please answer thoroughly

Problem 2: Screening using Probation (20 pts) Shuqi is hiring workers for General Electric. She knows that there are bad and good workers in the applicant pool, and decides to institute a probation scheme to screen out bad workers and screen in good workers. Under this probation scheme, workers will work at GE for one year. Afterwards, those deemed good workers will get promoted and earn a higher wage in the second year. Those deemed bad workers will be fired. Shuqi anticipates making mistakes in assessing worker quality. With 20% probability, a good worker will be mistaken as a bad worker and fired. With 15% probability, a bad worker will be mistaken as a good worker and promoted. Good workers expect to earn $70K per year if they do not work at GE. Bad workers expect to earn $50K per year if they do not work at GE. In this market, workers only think aboul working for the next two years, including the one year probation period. An effective probation scheme (W, W5) will lead only good workers to apply. W is the salary during the probation month, while W5 is the salary for each month of work if the worker were promoted to join GE's payroll. a. What is the expected salary from working at GE for good workers? (3 pts) Note: Express your answer in terms of thousands of dollars, Wy, and W,. b) What is the expected salary from working at GE for bad workers? (3 pts) Note: Express your answer in terms of Wy and Ws. From part c. on, you will be guided through completing the table below. (1) (2) (3) (4) (5) (6) Annual Salary Annual Salary Good Workers Bad Workers W, Wy Not GE GE Not GE GE 70 70 60 75 50 80 40 90 45 105 35 115 c. What is the one-year salary good workers can expect if they choose not to work at GE? Fill this out in the table above. Hint: This will be one number. Fill it out for all cells in column (3). (2 pts) d. What is the one-year salary bad workers can expect if they choose not to work at GE? Fill this out in the table above. Hint: This will be one number. Fill it out for all cells in column (5). (2 pts) e. What is the one-year salary good workers can expect if they work at GE? Fill this out in the table above. Hint: For each combination of Wi and Wy in columns (1) and (2), caleulate the expected salary based on the equation in a. Fill this out in the appropriate cell is column (4). (4 pts) f. What is the one-year salary bad workers can expect if they work at GE? Fill this out in the table above. Hint: For each combination of Wi and Wy in columns (1) and (2), caleulate the expected salary based on the equation in b. Fill this out in the appropriate cell is column (6). (4 pts) g. Of the options in the tables above, which probation scheme(s) (W, W53) can GE use to only induce good workers to apply? (2 pts)