Suppose that the inverse demand function is described by P = 120 the incumbent firm and q is the output of the entrant. Let both the labor cost and capital cost per unit be 30, i.e., w = r = 30. In addition, let each firm have a fixed cost of F1 = F2 200. In stage 1 of the game the incumbent can choose to invest in capacity (i.e. take part or all of its cost for capital). After observing this, the entrant decides whether or not to enter, and lastly the production levels are chosen.
a) Suppose that in stage one the incumbent invests in capacity K. Show that in stage two the incumbent's best response function is Q = 45 - q/2 when Q < K 2
b) What is the incumbent's best response function when Q > K and what is the entrant's best response function? Show your calculations.
c) What will the incumbent's profit be if it invests in capacity K = 30? Show your calculations.