Price, Income & Cross Elasticities of Demand

This section explains price, income & cross elasticities of demand covering, how to use formulae to calculate price, income, and cross elasticities of demand, interpreting numerical values of elasticities, income elasticity of demand (YED), factors influencing elasticities of demand, the significance of elasticities of demand to firms and government and the relationship between price elasticity of demand and total revenue. 

Understanding Price, Income, and Cross Elasticities of Demand

Price Elasticity of Demand (PED)

Definition: Price elasticity of demand measures the responsiveness of the quantity demanded of a good to a change in its price.

Formula:

$$\text{Price Elasticity of Demand (PED)} = \frac{\% \text{ Change in Quantity Demanded}}{\% \text{ Change in Price}}$$

• If PED > 1, demand is elastic (consumers are very responsive to price changes).
• If PED = 1, demand is unitary elastic (percentage change in quantity demanded equals percentage change in price).
• If PED < 1, demand is inelastic (consumers are less responsive to price changes).

Income Elasticity of Demand (YED)

Definition: Income elasticity of demand measures the responsiveness of quantity demanded to a change in consumer income.

Formula:

$$\text{Income Elasticity of Demand (YED)} = \frac{\% \text{ Change in Quantity Demanded}}{\% \text{ Change in Income}}$$

• If YED > 1, the good is a luxury good (demand increases significantly as income rises).
• If YED = 0, the good is a necessity (demand does not change with income changes).
• If YED < 0, the good is an inferior good (demand decreases as income rises).

Cross Elasticity of Demand (XED)

• Definition: Cross elasticity of demand measures the responsiveness of the quantity demanded of one good to a change in the price of another good.
• Formula:

$$\text{Cross Elasticity of Demand (XED)} = \frac{\% \text{ Change in Quantity Demanded of Good A}}{\% \text{ Change in Price of Good B}}$$

• If XED > 0, the goods are substitutes (an increase in the price of Good B leads to an increase in demand for Good A).
• If XED < 0, the goods are complements (an increase in the price of Good B leads to a decrease in demand for Good A).
• If XED = 0, the goods are unrelated (changes in the price of one good have no effect on the demand for the other).

Using Formulae to Calculate Price, Income, and Cross Elasticities of Demand

To calculate elasticities, you need the percentage changes in quantity demanded and the relevant factor (price, income, or the price of another good).

Price Elasticity of Demand (PED):

$$\frac{\text{Change in Quantity Demanded}}{\text{Original Quantity Demanded}} \times \frac{\text{Original Price}}{\text{Change in Price}}$$

Income Elasticity of Demand (YED):

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

Cross Elasticity of Demand (XED):

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

Interpreting Numerical Values of Elasticities

Price Elasticity of Demand (PED)

Perfectly Inelastic (PED = 0): Quantity demanded does not change with price changes (e.g., life-saving drugs).

Relatively Inelastic (PED < 1): Consumers are not very responsive to price changes (e.g., basic foodstuffs).

Unitary Elastic (PED = 1): The percentage change in quantity demanded is equal to the percentage change in price.

Relatively Elastic (PED > 1): Consumers are highly responsive to price changes (e.g., luxury goods).

Perfectly Elastic (PED = ∞): Any price change leads to no demand (e.g., highly competitive markets).

Income Elasticity of Demand (YED)

• Inferior Goods (YED < 0): As income increases, demand decreases (e.g., generic brands).
• Normal Goods (0 < YED < 1): As income increases, demand increases, but not as much (e.g., food items).
• Luxury Goods (YED > 1): As income increases, demand increases significantly (e.g., high-end cars, holidays).
• Necessities (YED = 0): Changes in income have no effect on demand (e.g., basic utilities).

Cross Elasticity of Demand (XED)

• Substitute Goods (XED > 0): An increase in the price of one good leads to an increase in demand for its substitute (e.g., tea and coffee).
• Complementary Goods (XED < 0): An increase in the price of one good leads to a decrease in demand for its complement (e.g., printers and ink cartridges).
• Unrelated Goods (XED = 0): Changes in the price of one good have no effect on the demand for another good (e.g., books and shoes).

Factors Influencing Elasticities of Demand

Several factors influence how elastic the demand for a good or service is:

• Availability of Substitutes: The more substitutes available, the more elastic the demand (e.g., if the price of one brand of cola increases, consumers can switch to other brands).
• Necessity vs Luxury: Necessities tend to have inelastic demand (e.g., petrol), while luxury goods tend to have elastic demand.
• Proportion of Income: Goods that take up a large proportion of income tend to have more elastic demand (e.g., cars), while smaller items (e.g., salt) have inelastic demand.
• Time Period: Over time, demand may become more elastic as consumers find substitutes or adjust their behaviour (e.g., the demand for petrol may become more elastic in the long run as electric cars become more widespread).
• Addictiveness: Products that are addictive (e.g., cigarettes) often have inelastic demand because consumers continue buying despite price rises.

Significance of Elasticities of Demand to Firms and Government

The Imposition of Indirect Taxes and Subsidies

• Taxation: Governments may impose indirect taxes (e.g., VAT) on goods. If demand is inelastic (PED < 1), consumers will bear most of the tax burden, as they are less responsive to price changes. If demand is elastic (PED > 1), firms may have to absorb part of the tax to avoid losing customers.
• Subsidies: Subsidies can be used to encourage consumption of certain goods. If demand is elastic, a subsidy will lead to a larger increase in quantity demanded.

Changes in Real Income

• Income Elasticity of Demand: When real income rises, the demand for normal and luxury goods will increase, while demand for inferior goods may fall. Governments use this information to predict consumption patterns and plan fiscal policies.

Changes in the Prices of Substitutes and Complementary Goods

• Cross Elasticity of Demand: If the price of a substitute rises, firms can expect an increase in demand for their products. On the other hand, if the price of a complement rises, demand for the related good may fall. This information is vital for firms to understand competitive and complementary market dynamics.

The Relationship Between Price Elasticity of Demand and Total Revenue

Total Revenue (TR): Total revenue is the total income a firm receives from selling its goods, calculated as:

$$TR = \text{Price} \times \text{Quantity Sold}$$ 

Relationship between PED and TR:

• If demand is inelastic (PED < 1), a rise in price will lead to an increase in total revenue, because the percentage decrease in quantity demanded is smaller than the percentage increase in price.
• If demand is elastic (PED > 1), a rise in price will lead to a decrease in total revenue, as the percentage decrease in quantity demanded will be larger than the percentage increase in price.
• If demand is unitary elastic (PED = 1), a change in price will not affect total revenue, as the percentage change in quantity demanded is exactly offset by the percentage change in price.

Summary

Price, income, and cross elasticities of demand are crucial concepts that help to understand consumer behaviour and market dynamics. Firms and governments use elasticities to make decisions about pricing, taxation, subsidies, and market regulation. By understanding how demand responds to price, income, and the prices of related goods, economic agents can make more informed decisions that optimise revenue and social welfare.