Consider the following variant of the Dixit model that we discussed in class: In the market for microwaves, there is an incumbent (firm 1) and a potential entrant(firm 2). The demand function is given by:P= 600.01(q1+q2) whereq1is the output of the incumbent andq2is the output of the entrant. Firms needtwo units of labourandone unit of capitalto produceone unit of output. Labour costsw= 10 per unit and capital costsr= 15 per unit. In addition, the entrant has to pay a fixed cost ofF2to enter this market. At periodT= 1, the incumbent chooses a level of capital investmentK1and at timeT= 2, firms compete in quantities by buying inputs and producing outputs

a)What is the range of possible levels of investment for firm 1 that could be a part of the equilibrium for this game? That is, what is the lowestK1that could be an optimal choice for firm 1 for some values of firm 2's fixed costF2? What is the highestK1that firm 1 could optimally choose?

b)What is the equilibrium outcome and profits of this game if the entrant has fixed costsF2= 1000?

c)What is the equilibrium outcome and profits of this game if the entrant has fixed costsF2= 2500?

d)What is the equilibrium outcome and profits of this game if the entrant has fixed costsF2= 4000?

Please answer all parts with a step by step explanation in detail.

Thank you :)