Cross elasticity of demand measures the degree of responsiveness of the quantity demanded of one good (B) to changes in the price of another good (A). It is measured as follows:
Ex = Percentage change in quantity demanded of B
Percentage change in Price of A.
This may be written mathematically as follows:
Ex = DQB/QB
= AQB · PA
In the case of complementary goods, such as cars and petrol, a face in the price of one will bring about an increase in the demand for the other. Thus we are considering a cut in price (-) bringing about a rise in demand (+). This therefore means that for complements, the Ex is negative.
Conversely, substitute goods such as butter and margarine might be expected to have a positive Ex because a rise in price of one (+) will bring about a rise in the demand for the other (+).
The value of Ex may vary from minus infinity to plus infinity. Goods which are close to complements or substitutes will tend to exhibit a high cross-elasticity of demand. Conversely, when there is little or no relationship between goods then the Ex will be near zero.