Question

2. (1.5 p) Consider perfectly competitive industry with identical firms. The long run average cots function of a typical firm is given by AC(q)- 24 - 49 + q. Market demand is given by c p)=100-2p. (a) Find the long run supply curve of the typical firm. (b) Find the number of firms in the industry in the long run equilibrium.

Answer 1

Answer 2

(a)

In the long run a perfect competitive form earns 0 profit because If they earn positive profit then new firm gets attracted and enters the market which shifts Market supply curve to the right and results in decrease in price and this will continue till Price(p) = AC(Average Total Cost) and If they earn negative profit then existing firm gets exits the market which shifts Market supply curve to the left and results in increase in price and this will continue till Price(p) = AC(Average Total Cost).

Note If P = AC then P*Q = AC*Q => TR = TC

where TR = Total revenue = P*Q and TC = Total Cost = AC*Q.

Thus in a long run in perfect competitive market, Profit = TR - TC = 0 => TR = TC => p*Q = AC*Q => p = AC-------------(1)

In order to maximize profit a perfect competitive market produces that quantity at which p = MC---------------------------------(2) where MC = Marginal Cost.

TC = AC*Q = (24 - 4q + q²)q = 24q - 4q² + q³

MC = d(TC)/dQ = 24 - 8q + 3q²

From (1) and (2) we have p = MC = AC

=> 24 - 8q + 3q² = 24 - 4q + q²

=> 2q² = 4q

=> q = 2

Hence Long run supply of the typical firm is : q = 2

(b)

When q = 2 then p = MC = AC = 24 - 4*2 + 2² = 20

When p = 20, Market demand (Q) = 100 - 2p = 100 - 2*20 = 60

Thus each firm is supplying 2 units and industry demand is 60 units.

Let there be n firms thus Total market supply = 2n.

So, At equilibrium Total Market supply = Total Market demand => 2n = 60

=> n = 30

Hence, In the long run equilibrium, Number of firms in the industry are 30 units.