A many-person Ramsey tax rule

Define the social marginal utility of an individual's income as the gain to society of a unit of consumption by the individual plus the value of his marginal propensity to pay taxes out of income. This concept rather than the social marginal utility of consumption (equal to the first term above) seems helpful in understanding optimal tax first order conditions. For example, with many consumers (and a poll tax as well as excise taxes) the change in aggregate compensated quantity demanded is proportional to the covariance between individual quantities demanded and social marginal utilities of income.