### Cross Elasticity of Demand

Some goods are related to each other. So a fall in the price of a commodity causes change in the demand for other commodity. As for example, demand for tea is related to the price of substitute, coffee. When the price of coffee increases, the demand for tea increases. Hence, cross elasticity of demand means the responsiveness of quantity demanded of a commodity to the change in price of other commodity. The cross elasticity of demand is defined as the percentage in the quantity demand of good x resulting from a 2 percent change in the price of good y.
According to C. E. Ferguson, “Cross elasticity is the proportionate change in the quantity demanded of good x divided by the proportionate change in the price of y.”
The formula to calculate cross elasticity is,

Cross Elasticity = Proportionate change in quantity demanded of x/Proportionate change in price of y

Symbolically, Ec = Δqx/Δpy x Py/Qx

The concept of cross elasticity can be illustrated by the help of a numerical example. Suppose that x and y are two substitute goods. Suppose when the initial price of y is \$4.50, the initial quantity of x is 60kg. Now when the price of y increases to \$5, the quantity demanded of x increases to 70kg. The cross elasticity is calculated as,

Ec = Δqx/Δpy x Py/Qx
= 10/5.0 x 4.5/60 = 3/2 = 1.5

1.5 coefficient shows that the cross elasticity is positive.

### Types of Cross Elasticity

The goods may be either substitutes or complements. So the cross elasticity is of two types as follows:
1. Positive Cross Elasticity (Ec > 1)
When two goods are substitutes of each other, the cross elasticity is positive. As for example, tea and coffee. The increase in price of one commodity leads to an increase in quantity demanded of other commodity. Because, people substitute one commodity for other. Positive Cross Elasticity
In the figure, demand curve DD shows positive cross elasticity. Because, with the increase in price X from OP to OP1, demand for Y has increased from OM to OM1.

2. Negative Cross Elasticity (Ec < 0)
When two goods are complements, cross elasticity is negative. As for example, shoe and shoelaces. The increase in price of one commodity causes fall in the quantity demanded of other commodity. Negative Cross Elasticity
In the figure, demand curve DD shows negative cross elasticity. Because due to the increase in price of X from OP to OP1, demand for Y has declined from OM to OM1.

When the goods are not related to each other, the cross elasticity is zero. As for example, book and coat. The change in price of one does not affect the demand for other. Hence, the demand curve will be a vertical straight line. But this is not counted as cross elasticity.