Hi - Could you please explain how to solve the following? d) e)

There are two incumbent firms, F1, F2 and also a potential entrant, F3. The steps of the game are: 1. F1 and F2 simultaneously choose outputs q1 E R+ and 92 E R4 re- spectively. 2. F3 observes q1, 92 and then chooses whether to enter the industry. If she does not, then 93 = 0 and she gets a payoff of zero, but. .. 3. if she has entered the industry, F3 chooses her own output level, 93 E Inverse demand is p = 12 - q1 - 92 - 93. Production costs are zero, but F3 would have to incur a fixed investment cost of 4 in order to enter the industry. d) How high would F3's payoff be if she does enter, (and then chooses q3 according to the best response you found in (c))? Your answer should be a function of q1 + 92, but 93 should have been substituted out. e) In step 2, F3 decides whether to enter the industry. She will enter if her payoff from entry (which you found in (d) ) is higher than zero. How high would q1 + 92 have to be, in order to persuade her not to enter? Assume that F3 will not enter if she would get exactly the same payoff from entering and staying out