  This work provides analysis of a variant of the Risk-Sharing Principal-Agent
problem in a single period setting with additional constant lower and upper
bounds on the wage paid to the Agent. First the effect of the extra constraints
on optimal contract existence is analyzed and leads to conditions on utilities
under which an optimum may be attained. Solution characterization is then
provided along with the derivation of a Borch rule for Limited Liability.
Finally the CARA utility case is considered and a closed form optimal wage and
action are obtained. This allows for analysis of the classical CARA utility and
gaussian setting.
