Consumer&Producer Surplus

Here is an interesting question on surplus:

Find the equilibrium price Po and the equilibrium demand Xo, and evaluate the consumer's surplus and producer's surplus.

Solution

Demand:p=-3x+21

Supply:p=9x^2/16, x>=0

Since at equilibrium, the curves intersect

=>-3x+21=9x^2/16

<->3x^2+16x-(16)(7)=0

<->(3x+28)(x-4)=0

As x>=0,

Hence equilibrium occurs when x=Xo=4,and the corresponding equilibrium price is p=(-3)(4)+(21)=9

Consumer surplus=Area A=(21-9)/2*(4)=24