Question

11. Supply and Demand - Application of Simultaneous Equations

(a) Find the equilibrium price and quantity in each of the following markets:

(i) Qd = 6 − 2p, Qs = 3 + p;

(ii) Qd = 10 – 5/2 p, Qs = 3 + p;

(iii) Qd = 1 − p, Qs = 3 + p. Comment on the situation in market (iii).

(b) What would be the effect of a purchase/sales tax of 1 cent per item in (ii) above, if p measures price in cents? Explain your answer.

Answer 1

Part A.

(i) Qd = 6 − 2p, Qs = 3 + p;

Equilibrium at Qd=Qs

6-2p=3+p

3p = 3

p=1, Q = 3+1 =4

(ii) Qd = 10 – 5/2 p, Qs = 3 + p;

10-5p/2 = 3+p (equate demand and supply equations)

p+5p/2 = 7

7p/2 = 72 (Simplification)

p = 2, q = 3+2 =5

(iii) Qd = 1 − p, Qs = 3 + p.

1-p = 3+p

2p = -2

p=-1, Q = 3-1 = 2 units (The commodity has a negative price which is only in case of bads like garbage etc for which we or the consumers pay. The price in actual market conditions cannot be negative except in case of bads which are paid for, to get rid off.)

Part B.

Qd = 10 – 5/2 p, Qs = 3 + p or p = Q-3, supply equation after tax p = Q-3+1 = Q-2 or Q = p+2;

10 – 5/2 p = p+2

p+5p/2 = 8

7p/2 = 8

p = 16/7 = 2.2857

q = 2.2857+2 = 4.2857

The price has increased and quantity at equilibrium has fallen. Due to the tax imposed on the commodity, both the buyers and sellers will bear the tax depending on the elasticity of demand and supply. The tax causes the price paid by buyers to rise and also creates deadweight loss for the society.