Many European politicians argue that the EU should set tougher emission targets than what is required by the Kyoto protocol, and moreover, that emission trading with other countries outside EU should be limited so as to keep emission quota prices high. One of the arguments, frequently cited for such a policy, is the need for technological development. However, the literature on climate change and technological innovation does not unambiguously support the need for setting high emission taxes today. In this paper we investigate the relationship between emission taxes and technological change further by modeling innovation activity explicitly. In our model both the amount of R&D and the amount of carbon abatement are decided in a decentralized way by the market as a response to an emission tax. Moreover, we introduce several distinct failures in the market for new innovations, among others, insufficient patent protection and intertemporal knowledge spillovers. Our findings suggest that governments should under some circumstances set a higher carbon tax today if we have technological change driven by R&D than if we have pure exogenous technological change. Based on numerical simulations these circumstances are (a) positive intertemporal knowledge spillovers and/or (b) weak patent protection.