Define and calculate price, income and cross elasticity of demand and price elasticity of supply, and explain their determinants and uses.

What this dot point is asking

Elasticity is a measure of responsiveness. It compares the percentage change in one variable with the percentage change in another, which makes it independent of the units used.

Price elasticity of demand (PED)

PED measures how quantity demanded responds to a change in the good's own price.

$PED = \dfrac{\% \Delta Q_d}{\% \Delta P}$

Because demand slopes downward, PED is negative, but we usually read its size (absolute value).

• If $|PED| > 1$ demand is elastic (quantity is very responsive).
• If $|PED| < 1$ demand is inelastic (quantity is not very responsive).
• If $|PED| = 1$ demand is unit elastic.

Determinants of PED include the number and closeness of substitutes (more substitutes means more elastic), whether the good is a necessity or a luxury (necessities are inelastic), the proportion of income spent on it, and the time period (demand is more elastic over a longer time).

PED and total revenue

Total revenue is $TR = P \times Q$. The link to PED is central to the exam:

• If demand is elastic, raising price reduces total revenue (the quantity fall outweighs the price rise).
• If demand is inelastic, raising price increases total revenue.
• If demand is unit elastic, total revenue is unchanged when price changes.

This is why producers of goods with few substitutes can raise prices and earn more, while a price rise for an item with many close rivals can backfire.

Income elasticity of demand (YED)

YED measures how demand responds to a change in income.

$YED = \dfrac{\% \Delta Q_d}{\% \Delta Y}$

• Normal goods have positive YED (demand rises with income).
• Luxuries have YED greater than 1; necessities have YED between 0 and 1.
• Inferior goods have negative YED (demand falls as income rises).

When the ABS reports rising household incomes, businesses use YED to predict which products will grow fastest.

Cross elasticity of demand (XED)

XED measures how the demand for one good responds to a change in the price of another.

$XED = \dfrac{\% \Delta Q_{dA}}{\% \Delta P_B}$

• Substitutes have positive XED (a dearer rival raises demand for your good).
• Complements have negative XED (a dearer complement lowers demand for your good).

Price elasticity of supply (PES)

PES measures how quantity supplied responds to price.

$PES = \dfrac{\% \Delta Q_s}{\% \Delta P}$

Supply is more elastic when firms have spare capacity, can store stock, and have more time to adjust. Agricultural goods are often inelastic in the short run because crops take time to grow.

In data-response questions, always show the formula, substitute the percentages, and then interpret the number in words, including what it implies for revenue or policy.