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)

0.5x^{2}+22x+170 =292.5

X^{2}+44x+340-585=0

x^{2}+44x-245=0

x^{2}+49x-5x-245=0

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

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

Q_{E }=5

P_{E = }19.5

Producers surplus = p_{E}q_{E ā }integral 0.5q+17 between 0 and 5

Consumers surplus =Integral 292.5 /(q+10) between 0 and 5 - p_{E}q_{EĀ}

Producers surplus = 19.5 *5 ā (q^{2}/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

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