The long run cost function for each (identical) firm in a perfectly competitive market is C(q) = q1.5 + 16q0.5 with long run marginal cost given by LMC = 1.5q0.5 + 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?
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
Let us calculate the quantity demanded at a price of $8
Number of firms in long run=Quantity demanded/Output of a firm=Q/q=1584/16=99
Now calculate the quantity demanded at a price of $8
Quantity demanded is zero at long run price. So, no firm will be there in long run at this demand function.
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