Lump-sum Taxes:

First Best analysis means that the government has a set of policy options sufficient for correcting whatever problems an economy has to restore the economy to the bliss point on its first best utilities possibilities frontier. Second best analysis is defined as the optimal policy of the government given that the bliss point is unattainable.

If efficiency is the only concern, an ideal tax system is one, which is consistent with Pareto optimality. Imposition of lump-sum  taxes, or, head tax as it is often referred to as, offers the classical solution as this kind of tax does not affect the optimum configurations attained by the consumers and the producers. Since, this kind of tax does not interfere with the decision making of the consumers and producers as neither income nor prices, which determine the equilibrium configurations, gets affected.

Therefore, it would have been ideal if the government could mobilise revenue only through this tax as the essential properties of a Pareto optimal allocation would have remained satisfied. Unfortunately, in a real world it offers no solution to a policy maker. Imposition of this tax is tantamount to treating all taxpayers on equal footing, which is unethical. It is impractical as well to rely on this tax as the only source. The government is always therefore in a Second Best environment where the government is left with no choice but to levy distortionary taxes. Moreover, other conditions necessary for a market efficient outcome like perfect  competition and absence of externalities are difficult to obtain in a real world. However, there are taxes other than lump-sum taxes, which satisfy Pareto optimal conditions. Under certain conditions, it has been shown that taxes on profits are neutral as the optimising decisions of the producers and consumers remain unaltered.

In presence of externalities, Pigouvian taxes (or, subsidies) can correct for deviations between private costs (or, benefits) and social costs (or, benefits) and help achieve Pareto optimal conditions. As in the majority of the cases, markets associated with externalities are 'missing' or non-existent. In such cases, determining a Pigouvian tax structure to achieve optimality would not be feasible.