Elasticity

Elasticity

Elasticity measures the responsiveness of quantity demanded (QD) or quantity supplied (QS) to changes in their determinants.

The Price Elasticity of Demand

Definition: Measures how much the quantity demanded of a good responds to a change in the price of that good. It indicates how price-sensitive buyers are for that good.
Formula: \frac{\% \Delta Q}{\% \Delta P} = \frac{\text{percentage change in quantity demanded}}{\text{percentage change in price}}

Example

Along a demand curve, price (P) and quantity (Q) move in opposite directions, resulting in a negative price elasticity.
Scenario:
- Price rises by 10%.
- Quantity falls by 15%.

Midpoint Method

The midpoint method is used to calculate elasticity to ensure consistent results regardless of the direction of change.
The formula incorporates a minus sign to make the price elasticity positive.

Numerical Example Using Midpoint Method

Consider the demand for photo sessions:
- Point A: Price = $200, Quantity = 12
- Point B: Price = $250, Quantity = 8

Interpretation of Elasticity

Elasticity indicates the responsiveness of one variable to a change in another.

Rubber Band Analogy

Two rubber bands holding the same weight (10 KG) illustrate elasticity.
- Less Elastic Band: Doesn't stretch as far.
- More Elastic Band: Stretches further.
- The more elastic band is more responsive to the weight applied.

Price Increase and Elasticity

If the price of two different goods increases by 10%:
- The good with the higher price elasticity will experience a greater fall in quantity demanded.

Intuition Check: Examples

Comparing two goods to determine which has a higher price elasticity of demand, given a 10% price increase.
Example 1: Insulin vs. Luxury Goods
- Price elasticity is generally higher for luxury goods compared to necessities like insulin.
Example 2: Broadly vs. Narrowly Defined Goods
- Price elasticity is higher when goods are defined narrowly.
Example 3: Sunscreen Brands
- Price elasticity is higher when close substitutes are available.

Gasoline: Short Run vs. Long Run

Consider a 20% price increase in gasoline.
- Short Run (Tomorrow): Limited behavioral changes.
- Long Run (Five Years): Consumers can adjust (e.g., buy smaller cars, move closer to work).
- Price elasticity is higher in the long run because consumers have more time to adjust their behavior.

Real-World Elasticities

Examples of price elasticities for various product categories:
- Eggs: 0.1
- Healthcare: 0.2
- Cigarettes: 0.4
- Rice: 0.5
- Housing: 0.7
- Beef: 1.6
- Peanut Butter: 1.7
- Restaurant Meals: 2.3
- Mountain Dew: 2.4

Demand Curve Shapes and Price Elasticity

General Rule: The flatter the demand curve, the greater the price elasticity of demand.
Elasticity Values:
- e = 0: Perfectly inelastic (vertical demand curve).
- e < 1: Inelastic.
- e = 1: Unit elastic.
- e > 1: Elastic.
- e = ∞: Perfectly elastic (horizontal demand curve).

Perfectly Inelastic Demand

Demand curve is vertical.
Consumers' price sensitivity: None.
Elasticity: 0
Example: \text{Price elasticity of demand} = \frac{\% \text{change in Q}}{\% \text{change in P}} = \frac{0\%}{10\%} = 0

Inelastic Demand

Demand curve is relatively steep.
Consumers’ price sensitivity: Relatively low.
Elasticity: < 1
Example: \text{Price elasticity of demand} = \frac{\% \text{change in Q}}{\% \text{change in P}} < \frac{10\%}{10\%} < 1

Unit Elastic Demand

Demand curve has an intermediate slope.
Consumers’ price sensitivity: Intermediate.
Elasticity: = 1
Example: \text{Price elasticity of demand} = \frac{\% \text{change in Q}}{\% \text{change in P}} = \frac{10\%}{10\%} = 1

Elastic Demand

Demand curve is relatively flat.
Consumers’ price sensitivity: Relatively high.
Elasticity: > 1
Example: \text{Price elasticity of demand} = \frac{\% \text{change in Q}}{\% \text{change in P}} > \frac{10\%}{10\%} > 1

Perfectly Elastic Demand

Demand curve is horizontal.
Consumers’ price sensitivity: Extreme.
Elasticity: Infinity
Example: \text{Price elasticity of demand} = \frac{\% \text{change in Q}}{\% \text{change in P}} = \frac{\text{any }\%}{0\%} = \infty

Elasticity Along a Linear Demand Curve

The slope of a linear demand curve is constant, but its elasticity is not.
Examples:
- E = \frac{200\%}{40\%} = 5.0
- E = \frac{67\%}{67\%} = 1.0
- E = \frac{40\%}{200\%} = 0.2

Price Elasticities and Total Revenue

Total Revenue (TR) = P x Q
A price increase has two effects on revenue:
- Higher revenue due to the higher price.
- Lower revenue due to selling fewer units.
The overall impact depends on the price elasticity of demand.

Price Elasticity and Total Revenue Relationship

For a price increase, if demand is elastic (E > 1):
- % change in Q > % change in P
- TR decreases because the fall in revenue from lower Q > the increase in revenue from higher P
For a price increase, if demand is inelastic (E < 1):
- % change in Q < % change in P
- TR increases because the fall in revenue from lower Q < the increase in revenue from higher P

Elastic Demand Example

Elastic demand (elasticity = 1.8)
- If P = $200, Q = 12, and revenue = $2400
- If P = $250, Q = 8, and revenue = $2000
- When demand is elastic, a price increase causes revenue to fall.

Inelastic Demand Example

Inelastic demand (elasticity = 0.82)
- If P = $200, Q = 12, and revenue = $2400
- If P = $250, Q = 10, and revenue = $2500
- When demand is inelastic, a price increase causes revenue to rise.

The Price Elasticity of Supply

Definition: Measures how much the quantity supplied of a good responds to a change in the price of that good.
Formula: \% \Delta Q / \% \Delta P = \frac{\text{percentage change in quantity supplied}}{\text{percentage change in price}}

Calculating Price Elasticity of Supply

The midpoint method is used to compute percentage changes.

Supply Curve Shapes and Price Elasticities of Supply

General Rule: The flatter the supply curve, the greater the price elasticity of supply.
Elasticity Values:
- e = 0: Perfectly inelastic (vertical supply curve).
- e < 1: Inelastic.
- e = 1: Unit elastic.
- e > 1: Elastic.
- e = ∞: Perfectly elastic (horizontal supply curve).

Perfectly Inelastic Supply

S curve is vertical.
Sellers’ price sensitivity: None.
Elasticity: 0
Example: \text{Price elasticity of supply} = \frac{\% \text{change in Q}}{\% \text{change in P}} = \frac{0\%}{10\%} = 0

Inelastic Supply

S curve is relatively steep.
Sellers’ price sensitivity: Relatively low.
Elasticity: < 1
Example: \text{Price elasticity of supply} = \frac{\% \text{change in Q}}{\% \text{change in P}} < \frac{10\%}{10\%} < 1

Unit Elastic Supply

S curve has an intermediate slope.
Sellers’ price sensitivity: Intermediate.
Elasticity: = 1
Example: \text{Price elasticity of supply} = \frac{\% \text{change in Q}}{\% \text{change in P}} = \frac{10\%}{10\%} = 1

Elastic Supply

S curve is relatively flat.
Sellers’ price sensitivity: Relatively high.
Elasticity: > 1
Example: \text{Price elasticity of supply} = \frac{\% \text{change in Q}}{\% \text{change in P}} > \frac{10\%}{10\%} > 1

Perfectly Elastic Supply

S curve is horizontal.
Sellers’ price sensitivity: Extreme.
Elasticity: Infinity
Example: \text{Price elasticity of supply} = \frac{\% \text{change in Q}}{\% \text{change in P}} = \frac{\text{any }\%}{0\%} = \infty

Real-World Example: Gasoline Consumption

Data from June 2007 and June 2008:
- June 2007: Per capita daily consumption = 1.32 gallons, average price = $3.05
- June 2008: Per capita daily consumption = 1.26 gallons, average price = $4.07
- Change in consumption (\DeltaQ) = -0.06
- Change in price (\DeltaP) = 1.02
- Average consumption = 1.29
- Average price = 3.56
Demand for gasoline is inelastic.

Considerations for Elasticity Calculation

It's important to ensure that the changes observed are due to price changes and not other factors.

Identifying Shifts in Supply and Demand

Need to determine whether there was a shift in the supply curve or the demand curve.
In the gasoline example:
- Supply curve shifted due to an increase in the price of oil (an input in making gasoline).
- To claim that we are looking at the demand curve, we need to argue that the demand curve DID NOT shift.

Determinants of Demand

We have to make sure other determinants of demand are held constant when calculating price elasticity
Tastes of consumers
Seasonality in demand – compare June to June to hold this fixed
Number of consumers – use per capita numbers to hold this fixed
Income – Gasoline is a normal good, income cannot change. Relatively stable from June 2007 to June 2008
Prices of substitutes and complements – look at consumer price index to confirm this information

Summary for Estimating Demand Elasticity

When estimating demand elasticity, hold fixed the other determinants of demand to isolate the impact of the change in price.
Also, consider the supply side.

Knowledge Check

Which two months could you use to determine the price elasticity of demand for eggs?
Need the information for the appropriate circumstances

Template for Supply and Demand

Concept of elasticity can be applied to capture how supply or demand changes in response to changes in any determinant.

The Income Elasticity of Demand

Definition: Measures how much the quantity demanded of a good responds to a change in the income of consumers.
Formula: \% \Delta Q / \% \Delta \text{Income} = \frac{\text{percentage change in quantity demanded}}{\text{percentage change in income}}
- Normal goods: > 0
- Inferior goods: < 0 (e.g., Ramen noodles)

Example

Given data for income, price of milk, quantity of milk, price of cookies, and quantity of cookies for January, February, March and April.

Calculating Income Elasticity of Milk

Use January and February data, as the price of milk and cookies remains the same, and income increases.
Midpoint method:
- \frac{11-9}{10} / \frac{45-35}{40} = \frac{2/10}{10/40} = \frac{4}{5} = 0.8
Milk is a normal good and a necessity.

The Cross-Price Elasticity of Demand

Definition: Measures how much the quantity demanded of one good responds to a change in the price of another good.
Formula: \% \Delta Q1 / \% \Delta P2 = \frac{\text{percentage change in quantity demanded of good 1}}{\text{percentage change in price of good 2}}
- Substitutes: > 0
- Complements: < 0

Example: Cross-Price Elasticity of Milk with Respect to Cookies

How does quantity demanded of milk change when the price of cookies changes?
Use March and April to calculate the cross-price elasticity!
Midpoint method: \frac{12-10}{11} / \frac{2-4}{3} = \frac{2/11}{-2/3} = -\frac{6}{22} \approx -0.2727
Milk and cookies are complements.