# Cross Elasticity of Demand

The cross elasticity of demand (or cross-price elasticity of demand)  ϵ AB  refers to the sensitivity of the demand for item A   q A   to changes in the price of item B  p B :

In microeconomics it is assumed that individuals’ utility (material well-being) depends on their access to/ consumption of bundles of items, and that individuals seek to maximise utility. The precise relationship between the consumption of particular items and an individual’s utility is determined by the individual’s preferences. Individuals are constrained in their consumption on the one hand by their budgets, i.e. how much money they have available to purchase items, and on the other hand by the prices of the items.  If the price of an item increases then the individual’s ability to obtain utility through consumption of that item is reduced.  It may be possible to obtain utility more efficiently through consumption of a different item instead.  The extent to which this is possible depends on the substitutability of other items with the item whose price has increased.

For example, an individual may like to consume hazelnuts and peanuts.  Ideally the individual likes to consume both types of nuts (due to diminishing marginal utility).  However if the price of one nut type, say peanuts, increases then the individual can afford fewer peanuts and may substitute forgone utility by reducing peanut consumption and replacing peanuts with hazelnuts.  Hazelnuts and peanuts are thus substitutes in consumption. Note that the reverse is then also true if the price of peanuts falls.  In that case the individual can afford more peanuts and will obtain utility more efficiently by reducing hazelnut consumption and increasing peanut consumption.  In the case of substitutes, the cross elasticity of demand is positive  ϵHazelnutsPeanuts > 0.

The interrelationship between items is key in the cross elasticity of demand.  Some items are consumed together as complements rather than as replacements or substitutes.  For example, fuel is required to power vehicles.  In the case of the price of either one of these items changing, demand for both goods will move in the same direction.  If the price of vehicles increases then demand for the vehicles will fall and because of this the demand for the fuel that powers the vehicles will also fall.  Likewise, if the price of fuel rises then demand for both fuel and vehicles will fall.  In the case of complements, the cross elasticity of demand is negative  ϵFuelVehicles < 0.

Other items have conceivably very little to do with each other.  For example, if the price of yoghurt changes then this would not be expected to affect the demand for smartphones.  The cross elasticity of demand between these items should be close to zero  ϵSmartphonesYoghurt ≈ 0.  However, note that insofar as the item whose price changes is an important constituent of individuals’ bundles of items in the economy, there will be an effect on budgets, which may then lead indirectly to change in the demand for other seemingly unrelated items.  See income elasticity of demand  for details of this type of effect.

As with the standard price elasticity of demand  for a single item, a cross elasticity of demand can be elastic (IϵAB≥ 1), unit elastic (IϵAB= 1), inelastic (IϵAB< 1), perfectly inelastic (IϵAB= 0) or (in theory) perfectly elastic (IϵAB→ ∞), reflecting the extent of the change in quantity demanded relative to a change in price.