Cross elasticity of demand:
The cross elasticity of demand measures the
percentage change in demand for a particular good caused by a change in another
good.
In the words of A. Koutsoyiannis-
"The
cross elasticity of demand is defined as the proportionate change in the
quantity demanded of X resulting from a proportionate change in the price of
Y."
Percentage Change in Quantity Demand
of One Good (Px)
Ec =
Percentage Change in Price of
Another good (Qy)
= ΔQy/ ΔPx X Qy/ Px
Implication
of Cross Elasticity of Demand:
For substitute goods, cross elasticity is
positive, for complementary goods cross elasticity is negative. Both are
discussed below:
(i)
Substitute goods:
For substitute goods, if the price of one good
increases, the demand of another good also increases. Imagine a demand schedule
of Tea and Coffee:
Px(Tea)
|
Qy(Coffee)
|
40
|
20
|
60
|
40
|
Now
we can draw a demand curve from the schedule:
Here, we can see that when the price of tea is 40 Tk
the demand of coffee is 20 units. When the price of tea increases to 60 Tk the
demand of coffee also increases 40 units.
From
the above schedule, we get:
ΔPx
= (Px1-Px) = 60-40 =20
ΔQy
= (Qy1-Qy) = 40-20 =20
Qy
= 20
Px
= 40
Putting
the value in income elasticity equation, we get:
Ec
= 20/20 X 40/20
= 2 (Positive)
(ii)
Complementary goods:
For complementary goods, if the price of one good
increases, the demand of another good decreases. Imagine a demand schedule of
Tea and Sugar:
Px(Tea)
|
Qy(Sugar)
|
40
|
100
|
60
|
50
|
Now
we can draw a demand curve from the schedule:
Here, we can see that when the price of tea is 40 Tk
the demand of sugar is 100 units. When the price of tea increases to 60 Tk the
demand of sugar decreases 50 units.
From
the above schedule, we get:
ΔPx = (Px1-Px) =
60-40 =20
ΔQy = (Qy1-Qy) =
50-100 =-50
Qy = 20
Px = 50
Putting
the value in income elasticity equation, we get:
Ec
= -50/20 X 40/100
= -1 (Negative)
At last we can conclude that for substitute goods
cross elasticity has positive relationship and for complementary goods cross
elasticity has negative relationship.