On atmosphere externality and corrective taxes

It has been argued that in the presence of an 'Atmosphere Externality' and competitive behavior by households, a uniform commodity tax on the externality-generating good attains the first best. It is demonstrated, however, that if income redistribution is desirable then personalized taxes are required for a second-best optimum. Each of these taxes is the sum of a uniform (across households) tax and a component, positive or negative, which depends on the household's income and demand elasticities. Second-best optimal indirect taxes and rules for investment in externality-reducing measures are also considered.