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.

The time period is the single most important determinant of supply elasticity. In the momentary period supply is almost perfectly inelastic because output is fixed. In the short run firms can vary some inputs (such as labour and raw materials) but not their plant, so supply is somewhat elastic. In the long run all inputs, including factory capacity, can change, so supply is most elastic. This is why a sudden rise in demand for a Tasmanian crop such as cherries pushes prices up sharply at first, then prices ease over later seasons as growers plant more trees and supply responds.

Why elasticity matters in practice

Elasticity is not just a calculation. Firms use price elasticity of demand to set prices that maximise revenue, choosing to raise price only where demand is inelastic. They use income elasticity to forecast which products will grow in a boom (luxuries) and which will hold up in a downturn (necessities and inferior goods). Governments use elasticity to design taxes: an excise on an inelastic good such as tobacco raises stable revenue, while the burden of any indirect tax falls mainly on whichever side of the market (buyer or seller) is more inelastic. Understanding all four elasticities therefore links directly to pricing, forecasting and policy.

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.