Since the Kyoto Protocol, the carbon tax has aroused such a large interest from economists, financial analysts as well as mathematicians because its modelling is not classical. In this work, we propose a model consisting of n producers that have the ability to reduce their carbon emissions in return for a certain cost. We assume that they can also trade on the certificates market. Our aim is to determine the price of the carbon certificates, which will lead us to a forward-backward SDE with some irregularity. Using a method of approximation, we are able to show the existence and uniqueness of a solution. As expected, we find that with the introduction of such a tax, the emissions decrease.