Nicholas Kaldor, James A. Mirrlees; A New Model of Economic Growth, The Review of Economic Studies, Volume 29, Issue 3, 1 June 1962, Pages 174–192, https:/

I. Two consumers, 3. — II. Many consumers, 12. — III. Varying supply price, 20. — IV. Varying marginal utility of income, 22.

set out the problem of using taxation and government production to maximize a social welfare function. We derived the first-order conditions, and considered the argument for efficiency in aggregate production. Here in Part II we consider the structure of optimal taxes in more detail. Part I contained five sections, and Part II begins at Section VI. In the sixth and seventh sections we consider commodity taxation in one- and many-consumer economies. In the eighth section we consider other kinds of taxes; and in the ninth, public consumption. In the tenth section we consider a rigorous treatment of the problem, giving a sufficient condition for the validity of the first-order conditions. To begin, we shall restate the notation and basic problem. Notation