Assume that the market demand in an industry is: P(Q) = 1 – Q, and that the cost functions of the firms are Ci(qi) = 0.5 qi + F, for all the firms i = 1, 2,…n, where m < 1, and F is the cost of entry into the industry. Consider the free entry sequential game in which the firms decide whether to enter into the market in the first stage, and in the second stage they decide output simultaneously.
-Find the best response function of (n) firm in the second stage of the game.
-Find the Nash equilibrium of the second stage.
-Find the number of firms and the output level of every firm that result from the perfect Nash equilibrium.