Consider an industry with inverse demand given by p = 12 – Q. There are two firms: the incumbent (I) and a potential entrant (E). The incumbent moves first by choosing a level of quantity qi from the...

help me

Extracted text: Consider an industry with inverse demand given by p = 12 – Q. There are two firms: the incumbent (I) and a potential entrant (E). The incumbent moves first by choosing a level of quantity qi from the interval (0, 4]. The entrant observes q1 and decides whether or not to enter and how much to produce if it enters (qE). There is no fixed cost of entry. If the entrant decides to stay out, its profit is zero and the incumbent enjoys a monopoly position. Suppose that both the incumbent and the entrant have identical marginal costs equal to c = 8. (a) Derive the subgame perfect equilibrium of this two-stage game. What are the quantities produced by the incumbent and the entrant? What are their profits?