Description
Find producer's surplus at the market equilibrium point if supply function is
p= 292.5/(x+10)
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Explanation & Answer
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 – integral 0.5q+17 between 0 and 5
Consumers surplus =Integral 292.5 /(q+10) between 0 and 5 - pEqE
Producers surplus = 19.5 *5 – (q2/4+17q) between 0 and 5
= 97.5 –(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
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