Hi - Could you please explain how to solve the following? i) j)

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 1R+ re- Spectively. 2. F3 observes q1,q2 and then chooses whether to enter the industry. If she does not, then 133 = 0 and she gets a payo" of zero, but. . . 3. if she has entered the industry, F3 chooses her own output level, 93 6 1m. Inverse demand is p = 12 ql qg (33. Production costs are zero, but F3 would have to incur a xed investment cost of 4 in order to enter the industry. 0 Now imagine that in step 1, F1 didn't take into account the possibility that his output could deter entry by F3. That is, he just chose ql to maximise his prots for an assumed xed level of qg and also subject to qg = B3(q1 + qg), the best-response function for F3 that you derived in (c). Solve this problem. You might wish to use the method of sub- stitution. Just as in question (g), your answer should be a function of Q2 but not of 93, ie. q1 = S ((12). Hint: If you are nding this prob- lem diieult, you might like to review the lecture notes on Steehelberg equilibrium. The method is quite similar, although you have to include F2 '3 output in your derivation now. Of course, neither of questions (g) or (i) describe the real problem faced by F1 in step 1. In fact, he has to account for both the possibility that entry might be deterred and the prot consequences of selling more output. Assume that his prots are higher from blocking entry than accommodating entry when Q2 3 7 but higher from accommodating entry when (12 > 7 (this assumption is not actually correct, but please answer this question as if it was correct). What would Fl's overall best response, B1(q2), be under this assumption