Question

A perfectly competitive firm faces a market price of $10 for its output X. It owns two plant A and B whose Total Cost are:
TCa=70+30Q+2Q^2
TCb=400-50Q+5Q^2.
Find the optimal quantity produced and sold by the firm so that they are maximising profit

Answer 1

TCa = 2Q² + 30Q + 70

TCb = 5Q² - 50Q + 400

P =10

MC =P

MC = dTC/dQ

MCa = 4Q + 30

MCb = 10Q - 50

MC = MCa + MCb

= 4Q + 30 + 10Q - 50

MC = 14Q -20

MC = P

14Q -20 = 10

14Q = 30

Q = 2.1