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This work provides analysis of a variant of the Risk-Sharing Principal-Agentproblem in a single period setting with additional constant lower and upperbounds on the wage paid to the Agent. First the effect of the extra constraintson optimal contract existence is analyzed and leads to conditions on utilitiesunder which an optimum may be attained. Solution characterization is thenprovided along with the derivation of a Borch rule for Limited Liability.Finally the CARA utility case is considered and a closed form optimal wage andaction are obtained. This allows for analysis of the classical CARA utility andgaussian setting.

The Risk-Sharing problem under limited liability constraints in a single-period model