Question

Suppose the value of demand and supply curves of a Commodity-X is given by the following two equations simultaneously:

Qd = 200 –10p Qs = 50 + 15p

i) Find the equilibrium price and equilibrium quantity of commodity X.

ii) Suppose that the price of a factor inputs used in producing the commodity has changed, resulting in the new supply curve given by the equation

Qs’ = 100 + 15p

Analyse the new equilibrium price and new equilibrium quantity as against the original equilibrium price and equilibrium quantity.

Answer 1

(i) We know that the equilibrium price and quantity are achieved at;
$Q_d=Q_s$
200- 10 p = 50 +15p
150 = 25p
Therefore, Equilibrium Price p = Rs 6
And, Equilibrium Quantity q = 200 – (10) (6) = 140 units

ii) If the price of factor of production has changed, then under the new conditions;
$Q_d=Q_s$
200- 10p = 100 + 15p
25p = 100
Therefore, Equilibrium Price p = Rs 4
And, Equilibrium Quantity q = 200 – (10)(4) = 160 units
Thus as the equilibrium price is decreasing the equilibrium quantity is increased.