels

--
- Mystery novels because they have close substitutes are a luxury good. Required textbooks are a necessity with no close substitutes

--
#### Beethoven recordings or classical music recordings in general

--
- Beethoven recordings have more elastic demand than classical music recordings in general. Beethoven recordings are a narrower market

--
#### Subway rides during the next 6 months or subway rides during the next 5 years

--
- Subway rides during the next five years have more elastic demand. Goods have a more elastic demand over longer time horizons

--
#### Root beer or water

--
- Root beer has more elastic demand than water. Root beer is a luxury with close substitutes, while water is a necessity with no close substitutes

---
# Question 2

#### Suppose that business travelers and vacationers have the following demand for airline tickets from New York to Boston:

##### a. As the price of tickets rises from $200 to $250, what is the price elasticity of demand for (i) business travelers and (ii) vacationers? (Use the midpoint method in your calculations.)

$$
`\begin{align}
E_B &= \frac{\frac{Q_{2} - Q_{1}}{0.5 \cdot (Q_{2} + Q_{1})}}{\frac{P_{2} - P_{1}}{0.5 \cdot (P_{2} + P_{1})}} = \frac{\frac{2,000 - 1,900}{1,950}}{\frac{250 - 200}{225}} = 0.23\\
E_V &= \frac{\frac{800 - 600}{700}}{\frac{250 - 200}{225}} = 1.32
\end{align}`
$$

---
# Question 2 (cont.)

##### b. Why might vacationers have a different elasticity from business travelers?

--
- The price elasticity of demand for vacationers is higher than the elasticity for business travelers because vacationers can choose a substitute more easily than business travelers

- For example, vacationers can choose a different mode of transportation (like driving or taking the train), a different destination, a different departure date, and a different return date. They may also choose to not travel at all. Business travelers are less likely to do so because their schedules are less adaptable.

---
# Question 3

### Suppose the price elasticity of demand for heating oil is 0.2 in the short run and 0.7 in the long run.

--
##### If the price of heating oil rises from $1.80 to $2.20 per gallon, what happens to the quantity of heating oil demanded in the short run? In the long run?

--
- The percentage change in price is equal to `$(2.20 – 1.80)/2.00 \times 100 = 20\%$`

--
- If the price elasticity of demand is `$0.2$`, quantity demanded will fall by `$0.2 \times 0.2 = 0.04 \Rightarrow 4\%$` in the short run

--
- If the price elasticity of demand is `$0.7$`, quantity demanded will fall by `$0.7 \times 0.2 = 0.14 \Rightarrow 14\%$` in the short run

--
##### Why might this elasticity depend on the time horizon?

--
- Over time, consumers can make adjustments to their homes by purchasing alternative heat sources such as natural gas or electric furnaces. Thus, they can respond more easily to the change in the price of heating oil in the long run than in the short run.

---
# Question 4

### A price change causes the quantity demanded of a good to decrease by 30 percent, while the total revenue of that good increases by 15 percent. Is the demand curve elastic or inelastic? Explain.

--
<h4>
  <ul>
  <li>If quantity demanded fell, price must have increased according to the law of demand</li>
  <li>For a price increase to increase total revenue, the percentage increase in the price must be greater than the percentage decline in quantity demanded</li>  
  <li>Therefore, demand is inelastic</li>
  </ul>
</h4>

---
# Question 5

#### Cups of coffee and donuts are complements. Both have inelastic demand. A hurricane destroys half the coffee bean crop. Use appropriately labeled diagrams to answer the following questions.

--
##### a. What happens to the price of coffee beans?

--
##### The effect on the market for coffee beans is shown in Figure 2.  When a hurricane destroys half of the crop, the supply of coffee beans decreases, the price of coffee beans increases, and the quantity decreases.

---
# Question 5

#### Cups of coffee and donuts are complements. Both have inelastic demand. A hurricane destroys half the coffee bean crop. Use appropriately labeled diagrams to answer the following questions.

--
##### b. What happens to the price of a cup of coffee? What happens to total expenditure on cups of coffee?

--
##### The effect on the market for cups of coffee is shown in Figure 2.  When the price of coffee beans, an important input into the production of a cup of coffee, increases, the supply of cups of coffee decreases, the price of a cup of coffee increases, and the quantity decreases. Because cups of coffee have an inelastic demand, when the price of a cup of coffee increases, the total expenditure on coffee increases.

---
# Question 5

#### Cups of coffee and donuts are complements. Both have inelastic demand. A hurricane destroys half the coffee bean crop. Use appropriately labeled diagrams to answer the following questions.

--
##### c. What happens to the price of donuts? What happens to total expenditure on donuts?

--
##### The effect on the market for donuts is shown in Figure 3.  When the price of coffee increases and the quantity demanded of coffee decreases, consumers demand fewer donuts because coffee and donuts are complements. When demand decreases, the price of donuts decreases.

---
# Question 6

#### The price of coffee rose sharply last month, while the quantity sold remained the same. Five people suggest various explanations:

- Leonard:Demand increased, but supply was perfectly inelastic

- Sheldon:Demand increased, but it was perfectly inelastic

- Penny:Demand increased, but supply decreased at the same time

- Howard:Supply decreased, but demand was unit elastic

- Raj:Supply decreased, but demand was perfectly inelastic

#### Who could possibly be right? Use graphs to explain your answer.

--
#### If the price of coffee rose sharply while the quantity sold remained the same, the explanations offered by Leonard, Penny, and Raj could be correct while the explanations offered by Sheldon and Howard are incorrect

---
# Question 6

---
# Question 7

Suppose that your demand schedule for pizza is as follows:

a. Use the midpoint method to calculate your price elasticity of demand as the price of pizza increases from $8 to $10 if
  
  (i) your income is $20,000 and
  
  (ii) your income is $24,000

$$
`\begin{align}
E_i &= \frac{\frac{Q_{2} - Q_{1}}{0.5 \cdot (Q_{2} + Q_{1})}}{\frac{P_{2} - P_{1}}{0.5 \cdot (P_{2} + P_{1})}} = \frac{\frac{40 - 32}{36}}{\frac{10-8}{9}} = 0.22/0.22 = 1\\
E_{ii} &= \frac{\frac{50-45}{47.5}}{\frac{10-8}{9}} = 0.11/0.22=0.5
\end{align}`
$$

---
# Question 7

Suppose that your demand schedule for pizza is as follows:

b. Calculate your income elasticity of demand as your income increases from $20,000 to $24,000 if
  
  (i) the price is $12 and
  
  (ii) the price is $16

$$
`\begin{align}
E_i &= \frac{\frac{Q_{2} - Q_{1}}{0.5 \cdot (Q_{2} + Q_{1})}}{\frac{I_{2} - I_{1}}{0.5 \cdot (I_{2} + I_{1})}} = \frac{\frac{30 - 24}{27}}{\frac{24,000 - 20,000}{22,000}} = 0.22/0.18 = 1.22\\
E_{ii} &= \frac{\frac{12-8}{10}}{\frac{24,000 - 20,000}{22,000}} = 0.40/0.18=2.22
\end{align}`
$$

---
# Question 8

#### The New York Times reported (Feb. 17, 1996) that subway ridership declined after a fare increase: “There were nearly four million fewer riders in December 1995, the first full month after the price of a token increased 25 cents to $1.50, than in the previous December, a 4.3 percent decline.”

--
a. Use these data to estimate the price elasticity of demand for subway rides.

--
- The percentage change in price (using the midpoint formula) is (1.50 – 1.25)/(1.375) × 100% = 18.18%. Therefore, the price elasticity of demand is 4.3/18.18 = 0.24, which is very inelastic

--
b. According to your estimate, what happens to the Transit Authority’s revenue when the fare rises?

--
- Because the demand is inelastic, the Transit Authority's revenue rises when the fare rises.

---
# Question 8

c. Why might your estimate of the elasticity be unreliable?

--
- The elasticity estimate might be unreliable because it is only the first month after the fare increase. As time goes by, people may switch to other means of transportation in response to the price increase. So the elasticity may be larger in the long run than it is in the short run