# The inverse demand function for taxi-apps is estimated to be p = 100−2Q. If the price increases from 20 to 30, then by how much does consumer surplus change?

The inverse demand function for taxi-apps is estimated to be p = 100−2Q. If the price increases from 20 to 30, then by how much does consumer surplus change?

Inverse demand function:

p = 100 – 2Q

2Q = 100 – p

Q = (100 – p) / 2

Q = 50 – 0.5p [Demand function]

When p = 20,

Q = 50 – (0.5 x 20) = 50 – 10 = 40

Consumer surplus (CS) is the difference between consumer’s maximum willingness to pay and actual price she pays, and is measured by the area between demand curve and price.

From demand function, when Q = 0, p = 100 [Reservation price]

CS = (1/2) x \$(100 – 20) x 40 = (1/2) x \$80 x 40

CS = \$1,600

When p = 30,

Q = 50 – (0.5 x 30) = 50 – 15 = 35

CS = (1/2) x \$(100 – 30) x 35 = (1/2) x \$70 x 35

CS = \$1,225

Change in CS = \$1,225 – \$1,600 = – \$375

So, CS decreases by \$375 when price increases to \$30.

Asked on February 13, 2018 in