Question

Suppose the following demand and supply function:

Q^d = 750 – 25P

Q^s = -300 + 20 P

       i.           Find equilibrium price and quantity

     ii.           Find consumer and producer surplus

Answer 1

(I)

At equilibrium Qd=Qs

$750 – 25p=-300+20p$

$750+300=20p+25p$

$1050=45p$

$P=23.33$

Substituting value of P in demand function

$=750-25(23.33)$

$=750-583.25$

$Q=166.7$

(ii)

Graphically the consumer and producer can be represented as

The consumer and producer surplus can be calculated with the formula:

Consumers|producers surplus=1/2× Base × Height

According to the graph mentioned above, P_s and P_D is also calculated. At both these price points quantity demanded and supplied are 0. 

$0=750-25P_D$

$25P_D=750$

$P_D=\frac{750}{25}$

$=30$

$0=-300+25P_S$

$20P_S=300$

$P_S=\frac{300}{20}$

$=15$

consumer and producer surplus are then calculated as

Consumer surplus$=\frac{1}{2}×166.7×(30-23.33)$

$=\frac{1}{2}×166.7×6.67$

$=555.94$

Producer surplus

$=\frac{1}{2}×166.7×(23.33-15)$

$=\frac{1}{2}×166.7×8.33$

$=694.31$