1. Assume that firm B (the potential entrant) assigns probability 'p' (1 > p > 0) to firm A's cost being $40 [and probability (1 - p) to firm A's cost being $60]. Show why (or why not) firm B wants to enter this market if firm A charges $100 in the first stage of the game. 

2. Assume firm B would enter if firm A charges $100 in the first stage of the game. Why would firm A wish to signal to firm B to not enter in the third stage? (Calculate the cost to firm A both types [the HI and the LO cost type of firm A] - for firm B entering in the third stage.) 

3. Identify TWO different ways (in the game or in reality) firm A might try to signal to firm B that firm A's costs are $40 (LO). 

4. What price could firm A type LO charge in the first stage that would credibly signal to firm Bthat its costs are actually LO ($40)? Show that firm A type HI ($60) would Not rationally charge that price in the first stage. Show that sending such a signal is net profitable to firm.