The inverse demand function for diamonds is P = 150 2Q, where Q is the total output for all firms in the market. The market for diamonds consists of two firms. Each firm has a marginal cost of 30 when producing diamonds.

1.) Find the Cournot equilibrium quantity for each firm, the resulting market price, and the profits for each firm.

2.) Find the Stackelberg equilibrium quantity for each firm, the resulting market price, and the profits for each firm supposing that Firm 1 is the industry leader.

3.) Assume the two firms collude and form a cartel. What is the resulting market price and profits for each firm?