Question

A firm operates in perfectly competitive markets with the following demand and cost functions:

TC=0.5Q²+100Q+50 Q=1000-4P

a) What is the long-run equilibrium price and quantity in the market?

b) How many firms are there in the industry in the long-run?

Answer 1

In the long run price, average total cost, and marginal cost all three are to one another.

P = ATC = MC

Total Cost

TC = 0.5Q2 + 100Q + 50

Marginal Cost

MC = dTC / dQ

MC = Q + 100

Average Total Cost

ATC = TC / Q

ATC = 0.5Q + 100 +50/Q

Equating both MC and ATC

0.5Q + 100 +50/Q = Q + 100

Q = 10

So each firm will produce 10 units of quantity. To find the price we will use this quantity in any of the above two equations.

P = MC = Q + 100

P = MC = (10) + 100

P = 110

Now we will use this price in the demand equation to find the market demand

Q = 1000 - 4P

Q = 1000 - 4(110)

Q = 560

Number of firms = Market Demand / Individual Demand

Number of firms = 560 / 10

Number of firms = 56