Adoption of a clean technology using a renewable energy

We consider a monopolistic firm producing a good while polluting and using a fossil energy. This firm can adopt a clean technology by incurring an investment cost decreasing exponentially with the adoption date. This clean technology does not pollute and has a lower production cost because it uses a renewable energy. We determine the optimal adoption date for the firm in the cases where it is regulated at each period of time and when it is not regulated. Interestingly, the regulated firm adopts the clean technology earlier than what is socially-optimal. However, the non-regulated firm adopts later than what is socially desired. The regulator can compensate the regulated firm for the loss incurred if he wants that it delays its adoption date to the socially-optimal one. Nevertheless, the regulator may be interested in letting the firm adopts earlier to encourage the diffusion of the use of green technologies in other industries.