Question

Suppose the demand and supply curves of salt are given by:
$Q_d=1,000-p,Q_s=700+2p$
(a) Find the equilibrium price and quantity.
(b) Now suppose that the price of an input used to produce salt has increased so that the new supply curve is:
$Q_s=400+2p$
How does the equilibrium price and quantity change? Does the change conform to your expectation?
(c) Suppose the government has imposed GST which raises the cost by $Rs.3$ per unit of output. How does it affect the equilibrium price and quantity?

Answer 1

(a) Market equilibrium is struck when:
Market Demand = Market supply
Or, $Q_d=Q_s$
$1000-p=700+2p$
$\Rightarrow 2p+p=1000-700$
$\Rightarrow 3p=300$
$\Rightarrow p=100$
wHEN $p=10, { Q }_{ d }=1000-p $

$=1000-100=900$
Equilibrium price = $100.$
Equilibrium quantity = $900$
(b) When price of an input used to produce salt has increased, new equilibrium price and equilibrium quantity is achieved when:
$1000-p=400+2p$
$\Rightarrow 2p+p=1000-400$
$\Rightarrow 3p=600$
$\Rightarrow p=200$
When $p=200$, $Q_d=1000-p$
$=1000-200=800$
New equilibrium price = $200.$
New equilibrium quantity = $800$.
Owing to increase in input price, supply curve shifts backward. Consequently, equilibrium price is expected to rise and equilibrium quantity is expected to fall., In tune with this expected result, the new equilibrium price has risen from $Rs.100$ to $Rs.200$ and equilibrium quantity has decreased from $900$ to$800$.
(c) When GST is imposed, the supply equation changes as under:
$Q_d=700+2(p-3)$ [ out of the price charged producer has to pay $Rs.3$ to the government ]
Equating supply and demand equations, the equilibrium price is achieved, as under:
$1000-p=700+2(p-3)$
$\Rightarrow 1000-p=700+2p-6$
$\Rightarrow 2p+p=1000-700+6$
$\Rightarrow 3p=306$
$\Rightarrow p=102$
Equilibrium quantity:
$1000-102=898$
Or
$700+2(102-3)=700+198$
$=898$
After GST,
Equilibrium price increases from $Rs.100$ to $Rs.102$.
Equilibrium quantity reduces from $900$ to $898$.