Cross elasticity of demand

Cross elasticity of demand (E_XY)

Cross elasticity of demand is a measure of demand for a product to the change in the price of related goods. In other words, the percentage change in quantity demanded of commodities due to the change in the price of a related commodity that may be substitute goods or complementary goods is called cross-elasticity of demand. It is symbolized by  E_XY and expressed as:

Where,
E_XY = Cross elasticity of demand between x and y goods
∆Q_X = Change in quantity demanded for x commodity
∆P_Y = Change in price of y commodity
P_Y = Initial price of y commodity
Q_X = Initial quantity demanded for x commodity

Types or degrees of cross elasticity of demand

1. Positive cross elasticity of demand (E_XY>0)

If any two goods are a close substitute to each other, then the cross elasticity of demand is said to be positive. For example; tea and coffee, when the price of tea increases demand for coffee also increase and vice versa.

In the above figure price of x goods and demand for y goods are shown along y-axis and x-axis respectively. When the price of x goods rises from P to P₁ then quantity demanded for y goods also rise from Q to Q₁. DD is the demand curve which is positively cross elastic.
I.e. E_XY > 0

2. Negative cross elasticity of demand (E_XY<0)

When two goods are complementary to each other, then the cross elasticity of demand is said to be negative. For example petrol and car, when the price of petrol increases the demand for car decreases and vice versa.

In the above figure price of x goods and demand for y goods are shown along y-axis and x-axis respectively. When the price of x goods rises from P₀ to P then quantity demanded for y goods decreases from Q₀ to Q. DD is the demand curve which is positively cross elastic. I.e.  E_XY < 0.

3. Zero cross elasticity of demand (E_XY=0)

Zero cross-elasticity of demand implies that the cross elasticity of demand would be zero when two goods x and y are not related to each other. The increase or decrease in the price of y goods will not affect the demand for x goods.

In the above figure price of y goods and demand for x goods are shown along y-axis and x-axis respectively. When the price of y goods rises from P₁ to P₂ and then to P₃ then the demand for x goods will not change. It remains the same at OQ. QD is the demand curve which is zero cross-elastic I.e. E_XY=0