Suppose the demand and supply curves of salt are given by: `0ltplt15`
`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 `q^(S)=400+2p.` How does the equilibrium price and quantity change?
(c) Suppose the goverment has imposed at tax of rupee 3 per unit on sale of salt. How does it affect the equilibrium price and quantity?

Explanation

(a) At equilibrium, `q^(D)=q^(S)`
It means, 1,000-p=700+2p
p= rupee 100
Putting the value of equilibrium price in the equation of demand curve, we get:
`q^(D)=1,000-100=900`
Equilibrium Price= rupee 100, Equilibrium Quantity=900 units
When price of input increases, the new supply curve becomes: `q^(S)=400+2p` To calculate new equilibrium price and quantity, equantity, equating `q^(D)" and q^(S)`
`1,000-p=400+2p`
p=rupee 200
Puting the value of equilibrium price in the equation of demand curve or supply curve, we get:
`q^(D)=1,000-200=800`
Equilibrium Price = rupee 200, Equilibrium Quantity=800 untis
Thus, the equilibrium price increases and equilibrium quantity falls due to rise in the price of inputs.
(c) When tax fo rupee 3 per unit sale is imposed on the commodity, then the new supply curve becomes:
`q^(S)=700+2(p-3)`
`q^(S)=700+2p-6`
`q^(S)=694+2p`
To calculate new equilibrium price and quantity, equating `q^(D)" and "q^(S)`
1,000-p=694+2p
p= rupee 102
Putting the value of equilibrium price in the equation of demand curve or supply curve, we get:
`q^(D)=1,000-102=898`
Equilibrium Price = rupee 102, Equilibrium Quantity=898 units Thus, the equilibrium price increases and equilibrium quantity falls due to tax of rupee 3 per unit on sale of salt.