3: A manufacturing company is looking to hire an agent to manage a new project. The agent can exert a high effort ( )or low effort ( ). The high effort increases the probability of project success, but it is more costly for the agent. The company wants to design a contract that ensures the agent will choose to exert high effort and will also be willing to accept the job. If the agent exerts high effort (), the probability of success is 0.8. If the agent exerts low effort ( ), the probability of success is 0.4. The agent's cost of exerting high effort is = 10, and the cost of exerting low effort is =2. The company's payoff is 100 if the project is successful and 0 if it is not. The agent's utility is given by: = , i.e. their wage minus their effort cost. The agent has an outside option with a utility of 5. (a) Design a contract ( , ) where is the wage if the project is successful and is the wage if the project fails. Write down the incentive compatibility and participation condition that ensures the agent will accept the