There are 10 firms in this market. Each firm has the following long-run cost function:

There are 10 firms in this market. Each firm has the following long-run cost function: TC = 200 + 0.5q^2 Market demand for paper is given by Qd=300-5p Suppose we are in the long run, so both labor and capital are variable.

a) What is the long-run market price?

b) How many firms will be in this market in the long run?

c) What is each firm’s producer surplus in the long run?

Expert Solution

1.
a) In the long run, price(p) = minimum of AC
AC = TC/q = (200 + 0.5q^2)/q = (200/q) + 0.5q
d(AC)/dq = (-200/q2) + 0.5 = 0
So, 200/q2 = 0.5
So, q2 = 200/0.5 = 400
So, q = 20
So, p = (200/q) + 0.5q = (200/20) + 0.5*(20) = 10 + 10 = 20
So, long-run market price is 20.

b) Qd = 300 - 5p = 300 - (5*20) = 300 - 100 = 200
Firms = Qd/q = 200/20 = 10 firms

c) Producer surplus = Profit = TR - TC = P*q - AC*q = (P-AC)*q = (20-20)*20 = 0

Rahul Sunny answered 2 years ago

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