Suppose the demand and supply curves of a Commodity X is given by the following two equations simultaneously:
Qd = 200 - p , Qs = 50 + 2p
(i) Find the equilibrium price and equilibrium quantity.
(ii) Suppose that the price of a factor of production producing the commodity has changed, resulting in the new supply curve given by the equation:
Qs'=80+2p`
Analyse the new equilibrium price and new equilibrium quantity as against the original equilibrium price and equilibrium quantity.

Explanation

Equilibrium price and equilibrium quantity are determined at a point where quantity demanded is equal to quantity supplied
`Qd=200-P" (given) and "Qs=50+2P" (given)"`
At equilibrium : Qd = Qs
Hence `200-P=50+2P" or "3P=150" "P=50`
`therefore` Equilibrium price = 50 and equilibrium quantity `= 200 - 50 " or "50+(2xx50)`
`=150"units or "=150 "units"`.
(ii) If the price of factor of production has changed and new supply curve is 80 + 2P then at equilibrium : Qd = Qs
`200-P=80+2P" or "3P=120" "P=40`
`therefore` Equilibrium price = 40 and equilibrium quantity =`200-40" or "80+2(40)`
=160 units or =160 units.
Thus as the equilibrium price falls from Rs.50 to RS.40, equilibrium quantity rises from 150 units to 160 units.