# The question is related to topic consumer surplus [closed]

Suppose the demand function is 12-3p=q and price falls from 3 to 1. How much is the change in consumer surplus?

Demand function in your question is given as

Q=12-3P

In order to find consumer surplus,we first find inverse demand function from it

Q=12-3P 12-Q=3P 12/3-Q/3=P 4-Q/3=P or P=4-Q/3

At P = 3 ,from inverse demand function, we get Q= 3

Since intercept in the inverse demand function is 4 and base is 3,we can calculate consumer surplus by using the formula for area of a triangle as ab/2 i.e 4x3/2=6

Similarly,when price falls to 1,we get value of Q=9

Here,area of triangle becomes 9x4/2=18,which is the new consumer surplus

Subtracting 6 from 18, we get the change in consumer surplus as 12