In the perfectly competitive gold ring market, B. & F. Baggins Enterprises is one of a number of identical firms supplying the market. The firm's long-run total cost function has the form TC(Q) = 36Q - 10Q₂ + Q_3. The Market demand is given by the equation P = 21 - 0.01Q

(a) Derive expressions for Baggins Enterprises' long-run average cost (AC) and long-run marginal cost (MC) as functions of Q.

(b) Determine the level of Q at which AC(Q) reaches its minimum value.

(c) In long-run equilibrium, what are the price p and quantity Q of gold rings exchanged and the total number of firms in the industry?

(d) Repeat (c) if (beginning at the equilibrium in (c)) market demand becomes P = 31 - 0.01Q, and briefly describe the adjustment process toward the new long-run equilibrium.