The study of the concept cross elasticity of demand plays a major role in forecasting the effect of change in the price of a good on the demand of its substitutes and complementary goods.

Therefore, it helps in deciding the price of a good by determining the change in the demand of its substitutes and complementary goods.

The demand for a good is generally associated with the demand for another good. Therefore, change in the price of one good produces change in the price of another good. The extent of relationship between two related goods can be measured by cross- elasticity of demand. In other words, cross-elasticity of demand measures the receptiveness of quantity demanded of a good with respect to change in the price of its substitute or complementary good.

Some of the definitions of cross-elasticity of demand are as follows:

In the words of Leibhafsky, “the cross elasticity of demand is a measure of the responsiveness of T to change in the price of X.”

According to Ferugson, “the cross-elasticity of demand is the proportional change in the quantity of good-X demanded resulting from a given relative change in the price of the related good-Y.”

It should be noted that the cross-elasticity of demand would be positive, when two goods are substitute of each other. This is because the increase in the price of one good increases the demand for the other. On the other hand, in case of complementary goods, the cross-elasticity of demand would be negative as increase in the price of one good decreases the demand for the other. For example, increase in the price of tea would result in the increase in the demand for coffee, whereas increase in the price of petrol would cause decrease in the demand for cars.

Measurement of Cross Elasticity of Demand:

Cross-elasticity of demand expresses the ratio of percentage change in demand of good X produced due to the percentage change in price of related good Y.

Therefore, the formula for cross-elasticity (ec) of demand is as follows:

ec = Percentage change in quantity demanded of X/Percentage change in price of Y

Percentage change in quantity demanded of X= New demand for X (∆QX)/Original demand for X (QX)

Percentage change in price of Y= New price for Y (∆PY/Original price for Y (PY)

The symbolic representation of the formula for cross elasticity of demand is as follows:

ec = ∆QX/QX: ∆PY/PY

ec = ∆QX/QX */PY/∆PY

ec = ∆QX/∆PY */PY/QX

∆QX can be calculated by subtracting original demand for X (QX) from increase in demand (QX1), which is as follows:

∆QX = QX1 – QX

Similarly, PY is the difference between the new price of Y (PY1) and original price for Y (PY).

It can be calculated by the following formula:

∆PY = PY1 -PY

Types of Cross Elasticity of Demand:

The numerical value of cross-elasticity of demand is not same for every related goods. It differs for different types of goods.

The various types of cross-elasticity of demand are as follows:

i. Positive Cross Elasticity of Demand:

Implies that the cross elasticity of demand would be positive when increase in the price of one good (X) causes increase in the demand for the other good (Y). In simple terms, cross elasticity would be positive for substitutes. For example, the quantity demanded for coffee has increased from 500 units to 550 units with increase in the price of tea from Rs. 8 to Rs. 10. Calculate the cross elasticity of demand and state the type of relationship between coffee (X) and tea(Y).

Solution:

QX1 =550 units

QX =500 units

PY1 = Rs. 10

PY = Rs. 8

Therefore, ∆QX = QX1 – QX = 550 – 500 = 50 units

Similarly, ∆PY = PY1 – PY = Rs. 2

Now ec = 50/2*8/500= 0.4

The cross elasticity of “demand is positive; therefore, X and Y are substitutes.

ii. Negative Cross Elasticity of Demand:

Refers to a situation when the rise in the price of one good (X) reduces the demand for the other good (Y). The cross elasticity of demand would be negative for complementary goods. For example, the quantity demanded for X decreases from 220 to 200 units with the rise in prices of Y from Rs. 10 to 12.

Now, the cross elasticity of demand would be as follows:

QX1 =200 units

QX =220 units

PY1 = Rs. 12

PY = Rs. 10

Therefore, ∆QX = QX1 – QX = 200 – 220= – 20 units

Similarly, ∆PY = PY1 – PY = Rs. 12 – Rs. 10 = Rs. 2

Now ec = – 20/2* 12/200= -0.6

The cross elasticity of demand is negative; therefore, X and Y are complementary to each other.

iii. 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. In other words, the increase or decrease in the price of one good (X) would not affect the demand of other good (Y).