Question

# The docking station industry is perfectly competitive. Each firm producing the stations has cost curve given...

The docking station industry is perfectly competitive. Each firm producing the stations has cost curve given by C = 400 + 20q + q2. (You may assume this is both the short-run and the long-run cost curve.) Currently, there are 50 firms producing the stations, and the market demand is given by Q = 2000 – 25p. The long-run market equilibrium price is?

(a) 20

(b) 60

(c) 80

(d) 40

In the above question, TC function and demand function is given

TC = 400 + 20q + q2

Q = 2000 - 25p

Now from the above TC function, MC function can be find out through differential.

There are some properties of differential

1) C = xn

example -

C = x3

C = 3x2

2) if equation has constant then after differential it will be 0

Now to the question

TC = 400 + 20q + q2

MC = 0 + 20 +2q

MC = 20 + 2q

Now we have MC, TC and demand function

In a long-run equilibrium, ATC equals Marginal Cost in perfect competition so

Equating ATC and MC

400 + 20q + q2 = q(20 + 2q)

400 + 20q + q2 = 20q + 2q2

q = 20

In a long-run equilibrium ATC = MC = P

MC = P

20 + 2q = P

20 + 2(20) = 60

P = 60

Hence the price will \$60

so option B is correct

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