What would be the equilibrium number of firms in a market of identical firms, when market demand function ($Q_d$), supply function of a single firm ($Q_{s1}$) and equilibrium price (P) are given as
$Q_d=180-2P$
$Q_{s1} = 15+ P$
$P = 15$
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5
We are given:
-
Market demand function: Qd = 180 − 2P
-
Supply function of a single firm: Qs₁ = 15 + P
-
Equilibrium price: P = 15
Step 1: Calculate market quantity demanded at P = 15
$Q_d$ = 180 − 2(15)
= 180 − 30
= 150
Step 2: Calculate quantity supplied by one firm at P = 15
Qs₁ = 15+15 = 30
Step 3: Find number of identical firms (n) required to supply 150 units
n×Qs₁= $Q_d$
⇒ n×30=150
⇒ n = 150/30 =5