Question 3: A manufacturing company is looking to hire an agent to manage a new project. The agent can exert a high effort (πππ»π»)or low effort (πππΏπΏ). 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 (πππ»π»), the probability of success is 0.8. If the agent exerts low effort ( πππΏπΏ), the probability of success is 0.4. The agent's cost of exerting high effort is πΆπΆπ»π»= 10, and the cost of exerting low effort is πΆπΆπΏπΏ =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: ππ = ππβπΆπΆ, i.e. their wage ππ minus their effort cost. The agent has an outside option with a utility of 5. (a) Design a contract (ππππ, πππΉπΉ) where ππππ is the wage if the project is successful and πππΉπΉ is the wage if the project fails. Write down the incentive compatibility and participation condition that ensures the agent will accept the contract and choose to exert high effort. (8 Marks) (b) Solve the conditions from (a) and find the optimal contract with two sets of payments such that the agent will accept the contract and choose to exert high effort. (8 Marks) (c) What is the companyβs expected profits under such contract? (2 Marks)