Elasticity: Price, Income and Cross Elasticity of Demand

Knowing that people buy less when prices rise is useful; knowing how much less is far more useful. Elasticity measures how strongly one variable responds to a change in another. A business deciding whether to raise prices, a government estimating the effect of a tax and an analyst forecasting sales all need elasticity.

Price elasticity of demand

PED is normally negative (price and quantity move in opposite directions), so economists often discuss its absolute value:

Absolute value of PED	Description	Meaning
Greater than 1	Elastic	Quantity responds more than proportionally to price
Equal to 1	Unit elastic	Quantity responds proportionally
Less than 1	Inelastic	Quantity responds less than proportionally
0	Perfectly inelastic	Quantity does not respond at all

Elasticity and total revenue

Total revenue = price × quantity. The effect of a price change on revenue depends on elasticity:

Demand is	Raise price → revenue	Cut price → revenue
Elastic	Falls	Rises
Unit elastic	Unchanged	Unchanged
Inelastic	Rises	Falls

This is why sellers of essentials with few substitutes can raise prices without losing much revenue, while sellers in competitive markets cannot. Along a straight-line demand curve, elasticity changes: demand is elastic at high prices and inelastic at low prices, and revenue is highest where demand is unit elastic.

What makes demand elastic or inelastic

• Availability of substitutes — the more substitutes, the more elastic. Demand for one brand of tea is more elastic than demand for tea in general.
• Necessity versus luxury — necessities such as basic food and medicine tend to be inelastic.
• Share of income — goods that take a large share of the budget tend to be more elastic.
• Time — demand becomes more elastic over time as people find alternatives (for example, switching to fuel-efficient vehicles after fuel prices rise).
• Definition of the market — narrowly defined markets are more elastic.

Income elasticity of demand

• YED > 1: luxury or income-elastic goods (foreign travel, dining out).
• 0 < YED < 1: normal necessities (basic food, utilities).
• YED < 0: inferior goods, bought less as incomes rise.

If incomes rise by 10% and demand for restaurant meals rises by 15%, YED = 1.5. Businesses use income elasticity to forecast sales across the business cycle — see revenue forecasting.

Cross elasticity of demand

• XED > 0: substitutes. If the price of coffee rises 10% and tea demand rises 4%, XED = 0.4.
• XED < 0: complements. If petrol prices rise and demand for large cars falls.
• XED ≈ 0: unrelated goods.

Competition authorities use cross elasticity to judge whether products are in the same market.

Price elasticity of supply

Supply is more elastic when firms have spare capacity, inputs are easy to obtain, products can be stored, and when there is more time to adjust. Agricultural supply is often inelastic in the short run because crops take a season to grow — which is why weather shocks can cause large price swings, as shown in demand and supply.

Uses in business and policy

• Pricing: firms facing inelastic demand have more pricing power — one of the features of the market structures with few competitors.
• Tax incidence: a tax falls more heavily on whichever side of the market is less elastic. Taxes on goods with inelastic demand raise more revenue and change behaviour less.
• Forecasting: elasticities convert expected price or income changes into expected sales changes.
• Exchange rates: how much a currency depreciation improves the trade balance depends on the elasticity of export and import demand.

Limitations

Elasticity estimates come from past data and can change as markets, incomes and technology change. The midpoint formula measures an average response over a range, not at a single point. And other factors usually change at the same time as price, so isolating the true response requires careful statistical work.

Common mistakes

• Forgetting the negative sign or mixing absolute values with signed values.
• Using simple percentage changes for large price moves, which gives different answers for rises and falls.
• Assuming a product has one fixed elasticity at all prices.
• Confusing elasticity with the slope of the demand curve.