Confronted with political opposition to the implementation of efficient carbon pricing, climate policy relies on alternative policy interventions, at a cost in terms of welfare and public finance. In order to evaluate this cost, this paper studies, in the context of the energy transition, second best climate policies constrained to keeping a constant level of the carbon tax and combining it with subsidies to carbon-free electricity generation. This subsidies can take the form of a feed-in premium paid to electricity produced from carbon-free sources, or of subsidies to investment in green capacity. Within a stylized dynamic model where energy may be produced with fossil or carbon-free sources and climate policy aims at satisfying a carbon budget, we define and characterize the carbon pricing gap. We show that if the constant carbon tax is small and therefore the carbon pricing gap large, the subsidy to carbon-free sources should be so large to foster rapid build up of green capacity that it would imply large investment costs and huge financial burden on the public budget, and a large welfare loss. We calibrate the model to the European energy market to obtain orders of magnitude of the effects.