The producer's surplus at Q = a for the supply function P = 6 + 8Q
Is known to be 400. Find the value of a.
A)25
B)5
C)20
D)10
E)15

Question

Quizplus · Accepted Answer

The producer's surplus is the area above the supply curve and below the price level at Q = a. The supply function is P = 6 + 8Q. At Q = a, the price is P = 6 + 8a. The producer's surplus is given by the integral from 0 to a of (P - supply price) dQ, which equals 400. Solving the equation 400 = ∫(0 to a) (6 + 8a - (6 + 8Q)) dQ gives a = 10.

The Producer's Surplus at Q = a for the Supply