Question

1. Given the following demand and supply functions Qd = 500 - 3P Qs = 100 + 5P Calculate; i. The equilibrium price and the equilibrium quantity ii. The consumer surplus iii. The producer surplus)R​

Answer 1

Given:

The demand and supply functions are:

$Q_d=500-3P$

$Q_s=100+5P$

To find:

i. The equilibrium price and the equilibrium quantity.

ii. The consumer surplus .

iii. The producer surplus.

Explanation:

(i) At equilibrium, the demand and supply are equal. So, equating both functions, we get

$500-3P=100+5P$

$500-100=3P+5P$

$400=8P$

Divide both sides by 8, we get

$\dfrac{400}{8}=P$

$50=P$

Putting $P=50$ in the demand function, we get

$Q_d=500-3(50)$

$Q_d=500-150$

$Q_d=350$

Therefore, the equilibrium price is 50 and the equilibrium quantity is 350.

(ii)

The area under the demand curve and above the equilibrium price is known as consumer surplus. It is represent by the green area in the below figure.

The area of a triangle is:

$A=\dfrac{1}{2}\times base \times height$

So, the area of consumer surplus is:

$A=\dfrac{1}{2}\times 50 \times (500-350)$

$A=25 \times 150$

$A=3750$

Therefore, the consumer surplus is 3750.

(iii)

The area above the supply curve and below the equilibrium price is known as producer surplus. It is represent by the purple area in the below figure.

So, the area of producer surplus is:

$A=\dfrac{1}{2}\times 50 \times (350-100)$

$A=25 \times 250$

$A=6250$

Therefore, the producer surplus is 6250.