Question

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

Answer 1

(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

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

$=\frac{1}{2}\times166.75\times8.33$

$=694.51$