A Class of Explicit optimal contracts in the face of shutdown

Résumé

What type of delegation contract should be offered when facing a risk of the magnitude of the pandemic we are currently experiencing and how does the likelihood of an exogenous early termination of the relationship modify the terms of a full-commitment contract? We study these questions by considering a dynamic principal-agent model that naturally extends the classical Holmström-Milgrom setting to include a risk of shutdown before the maturity of the contract. We obtain an explicit characterization of the optimal wage along with the optimal action provided by the agent when the shutdown risk is independent of the inherent agency problem. The optimal contract is linear by offering both a fixed share of the output which is similar to the standard shutdown-free Holmström-Milgrom model and a linear prevention mechanism that is proportional to the random lifetime of the contract. We then extend the model in two directions. We first allow the agent to control the intensity of the shutdown risk. We also consider a structural agency model where the shutdown risk materializes when the state process hits zero.