Price elasticity is measured as a ratio of the proportionate change in demand to a proportionate change in price. Thus, price elasticity of demand, Ep° is given as

where, Q2 = quantity demanded at price P2

Ql = quantity demanded at price P1

?Q = change in quantity demanded due to a change in price (?P)

Q = initial level of demand at initial price P

Price elasticity will be discussed in detail later in the section.

#### 2. Income elasticity:

Income elasticity of demand is defined as the responsiveness of demand to a change in income, while all other things remain unchanged. It is measured as a ratio of proportionate change in quantity demanded to a proportionate change in income while other things remain unchanged. Thus, income elasticity of demand, EYD, is given as

Where, Q2 = quantity demanded at an income Y2

Q1 = quantity demanded at an income Y1

?Q = change in demand due to a change in income (?Y),

Q = initial demand at initial level of income, Y

#### 3. Cross Price Elasticity:

It is defined as the responsiveness of demand for good A to a change in price of good B, while other things remain unchanged.

Cross price elasticity is measured as a ratio of the proportionate change in demand of good A to a proportionate change in price of good B.

Thus, cross price elasticity, EpD (cross), is given as

Where, Q2A = quantity demanded of good A at price P2B of B

Q1A = quantity demanded of good A at price PXB of B

?QA = change in demand of good A due to a change in price of good B (?PB)

QA = quantity demanded of good A at a price PB of B

Before proceeding to the detailed study of price elasticity, let us construct some numerical illustrations to demonstrate calculations of the elasticities defined above.

Illustration 2.1

(j) Calculate price elasticity of demand when a rise in price from Rs 10 per unit to Rs 12 per unit lowers the demand from 1,000 units to 800 units in a local store.

(ii) When income of a consumer increases from Rs 10,000 to Rs 12,000, his demand for a product rises from 20 t j 30 units of a product. Calculate income elasticity of demand.

(iii) When price of tea in a local cafe rises from Rs 4 a cup to Rs 5 a cup, demand for coffee rises from 30 cups a day to 40 cups a day despite no change in coffee prices. Calculate cross price elasticity of demand.

(iv) A 20% rise in price of ink leads to 30% fall in the demand of ink-pens, calculate the cross price elasticity of demand. 