Suppose the following demand and supply function:
Qd = 750 – 25P
Qs = -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”
Ps and Pd 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”