Supposethe demand and supply curves of salt are given by:

q ^D = 1,000 − p q ^S = 700 + 2p

(a) Findthe equilibrium price and quantity.

(b) Now, suppose that the price of an input that used to produce salthas increased so, that the new supply curve is

q ^S = 400 +2p

How does the equilibrium price and quantity change? Does the changeconform to your expectation?

(c) Suppose the government has imposed a tax of Rs 3 per unit of saleon salt. How does it affect the equilibrium rice quantity?

q^d= 1000 − p — (1)

q^s= 700 + 2p — (2)

(a) Atequilibrium

q^d= q^s

1000 −p = 700 + 2p

300 = 3 p

100 = p

p =Rs 100

q^d= 1000-100 [Substituting the value of p in equation(1)]

= 900units

So, theequilibrium price is Rs 100 and equilibrium quantity is 900 units.

(b) Newquantity supplied (q′_s)

q′_s= 400 + 2p

Atequilibrium q^d = q′^s

1000 − p = 400 + 2p

600 = 3p

200 = p

p = Rs 200

Prior tothe increase in the price of input, the equilibrium price was Rs 100,and after the rise in input’s price, the equilibrium price isRs 200.

So thechange in the equilibrium price in Rs 100 (200 − 100).

q^d= 4000 − 200 [Subtitling the value of p inequation (1)]

= 800units

The changein the equilibrium quantity is 100 units (i.e. 900 − 800units).

Yes, thischange is obvious, as due to the change in the input’s price,the cost of producing salt has increased that will shift the marginalcost curve leftward and move the supply curve to the left. A leftwardshift in the supply curve results in a rise in the equilibrium priceand a fall in the equilibrium quantity.

(c) Theimposition of tax of Rs 3 per unit of salt sold will raise the costof producing salt. This will shift the supply curve leftwards and thequantity supplied equation will become

y^s= 700 + 2 (p − 3)

Atequilibrium

y^d= y^s

1000 −p = 700 +2 (p − 3)

1000 −p = 700 +2p − 6

306 = 3p

= p

p = Rs 102

Substitutingthe value of p in equation (1)

y^d = 1000 − p

y^d = 1000 − 102

y^d = 898 units

Thus, theimposition of tax of Rs 3 per unit of salt sold will result in anincrease in the price of salt from Rs 100 to Rs 102. The equilibriumquantity falls from 900 units to 898 units.