A perfectly competitive, profit maximizing firms earns zero economic profit in the long run. The firm's total cost is: TC= a + bQ^2. Use only the...

A perfectly competitive, profit maximizing firms earns zero economic profit in the long run. The firm's total cost is: TC= a + bQ^2. Use only the cost curve given

a. Determine mathematically the level of output the firm will produce in the long run

b. show mathematically if its amount differs from the amount of output the firm would produce in the short run

c. Explain why a perfectly competitive firm earns zero economic profit in the long run