Question 2 (30 marks, each part is worth 10 points)

Suppose the market demand curve is p = 30 - q. There is a incumbent dominant firm in the market with cost function c_d(q_d) = q_d, where the subscript "d" denotes the dominant firm. An entrant firm wants to enter the market. If it enters the market it incurs a entry cost F. Hence, the entrant's cost function is c_e(q_e) = F + q_e where the subscript "e" denotes the entrant.

i. Suppose the dominant firm behaves passively and allows the entrant to enter. Calculate the dominant firm's entry-allowing output strategy. Also calculate the market price and each firm's profit. Also find the entry cost at which the entrant's entry is blockaded and the monopoly outcome is restored. So you have to calculate the monopoly outcome when the dominant firm is the only firm in the market and there is no threat of entry.

ii.Suppose the dominant firm behaves aggressively and deters the entrant's entry. Determine the dominant firm's entry-deterring output strategy and explain the relationship between this output and the entrant's entry cost. Also determine the market price and the dominant firm's entry-deterring profit. What is their relationship to the entry cost?

iii.Draw in one diagram the dominant firm's entry-allowing and entry-deterring profits' as functions of the entry cost F which is measured along the horizontal axis. Let F* be the entry cost at which the two profits are the same. Calculate F* and explain what output strategy will the dominant firm choose if the entry cost is less than F* and what strategy will the dominant firm choose if the entry cost is more than F*.