Question

The long run cost function for each (identical) firm in a
perfectly competitive market is *C(q)* =
*q*^{1.5} + 16*q*^{0.5} with long run
marginal cost given by LMC = 1.5*q*^{0.5} +
8*q*^{-0.5}, where *q* is a firm’s
output. The market demand curve is *Q* = 1600 –
2*p*, 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 – 20*p*?

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.**

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