Elasticity: The Responsiveness of Demand and Supply (Microeconomics CH6 Study Notes)

Elasticity: The Responsiveness of Demand and Supply

Introduction

Elasticity is a central concept in microeconomics, measuring how much one economic variable responds to changes in another. In this chapter, we focus on the responsiveness of demand and supply to changes in price and other factors, and how these responses affect market outcomes such as total revenue.

Price Elasticity of Demand and Its Measurement

Definition and Formula

The price elasticity of demand quantifies how much the quantity demanded of a good changes in response to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

• Formula:

$\varepsilon_D = \frac{\%\Delta Q}{\%\Delta P}$

• Key Point: The price elasticity of demand is usually negative, since price and quantity demanded move in opposite directions.

• Interpretation: A larger (in absolute value) negative elasticity means greater responsiveness.

Terminology

• Elastic Demand: $|\varepsilon_D| > 1$ Quantity demanded changes by a greater percentage than price. Example: A 10% increase in price leads to more than a 10% decrease in quantity demanded.

• Inelastic Demand: $|\varepsilon_D| < 1$ Quantity demanded changes by a smaller percentage than price. Example: A 10% increase in price leads to less than a 10% decrease in quantity demanded.

• Unit Elastic Demand: $|\varepsilon_D| = 1$ Quantity demanded changes by exactly the same percentage as price.

Calculating Price Elasticity of Demand

To calculate elasticity, use the midpoint formula for percentage changes:

• Midpoint Formula:

$\%\Delta Q = \frac{Q_2 - Q_1}{(Q_2 + Q_1)/2} \times 100$ $\%\Delta P = \frac{P_2 - P_1}{(P_2 + P_1)/2} \times 100$

Then, plug these values into the elasticity formula above.

• Example: If the price of Coca-Cola drops from $1.50 to $1.30 and sales rise from 2,000 to 2,500 gallons, calculate:

$\%\Delta Q = \frac{2500 - 2000}{(2500 + 2000)/2} \times 100 = 22.22\%$ $\%\Delta P = \frac{1.30 - 1.50}{(1.30 + 1.50)/2} \times 100 = -14.29\%$ $\varepsilon_D = \frac{22.22}{-14.29} = -1.56$

This demand is elastic because the absolute value is greater than 1.

Special Cases of Elasticity

• Perfectly Inelastic Demand: $\varepsilon_D = 0$ Quantity demanded does not change as price changes. Demand curve is vertical.

• Perfectly Elastic Demand: $\varepsilon_D = \infty$ Quantity demanded is infinitely responsive to price. Demand curve is horizontal.

• Unit Elastic Demand: $\varepsilon_D = 1$ Proportional change; demand curve has a specific slope.

Determinants of Price Elasticity of Demand

Factors Affecting Elasticity

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

• Passage of Time: Demand is more elastic in the long run as consumers adjust.

• Luxury vs. Necessity: Luxuries have more elastic demand; necessities are less elastic.

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

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

Example: Gasoline has few substitutes and is a necessity, so its demand is inelastic. Brand-name jeans have many substitutes, so demand is elastic.

Relationship Between Price Elasticity of Demand and Total Revenue

Total Revenue and Elasticity

Total Revenue (TR) is the total amount received by sellers, calculated as price times quantity sold:

$TR = P \times Q$

• If demand is elastic: Lowering price increases total revenue.

• If demand is inelastic: Lowering price decreases total revenue.

• If demand is unit elastic: Total revenue remains unchanged when price changes.

Elasticity Type	Effect of Price Decrease on TR	Effect of Price Increase on TR
Elastic	TR increases	TR decreases
Inelastic	TR decreases	TR increases
Unit Elastic	No change	No change

Example: If a price cut leads to a proportionally larger increase in quantity demanded, total revenue rises (elastic demand).

Other Demand Elasticities

Cross-Price Elasticity of Demand

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

$\text{Cross-Price Elasticity} = \frac{\%\Delta Q_A}{\%\Delta P_B}$

• Substitutes: Positive cross-price elasticity (e.g., Coke and Pepsi).

• Complements: Negative cross-price elasticity (e.g., printers and ink).

• Unrelated goods: Zero cross-price elasticity.

Relationship	Sign of Elasticity	Example
Substitutes	Positive	iPhones and Android phones
Complements	Negative	Smartphones and apps
Unrelated	Zero	Smartphones and peanut butter

Income Elasticity of Demand

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

$\text{Income Elasticity} = \frac{\%\Delta Q}{\%\Delta I}$

• Normal Goods: Positive income elasticity. Quantity demanded increases as income rises.

• Inferior Goods: Negative income elasticity. Quantity demanded decreases as income rises.

• Necessities: Income elasticity between 0 and 1.

• Luxuries: Income elasticity greater than 1.

Type of Good	Income Elasticity	Example
Normal, Necessity	Positive, < 1	Bread
Normal, Luxury	Positive, > 1	Caviar
Inferior	Negative	Low-quality meat

Price Elasticity of Supply and Its Measurement

Definition and Formula

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

$\varepsilon_S = \frac{\%\Delta Q_S}{\%\Delta P}$

• Calculation: Use the midpoint formula for percentage changes, similar to demand elasticity.

Determinants of Price Elasticity of Supply

• Ability to Change Output: If firms can quickly adjust production, supply is more elastic.

• Time Period: Supply is more elastic in the long run as firms can adjust resources.

Example: Agricultural products have more elastic supply in the long run; parking spaces are perfectly inelastic in the short run.

Polar Cases of Supply Elasticity

• Perfectly Inelastic Supply: $\varepsilon_S = 0$ Quantity supplied does not change as price changes. Supply curve is vertical.

• Perfectly Elastic Supply: $\varepsilon_S = \infty$ Quantity supplied is infinitely responsive to price. Supply curve is horizontal.

Using Price Elasticity of Supply to Predict Price Changes

• If supply is inelastic, an increase in demand leads to a large increase in price.

• If supply is elastic, an increase in demand leads to a smaller increase in price.

Summary Table: Elasticities

Elasticity Type	Formula	Interpretation
Price Elasticity of Demand	$\frac{\%\Delta Q}{\%\Delta P}$	Responsiveness of quantity demanded to price changes
Cross-Price Elasticity	$\frac{\%\Delta Q_A}{\%\Delta P_B}$	Responsiveness of demand for one good to price changes in another
Income Elasticity	$\frac{\%\Delta Q}{\%\Delta I}$	Responsiveness of demand to income changes
Price Elasticity of Supply	$\frac{\%\Delta Q_S}{\%\Delta P}$	Responsiveness of quantity supplied to price changes

Practice Questions

• What does price elasticity of demand measure?

• How does total revenue change when demand is elastic vs. inelastic?

• What factors determine the price elasticity of supply?

• How do cross-price and income elasticities classify goods?

Additional info: Some context and examples were inferred and expanded for clarity and completeness, including formulas, tables, and academic explanations.