Question

Suppose there is a monopolistically competitive market with n identical firms, such that each firm produces the same quantity, q. Further, the market is in the monopolistically competitive long-run equilibrium. You are given the following: Inverse market demand: P 10-Q Total market output: Qnxq Marginal revenue: MR 10n+ 1)xq Total cost: C(q)-5+q Marginal cost: MC 2xq In long-run equilibrium, each firm earns zero economic profit. In long-run equilibrium, the number of firms, n, is and each firm produces units) of output at an eqjuilibium price of s(Read carefully The number of firms must be an integer. Round output to three decimal places and round the price to the nearest penny)

Answer 1

In a monopoly,

MC = MR

TR = P*Q = 10Q - Q²

MR = d(TR)/dQ = 10 - 2Q

MC = 2Q already given.

So,

2Q = 10Q - Q²

Q² = 8Q

Q* = 8

P* = 10(8) - 8² = 80-64 = 16

MINIMUM of LAC is output of each firm.

LAC = 5/Q + Q

d(LAC)/dQ = -5/Q² +1 = 0

or, 1 = 5/Q²

or,Q² = 5

or, Q = 2.236

So, number of firms (n) = 8/2.236 = 3.577 which is equal to 3.

ANSWERS IN ORDER

3

2.236

16