Question

Find the producer's surplus at Q = 9 for the following supply functions:

(a) P = 12 + 2Q

(b) P = 20√Q + 15

Answer 1

a) =$P=12+2Q$

At Q=9,P=12+18=30

Therefore producer's surplus =$P. Q-\int PdQ$

$=(30)(9)-\int(12+2Q)dQ$

$=270-[12Q+Q^2] ^9_0$

$=270-[108+81]$

$=81$

b) $P=20\sqrt{Q}+15$

At Q=9,$P=20\sqrt{9}+15 =75$

Producer's Surplus =$PQ-\int PdQ$

$=(75)(9)-\int 20\sqrt{Q}+15 dQ$

$=675-[20\frac {Q^{\frac {3} {2} }}{\frac {3} {2}} +15Q]^9_0$

$=675-495$

$=180$