My Math Forum Consumer's surplus

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 January 16th, 2014, 09:49 PM #1 Senior Member   Joined: Sep 2012 Posts: 112 Thanks: 0 Consumer's surplus Q. The demand & supply functions respectively are: $P_d= (6-x)^2 &P_s= 14+x$ Find the consumer surplus if the demand and price are determined under perfect competition. I tried to solve this problem as follows:- Under perfect competition, the equilibrium condition is $P_d = P_s or, (6-x)^2 = 14+x or, x = 11 or 2$ At x=11, price(p)= 25 At x=2, price(p)= 16 At x=11 & p=25, the consumer's surplus turns out negative, while at x=2 & p= 16, the consumer's surplus is positive. So what should I conclude? Should I write the conclusion as follows? Since at x=11 & p=25 the consumer's surplus is negative, (11,25) can't be the equilibrium point. Hence the equilibrium point is (2,16) where the consumer's surplus is 56/3 units.

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