Three price-taking firms produce pencils (a homogeneous good). Firm 1 has a marginal cost MC1(q) = 10 + 2q and average cost of AC1(q) = 100/q + 10 + q. Firm 2 has a marginal cost of MC2 = 8 + 4q and an average cost of AC2 = 250/q + 8 + 2q. Firm 3 has a marginal cost of MC3 = 10 + q and an average cost of AC3 = 500/q + 10 + 0.5q

(a) Find the short and long run shut down prices for each firm.

(b) What is the supply function for firm 1? Write this as an equation and draw a graph.

(c) What are the long-run supply functions for firms 2 and 3? Write this as an equation and draw a graph (each firm on a separate graph).

(d) What is the market supply function? (Assume no other firms enter.) Write this as an equation and draw a graph.

(e) Which firms produce when the market price is $40? What is their total output? When the price rises to $70?

(f) What is the total producer surplus when the price is $40? $70?