Consumer and Producer Surplus using algebra to calculate

Question

Calculate the consumer and producer surplus in the following market:

Inverse Demand function: P = -Q + 12

Supply function: P = 2Q + 6

Answer 1

4 and 16

consumer surplus is the area of the triangle formed by the demand curve, the y-axis and the price line, P=10

set the 2 curves equal, to get -Q+12=2Q+6 or Q=2 then P=-2+12=10

at Q=0 P=12

12-10=2

the consumer surplus triangle is 2x2 1/2 the area is (1/2)2(2) = 2

producer surplus is the area is a triangle formed by the supply curve, P=6, and the line Q=4, that's height 4 and base 2 or area = 4 plus a square 2x6=12 producer surplus is 4+12=16