Price Elasticity of Demand (PED)

Price elasticity of demand (PED) measures the responsiveness of quantity demanded to a change in price. It's a crucial concept in economics for understanding consumer behavior and how changes in price affect market outcomes.

Definition

PED is calculated as the percentage change in quantity demanded divided by the percentage change in price.

$$PED = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}$$

Formula

The formula for PED is:

$$PED = \frac{\Delta Q / Q}{\Delta P / P}$$

Where:

• $\Delta Q$ = Change in quantity demanded
• $Q$ = Initial quantity demanded
• $\Delta P$ = Change in price
• $P$ = Initial price

Types of Demand Elasticity

1. Elastic Demand: PED > 1. A significant change in quantity demanded occurs with a small change in price.
2. Inelastic Demand: PED < 1. A small change in quantity demanded occurs with a large change in price.
3. Unit Elastic Demand: PED = 1. The percentage change in quantity demanded is equal to the percentage change in price.

Factors Affecting PED

• Availability of Substitutes: More substitutes lead to more elastic demand.
• Necessity vs. Luxury: Necessities tend to have inelastic demand. Luxuries tend to have elastic demand.
• Proportion of Income Spent: Goods that represent a large proportion of income tend to have more elastic demand.
• Time Horizon: Demand tends to become more elastic over longer time horizons.

Table Summary of PED Types

Type of Elasticity	PED Value	Consumer Response
Elastic	> 1	Quantity demanded changes significantly with price changes.
Inelastic	< 1	Quantity demanded changes little with price changes.
Unit Elastic	= 1	Percentage change in quantity demanded equals percentage change in price.

Income Elasticity of Demand (YED)

Income elasticity of demand (YED) measures the responsiveness of quantity demanded to a change in consumer income.

Definition

YED is calculated as the percentage change in quantity demanded divided by the percentage change in income.

$$YED = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Income}}$$

Formula

The formula for YED is:

$$YED = \frac{\Delta Q / Q}{\Delta Y / Y}$$

Where:

• $\Delta Q$ = Change in quantity demanded
• $Q$ = Initial quantity demanded
• $\Delta Y$ = Change in income
• $Y$ = Initial income

Types of Demand Elasticity

1. Normal Goods: YED > 0. As income increases, quantity demanded increases.
2. Inferior Goods: YED < 0. As income increases, quantity demanded decreases.

Examples

• Normal Good: A luxury car. As income rises, demand for the car increases.
• Inferior Good: Generic tea. As income rises, people switch to branded tea, decreasing demand for generic tea.

Cross Elasticity of Demand (XED)

Cross elasticity of demand (XED) measures the responsiveness of quantity demanded of one good to a change in the price of another good.

Definition

XED is calculated as the percentage change in quantity demanded of one good divided by the percentage change in the price of another good.

$$XED = \frac{\text{Percentage Change in Quantity Demanded of Good A}}{\text{Percentage Change in Price of Good B}}$$

Formula

The formula for XED is:

$$XED = \frac{\Delta Q_A / Q_A}{\Delta P_B / P_B}$$

Where:

• $\Delta Q_A$ = Change in quantity demanded of Good A
• $Q_A$ = Initial quantity demanded of Good A
• $\Delta P_B$ = Change in price of Good B
• $P_B$ = Initial price of Good B

Types of Demand Elasticity

1. Substitutes: XED > 0. When the price of Good B increases, the demand for Good A increases.
2. Complements: XED < 0. When the price of Good B increases, the demand for Good A decreases.

Examples

• Substitutes: Coffee and tea. If the price of coffee increases, demand for tea will increase.
• Complements: Cars and petrol. If the price of petrol increases, demand for cars will decrease.