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So far you learned that price and income play a role in determining elasticity of demand. They both are factors that determine
the degree at which quantity demanded changes. For certain goods we saw relatively large changes in quantity demanded when
price or income changes, while for certain other goods, the changes in quantity demanded are relatively small. Yet, for some
goods the changes in price or income cause a correspondingly equal change in quantity demanded. In extreme cases, we saw no
changes at all to quantity demanded regardless of price or income changes or an indefinite change even with the slightest
change in price or income.
Now we are going to look at another factor that can determine the elasticity of demand. We will study how the price changes
of one good, say good A, can affect the elasticity of demand of another related good, say good B. This is known as cross elasticity
of demand.
In determining the cross elasticity of demand we will look at two different products. On one, we will look at the percentage
change in price, and on the other we will study the percentage change in quantity as the result of the change in price of
the former good. Please remember that the study of cross elasticity of demand is on related goods only, that is, either substitute
or complementary goods.
How do we do this? First, calculate the change in price of product A using the following formula:
Change in Price
(P1 + P2)/2
Then, calculate the change in quantity of product B using the following formula.
Change in Quantity
(Q1 + Q2)/2
Lets use this example to complete the calculations:
The price of fountain pens (product A) increases from RM100 per unit to RM120 per unit. This price increase results in
the decrease in demand for ink (product B), and the demand falls from 20 units to 16 units.
Change in price of product A
= RM20
Change in Quantity Demanded of Product B = 4 units
The change in price is:
_____20____
(100 + 120)/2
0.10 (or 10%)
The change in quantity demanded is:
____4_____
(20 + 16)/2
0.22 (or 22%)
Here you see that a 10% increase in price of fountain pens resulted in a 22% fall in quantity demanded for ink. If you
take the change in quantity demanded figure (0.22) and divides it with the change in price figure (0.10); you will get a figure
of 2.2. What the 2.2 means is "a 1% increase in price of fountain pens results in a 2.2% decrease in quantity demanded for
ink. (Since the change in quantity demanded is greater than 1, we say ink has a cross elastic demand).
The complete formula for calculating cross elasticity of demand is as follows:
Change in QD of Product B divide by Change in P of Product A
(Q1 + Q2)/2
(P1 + P2)/2
After doing the appropriate calculations, make the appropriate conclusion. Pick any one below:
- The change in price of product A will cause a relatively larger change in the quantity demanded of product B. A 1% change
in price of product A will result in a greater than 1% change in quantity demanded for product B. In this case, we say that
the demand for product B is cross elastic.
- The change in price of product A will cause a relatively smaller change in the quantity demanded of product B. A 1% change
in the price of product A will result in a smaller than 1% change in quantity demanded for product B. In this case, we say
that the demand for product B is cross inelastic.
- The change in price of product A will cause a correspondingly equal change in quantity demanded of product B. A 1% change
in the price of product A will result in an equal 1% change in quantity demanded for product B. In this case, we say the demand
for product B is unit elastic.
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