The Evolution of Welfare Economics

The New Welfare Economics identified conditions for what it called a general social optimum. This problem was solved without assumptions of interpersonally comparable or measurable utility.
 
Bergson, A. A reformulation of certain aspects of welfare economics. QJE 1938
 
Lange, O. The foundations of welfare economics. Econometrica 1942

A Bergson Social welfare function maps consumption and production to $\mathbb{R}$. \begin{equation*} \text{Welfare}=W\bigl(U_1(x_1),\ldots,U_N(x_N)\bigr) \end{equation*} He derives the marginal conditions that characterize optimality. Lange maxes $U_i$ subject to all $U_j$ fixed and technology and resource constraints to get P.O. The welfare theorems and public economics are the chief accomplishments of the NWE.