There are two effort level for the agent and they are eH$,$eL$.$For the agent the cost for high effort is $600$and the cost for low effort is $0.$The reservation utility for the agent is $400.$When the agent is working for the principal, there can be three levels of profit and they are $($x$1,$x$2,$x$3)=($$$1,000,000,$$$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 ttal utility would be u$=$w$$c$($e to the power of k$)$where k$=$H$,$L $.$When the effort level is high the probabilities that each result would happen are $($pH$1,$pH$2,$pH$3)=(1/4,1/4,1/2).$When the effort level is low they are $($pL$1$H$,$pL$2$H$,$pL$3)=(1/2,1/4,1/4).(1)$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 $($w$1,$w$2,$w$3)?(2)$If the principal cannot observe the effort level of the agent, what will be $($w$1$w$2$w$3)?$And what will be the effort level of the agent in that case? What will be the profit of the principal?