Dynamic Adverse Selection with Flow Limited Liability: A Closed-Form Approach to Price Regulation

This paper studies a continuous-time regulatory problem in which a firm holds persistent private information about demand and is subject to a flow limited-liability constraint. The regulator regulates prices through a dynamic mechanism that ensures truthful reporting of the evolving type. Limited liability imposes a state-dependent lower bound on the firm’s instantaneous utility, inducing a reflecting boundary in continuation utility and giving rise to a tractable singular-control representation. We derive closed-form expressions for the optimal pricing rule and the associated continuation-utility function, and we characterize the optimal up-front transfer required to induce truthful revelation of the firm’s initial type. The resulting contract is fully explicit and highlights how limited liability shapes information rents and regulatory distortions over time.