What is cross elasticity of demand? Discuss the implication of cross elasticity of demand. Or, Explain why the cross price elasticity of demand is positive for commodities that are substitutes but negative when commodities are complementary.

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.