Consider the following demand and supply function of the commodity :
`Q^(D)=160=2P" , "Q^(S)=-40+2P`
(i) Find equilibrium price.
(ii) Find equilibrium quantity.
(iii) Which situation arises when market price is Rs.30 ?
(iv) Which situation arises when market price is Rs.60 ?

Explanation

Equilibrium price is determined at that point where market demand is equal to market supply i.e.,
`Q^(D)=Q^(S)`
`160-2P=-40+2P`
`-4P=-40-160`
`P=(-120)/(-4)`
P = 50
`therefore` Equilibrium price is Rs.50.
(ii) The equilibrium quantity is calculated by substituting the equilibrium price into either demand or supply function since at equilibrium, quantity demanded and quantity supplied are equal.
`Q^(D)=160-2P=160-2(50)=160-100=60" units"`
`Q^(S)=-40+2P=-40+2(50)=-40+100=60" units"`
(iii) When market price is Rs.30, then
`Q^(D)=160-2P=160-2(30)=100"units"`
`Q^(S)=-40+2P=-40+2(30)=20"units"`
`Q^(D)gtQ^(S)`
`100gt20`
This is a situation of excess demand or shortage of supplyy, because `Q^(S)gtQ^(S)`.
(iv) When market price is Rs.60, then
`Q^(D)=160-2P=160-2(60)="40 units"`
`Q^(S)=-40+2P=-40+2(60)="80 units"`
`Q^(D)ltQ^(S)`
`40lt80`
This is a situation of supply or surplus because `Q^(D)ltQ^(S)`.