1. Consider a principal agent problem. The principal is hiring an agent. The agent can put high effort e or low effort e. If the agents puts high effort, the output for the principal is q 20 with probability 3/4 and q = 1 with probability 1/4. If the agent puts low effort, the output is q = 20 with probability 1/4 and q = 1 with probability 3/4. The principal decides to pay the agent w. (Assume that the utility of the agent is linear and risk neutral). The cost of effort for the agent is c(e) 0.1 and c(e) = 0 for high and low effort respectively. The reservation wage (outside option) of the agent is 0.1. The principal wants to maximize expected profits. (6 points) = = a) Assume that there is no hidden information and effort can be observed. Further assume that the principal wants to hire an agent with high effort. Set up the maximization problem of the principal and solve for expected profits. (2 points) b) Now assume that the principal wants to hire an agent with low effort. What will be wages and the profit level? Will the principal hire an agent with high or low profit? (1 point) c) Assume now that the principal cannnot observe the agent's effort (hid- den action) but can offer a contract with different wages for different output outcomes. What is the incentive compatibility constraint when the principal wants high effort? (1 point) d) What will be the participation constraint when there is hidden action and the principal wants to induce high effort? (1 point) e) Using your answers to parts c an d, find the wage level in case of low and high output when the principal wants to induce high effort? (1 point)