Price, Income and Cross Elasticity of Demand

This section details the concepts of price elasticity of demand, income elasticity of demand, and cross elasticity of demand. These elasticities are crucial for understanding consumer behaviour and how changes in price, income, or the price of related goods affect the quantity demanded.

Price Elasticity of Demand (PED)

Price elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Formula:

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

Interpretation of PED values:

• Elastic Demand ($|PED| > 1$): Quantity demanded is highly responsive to price changes. A small change in price leads to a relatively large change in quantity demanded.
• Inelastic Demand ($|PED| < 1$): Quantity demanded is not very responsive to price changes. A change in price leads to a relatively small change in quantity demanded.
• Unit Elastic Demand ($|PED| = 1$): Quantity demanded changes proportionally to the change in price.
• Perfectly Elastic Demand ($PED = \infty$): Consumers will not buy any quantity if the price is above a certain level.
• Perfectly Inelastic Demand ($PED = 0$): Quantity demanded does not change regardless of the price.

Factors affecting PED:

• Availability of substitutes
• Necessity vs. luxury
• Proportion of income spent on the good
• Time horizon

Income Elasticity of Demand (YED)

Income elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in consumer income. It is calculated as the percentage change in quantity demanded divided by the percentage change in income.

Formula:

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

Interpretation of YED values:

• Normal Goods ($YED > 0$): As income increases, the quantity demanded of the good increases.
• Luxury Goods ($YED > 1$): As income increases, the quantity demanded of the good increases at a proportionally faster rate.
• Inferior Goods ($YED < 0$): As income increases, the quantity demanded of the good decreases.

Cross Elasticity of Demand (XED)

Cross elasticity of demand measures the responsiveness of the quantity demanded of one good to a change in the price of another good. It is calculated as the percentage change in quantity demanded of one good divided by the percentage change in the price of the other good.

Formula:

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

Interpretation of XED values:

• Substitutes ($XED > 0$): As the price of good B increases, the quantity demanded of good A increases.
• Complements ($XED < 0$): As the price of good B increases, the quantity demanded of good A decreases.

Elasticity	Formula	Interpretation
Price Elasticity of Demand (PED)	$PED = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Price}}$	Responsiveness of quantity demanded to a price change.
Income Elasticity of Demand (YED)	$YED = \frac{\text{Percentage Change in Quantity Demanded}}{\text{Percentage Change in Income}}$	Responsiveness of quantity demanded to a change in income.
Cross Elasticity of Demand (XED)	$XED = \frac{\text{Percentage Change in Quantity Demanded of Good A}}{\text{Percentage Change in Price of Good B}}$	Responsiveness of quantity demanded of one good to a price change in another good.