A Comment on the Theory of Second Best

Abstract

In a comment published in the Review of Economic Studies Professors Santoni and Church (1972) corrected a mathematical flaw which existed in Lipsey's and Lancaster's (1956) seminal article on the theory of second best. The correction of that error, although it had no effect on the statement of the general theorem of second best, had a significant impact on the necessary conditions for the attainment of the second best position. Professors Santoni and Church, however, in their analysis on the equivalence of first best and second best optimality conditions, missed a point which is important because it proves a theorem whose position in the literature of Welfare Economics goes back at least as far as Pigou (1932). We may paraphrase this theorem as follows. If there is a distortion in some sector of the economy, then the Pareto and second best solutions for the rest of the economy are equivalent if the marginal rate of substitution (transformation) between any two industries is equal to the marginal rate of distortion between these two industries. In this comment we will provide a rigorous proof of this theorem and also give an economic example which validates the theorem under quite general conditions. In formulating the proof we will employ the same notation as that employed by