Optimal state-contingent regulation under limited liability

We consider an optimal regulation model in which the regulated firm's production cost is subject to random, publicly observable shocks. The distribution of these shocks is correlated with the firm's cost type, which is private information. The regulator designs an incentive-compatible regulatory scheme, which adjusts itself automatically ex post given the realization of the cost shock. We derive the optimal scheme, assuming that there is an upper bound on the financial losses that the firm can sustain in any given state. We first consider a two-type, two-state case, and then extend the results to the case of a continuum of firm types and an arbitrary finite number of states. We show that the first-best allocation can be implemented if the state of nature conveys enough information about the firm's type and/or the maximal loss that the firm can sustain is sufficiently large. Otherwise, the solution is characterized by classical second-best features.