Question

The docking station industry is perfectly competitive. Each firm producing the stations has long-run cost curve given by C = 400 + 20q + q2. (You may assume this is both the short-run and the long-run cost curve.) The market demand is given by Q = 3000 – 25p. The long-run equilibrium number of firms is _____.

(a) 20

(b) 60

(c) 75

(d) 45

Answer 1

In long run in perfect competition, price equals minimum of AC

So AC = 400/q + 20+ q

Now differentiate it with respect to q & put it equal to zero

-400/q^ 2 +1 = 0

1= 400/q^2

So q*^2 = 400

So AC is minimal when q* = 20

Now minimum of AC is 400/20 + 20 +20 = 60

Thus price in long run = 60

Now total market demand is = 3000-25*60

= 1500

Now each firm produces According to its supply curve, which is rising segment of MC curve

MC : P = 20+2q

So at price equals 60, 60= 20+2*q

Output per firm = 20

Thus total number of firms = total market demand / output per firm

= 1500/20 = 75

option c is right