Suppose in a perfectly competitive industry that the market supply and demand forces combine to produce a short-run equilibrium price of $70. Suppose further that a single firm in this industry has a weekly total cost function expressed by the equation:
TC = 200 + 25q - 6q^2 + (1/3)q^3 .
(a) Calculate the equations facing the firm: demand, MR, and AR.
(b) Calculate the following cost equations of this firm: TFC, TVC, AFC, AVC, MC, and ATC.
(c) What is this firm's profit maximizing level of output? What are its profits?
(d) At what level of (q) will this firm shut down its operations?