Cross elasticity of demand

Indian Economy glossary

Also called: Cross-price elasticity of demand, XED · Topic: Consumer Behaviour, Demand and Elasticity · NCERT: Beyond NCERT

Meaning

Cross elasticity of demand (eXY) measures how much the quantity demanded of one good (X) changes when the price of another good (Y) changes. The buyer's income and the price of X itself are held constant.

  • Formula: eXY = % change in quantity demanded of X ÷ % change in price of Y
  • The sign of eXY tells you how the two goods are related. Its size tells you how strong that link is.

It matters because firms, tax authorities and regulators need to know the effect of one price change on the demand for other goods, not only on the good whose price changed.

Explanation

How it works: read the sign

Sign of eXY Relationship Logic Example
Positive Substitutes (one can be used in place of the other) Y becomes costlier → people switch to X → demand for X rises Coffee price up → tea demand up
Negative Complements (goods used together) Y becomes costlier → people use less of Y and so less of X too Sugar price up → tea demand down
About zero Unrelated goods A price change in one has no effect on the other Salt and shoes
  • Why the sign works this way:
  • For substitutes, the price of Y and the demand for X move in the same direction, so the ratio is positive.
  • For complements, they move in opposite directions, so the ratio is negative.

Worked examples

  • Substitutes (tea and coffee):
  • The price of coffee rises by 20%.
  • Demand for tea rises by 10%.

  • eXY = +10 ÷ +20 = +0.5. The sign is positive, so tea and coffee are substitutes.

  • Complements (tea and sugar):

  • The price of sugar rises by 20%.
  • Demand for tea falls by 6%.
  • eXY = −6 ÷ +20 = −0.3. The sign is negative, so tea and sugar are complements.

Size: how strong is the link?

  • A large positive eXY means close substitutes.
  • Buyers switch easily from one good to the other.

  • Example: two brands of the same kind of tea.

  • A small positive eXY means weak substitutes.

  • Some buyers switch, but most stay with what they already buy.

  • A large negative eXY means strong complements.

  • The goods are almost always used together, like a car and fuel.

  • eXY close to zero means the goods have almost nothing to do with each other.

Points that make the concept exact

  • eXY and eYX need not be equal.
  • A rise in the price of coffee may push many people to tea.
  • The same % rise in the price of tea may push fewer people to coffee.

  • So always check which good's price changed and whose demand is being measured.

  • The demand curve shifts; there is no movement along it.

  • A change in the price of Y shifts the whole demand curve of X. For substitutes it shifts right; for complements it shifts left.

  • A movement along X's demand curve happens only when X's own price changes.

  • It puts a number on the "related goods" rule. The textbook rule says that the price of related goods is one of the things that decides demand. eXY measures that effect.

In India

No official body publishes cross elasticities the way MoSPI publishes CPI or HCES data. The concept shows up in everyday Indian markets and in policy.

  • Tea, coffee and sugar: these are the standard textbook pairs.
  • Tea and coffee are substitutes (positive eXY).

  • Tea and sugar are complements (negative eXY).

  • Fuel and vehicles:

  • Petrol and petrol cars are complements. When fuel is taxed heavily, demand for the vehicles that use it can fall.

  • Other options, such as other fuels or public transport, act as substitutes, so their demand can rise.

  • Taxes on "sin" goods (tobacco, alcohol):

  • These goods have price inelastic demand, meaning buyers purchase almost the same amount even when the price rises. So taxes on them give stable revenue.
  • If a cheaper substitute is taxed less, some buyers move to it rather than stopping. The tax then protects health less than intended.

  • Cross elasticity tells the government how much of this switching to expect.

  • Firms' pricing:

  • Companies track how their sales react when a rival cuts its price. That reaction is a cross elasticity.
  • Festival and online discounts on electronics and apparel draw buyers away from close substitutes.

Don't confuse with

  • Price elasticity of demand (own-price): this links the demand for X to the price of X itself. Its sign is normally negative. Cross elasticity links the demand for X to the price of a different good, Y.
  • Income elasticity of demand (eY): this links demand to the buyer's income. Its sign separates normal and inferior goods (necessity 0–1, luxury above 1, inferior below 0). Cross elasticity's sign separates substitutes and complements.
  • Inferior good vs complement: both have a negative sign, but in different formulas. A negative eY means an inferior good. A negative eXY means complements. Exam options often swap these two.
  • Shift vs movement along the demand curve: a change in the price of a related good shifts X's demand curve. A change in X's own price causes a movement along it.

Prelims Hooks

  • Formula: eXY = % change in quantity demanded of X ÷ % change in price of Y.
  • Positive → substitutes (tea–coffee). Negative → complements (tea–sugar). About zero → unrelated (salt–shoes).
  • Worked figure: coffee price +20% and tea demand +10% gives eXY = +0.5, so they are substitutes. Sugar price +20% and tea demand −6% gives eXY = −0.3, so they are complements.
  • A larger positive eXY means closer substitutes.
  • Trap: a negative sign does not always mean "inferior good". That is true only for income elasticity. For cross elasticity, a negative sign means complements.
  • Trap: eXY and eYX are not always equal. Switching between two goods can be stronger in one direction than the other.

Mains Points

  • Competition policy and market power:
  • Regulators such as the Competition Commission of India (CCI) have to decide which products compete with each other before they can judge a merger or a claim of dominance.

  • Goods with a high positive cross elasticity belong to the same market. If the market is drawn too narrowly, one firm looks dominant when it is not. If it is drawn too widely, real monopoly power can be missed.

  • Design of "sin" and fuel taxes:

  • Taxes on goods with inelastic demand give stable revenue, but they tend to be regressive, meaning they take a bigger share of income from the poor than from the rich.
  • If close substitutes are taxed less, buyers switch to them. Revenue and health goals can then both fail.

  • Tax rates on substitutes should be set together. They can be paired with nudges (behavioural economics, Economic Survey 2018-19, chapter 2) instead of relying on price alone.

  • Price shocks spread through related goods:

  • When the price of one food rises sharply, demand shifts to its substitutes and falls for its complements.
  • Price policy for one commodity, such as a Price Stabilisation Fund release or a subsidy, also affects the markets for its substitutes and complements.
  • So a price shock in one staple can push up prices of its substitutes. Supply-side tools such as buffer stocks and Operation Greens' TOP to TOTAL transport and storage subsidy [1] should be planned for groups of related goods, not one crop at a time.

Related concepts

Read more

Sources

  1. 1Subsidy under Operation Greens a step towards Aatma Nirbhar Bharat (PIB)pib.gov.in · tier 1