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.

What do the price elasticity of demand, the income elasticity of demand measure in general?

Elasticity means the degree of responsiveness of quantity affected by a change in any one of the forces behind the demand. There are three measures of demand elasticity. They are:

1. Price elasticity of demand:

Price elasticity of demand defines the ratio of the percentage change in quantity demand of a commodity due to a percentage change in price.

According to R. G. Lipsey-

"The price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price that brought it about."

         Percentage change in quantity demanded

Ed =                                                                      =Δ Q ÷ Q / Δ P ÷ P = Δ Q ÷ Q X P ÷ Δ P

                Percentage change in price

= ΔQ ÷ Δ P X P ÷ Q

Here, ΔQ = Change in quantity demand

ΔP = Initial quantity

P = Change in price

Q = Initial price

Imagine a demand schedule:

Price	Quantity demand
10	100
8	120

When the price of a particular commodity is Tk. 10, the demand is 100 units. But when price decreases to 8, the demand   increases Tk. 120.

From the above schedule, we get:

ΔQ = (Q1 - Q) = 120 - 100 = 20

ΔP = (P1 - P) = 8 - 10 = -2

P = 10

Q = 100

Putting the value in the equation of price elasticity of demand, we get:

Ed = 20/-2 X 10/100

= |-1| [using absolute value]

= 1

2. Income Elasticity of Demand:

Income elasticity of demand measures the percentage change in quantity demand caused by percentage change in income.

According to R. G. Lipsey-

"The responsiveness of demand for a commodity to change in income is termed income elasticity of demand."

         Percentage Change in Quantity Demand

Ey =                                                                     = ΔQd/ ΔY X Y/ Qd

              Percentage Change in Income

For normal goods income elasticity is positive, but for inferior goods income elasticity is negative. Example:

(i) Normal goods: We know, if the income of people increases the demand of normal goods increases. If income decreases the demand also decreases. Imagine a demand schedule:

Income (Y)	Quantity Demand (Qd)
100	10
110	20

Here, the income of man increases 100 to 110, the demand of the man also increases 10 to 20 units. Now,

ΔQd = (Q1-Q) = 20-10 =10

ΔY   = (Y1-Y) = 110-100 =10

Qd = 10

Y   = 100

Putting the value in income elasticity equation, we get:

Ey = 10/ 10 X 100/ 10

     =10 (Positive)

(ii) Inferior goods:

For inferior goods, the income of buyer increases, the demand of goods decreases and income decreases demand increases. Imagine a demand schedule:

Income (Y)	Quantity Demand (Qd)
100	10
110	5

Here, the income of man increases 100 to 110, the demand of the man decreases 10 to 5 unit. Now, from the above schedule, we get:

ΔQd = (Q1-Q) = 5-10 = -5

ΔY = (Y1-Y) = 110-100 =10

Qd = 5

Y   = 110

Putting the value in income elasticity equation, we get:

Ey = -5/ 10 X 110/ 5

     = -11(Negative)

At last we can say, if the elasticity is positive the good in normal and if the elasticity is negative then the good in inferior.

What is elasticity of demand?

Elasticity of demand is a major of how changing quantity demand due to change in its price. That is,

                                     Percentage change in quantity demand

                       Ed =               

                                            Percentage change in price

According to Prof. A. Marshall-

“The degree of rapidity or slowness with which demand changes with every change in price is known as elasticity of demand."

In the words of Lipsey-

"Elasticity of demand is the measure of the responsiveness of the quantity demanded to change in price."

In mathematical terms, elasticity of demand is-

           % Δ Qd                    Δ Qd ÷ Qd X 100             Δ Qd ÷ Qd

Ed =                             =                                    =                             = Δ Qd /Qd X P /Δ P

             % Δ P                     Δ P ÷ P X 100                     Δ P ÷ P

     = Δ Qd /Δ P X P / Qd

What do you mean by elasticity?

Generally elasticity means the rate of change. In economics, elasticity is the measurement of how changing one economic variable affects others. There are several factors related to elasticity. For example, elasticity of demand, supply, income, expenditure, cross etc.