Suppose the following demand and supply function:

Q^{d} = 750 – 25P

Q^{s} = -300 + 20 P

i. Find the equilibrium price and quantity

ii. Find consumer and producer surplus

(i)“Qd=Qs”

“750-25p=-300+20p”

“750+300=20p+25p”

“1050=45p”

“p=23.33”

“Q=750-25(23.33)”

“=750-583.25”

“Q=166.75”

(ii) consumer/producer surplus“=\frac{1}{2}\times base\times height”

P_{s} and P_{d} are also calculated at points where quantity demanded and supplied are 0.

“0=750-25P_d”

“25P_d=750”

“Pd=\frac{750}{25}”

“=30”

“o=-300+20P_s”

“20P_s=300”

“P_s=\frac{300}{20}”

“=15”

The consumer and producer surplus are then calculated as follows

consumer surplus

“=\frac{1}{2}\times166.75\times(30-23.33)”

“=\frac{1}{2}\times166.75\times6.67”

“=556.11”

producer surplus

“=\frac{1}{2}\times166.75\times(23.33-15)”

“=\frac{1}{2}\times166.75\times8.33”

“=694.51”