Question 24: Suppose the demand and supply curves of salt are given by:
(a) Find the equilibrium price and quantity.
(b) Now, suppose that the price of an input that used to produce salt has increased so, that the new supply curve is qs = 400 + 3p
How does the equilibrium price and quantity change? Does the change conform to your expectation?
(a) Suppose the government has imposed at ax of Rs 3 per unit of sale on salt. How does it affect the equilibrium rice quantity?
Answer:
qD = 1000 – p- (1)
qs = 700 + 2 p –(2)
(a) At equilibrium
qd = qs
1000 - p = 700 + 2p
300 = 3 p
P = Rs100
qd = 1000 - 100 [Substituting the value of p in equation (1)]
= 900 units
So, the equilibrium price is Rs 100 and equilibrium quantity is 900 units.
(b) New quantity supplied '
qs = 400 + 2p
At equilibrium qd = qs
1000 - p = 400 + 2p
600 = 3p
200 = p
p = Rs 200
Prior to the increase in the price of input, the equilibrium price was Rs
100, and after the rise in input's price, the equilibrium price is Rs 200.
So the change in the equilibrium price in Rs 100 (200 - 100).
qd = 4000 - 200 [Subtitling the value of p in equation (1)]
= 800 units
The change in the equilibrium quantity is 100 units (i.e. 900 - 800 units).
Yes, this change is obvious, as due to the change in the input's price,
the cost of producing salt has increased that will shift the marginal cost
curve leftward and move the supply curve to the left. A leftward shift in
the supply curve results in a rise in the equilibrium price and a fall in the
equilibrium quantity.
(c) 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
ys = 700 + 2 (p - 3)
At equilibrium
Yd=Ys
1000 - p = 700 +2 (p - 3)
1000 - p = 700 +2p – 6
306 =
p = Rs 102
Substituting the value of p in equation (1)
yd = 1000 – p
yd = 1000 – 102
yd = 898 units
Thus, the imposition of tax of Rs 3 per unit of salt sold will result in an
increase in the price of salt from Rs 100 to Rs 102. The equilibrium
quantity falls from 900 units to 898 units.
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