Question

Suppose the demand and supply curves of salt are given by. q^D = 1000 – P q^S = 700 + 2P 

1. Find the equilibrium price and quantity 

2. Suppose that the price of input used to produce salt has increased so that the supply curve is q^S = 400 + 2P How does the equilibrium price and quantity change? Does the change conform to your expectation?

3. Suppose the government has imposed a tax of 3 per unit of salt. How does it affect the equilibrium price and quantity?

Answer 1

1. equilibrium price and quantity 

q^D = 1000 – P 

q^S = 700 + 2P 

For equilibrium 

q^D = q^S 1000 – P = 700 + 2P 

1000 – 700 = 3 P 

3P = 300 P = 300/3 = 100 

Put the value of P in supply equation 

q^S = 700 + 2P 

q^S = 700 + 2×100 

q^S =700 + 200 = 900

Therefore the equilibrium price = ? 100 and

the equilibrium quantity is = 900 units

2. For equilibrium q^D = q^S 

1000 – P = 400 + 2P 

1000 – 400 = 3P 

600 = 3 P 

P = 600 / 3 = 200 

Put the value of P in demand equation 

Q^D = 1000 – P 

Q^D = 1000  – 200 = 800 

Therefore the equilibrium price = ₹200 and the equilibrium quantity is = 800 units This change confirms to our expectations, i.e., rise in input prices raises prices and lowers supply.

3. q^D = 1000 – P 

q^S = 700 + 2P

When ₹3 as tax is imposed on sale of salt the new demand and supply function will change 

q^D = 1000 – (P + 3) 

q^S = 700 + (2P +3) 

In part A equilibrium price was ₹100 which goes up to ₹103 with imposition of tax 

q^D = 1000 – (100 + 3) = 1000 – 103 =897 

q^S = 700 + (2P + 3) 

= 700 + 2(100 + 3) 

= 700 + 2×103 

= 700 + 206 

= 906 q^D < q^S 

Therefore, new price and quantity has to be adjusted.