I need some economics help please. ?

Question

The hamilton Company is a member of a perfectly competitive industry. Like all members of the industry, its total cost function is TC = 25,000 + 150Q + 3Q^2 where TC is the firm's monthly total cost (in dollars) and Q is the firm's monthly output.

a) If the industry is in long-run equilibrium, what is the price of the Hamilton Company's product?

b) What is the firm's monthly output?

Answer 1

There is not enough information to solve this problem.  A price is necessary.

Answer 2

a)

In long-run for perfect competition output is on minimum of ATC, thus

(TC/Q) = ATC

(ATC)'=0

(25000/Q + 150 +3Q) ' = 3 - 25000/Q² = 0

3 = 25000/Q²

25000/3 = Q²

Q=50√(10/3) ≈91.2871

In long-run there is no profits for perfect competition, thus TR-TC=0

TR=TC

TC=25000 + 150 * 50√(10/3) + 3 * 50 * 50 * 10/3 =

= 50000+2500√3≈63693.1

TR=P*Q = P * 50√(10/3)

P * 50√(10/3) = 50000+2500√3

P = (50000+2500√3) / 50√(10/3) = 150 + 100√3≈ 697.723

b)

Q=50√(10/3) ≈91.2871