Elasticity: The Responsiveness of Demand and Supply

Elasticity: The Responsiveness of Demand and Supply

Introduction

Elasticity is a fundamental concept in microeconomics that measures how much one economic variable responds to changes in another. This chapter explores the different types of elasticity, their determinants, and their implications for markets and policy.

The Price Elasticity of Demand and Its Measurement

Definition and Calculation

The price elasticity of demand quantifies how much the quantity demanded of a good responds to a change in its price. It is calculated as:

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

• Elasticity is typically negative, as price and quantity move in opposite directions.

• To avoid ambiguity in percentage changes, economists use the midpoint formula:

$\text{Price elasticity of demand} = \frac{(Q_2 - Q_1) / ((Q_1 + Q_2)/2)}{(P_2 - P_1) / ((P_1 + P_2)/2)}$

Elasticity Terminology

• Elastic demand: Absolute value of elasticity > 1. Quantity demanded changes more than price.

• Inelastic demand: Absolute value of elasticity < 1. Quantity demanded changes less than price.

• Unit-elastic demand: Absolute value of elasticity = 1. Quantity and price change proportionally.

• Perfectly elastic: Elasticity equals infinity. Any price change causes quantity demanded to fall to zero.

• Perfectly inelastic: Elasticity equals zero. Quantity demanded does not change with price.

Solved Example: Calculating Price Elasticity

• Suppose the price of Coca-Cola drops from $1.50 to $1.30, and sales rise from 2,000 to 2,500 gallons.

• Average quantity: (2,000 + 2,500)/2 = 2,250

• Average price: ($1.50 + $1.30)/2 = $1.40

• Percentage change in quantity: $(2,500 - 2,000)/2,250 \times 100 = 22.2\%$

• Percentage change in price: $(1.30 - 1.50)/1.40 \times 100 = -14.3\%$

• Elasticity: $\frac{22.2\%}{-14.3\%} = -1.6$ (elastic)

Observations About Elasticity

• Flatter demand curves have higher elasticity at the same point.

• Vertical demand curve: perfectly inelastic (elasticity = 0).

• Horizontal demand curve: perfectly elastic (elasticity = infinity).

Summary Table: Price Elasticity of Demand

If demand is...	Absolute value of price elasticity	Effect
Elastic	Greater than 1	Quantity changes a lot
Inelastic	Less than 1	Quantity changes little
Unit elastic	Equal to 1	Quantity changes proportionally
Perfectly elastic	Infinity	Any price change causes quantity to fall to zero
Perfectly inelastic	Zero	Quantity does not change

The Determinants of the Price Elasticity of Demand

Key Determinants

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

• Passage of time: Elasticity is higher in the long run as consumers adjust.

• Luxury vs. necessity: Luxuries have higher elasticity than necessities.

• Definition of the market: Narrowly defined markets have more elastic demand.

• Share of budget: Goods that take up a larger share of the budget have more elastic demand.

The Relationship between Price Elasticity of Demand and Total Revenue

Total Revenue and Elasticity

Total revenue is the product of price and quantity sold. The effect of price changes on total revenue depends on the elasticity of demand:

• If demand is inelastic, a price decrease reduces total revenue.

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

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

Summary Table: Price Elasticity and Revenue

If demand is...	Price change	Effect on revenue
Elastic	Increase	Reduces revenue
Elastic	Decrease	Increases revenue
Inelastic	Increase	Increases revenue
Inelastic	Decrease	Reduces revenue
Unit elastic	Increase or decrease	No effect on revenue

Elasticity Along a Linear Demand Curve

Elasticity is not constant along a linear demand curve. At high prices and low quantities, demand is elastic; at low prices and high quantities, demand is inelastic.

Other Demand Elasticities

Cross-Price Elasticity of Demand

The cross-price elasticity of demand measures how the quantity demanded of one good responds to a change in the price of another good:

$\text{Cross-price elasticity} = \frac{\text{Percentage change in quantity demanded of Good A}}{\text{Percentage change in price of Good B}}$

• Positive for substitutes

• Negative for complements

• Zero for unrelated goods

Income Elasticity of Demand

The income elasticity of demand measures how the quantity demanded responds to changes in income:

$\text{Income elasticity} = \frac{\text{Percentage change in quantity demanded}}{\text{Percentage change in income}}$

• Positive but less than 1: normal and necessity

• Positive and greater than 1: normal and luxury

• Negative: inferior good

Summary Table: Cross-Price and Income Elasticity

Type	Elasticity Value	Example
Substitutes	Positive	Two brands of smartphones
Complements	Negative	iPhones and apps
Unrelated	Zero	iPhones and peanut butter
Normal, necessity	Positive < 1	Bread
Normal, luxury	Positive > 1	Caviar
Inferior	Negative	High-fat meat

Using Elasticity to Analyze the Disappearing Family Farm

Elasticity and Agricultural Markets

Productivity gains in farming have led to a large increase in supply, but because demand for agricultural products is inelastic and has low income elasticity, prices have fallen sharply. This has made small-scale farming less profitable, resulting in fewer family farms.

The Price Elasticity of Supply and Its Measurement

Definition and Calculation

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

$\text{Price elasticity of supply} = \frac{\text{Percentage change in quantity supplied}}{\text{Percentage change in price}}$

• Calculated using the midpoint formula, similar to demand elasticity.

Determinants of Price Elasticity of Supply

• Ability to alter production: More flexibility means higher elasticity.

• Time period: Supply is more elastic in the long run.

Polar Cases

• Perfectly inelastic supply: Vertical supply curve; elasticity = 0.

• Perfectly elastic supply: Horizontal supply curve; elasticity = infinity.

Summary Table: Price Elasticity of Supply

If supply is...	Value of price elasticity	Effect
Elastic	Greater than 1	Quantity supplied changes a lot
Inelastic	Less than 1	Quantity supplied changes little
Unit elastic	Equal to 1	Quantity supplied changes proportionally
Perfectly elastic	Infinity	Any price change causes infinite change in quantity supplied
Perfectly inelastic	Zero	Quantity supplied does not change

Using Price Elasticity of Supply to Predict Changes in Price

Effect of Demand Changes

When demand increases, the effect on equilibrium price depends on the elasticity of supply:

• If supply is inelastic, price rises significantly.

• If supply is elastic, price rises only slightly.

Summary of Elasticities

Key Formulas and Classifications

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

• Cross-Price Elasticity: $\frac{\text{Percentage change in quantity demanded of one good}}{\text{Percentage change in price of another good}}$

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

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

Elasticity Type	Value	Classification
Price Elasticity of Demand	>1	Elastic
Price Elasticity of Demand	<1	Inelastic
Price Elasticity of Demand	=1	Unit elastic
Cross-Price Elasticity	Positive	Substitutes
Cross-Price Elasticity	Negative	Complements
Cross-Price Elasticity	Zero	Unrelated
Income Elasticity	Positive < 1	Normal, necessity
Income Elasticity	Positive > 1	Normal, luxury
Income Elasticity	Negative	Inferior
Price Elasticity of Supply	>1	Elastic
Price Elasticity of Supply	<1	Inelastic
Price Elasticity of Supply	=1	Unit elastic