There are two effort level for the agent and they are eH$,$eH$.$ 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 $($xHxHxH$)=($$$1,000,000,$$$4,000,000,$$$9,000,000).$ The principal is risk neutral and the agent is risk averse. The agent$$s utility from the wage, w$,$ would be $$w$.$ The agent$$s total utility would be u$=$w$$c$($eH$)$ where k$=$H$,$L$.$ When the effort level is high the probabilities that each result would happen are $($pHH$,$pHH$,$pHH$)=($H H $,$ H H $,$ H H $).$ When the effort level is low they are $($pH H$,$pH H$,$pH H$)=($H H $,$ H H $,$ H H $).(1)$ 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 $($wHwHwH$)?(2)$ If the principal cannot observe the effort level of the agent, what will be $($wHwHwH$)?$ And what will be the effort level of the agent in that case? What will be the profit of the principal?