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
%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
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