Long-lived public infrastructure (for example roads) complements private goods (cars) and may perpetuate carbon-intensive demand patterns and technologies far into the future. Thus, climate policy must combine `direct' instruments such as carbon taxation with public investment shifts (from roads towards rails or bicycle paths). This is particularly important and complex because infrastructure supply changes slowly and carbon taxation may be politically constrained:
This paper shows that if carbon taxation is non-optimal, infrastructure provision should be used to actively change private behavior. Nevertheless, if one instrument is restricted, the other may also have to be less ambitious: Intuitively, if clean infrastructure provision is non-optimal, polluting should also be penalized less (and vice versa), unless welfare gains from environmental quality are large.
More precisely, for two public goods complementing private goods in utility, general second-best policy conditions are derived and applied to a specific utility function. Constrained public spending composition leaves the (Pigouvian) tax rule unchanged, but constrained taxation implies that the environmental externality enters the condition for public spending composition.
Nevertheless, the second-best level of either policy instrument is below its first-best when `dirty' consumption is sufficiently important in utility.