Question

Consider the following demand and supply functions for a good.

Quantity demanded = 160 - 2p

Quantity supplied = - 40 + 2p

(i) Calculate the equilibrium price and quantity.

(ii) Find out a price at which there is excess demand.

(iii) Find out a price at which there is excess supply.

Answer 1

(i) Quantity demanded = 160 - 2p
Quantity supplied = - 40 + 2p
Equilibrium is attained at a point where market demand is equal to market supply, i.e,
Quantity demanded = Quantity supplied
Hence, 160 - 2p = -40 + 2p
160 + 40 = 2p + 2p
200 = 4p
$p=\frac{200}{4}=50$
Hence, equilibrium price = Rs. 50
Equilibrium quantity will be
Quantity demanded = Quantity supplied
$=160-2p=160-2\times 50$
= 160 - 100 = 60

(ii) At any price below the equilibrium price there will be excess demand
Let us take at price Rs. 20
At p = Rs. 20
Quantity demanded = 160 - 2p
$=160-2\times 20=160-40$
= Rs. 120
Quantity supplied = - 40 + 2p
$=-40+2\times 20=-40+40$
=0
Quantity demanded > Quantity supplied
[excess demand]
Also it can be concluded that at Rs. 20 there will be no supply of the commodity, hence between 20 < p < 50, there will be excess demand.
(iii) At any price above equilibrium, there will be excess supply.
Let us take at price = Rs. 80
Quantity demanded = 160 - 2p
$=160-2\times 80=160-160$
= 0
Quantity supplied = - 40 + 2p
$=-40+2\times 80=-40+160$
= 120
Qunatity demanded < Quantity supplied
[excess supply]
Also, it can be concluded that at p = Rs. 80 demand will be zero, hence there will be excess supply between 50 < p < 80.