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.) The market demand is given by Q = 4000 - 25p. The long run equilibrium number of firms is: ______

Answer 1

We know under Perfect competition long run equilibrium is given as :-

P = AC

where AC is minimum.

So, Given

As,

So, For minimizing AC we will find first order condition.

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So, Individual firms produce q = 20 units of output.

Now, We know P = AC

So, At q =20

Hence,

Now,

We know under perfect competition there is a fixed market price.

So, At P = 60 Market Demand is :-

So, Market output Q = 2500 units

Now we know,

So,

Hence,

The long run equilibrium number of firms is 125