3. Market demand is given by p = 12 - Q. There are two firms: the incumbent firm (1) and the entrant firm (E). Incumbent moves first by choosing quantity q from the interval [0, 4]. The entrant observes q and decides whether or not to enter and how much to produce if he enters (qe). There is no fixed cost of entry. If the entrant decides to stay out, his profit is zero and the incumbent enjoys a monopoly position. Suppose that both incumbent and entrant have identical marginal costs equal to c = 8. (a) What is the (subgame perfect) equilibrium of this game? What are the quantities produced by the incumbent and entrant? What are their profits? (b) What is the minimum quantity that must be produced by the incumbent to deter entry (to make entry unprofitable)? In this game, will the incumbent ever try to deter entry by increasing quantity