Elasticity in Microeconomics: Price, Income, and Cross Elasticities of Demand and Supply

Elasticity in Microeconomics

Introduction to Elasticity

Elasticity measures how much one variable responds to changes in another variable. In microeconomics, elasticity is crucial for understanding how price, income, and other factors affect the quantity demanded and supplied of goods and services.

• Elasticity of demand shows how quantity demanded responds to price changes.

• Elasticity of supply shows how quantity supplied responds to price changes.

• Other elasticities include income elasticity and cross elasticity.

Price Elasticity of Demand

Definition and Interpretation

The price elasticity of demand quantifies the responsiveness of quantity demanded to changes in price. It is a key concept for predicting consumer behavior and market outcomes.

• Formula: $\text{Price Elasticity of Demand} = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in price}}$

• If elasticity > 1: Elastic demand (quantity demanded changes by a larger percentage than price).

• If elasticity < 1: Inelastic demand (quantity demanded changes by a smaller percentage than price).

• If elasticity = 1: Unit elastic demand (percentage changes are equal).

Calculating Price Elasticity of Demand

Elasticity is calculated using average values to avoid ambiguity when moving between two points on a demand curve.

• Midpoint formula: $\text{Elasticity} = \frac{(Q_2 - Q_1)}{(Q_2 + Q_1)/2} \div \frac{(P_2 - P_1)}{(P_2 + P_1)/2}$

• Use absolute values for interpretation.

• Elasticity is usually negative due to the law of demand, but the magnitude is used for classification.

Elasticity Along a Linear Demand Curve

Elasticity varies along a straight-line demand curve. It is higher (more elastic) at higher prices and lower quantities, and lower (more inelastic) at lower prices and higher quantities.

• At the midpoint, demand is unit elastic.

• Above the midpoint, demand is elastic.

• Below the midpoint, demand is inelastic.

Perfectly Elastic and Inelastic Demand

• Perfectly elastic demand: Quantity demanded changes infinitely with any price change (horizontal demand curve).

• Perfectly inelastic demand: Quantity demanded does not change with price (vertical demand curve).

Total Revenue and Elasticity

Relationship Between Elasticity and Total Revenue

Total revenue is the product of price and quantity sold. Elasticity determines how changes in price affect total revenue.

• If demand is elastic, a price increase decreases total revenue.

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

• If demand is unit elastic, total revenue is maximized.

Determinants of Price Elasticity of Demand

Key Factors

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

• Proportion of income spent: Goods that take a larger share of income have more elastic demand.

• Necessities vs. luxuries: Necessities tend to have inelastic demand; luxuries are more elastic.

• Time horizon: Demand is more elastic over longer periods.

Cross Elasticity of Demand

Definition and Application

Cross elasticity of demand measures how the quantity demanded of one good responds to changes in the price of another good.

• Formula: $\text{Cross Elasticity of Demand} = \frac{\text{Percentage change in quantity demanded of Good A}}{\text{Percentage change in price of Good B}}$

• If cross elasticity > 0: Goods are substitutes.

• If cross elasticity < 0: Goods are complements.

Income Elasticity of Demand

Definition and Application

Income elasticity of demand measures how quantity demanded changes as consumer income changes.

• Formula: $\text{Income Elasticity of Demand} = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in income}}$

• If income elasticity > 1: Normal good and income elastic.

• If income elasticity < 1 but > 0: Normal good and income inelastic.

• If income elasticity < 0: Inferior good.

Elasticity of Supply

Definition and Calculation

The elasticity of supply measures the responsiveness of quantity supplied to changes in price.

• Formula: $\text{Elasticity of Supply} = \frac{\text{Percentage change in quantity supplied}}{\text{Percentage change in price}}$

• Elastic supply: elasticity > 1

• Inelastic supply: elasticity < 1

• Unit elastic supply: elasticity = 1

Determinants of Elasticity of Supply

• Resource substitution possibilities: Supply is more elastic if resources can be easily shifted between uses.

• Time frame: Supply is more elastic in the long run than in the short run.

Glossary of Elasticities

Elasticity Type	Magnitude	Interpretation
Price Elasticity of Demand	Elastic (>1), Inelastic (<1), Unit Elastic (=1)	Elastic: Quantity demanded changes more than price. Inelastic: Quantity demanded changes less than price. Unit elastic: Changes are proportional.
Cross Elasticity of Demand	Positive (substitutes), Negative (complements)	Positive: Goods are substitutes. Negative: Goods are complements.
Income Elasticity of Demand	Positive (>0, normal goods), Negative (<0, inferior goods)	Positive: Normal goods. Negative: Inferior goods.
Elasticity of Supply	Elastic (>1), Inelastic (<1), Unit Elastic (=1)	Elastic: Quantity supplied changes more than price. Inelastic: Quantity supplied changes less than price. Unit elastic: Changes are proportional.

Examples and Applications

• Price elasticity of demand for food: If the price of food rises, the quantity demanded falls, but the degree depends on the elasticity.

• Cross elasticity: If the price of tea rises, demand for coffee (a substitute) increases.

• Income elasticity: As income rises, demand for luxury goods increases more than for necessities.

Summary Table: Real-World Elasticities

Good or Service	Price Elasticity of Demand
Restaurant meals	2.27
Automobiles	1.55
Gasoline	0.20
Electricity	0.13
Clothing	0.47
Food	0.12