when the price of the commodity X changes from 40 to 20, its demand increases by 20 units. if the price elasticity ofdemand is 0.5 calculate the final quantity for commodity X.
Answers
Answer:
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%.
Answer : Final quantity : 100
Explanation: Es ( Elasticity of demand ) = ΔQ/ΔP x P/Q
Here Es = 0.5 , ΔQ =20 (40 - 20 ) , ΔP = 20 , P = 40
=> 0.5 = 20/20 x 40/Q
=> Q = 80
Change in Quantity = 20
Initial Quantity = 80
Final Quantity = 80 + 20
= 100