Economics Homework Help

Consider the relationship between a company and its employees, employees are divided into highly productive H type and low productive L type. When an employee performs work for x hours, he/she gets a reward w for it. However, the employees have no place to work other than this company. H type employees produce 8√x results from x hours of work, while L type employees produce 4√x results. Corporate profit is results from the employees’ results minus the remuneration w and the utility of the employee is defined by u = w – x.

Problem;

The company does not know the type of employee (Information Asymmetry), but knows that the ratio of H type is 1/3 and the ratio of L type is 2/3. Find the combinations or contracts (x, w) that enable the screening of employees but at the same time, maximizes the profit of the company. Show your calculation