Question

When price of commodity X changes from ₹ 40 per unit to ₹ 20 per unit, its demand increases by 20 units. If price elasticity of demand is 0.5, calculate the initial and final quantity demanded of commodity X.

Answer 1

Initial Price P₁ = ₹ 40

New Price P₂ = ₹ 20

Change in Quantity Demanded = +20 units

Price Elasticity of Demand e_P = 0.5

e_P = `"% change in quantity​"/"% change in price"`

% change in price = `(P_2 - P_1)/P_1 xx 100`

= `(20 - 40)/40 xx 100`

= `(-20)/40 xx 100`

= −50%

0.5 = `"% change in quantity"/-50`

% change in quantity = 0.5 × (−50)

= −25%

Since the price decreased, demand increased, so the actual change is +25%

Q₁ + 20 = 1.25Q₁

⇒ 20 = 0.25Q₁

⇒ Q₁ = `20/0.25`

= 80

Q₂​ = Q₁ ​+ 20

= 80 + 20

= 100

Initial Quantity Demanded Q₁ = 80 units

Final Quantity Demanded Q₂ = 100 units