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.

Explanation

(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.