please answer thoroughly

Problem 1: Benefits of Screening (20 pts) General Motors and Chrysler both hire engineers. Applicants are of five types, given by the table below. Neither firm knows the worker type unless they screen workers. The table below shows the proportion of each worker type in the labor pool, as well as each worker type's productivity (in thousands of dollars) at each firm. Both companies will pay workers $100K. The cost of screening per worker is $2015. Type A B C D E Percent of Labor Pool 10 25 25 25 15 Productivity at General Motors -100 50 110 150 200 Chrysler 50 90 110 125 150 a. Without screening, what is the average productivity per hired worker at each firm? (3 pts) b. What is the average profit per worker for each firm without screening? (2 pts) c. Which firm(s) will operate at positive (or 0) profit without screening? (2 pts) d. With screening, what is the average productivity per worker for each firm? (3 pts) e. What is the average cost of screening per hired worker for each firm? (2 pts) f. With screening, what is the average profit per worker for each firm? (2 pts) g. What is the profit gain to screening for each firm? (2 pts) h. Which firm gains more from screening? Why? (2 pts) j- Will GM choose to operate? If so, with or without screening? Will Chrysler choose to operate? If so, with or without screening? (2 pts) 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) Problem 3: True/False/Uncertain (10 pts) State whether each of the sentences below is true, false, or uncertain based on the concepts discussed in class. Most importantly, justify vour explanation. a. In the hiring context, there is often asymmetric information, in which the worker knows more about her productivity than the manager does. This can lead to adverse selection, where most of the candidates for a job do not meet the manager's qualifications. (2 pts) b. An example of screening is when a worker chooses to get a master's degree because it reveals that he is high-ability. (2 pts) c. All else equal, when it takes a long time to determine a worker's productivity, firms are less likely to hire risky over safe workers. (2 pts) d. All employers benefit from screening. (2 pts) e. Noncompete agreements are especially useful in environments with high turnover. (2 pts)