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W2. Toughest Inc (\"I") is a monopoly in the production of graphene in Italy; W1] is a maa] entrant planning to enter the market. If NT enters, the industry will be a Cournot duopoly i.e. the 2 rms will choose output levels Q1- and Q-N simultaneously in the post-entry stage [stage 2). The market demand curve is P = 160 Q where Q = QN+ 01-1 Toughest Inc chooses capacity level K in the pre-entry stage. Wobserves this move in stage I (pm-entry stage). Each unit costs w = $6 to produce. In addition, there is the cost of capacity r = $6 per unit. =2: The marginal cost ofproduction for each rm is MC = 12 ifeither no capacity is previously chosen (as in the case of W or (for Toughest Inc) if 01- > K level chosen in stage 1_ Fixed costs of production are F. As a monopoly in the market, Wmt-maximizing output and price are: * = 74 and l\" = 86 a) For stage 2: Compute the best-response mctions of Wand Toughest in the case that (i) Toughest produces QT> K and (ii) Toughest produces Q.- s K (iii) Indicate the best-response functions on the graph below by using your computations in (i) and (ii) to ll in the blanks at each \"'3\" b) The capacity required to produce the monopoly level of output Opus K = 74. What is the Nash equilibrium ofthe stage 2. game? Explain your answers Indicate the entrant's output level on the graph. c) Suppose the K-level chosen by the monopoly in stage I is K = 7-1- then in the Nash equilibrium ofthe stage 2 game, the entrant's prots are l'IN = 1369 - F. The incumbent's prot is l'lr= 2738 F We know that ifF 2 I369 entrant will stay out. Suppose F = 1300. Now Toughest has to decide whether to predate entry by choosing a K-level large enough in the pre-entry stage and then in stage 2 setting QT equal to that large K in the post-entry game. The solution to the stage 1 game is to nd this K-level that predates entry. \"I F J L (i) Show that if F = 1300 then K = 1"? is large enough to predate entry. (ii) Show that the incumbent will want to predate entry best response function %