Question

Suppose we have a perfectly competitive market where at the equilibrium price the total market demand is 300 units. Each individual firm in the market has a cost function C(Q) = 50 -2Q + 1.4Q^2. The number of firms this market can support in the long run is _____? Hint: There can be a fraction of a firm. Hint two: Round your answer to two decimal places

Answer 1

P (long run) = min Average cost

Average cost (AC) = C/Q = 50/Q - 2 + 1.4Q

AC is minimum where d(AC)/dQ = 0

50/Q² = 1.4

Q = 5.98 units

Number of firms = Total demand/6 = 300/6 = 50.2 firms