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Calculation of profits and output in a Duopoly.

Suppose the steel industry consists of only 2 firms: BIG STEAL (BS) and P-LOOTER (PL). Their costs are TC_M = 4Q_M = and TC_PL = 4Q_PL. The steel industry demand curve is:
P = 10-(1/2)Q       Where Q=Q_M + Q_PL
1.Each firm expects the other to behave as a cournot deopolist choosing the output level myuch profits will each firm make? Draw the reaction curve for each firm.
2.Suppose instead of acting as a cournot duopolist BIG STEAL is the dominant firm and acts as a stackelberg duopolist by choosing its output first. P-LOTER makes its output decision after observing BIG STEAL'S output. How much profits will each firm make?
3.Suppose instead of either the cournot or stackelberg solutions the duopolists decide to collude. How much profits will each firm make?
4.Confirm that output in the Cournot solution is 2/3rds of the output that would occur if the firms were perfect competitors.

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