Calculus II Consumer and Producer's Surplus

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Find producer's surplus at the market equilibrium point if supply function is

p=0.5x+17 and the demand function is 

p= 292.5/(x+10)

Sep 26th, 2017

0.5x2+22x+170 =292.5

X2+44x+340-585=0

x2+44x-245=0

x2+49x-5x-245=0

x(x+49)-5(x+49)=0

(x+49)(x-5) =0

QE  =5

PE = 19.5

Producers surplus = pEqE ā€“ integral 0.5q+17  between 0 and 5

Consumers surplus =Integral 292.5 /(q+10) between 0 and 5 - pEqEĀ­

Producers surplus = 19.5 *5 ā€“ (q2/4+17q) between 0 and 5

  = 97.5 ā€“(25/4+85)= 97.5 -91.25 = 6.25

Consumers surplus = 292.5 ln(q+10) between 0 and 5 -97.5

  =292.5 ln (15/10)-97.5

  =118.5985-97.5= 21.0985


Feb 26th, 2015

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