Elasticity and Its Applications – Microeconomics Study Notes

Elasticity and Its Applications

Introduction to Elasticity

Elasticity is a fundamental concept in microeconomics that measures how much buyers and sellers respond to changes in market conditions. It is crucial for understanding how various factors such as price, income, and the prices of related goods affect the quantity demanded and supplied in a market.

• Elasticity: The responsiveness of quantity demanded (Qd) or quantity supplied (Qs) to a change in one of its determinants.

• Applications: Elasticity helps analyze the effects of pricing decisions, taxation, and market shocks on revenue and expenditure.

Main Questions Addressed in This Chapter

• What is elasticity?

• What kinds of issues can elasticity help us understand?

• What is the price elasticity of demand?

• How is it related to the demand curve?

• How is it related to revenue and expenditure?

• What are the income and cross-price elasticities of demand?

• What is the price elasticity of supply?

• How is it related to the supply curve?

Price Elasticity of Demand

Definition and Formula

The price elasticity of demand measures how much the quantity demanded of a good responds to a change in its price. It is a key indicator of buyers’ price sensitivity.

• Formula:

$\text{Price Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}$

• Along a demand curve, price and quantity move in opposite directions, making price elasticity negative. However, economists often report the absolute value.

Calculating Percentage Changes

To compute elasticity, percentage changes are calculated using the midpoint method for accuracy.

• Midpoint Method Formula:

$\text{Percentage Change} = \frac{\text{New Value} - \text{Initial Value}}{\text{Midpoint}} \times 100$

• Example: If price increases from $2,000 to $2,500 and quantity falls from 12 to 8, the percentage change in price and quantity can be calculated using the midpoint method.

Determinants of Price Elasticity of Demand

Several factors influence the price elasticity of demand:

• Availability of close substitutes: More substitutes make demand more elastic.

• Narrowly vs. broadly defined goods: Narrowly defined goods (e.g., Mountain Dew) have more elastic demand than broadly defined goods (e.g., soda).

• Necessities vs. luxuries: Luxuries have more elastic demand than necessities (e.g., Rolex watches vs. insulin).

• Time horizon: Demand is more elastic in the long run than in the short run.

Types of Demand Elasticity

Demand elasticity can be classified as follows:

• Elastic: Elasticity > 1 (quantity demanded changes more than price)

• Inelastic: Elasticity < 1 (quantity demanded changes less than price)

• Unit elastic: Elasticity = 1 (quantity demanded changes exactly as price)

• Perfectly inelastic: Elasticity = 0 (quantity demanded does not change with price; vertical demand curve)

• Perfectly elastic: Elasticity = ∞ (quantity demanded changes infinitely with any price change; horizontal demand curve)

Examples from the Real World

Good	Elasticity	Interpretation
Healthcare	0.1	Very inelastic
Restaurant Meals	2.3	Very elastic
Cheerios	3.7	Highly elastic
Mountain Dew	4.4	Extremely elastic
Gasoline (short run)	0.2	Inelastic
Gasoline (long run)	0.7	More elastic
Insulin	~0	Perfectly inelastic
Rolex Watches	>1	Elastic

Elasticity and Total Revenue

Relationship Between Elasticity and Revenue

Total revenue (TR) is the product of price and quantity sold:

$\text{Total Revenue} = P \times Q$

• If demand is elastic, a price increase causes total revenue to decrease.

• If demand is inelastic, a price increase causes total revenue to increase.

Example: Raising the price of insulin (inelastic demand) increases total revenue, while raising the price of luxury cruises (elastic demand) decreases total revenue.

Other Types of Elasticity

Income Elasticity of Demand

Measures how much the quantity demanded of a good responds to changes in consumer income.

$\text{Income Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Income}}$

• Normal goods: Income elasticity > 0

• Inferior goods: Income elasticity < 0

Cross-Price Elasticity of Demand

Measures how much the quantity demanded of one good responds to a change in the price of another good.

$\text{Cross-Price Elasticity of Demand} = \frac{\text{Percentage Change in Quantity Demanded of Good 1}}{\text{Percentage Change in Price of Good 2}}$

• Substitutes: Cross-price elasticity > 0

• Complements: Cross-price elasticity < 0

Price Elasticity of Supply

Definition and Formula

The price elasticity of supply measures how much the quantity supplied of a good responds to a change in its price.

$\text{Price Elasticity of Supply} = \frac{\text{Percentage Change in Quantity Supplied}}{\text{Percentage Change in Price}}$

• Elastic supply: quantity supplied responds substantially to price changes.

• Inelastic supply: quantity supplied responds only slightly to price changes.

Types of Supply Elasticity

• Elastic: Elasticity > 1

• Inelastic: Elasticity < 1

• Unit elastic: Elasticity = 1

• Perfectly inelastic: Elasticity = 0 (vertical supply curve)

• Perfectly elastic: Elasticity = ∞ (horizontal supply curve)

Determinants of Supply Elasticity

• Flexibility of sellers to change quantity supplied

• Time horizon: supply is more elastic in the long run

Applications of Elasticity

Policy Implications

• Drug interdiction: Reducing supply of illegal drugs increases price and may increase drug-related crime if demand is inelastic.

• Drug education: Reducing demand for illegal drugs lowers both price and quantity, reducing drug-related crime.

• Taxation: The effect of taxes on quantity and revenue depends on elasticity.

Elasticity in Different Markets

• Markets with inelastic supply (e.g., parking spots) experience larger price changes when demand increases.

• Markets with elastic supply (e.g., wheat) experience larger quantity changes when demand increases.

Summary Table: Types of Elasticity

Type	Formula	Interpretation
Price Elasticity of Demand	$\frac{\% \Delta Q^d}{\% \Delta P}$	Responsiveness of quantity demanded to price
Income Elasticity of Demand	$\frac{\% \Delta Q^d}{\% \Delta \text{Income}}$	Responsiveness of quantity demanded to income
Cross-Price Elasticity of Demand	$\frac{\% \Delta Q^d_1}{\% \Delta P_2}$	Responsiveness of quantity demanded of one good to price of another
Price Elasticity of Supply	$\frac{\% \Delta Q^s}{\% \Delta P}$	Responsiveness of quantity supplied to price

Key Takeaways

• Elasticity quantifies how much quantity demanded or supplied responds to changes in price, income, or other goods’ prices.

• Elasticity affects total revenue, market outcomes, and policy effectiveness.

• Understanding elasticity is essential for making informed business and policy decisions in microeconomics.