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.