Adoption of a cleaner technology by a monopoly under incomplete information

We consider a monopolistic firm producing a good while polluting. This firm can adopt a cleaner technology within a finite time by incurring an investment cost decreasing exponentially with the adoption date. The firm is induced to adopt the cleaner technology at the socially optimal date by an appropriate innovation subsidy. In the incomplete information context, the firm has private information concerning the cost of acquiring new technology. Interestingly, the regulator can induce the firm to reveal the true value of its private information by a contract consisting of an adoption date which is increasing with the value of the innovation cost parameter announced by the firm, and a R&D subsidy which is decreasing with the value of the innovation cost parameter announced by the firm. Nevertheless, the socially optimal adoption date of incomplete information is delayed with respect to the complete information one.