Suppose the demand and supply curves of salt are given by:
qD = 1,000 – p qS = 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
qS = 400 + 2p
How does the equilibrium price and quantity change? Does the change conform to your expectation?
(c) Suppose the government has imposed a tax of Rs 3 per unit of sale of salt. How does it affect the equilibrium price and quantity?
(a) Find the equilibrium price and quantity.
At equilibrium point qD = qS
1000 – p = 700 + 2p
300 = 3p
p = 100
Therefore, equilibrium price is Rs 100
qD = 1,000 – p
= 1000 – 100
= 900 units
Therefore, equilibrium quantity is 900 units
(b) Now suppose that the price of an input used to produce salt has increased so that the new supply curve is
qS = 400 + 2p
How does the equilibrium price and quantity change? Does the change conform to your expectation?
Now for equilibrium price
1000 – p = 400 + 2p
600 = 3p
p = 200
Therefore, equilibrium price is Rs 100
qs = 400 + 2p
= 800
Therefore, equilibrium quantity is 800 units
The equilibrium quantity has decreased because the cost of production has increased which will shift the marginal cost curve leftward and move the supply curve towards the left, the leftward shift in the supply curve will result in increase in equilibrium price and fall in equilibrium quantity.
(c) Suppose the government has imposed a tax of Rs 3 per unit of sale of salt. How does it affect the equilibrium price and quantity?
The imposition of tax of Rs 3 per unit of salt sold will raise the cost of producing salt. This
will shift the supply curve leftwards and the quantity supplied equation will become
qs= 700 + 2 (p - 3)
At equilibrium point qD = qS
1000 – p = 700 + 2 (p – 3)
1000 – p = 700 + 2p - 6
1000 – 694 = 3p
p = 102
Therefore, equilibrium price is Rs 102
qd = 1000 – p
= 1000 – 102
= 898
Therefore, equilibrium quantity is 898 units