A risk neutral principal is hiring a risk averse agent. When hired, the agent can either work

hard $($a $=1)$ or shirk $($a $=0).$ The principal$$s gross profit q depends on the agent$$s action a and

the state of the world, denoted by $!2$ f$!1$;$!2$;$!3$g$.$ The values of q$,$ as well as the probabilities

of each state, are summarized in Table $1$ below. The principal$$s and agent$$s $($Bernoulli$)$ utility

functions are given by v$($q; w$)=$ q $$ w and u$($w; a$)=$

p

w $2$a$,$ respectively, where w $0$ is

the wage payment from the principal to the agent. By working elsewhere, the agent can get

the reservation utility of $2.$ Throughout this problem, assume the realized value of q is always

contractible. Also assume that the agent cannot observe $!$ when he chooses a$.$