Question

LAC is given as ? + 100/? . LMC is given as 2Q.

(a) Find individual firm’s production when it is long term equilibrium.

(b) When market demand is ? = 5000 − 100?, find market equilibrium quantity and number of firms.

Answer 1

(a)

Assuming it is a perfect competitive market, In a long run Each firms under perfect competitive market earns 0 profit

Profit = 0 means TR= TC where TC = Total Cost = LAC*Q and TR = Total revenue = PQ

=> PQ = LAC*Q => P = LAC

In order to maximize profit a perfect competitive market produces that quantity at which P = LMC

Thus we have P = LAC = LMC

=> Q + 100/Q = 2Q

=> 100/Q = Q

=> Q = 10

Hence Individual Firm production = 10 units when it is in long term equilibrium

(b)

As discussed above P = LAC = LMC => P = 10 + 100/10 = 20

Thus each firm will charge Price = 20 and hence Market price = 20

Demand is given by: Q = 5000 − 100P and Market price = 20

=> Q =  5000 − 100*20 = 3000

Hence Equilibrium quantity = 3000.

As discussed above that each firm will produce 10 units.

Let number of firms be n

Hence Total supply = 10n

These n firms should produce 3000 units

Thus 10n = 3000

=> n = 300

Hence, Number of firms = 300 firms