Question #270193

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



(a) P = 12 + 2Q



(b) P = 20√Q + 15

1
Expert's answer
2021-11-25T20:53:01-0500

a) =P=12+2QP=12+2Q

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


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


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


=270[12Q+Q2]09=270-[12Q+Q^2] ^9_0


=270[108+81]=270-[108+81]


=81=81


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


At Q=9,P=209+15=75P=20\sqrt{9}+15 =75


Producer's Surplus =PQPdQPQ-\int PdQ


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


=675[20Q3232+15Q]09=675-[20\frac {Q^{\frac {3} {2} }}{\frac {3} {2}} +15Q]^9_0


=675495=675-495


=180=180


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