THE POLITICAL ECONOMY THEOREM

Welfare maximization is constrained by the ultimate frontier of efficient allocations, with a unique, interior optimum. By the second welfare theorem, such an optimum depends on a specific wealth distribution out of innumerable ones at given prices, whereby the state cannot refrain from redistributing. Such has long been known by the profession, but it never received a mathematical formalization, which this article takes up. Building on the literature, this research also presents two simplified proofs to the two welfare theorems and a mathematical formalization of the resolution to the compromise between equity and efficiency, for the additional constraint binds the social welfare function in equity and it originates the ultimate possibility frontier in efficiency.