My paper firm generates a monthly profit of $500,000 as I dump a noxious affluent into the nearby river due to the absence of law or regulation. Your downstream brewery must therefore filter the water before it is used to make beer which, in turn, costs you $50,000. Your current profits of $200,000 per month could obviously increase if you did not have to clean the water.
Should there be a private solution? If so, sketch out the form it might take. Might government have a role? Why or why not?