Question

Assume that demand for a commodity is represented by the equation P = 30 - 0.4Qd and supply by the equation P = 6 + 0.2Qs, where Qd and Qs are quantity demanded and quantity supplied, respectively and P is price. The market will clear at        
A
P = 14 and Q = 40.
B
P = 40 and Q = 14.
C
P = 20 and Q = 6.
D
P = 6 and Q = 20.

Answer 1

A market is clear when the quantity demanded and quantity supplied become equal. This means market is clear at equilibrium point.

Qd = Qs

The given demand function is

P = 30 - 0.4Qd

The given supply function is

P = 6 + 0.2Qs

When Qd = Qs

30 - 0.4Qd = 6 + 0.2Qs

30 - 6 = 0.4Qd + 0.2Qs

24 = 0.6 Q (Q = quantity)

Q = 24/0.6 = 40

Substitute Q = 40 in either demand or supply function

P = 30 - 0.4 * 40

= 30 - 16

= 14

Therefore the market will clear at

P = 14

Q = 40