Question

Suppose the demand and supply curves of a commodity are given as:
$Y^d=200-p$
$Y^s=120+p$
(i) Find the equilibrium price and equilibrium quantity.
(ii) Also show that at a price of Rs. 30, there is excess demand and at a price of Rs. 45, there is excess supply.

Answer 1

(i) At equilibrium price, Qd=Qs
$\therefore 200-p=120+p\Rightarrow 2p=80\Rightarrow p=40$
Equilibrium price = Rs. 40
Putting the value of equilibrium price Rs. 40 into either the demand curve equation or supply curve equation, we get
Qd=200-p=200-40=160
Qs=120+p=120+40=160
(ii) Now at, p= Rs. 30
$\therefore Y^d=200-p=200-30=170$
$Y^s=120+p=120+30=150$
$\therefore Atp=Rs.30,$ excess demand = $Y^d-Y^s=170-150=20$
Now at p=45,
$Y^d=200-p=200-45=155$
$Y^s=120+p=120+45=165$
$\therefore Atp=45$, excess supply= $Y^s-Y^d=165-155=10$