Question

The long run cost function for each (identical) firm in a perfectly competitive market is  C(q) = q^1.5 + 16q^0.5 with long run marginal cost given by LMC = 1.5q^0.5 + 8q^-0.5, where  q is a firm’s output. The market demand curve is  Q = 1600 – 2p, where Q  is the total output of all firms and p  is the price of output.

(a) Find the long run average cost curve for the firm. Find the price of output and the amount of output produced by each firm in a long run equilibrium.

(b) Find the number of firms in the long run equilibrium. What happens in the long run if the market demand curve shifts to Q = 160 – 20p?

Answer 1

a)

Long run average cost is given by

Set LRAC=MC to determine the value of q where LRAC is minimized

q=16 (optimal output produced by a firm in long run)

Minimum LRAC is given as

Long run price=Minimum LRAC=$8

b)

Let us calculate the quantity demanded at a price of $8

Q=1600-2p=1600-2*8=1584

Number of firms in long run=Quantity demanded/Output of a firm=Q/q=1584/16=99

If Q=160-20p

Now calculate the quantity demanded at a price of $8

Q=160-20p=160-20*8=0

Quantity demanded is zero at long run price. So, no firm will be there in long run at this demand function.