A homogeneous products duopoly faces a market demand function given by P-a-Q, where Q Q1 + Q2 and a-300. Both firms have constant marginal costs MC-100. There are no fixed costs a) What is firm 1’s optimal quantity given that firm 2 produces an output of 50 units per year? And what is frm’s 1 quantity if firm 2 produces 20 units? 4 marks) b) Derive the equation of each firm’s reaction function and provide a graphical explanation to comment your results 4 marks) c) What is the Cournot equilibrium quantity per firm and price in this market? (6 marks d) What would be the market equilibrium quantity and price if the two firms were 8 marks) perfectly competitive? Please comment results comparing them to the ones obtained in the Cournot equilibrium