q1 microeconomics

Question 1 Decima is a producer of widgets and can produce 5 widgets per hour of labor. Decima is able to sell as many widgets as it wishes at $2 per widget. Meanwhile, Hooli is a producer of FizzBs can produce 5 FizzBs per hour of labor. Hooli can sell as many FizzBs as it wishes at $2 per FizzB. The two firms, both located in Philadelphia, compete for the same workers by simultaneously offering a wage. The wage offer is denominated in dollars per hour of labor, and must be rounded to the nearest cent. Suppose Wooster is looking for a job at one of the two firms, and will accept whichever job offers a higher wage (if both firms offer the same wage, he flips a fair coin to decide which offer he will accept). 1. There are three Equilibria in this game: when both firms offer $10/hr, when both firms offer $9.99/hr, and when both firms offer $9.98/hr. Pick one of these Equilibria and show that it is a Equilibrium. 2. Are there any other Equilibria? Justify your answer. Now suppose that Decima can, instead, produce 7 widgets per hour of labor, while Hooli still, can only, produce 5 FizzBs per hour of labor. 3. Show that there cannot be a Equilibrium where Hooli offers a higher wage than Decima. 4. Show that "Decima offers $10.01/hr and Hooli offers $10/hr" is a Equilibrium. Is this Equilibrium unique