Hi - Could you please explain how to solve the following? f) g) h)

There are two incumbent rms, F1,F2 and also a potential entrant, F3. The steps of the game are: 1. F1 and F2 simultaneously choose outputs (11 e R+ and qg e R+ re- spectively. 2. F3 observes (11,412 and then chooses whether to enter the industry. If she does not, then (13 = 0 and she gets a payo? of zero, but. .. 3. if she has entered the industry, F3 chooses her own output level, (13 e R+. Inverse demand is p = 12 q1 qg (13. Production costs are zero, but F3 would have to incur a xed investment cost of 4 in order to enter the industry. f) Write down F1's payoffs. Remember that he doesn't have any costs. g) Now we investigate how much F1 would have to produce in order to successfully deter F3's entry. Imagine that in step 1, F1 decided to produce just enough so that it would not be worthwhile for F3 to enter the industry (but no more than that). Continue to assume that if F3 was just indifferent about entry, then she would stay out. How much would F1 have to produce to deter entry? Your answer should be a function of qg but not of 93, ie. of the form q1 = D(q2).1 Your answer to question (e) may be useful here. h) How high would Fl's prots be, if he followed the strategy you iden- tied in the previous question? Your answer should be a function of 9'2