HI could you please explain how to solve questions a) b) c)?

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 Q2 6 R+ re- spectively. 2. F3 observes q1,q2 and then chooses whether to enter the industry. If she does not, then .33 = 0 and she gets a payoff of zero, but. . . 3. if she has entered the industry, F3 chooses her own output level, (13 e R+. Inverse demand is p = 12 11 (12 Q3. Production costs are zero, but F3 would have to incur a xed investment cost of 4 in order to enter the industry. a) In step 3, F3 chooses (13 to maximise her prots, given an observed level of (11 + (12. Write down a mathematical expression for her prots, price times quantity less entry costs. Your expression should involve (11, Q2, (13, but price should have been substituted out. b) Take F3's rst-order condition wrt (13. c) Solve your condition from question (b) for Q3. The result should be F3's best response function, :13 = B3 (q1 + (12). d) How high would F3's payoff be if she does enter, (and then chooses 913 according to the best response you found in (c))? Your answer should be a function of q1 + (12, but (13 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 + (12 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