14 M. FAY, D. MARTIMORT, S. STRAUB This expression is remarkable. While under self-finance or traditional procurement, the firm is making zero profit, it now always enjoys some positive rent from having signed a debt contract with outside financiers while being privately informed on its costs. The firm’s rent is proportional to the demand for the service, namely 1 _−H_ ( _p_ ). That it depends positively on its scale of activities is a rather intuitive result since the proportionality followsrent is alsofromproportionalthe fact thattoaudita secondcosts termare counted�0 _c_ ˆ<sup>_F_(</sup><sup>_c_)</sup> per<sup>_dc_,which</sup> unit of<sup>comes</sup> demand.<sup>from</sup> In<sup>the</sup> addition,<sup>factthat,</sup> the with a debt contract, the firm repays financiers less than what it gets whenever its cost realization falls below the threshold _c_ ˆ. For all cost realizations _c ≤ c_ ˆ (so no audit) and for those benefits over all infra-marginal costs then gives a payoffeach unit of demand, the firm enjoys some gain ˆ _c−c_ from such low repayment. Integrating�0 _c_ ˆ<sup>(ˆ</sup><sup>_c−c_)</sup><sup>_dF_(</sup><sup>_c_) =</sup> �0 _c_ ˆ<sup>_F_(</sup><sup>_c_)</sup><sup>_dc_</sup> where the equality follows from a simple integration by parts.

The firm’s rent is of course socially costly and both the pricing of the service and the debt contract will be modified accordingly to account for these extra costs. Equation (2.16) already shows how this may happen. First, by raising the regulated price and decreasing demand, the public authority is able to reduce this rent. Second, increasing the audit zone and choosing a lower threshold also helps.

On more technical grounds, we may notice that Condition (2.16) also establishes a one-to-one relationship between the firm’s payoff _U_ ( _p,_ ˆ _c_ ) and the face value of debt, or alternatively the threshold _c_ ˆ above which outside financiers audit the project. In other words, controlling the firm’s profit through prices and subsidies allows the public authority to indirectly command the firm’s level of debt. Although the public authority has no direct control of the debt contract in practice, it may make the venture more attractive for outside financiers and change the cost of outside finance by simply increasing the public subsidy or raising the regulated prices so as to boost revenue from the service. This simple observation will later allow us to write the social welfare maximization in terms of _p_ and _c_ ˆ; understanding that the public authority indirectly commands access to outside finance. For the time being, it is important to stress that a lower likelihood of ˆ audit (i.e., a greater value of _c_ ) and a lower level of debt also means that the firm obtains a greater information rent.

# 2.3. _The Optimal Regulatory Charter_

The optimal regulatory charter consists of a regulated price _p_ , a public subsidy _T_ , together with a financial contract which is optimally designed by competitive lenders given this regulatory contract. Using the expression of _U_ ( _p,_ ˆ _c_ ), social welfare becomes: where we again make explicit the dependence on ( _p,_ ˆ _c_ ). This expression highlights how the social cost of audit is counted in the public authority’s objectives. Since financiers are competitive, the private cost of audit ends up being borne by the firm itself and it can be recouped through extra public subsidies, whose social cost is (1+ _λ_ )(1 _−H_ ( _p_ )) _μ_ (1 _−F_ (ˆ _c_ )).

The properties of the optimal regulatory charter are summarized in the next proposition.

Proposition 1 _Suppose that financiers are competitive. The optimal regulatory charter_ ( _p_<sup>_∗_</sup> _,_ ˆ _c_<sup>_∗_</sup> ) _entails the following properties._