Question

The demand and supply functions of a commodity are given as follows:
Qd = 40 – lnp Qs = lnp – 20.
Find the equilibrium price and quantity
Sketch the graphs of supply and demand on a well labeled diagram and shade the regions representing producer’s and consumer’s surplus.
Compute the consumer surplus

Answer 1

a. Equilibrium is when Qd$=$ Qs

Qd$=$ 40$-$ Inp

Qs$=$ Inp$-$ 20

40$-$ Inp$=$ Inp$-$ 20

40$+$ 20$=$ 2Inp

60$=$ 2Inp

Inp$=$ 30

Substituting for Qd$=$ 40$-$ 30$=$ 10

Qs$=$ 30$-$ 20$=$ 10

b.The following supply and demand curve shows both producer and consumer surplus regions

c. Consumer surplus

We will use the area of a triangle($\frac {1}{2}$ bh$)$

First we find the total area minus Producer surplus because of the shape

Total area$=$ $\frac {1}{2}$$×$ $(40-10)$$×$ 10

$=$ 150

Producer surplus area

$=$ $\frac {1}{2}$ $×(20-10)×10=50$

CS$=150-50$

Consumer surplus$=$ 100