Question

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

Answer #1

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

TC = 400 + 20q + q^{2}

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 = x^{n}

^{ }_{}

example -

C = x^{3}

C = 3x^{2}

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

Now to the question

TC = 400 + 20q + q^{2}

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 + q^{2} = q(20 + 2q)

400 + 20q + q^{2} = 20q + 2q^{2}

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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