A competitive firm’s cost of production is C(Q) = Q^3-20Q^2+125Q. The firm’s problem is to choose the value of Q>=0 that maximizes its profit.
(a) If the market price is 48, then find all points (if any) that satisfy the FOC, and determine whether each of those points satisfies the local SOC. Calculate the profit-maximizing quantity. (Justify your answer carefully.) Calculate the firm’s maximized profit.
(b) Repeat part (a), assuming that the market price is 24.
(c) Draw a picture of the firm’s supply curve. You should show the exact coordinates of the points where Q=0, Q=10, and Q=20.
(d) In what circumstances should the firm choose Q=5?
(e) If this were a free entry industry, then what would be the long run equilibrium price?