Game Theory Assignment 2 (final)

There are two effort level for the agent and they are . For the agent the cost for high effort is 500 and the cost for low effort is 0. The reservation utility for the agent is 500. When the agent is working for the principal, there can be three levels of profit and they are . The principal is risk neutral and the agent is risk averse. The agent’s utility from the wage, w, would be . The agent’s total utility would be where . When the effort level is high the probabilities that each result would happen are . When the effort level is low they are .

In the ideal case where the principal can observe the effort level of the agent, what will be the wage system like? In other words, what will be ?
If the principal cannot observe the effort level of the agent, what will be ? And what will be the effort level of the agent in that case? What will be the profit of the principal? Explain