Question

The price elasticity of demand of commodity X is half of the price elasticity of demand
of commodity Y. A 10% rise in the price of commodity Y reduces its demand from 200 to 150
units. Calculate the percentage rise in demand of commodity X when its price falls by 20%.

Answer 1

Given, percentage change in price =(−)10%

Q=150 units;Q

1

=180 units;△Q=Q

1

−Q=(180−150)units=30 units

Percentage change in quantity demanded =

Q

△Q

×100

=

150

30

×100=20%

Price elasticity of demand (E

d

)=(−)

Percentage change in price

Percentage change in quantity demanded

=(−)

−10%

20%

=2

When demand rises from 150 to 210 units:

E

d

=2

Q=150 units;Q

1

=210 units;△Q=Q

1

−Q=(210−150)units=60 units

Percentage change in quantity demanded =

Q

△Q

×100

=

150

60

×100=40%

Price elasticity of demand (E

d

)=(−)

Percentage change in price

Percentage change in quantity demanded

2=(−)

Percentage change in price

40%

Percentage change in price =

2

−40%

=20%

Price elasticity of demand =2.

Percentage fall in price =20%.