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

Equilibrium price and equilibrium quantity are determined at a point where quantity demanded is equal to quantity supplied `Q_(d)=200-10p" "Q_(s)=50+10P`
At equilibrium: `" "Q_(d)=Q_(s)`
`200-10P=50+15P`
25P = 150
P = 6
Equilibrium quantity `Q_(d)=200-10P`
`=200-10(6)=200-60=140`units
`Q_(s)=50+15P`
`50+15(6)=50+90=-140`units
Equilibrium price = Rs.6
Equilibrium quantity = 140 units
(ii) When price of a factor input used in producing the commodity has changed, resulting in a new supply curve,
`Q_(s)=100+15P`
New equilibrium price :
`200-10P=100+15P or 25P=100`
P = 4
New equilibrium quantity
`Q_(d)=200-10P=200-10(4)=200-40=160`
`Q_(s)=100+15P=100+15(4)=100+60=160`
As equilibrium price reduced from Rs.6 to Rs.4 per unit, equilibrium quantity increased from 140 units to 160 units.