Selling to a principal and a budget-constrained agent

We analyze a model of selling a single object to a principal-agent pair who want to acquire the object for a firm. The principal and the agent have different assessments of the object's value to the firm. The agent is budget-constrained while the principal is not. The agent participates in the mechanism, but she can (strategically) delegate decision-making to the principal. We derive the revenue-maximizing mechanism in a two-dimensional type space (values of the agent and the principal). We show that below a threshold budget, a mechanism involving two posted prices and three outcomes (one of which involves randomization) is the optimal mechanism for the seller. Otherwise, a single posted price mechanism is optimal.