Elasticity

Introduction to Elasticity

Elasticity is a fundamental concept in microeconomics that measures how responsive one variable is to changes in another. In the context of markets, elasticity helps us understand how quantity demanded or supplied reacts to changes in price, income, or the price of related goods.

• Price Elasticity of Demand: Measures responsiveness of quantity demanded to price changes.

• Income Elasticity of Demand: Measures responsiveness of quantity demanded to changes in consumer income.

• Cross Elasticity of Demand: Measures responsiveness of quantity demanded to changes in the price of substitutes or complements.

• Elasticity of Supply: Measures responsiveness of quantity supplied to price changes.

Price Elasticity of Demand

Definition and Calculation

The price elasticity of demand is a units-free measure of the responsiveness of the quantity demanded of a good to a change in its price, holding all other factors constant.

• Formula:

• To calculate, use the average price and average quantity between two points.

• Express changes as percentages of the averages:

Example: If price falls from $20.50 to $19.50 and quantity demanded rises from 9 to 11 pizzas per hour:

• Average price = $20

• Average quantity = 10 pizzas

• Elasticity =

Properties of Elasticity

• Units-Free: Elasticity is independent of the units used for price or quantity.

• Sign: The formula yields a negative value (since price and quantity move in opposite directions), but the magnitude (absolute value) is used for interpretation.

Types of Price Elasticity of Demand

• Perfectly Inelastic Demand: Elasticity = 0; quantity demanded does not change as price changes. Demand curve is vertical.

• Unit Elastic Demand: Elasticity = 1; percentage change in quantity equals percentage change in price. Demand curve has a declining slope.

• Inelastic Demand: Elasticity < 1; quantity demanded changes less than price.

• Elastic Demand: Elasticity > 1; quantity demanded changes more than price.

• Perfectly Elastic Demand: Elasticity = ∞; quantity demanded changes infinitely with a tiny change in price. Demand curve is horizontal.

Elasticity Along a Linear Demand Curve

• Elasticity varies along a straight-line demand curve.

• At the midpoint: demand is unit elastic.

• Above the midpoint: demand is elastic.

• Below the midpoint: demand is inelastic.

Example calculations along a demand curve:

• Price falls from $25 to $15, quantity from 0 to 20: Elasticity = 4 (elastic)

• Price falls from $10 to $0, quantity from 30 to 50: Elasticity = 0.25 (inelastic)

• Price falls from $15 to $10, quantity from 20 to 30: Elasticity = 1 (unit elastic)

Factors Influencing Price Elasticity of Demand

• Closeness of Substitutes: More substitutes make demand more elastic. Necessities (few substitutes) are inelastic; luxuries (many substitutes) are elastic.

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

• Time Elapsed Since Price Change: Demand becomes more elastic over time as consumers adjust.

Total Revenue and Elasticity

Relationship Between Total Revenue and Elasticity

Total revenue is the product of price and quantity sold. Changes in price affect total revenue depending on the elasticity of demand.

• If demand is elastic, a price cut increases total revenue.

• If demand is inelastic, a price cut decreases total revenue.

• If demand is unit elastic, a price cut leaves total revenue unchanged.

Total Revenue Test

• Observe changes in total revenue after a price change to estimate elasticity.

• If total revenue rises after a price cut, demand is elastic.

• If total revenue falls after a price cut, demand is inelastic.

• If total revenue remains unchanged, demand is unit elastic.

Income Elasticity of Demand

Definition and Calculation

The income elasticity of demand measures how the quantity demanded of a good responds to changes in consumer income, holding other factors constant.

• If elasticity > 1: demand is income elastic; the good is a normal good.

• If 0 < elasticity < 1: demand is income inelastic; the good is a normal good.

• If elasticity < 0: the good is an inferior good.

Cross Elasticity of Demand

Definition and Calculation

The cross elasticity of demand measures the responsiveness of demand for a good to changes in the price of a substitute or complement.

• For substitutes: cross elasticity is positive.

• For complements: cross elasticity is negative.

Example: If the price of burgers (a substitute for pizza) rises, the quantity of pizza demanded increases. If the price of soft drinks (a complement to pizza) rises, the quantity of pizza demanded decreases.

Elasticity of Supply

Definition and Calculation

The elasticity of supply measures the responsiveness of the quantity supplied to a change in the price of a good, holding other factors constant.

• Perfectly Inelastic Supply: Elasticity = 0; supply curve is vertical.

• Unit Elastic Supply: Elasticity = 1; supply curve is linear and passes through the origin.

• Perfectly Elastic Supply: Elasticity = ∞; supply curve is horizontal.

Factors Influencing Elasticity of Supply

• Resource Substitution Possibilities: Easier substitution among resources increases elasticity.

• Time Frame for Supply Decision:

  • Momentary supply: Perfectly inelastic; quantity supplied is fixed immediately after a price change.

  • Short-run supply: Somewhat elastic.

  • Long-run supply: Most elastic; producers have time to fully adjust.

Glossary of Elasticity Measures

Additional info: The notes above expand on the brief points in the slides, providing definitions, formulas, and examples for each type of elasticity, as well as the factors influencing them. The table summarizes the main elasticity measures for quick reference.