Question:

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 = 60?0.01(q1 +q2) where q1 is the output of the incumbent and q2 is the output of the entrant. Firms need two units of labourand one unit of capital to produce one unit of output. Labour costs w = 10 per unit and capital costsr = 15 per unit. In addition, the entrant has to pay a fixed cost of F2 to enter this market. At period T = 1, the incumbent chooses a level of capital investment K?1 and at time T = 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 lowest K?1 that could be an optimal choice for firm 1 for some values of firm 2's fixed cost F2? What is the highest K?1 that firm 1 could optimally choose?

b)What is the equilibrium outcome and profits of this game if the entrant has fixed costs F2 = 1000?

c)What is the equilibrium outcome and profits of this game if the entrant has fixed costs F2 = 2500?

d)What is the equilibrium outcome and profits of this game if the entrant has fixed costs F2 = 4000?

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

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