Question

Suppose the value of demand and supply curves of a commodity-X is given by the following two equation simultaneously:
`Q_(d) = 200 - 10 p " " Q_(s) = 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 eqation
`Q_(s) = 100 + 15 p`
Analyse the new equilibrium 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 - 10p = 50 + 15p`
`150 = 25 p`
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 - 10 p = 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.