The optimal pollution tax becomes complicated when allowance is made f
or endogenous innovation, under a patent system. However, if anything,
it is below marginal environmental damages, to counteract monopoly pr
icing by the patent holder, the common pool effect associated with res
earch and a possible excess of patent holder revenue over the social b
enefits from innovation when environmental damages are convex. In case
s where patents are weak at securing appropriability, for example when
rivals can easily imitate around patented technologies, awarding rese
arch prizes or contracts is probably more efficient than raising the p
ollution tax.