Question

Suppose the demand and supply curves of salt are given by:
Qd = 1000 - p
Qs = 700 + 2p
(a) Find the equilibrium price and quantity.
(b) Now suppose that the price of an input used to produce salt increased so that the new supply curve is
Qs = 400 + 2p
How does the equilibrium price and quantity change?
(c) Suppose that the government has imposed a tax of Rs. 3 per unit of sale. How does it affect the equilibrium price and quantity?

Answer 1

(a) At equilibrium price, Qd=Qs
$\therefore 1000-p=700+2p\Rightarrow 3p=300\Rightarrow p=100$
Now we put the value of equilibrium price into either the demand curve equation or the supply curve equation
Qd= 1000-p=1000-100= 900
or Qs= 700+2p=700+2(100)= 900
Thus, the equilibrium quantity is 900 units.

(b) Now when the price of input used increases, then the new supply curve becomes
Qs= 400+2p (New supply curve)
Now for equilibrium, Qd=Qs (New)
$\therefore 1000-p=400+2p$
$\Rightarrow 3p=600\Rightarrow p=200$
Equilibrium price = Rs. 200
Substituting p=200 into either demand or new supply equation, we get
Equilibrium quantity = 1000-p =1000-200 =800 (Demand side)
or Equilibrium quantity $=400+2p=400+2\times 200=800$ (supply side)
Thus, the equilibrium price increases and equilibrium quantity falls due to rise in the price of inputs.

(c) When tax of Rs. 3 per unit of sale is imposed on the commodity, then the new supply curve becomes
Qs= 700 + 2(p-3)
$\Rightarrow Qs=700+2p-6\Rightarrow Qs=694+2p$
Now for equilibrium, Qd = Qs
1000 - p = 694 + 2p
1000 - 694 = 3p
$\Rightarrow 3p=306\Rightarrow p=102$
Equilibrium price = Rs. 102
Substituing p = 102 to either demand or supply equation, we get
Equilibrium quantity = 1000 - 102 = 898
Thus, the equilibrium price increases and equilibrium quantity decreases.