Question

The price elasticity of demand of a good is 0.5. The consumer buys 50 units of the good at a price of ₹ 10 per unit. At what price will the consumer by willing to buy 60 units?

Answer 1

Price Elasticity of Demand (e_p) = 0.5

Initial Quantity Q₁ = 50 units

New Quantity Q₂ = 60 units

Initial Price P₁ = ₹ 10

Need to find: New Price (P₂) at which the consumer buys 60 units

% change in quantity demanded = `(Q_2-Q_1)/Q_1xx100`

= `(60-50)/50xx100`

= `10/50xx100`

= 20%

Price Elasticity of Demand = `"% change in quantity​"/"% change in price​"`

0.5 = `20/"% change in price​"`

% change in price​ = `20/0.5`

= 40%

Since quantity increased, and elasticity is positive in calculation, this must be due to a fall in price, so:

% change in price = −40%

P₂ = `P_1 + ((-40)/100xxP_1)`

= `₹ 10 - (40/100xx₹10)`

= ₹ 10 − ₹ 4

= ₹ 6