Question

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?

Answer 1

(i) At equilibrium price `Q^(D)=Q^(S)`
`1000-P=700+2P`
`2P+P=1000-700`
3P = 300 or P = 100
Equilibrium price = Rs. 1000
Equilibrium quantity `Q^(D)=1000-P=1000-100=900"units"`
`Q^(S)=700+2P=700+(2xx100)=900"units"`
(ii) New supply curve is : `Q^(S)=400+2P`
At equilibrium price:
`Q^(D)=Q^(S)`
`1000-P=400+2P`
`2P+P=1000-400`
`3P=600" or "P=200`
Equilibrium price =Rs.200
Equilibrium quantity `Q^(D)=100-P=1000-200=800"units"`
`Q^(S)=400+2P=400+(2xx200)=800"units"`
(iii) New supply curve equation after tax of Rs.3 per unit on sale is imposed.
`Q^(S)=700+2(P-3)=700+2P-6=694+2P`
At equilibrium price: `Q^(D)=Q^(S)`
`1000-P=694+2P`
`1000-694=2P+P`
`3P=306" or "P=102`
Equilibrium price has increased from Rs.100 to Rs.102.
Equilibrium quantity : `Q^(D)=1000-P=1000-102=898"units"`
`Q^(S)=694+2P=694+(2xx102)=694+204=898"unit"`
Equilibrium quantity has decreased from 900 to 898 units.