# A4 Optimal Taxation in the Second Best Case

## A4.1 The Modified Ramsey Rule

If *в =* 1, Eq. (9.A21) will be reduced to the standard Ramsey rule. In other words, if the government is concerned with steady state utility only, we have the standard Ramsey rule as well as the golden rule. The standard Ramsey rule describes the static efficiency point.

There is an important difference between our modified Ramsey rule and the standard static Ramsey rule even if we are only concerned with long-run welfare, ignoring transition *(в =* 1). Our rule is derived under the assumption that all effective taxes are available in the sense that the government can choose all consumer prices (q_{1}, q_{2}, q_{3}). This is because one cannot normalize q in a dynamic system (unless lump sum taxes are available).

Atkinson and Sandmo (1980) derived the standard Ramsey rule in the circumstance where debt policy is employed to achieve a desired intertemporal allocation. This rule (and hence the golden rule) is, however, also relevant to the second best solution where neither lump sum taxation nor debt policy is available. This is because changes in consumption taxes and labor income taxes have lump sum timing effects. Namely, an increase in consumption taxes with a reduction in labor income taxes is equivalent to an increase in lump sum taxes in the second period of life with a reduction in lump sum taxes in the first period of life. This tax timing effect is explained in the main text of the current chapter.