Consider two firms, Firm A and Firm B, who compete as duopolists. Each firm produces an identical product. The total inverse demand curve for the industry is = 250 − ( + ). Firm A has a total cost curve ( ) = 100 + 2 . Firm B has a total cost curve ( ) = 100 + 2. a. Suppose for now, only Firm A exists ( = 0). What is the Monopoly equilibrium quantity and price? What is Firm A's profit? b. Find the Nash Cournot equilibrium price and output level. What are the firms' profits? c. Find the equilibrium price and output level in the market if firm A acts as a Stackelberg leader. What are the firms' profits? d. Suppose that the two firms are able to form a cartel. Derive the output each firm will produce, the market price, and the total profit under the cartel solution. e. Compare the Cournot, Stackelberg, and Cartel outcomes to the monopoly outcome you calculated in part a.