Cross Elasticity of Demand

Cross elasticity is the ratio of the percentage change in the quantity requested for one good to the percentage change in the price of another good, all other things being equal.

In other words, it assesses how responsively the quantity of X good desired is to changes in Y good's price. It has a relationship to complements and substitutes.

Thus,

Exy = Proportionate change in quantity demand for good X / Proportionate change in price of good Y
=( ∆Qx/Qx)/ (∆Py/Py)
= (∆Qx/∆Py) × (Py/Qx)

Where Qx= initial quantity demand for good X
∆Qx= Change in quantity demanded for good X
Py= initial price for good Y
∆Py= Change in price for good Y

X and Y goods are related goods.

OR

Exy= Percentage change in quantity demand for good X / Percentage change in price for good Y

Types of Goods

Complementary goods: A good is considered complementary if its usage is directly connected to the use of a matched or associated good. If using more of good X necessitates using more of good Y, then two commodities (X and Y) are complementary. For instance, demand for one commodity, such as printers, will inevitably lead to demand for another good, such as ink cartridges. If the price of a product, such as a printer, drops, demand rises (people buy more), and whether or not the price of the product drops as well, people will typically buy more of the complementary product (ink cartridges). Similar to this, if the price of one commodity, such as a printer, increases, the demand for its matched or complementary good, such as ink cartridges, decreases as well.

Substitute goods: A good that can be employed in the other's alternative goods is referred to as a substitute good. These goods are viewed as being inverse of or opposed to complimentary goods in economics. If good A can be used in place of good B, then goods A and B are substitutes. For instance, if the price of Coca-Cola drops, demand for one good, let's say Fanta, rises automatically. If you buy one of a substitute good, you probably won't buy another. Apple Macs and Microsoft Windows-based personal computers are two examples of alternatives. The market is competitive with substitute products.

Numerical Example:
The price of Toyota car rises from $4000 to $5000 and demand for Nissan car increases from 200 units to 250 units. Find the cross elasticity of Nissan car.

Solution:
Here,
Initial price (Py) = $4000
Final price = $5000
Change in price (∆Py) = 5000-4000 = 1000
Initial demand (Qx) = 200
Final demand = 250
Change in demand (∆Qx)= 250-200 = 50
Exy =( ∆Qx/∆Py) / (Py/Qx)
= (50/1000)×(4000/200)
= 1

Types of Cross Elasticity of Demand

There are three types of cross elasticity of demand.

• Positive cross elasticity
• Negative cross elasticity
• Zero cross elasticity

Positive cross elasticity of demand (Exy =+ve): Cross elasticity will be positive if demand for one thing, let's say X, varies favorably with the price of another good, let's say Y. If two goods can be substituted for one another, positive cross elasticity is seen. Coca-cola and Fanta are ideal illustrations of positive cross-elasticity of demand. The demand for Fanta will grow from 1000 units to 2000 units when the price of Coca-Cola increases from Rs. 10 to Rs. 15. Additionally, when Coca-price Cola's drops from Rs. 12 to Rs. 10, the demand for Fanta will drop from Rs. 1000 to Rs. 800.

Negative cross elasticity of demand (Exy=-ve): Cross elasticity will be negative if the quantity requested for one thing, let's say X, varies adversely with the price of another good, let's say Y. If two products are complementary, negative cross elasticity is seen. Pens and ink, printers, and ink cartridges, for instance, are ideal illustrations of negative cross elasticity of demand. The quantity of ink required will decrease from 30 units to 25 units when the price of the pen increases from Rs. 22 to Rs. 25. The number of ink cartridges required will go from 30 to 25 when the price of printers drops from Rs. 13,000 to Rs. 12,000.

Zero cross elasticity of demand (Exy=0): Cross elasticity will be equal to zero if there is no change in the quantity required for one good, say X, as a result of a change in the price of another good, say Y. If two things are unrelated, there is zero cross elasticity. The ideal instances of zero cross elasticity of demand are milk, gas, and cars. The amount of gasoline required, or 1000 liters, remains same when the price of milk rises or increases from Rs. 18 to Rs. 22 per liter. The amount of gasoline required, 1000 liters, remains the same when the price of milk drops from Rs. 22 per liter to Rs. 20 per liter.

Let us take following example:

• The quantity of Pepsi demanded would increase from 1000 units to 2000 units when the price of coke increases from Rs. 10 to Rs. 12.
• The quantity of ink required will decrease from 30 units to 20 units when the price of the pen increases from Rs. 20 to Rs. 25.
• The amount of gasoline required, 1000 liters, remains constant when the price of milk increases from Rs. 20 per liter to Rs. 22 per liter.

Computation of Cross elasticity by using formula: Exy = (∆Qx/∆Py) × (Py/Qx)

Reference

Koutosoyianis, A (1979), Modern Microeconomics, London Macmillan