2. (Entry deterrence] An industry is currently monopolised by an incum- bent, rm 1. A challenger, rm 2, is considering entry, which entails a xed cost setup cost I = 300 in addition to its production cost. If the challenger enters, the two rms compete as in the Cournot duopoly. If the challenger stays out, its prots are zero and the incumbent obtains monopoly prots. The market demand is given by P[Q) = 90 Q, where Q denotes the aggregate output supplied to the market. a] '3} Suppose that, for each rms, the cost of producing 9 units of output is cq, where c = 30 is a constant marginal cost. The interpretation is that both rms have a access to the same production technology. Calculate the Cournot outputs and the rms' resulting prots if the chal- lenger decides to enter the market. Calculate rm 1's monopoly output and prots if the challenger decides not to enter the market. (Hint: See Osborne1 Section 7.2} Now suppose that, before the challenger decides whether to enter the market, the incumbent can invest in a better production technology, at some xed cost A = 600. thereby halving its marginal production cost to c1 = 15. The challenger can observe the incumbent's decision to upgrade its production technology or not. Calculate the Cournot outputs and the firms' resulting prots if the chal- lenger decides to enter the market. (We now have asymmetric Cournot duopoly, where rm 1's marginal cost is c; and rm 2's marginal cost is c 5 c1.) Calculate rm 1's monopoly output and prots if the challenger decides not to enter the market. Draw the extensive form game representing the incumbent's decision to invest in the new technology or not, and the challenger's decision, upon observing the incumbent' choice, whether to enter the market or not. Use the payos calculated in a} and b}. Solve this entry game using backwards induction. d) Discuss the following statement: "Although investing in a better produc- tion technology is not beneficial for a monopoly in the absence of chal- lengers, such an investment is worthwhile if it deters entry by potential challengers." e) Discuss the following statement: "In the model above, the incumbent can only successfully deter entry if the setup cost f for the challenger is sufficiently high.&quot