Contractual Design with Correlated Information under Limited Liability

We examine contractual design in a principal-agent model under two forms of limited liability: nonnegative constraints on the transfer payments to, and the profits of, the agent. We show that when limited liability is a binding constraint, the principal cannot implement the first-best solution and the agent earns rents from private information. Limited liability is a binding constraint in the nonnegative transfers model only when a signal is insufficiently responsible to type (inelastic). Further, as the production rule and profits are continuous in the type elasticity of the signal density function, the level of the inefficiency is less than that which obtains with no signal. If a signal is sufficiently responsive to type (elastic) in this environment, then the principal can implement the first-best allocation and the value of the agent's private information is zero. We show that limited liability will always be a binding constraint in the nonnegative ex post profits model, regardless of the information content of the signal. The production rule and welfare are increasing in the informativeness of the signal.