Consider a market that is currently occupied by only Firm 1 (the incumbent). The incumbent has a linear cost function C(qI) = IOqI. The inverse demand curve is P = 50 0.1Q for Q G [0, 500]. ** Part a (5 marks) If the incumbent acts as a simple monopolist (i.e. there is no entry), find the monopoly output. ** Part b (5 marks) If the incumbent acts as a simple monopolist, find the monopoly price. ** Part c (5 marks) Now suppose that a potential entrant appears and he considers whether to enter the market. In case the potential entrant enters, he would become the Stackelberg follower; the incumbent would be the Stackelberg leader. The potential entrant has a cost function C(qE) = 320 + 10q E. If q I is fixed to the monopoly output, what is the potential entrant's profit maximization problem in case he enters the market? ** Part d (5 marks) If the potential entrant enters the market, what is his choice of quantity qE given qI is the monopoly output you solved in part a? ** Part e (5 marks) Show whether the potential entrant finds it profitable to enter the market following your calculations in part d. ** Part f (5 marks) Now suppose that q I can be freely chosen by the incumbent. What is the best response function of the potential entrant in case he enters? ** Part g (5 marks) Find the limit output (the minimum level of q I that can make the potential entrant having a negative profit if entry actually happens). ** Part h (5 marks) Show that for incumbent output q I greater than the limit output, the profit is strictly decreasing in qI