Question

The current price for a good is $20, and 100 units are demanded at that price. The price elasticity of demand for the good is -2. When the price of the good drops by 5% to $19, consumer surplus: Increases or decreases by $__?

Answer 1

Answer

%change in quantity =%change in price * elasticity

=-5*(-2)

=10%

the quantity increases by 10%

New quantity =100*1.1=110

there are two-point on the line

(110,19) and (100,20)

the demand function is the form of

P=a+bQ

b=slope=change in price /change in quantity =(20-19)/(100-110)=-0.1

then the function is

P=a-0.1Q

using a point ((100,20)

20=a-0.1*100

a=20+10=30

now the function is

P=30-0.1Q

verifying it using the other point

Q=110 then P=30-0.1*110=19 so it is same as given

consumer surplus is the area below demand curve and above price

consumer surplus =0.5*(Y-axis intercept of the demand curve -P)*Q

consumer surplus before price change =0.5*(30-20)*100=500

after price change =0.5*(30-19)*110=605

change in it =605-500=105

the consumer surplus increases by $105