Before revision: We give an existence result for the principal-agent problem with adverse selection under general preferences and non-compact allocation space. The result is mainly based on the fact that the principal can always improve a feasible contract by another one which makes larger profit than the outside option from any type of agent. We also treat the case of type-dependent budget constraints.
After revision: We give an existence result for the principal-agent problem with adverse selection under general assumptions on preferences and allocation spaces. Instead of assuming that the allocation space is finite-dimensional or compact, we consider a more general coercivity condition which takes into account the principal's cost and the agents' preferences. Our existence proof is simple and flexible enough to adapt to partial participation models as well as to the case of type-dependent budget constraints.