# Cross elasticity of demand

There is cross elasticity of demand when demand for a commodity changes due to a change in the price of another related commodity. In fact cross elasticity of demand measures the change in demand of a commodity (say coffee) when the prices of another related commodity (say tea) changes by small amount. There is positive cross-elasticity of demand when two goods are substitutes of each other increase in the price of one increases the demand for other. There is negative cross-elasticity of demand for complementary goods because increase in the price of goods decreases the demand for its complementary goods.

## Definition

According to Ferguson 'cross elasticity of demand is proportional change in the quantity of x demanded resulting from a given relative change in the price of relative good y'.

## Formula:

The formula for measurement of cross elasticity of demand is as follows:

Ecr = Proportionate change in demand for x / Proportionate change in the prices of y

For example when price of tea increases from \$10 to \$15 per kilogram and as a result demand for coffee increases from 20 tones to 30 tones per month price of coffee remaining constant. If we put values in the formula the result is: Δq ÷ Δp × p ÷ q

In the example; Δq = 30 - 20 =10; q = 20; Δp = 15 - 10 = 5; p = 10

Putting the values in the question the result is; Ecr = 10 ÷ 5 ×10 ÷ 20 = 1

The same formula is used to measure cross-elasticity of demand for a commodity in response to change in the price of its complementary goods. The example of complementary goods is petrol to car. When the price of car increases there is decrease in the demand for petrol.

## Classification of commodities

### Substituted goods

The cross elasticity of demand for substitute goods is positive. The example of such goods is tea and coffee. Increase in the price of coffee leads to rise in the demand for tea. There is positive relationship between increase in price of coffee and increase in demand for tea.

### Complementary goods

The cross elasticity of demand for complementary goods is negative. The example of such goods is car and petrol. The increase in price of car decreases the demand for petrol and vice versa.

### independent goods

The cross elasticity of demand for independent goods is zero. The example of such goods is car and sugar. There is no price relationship between car and sugar. When price of car increases its demand falls but demand for sugar remains the same.