I'm reading Intermediate Microeconomics: A Modern Approach by Hal Varian. On page 606, he states:
The Second Theorem of Welfare Economics states that as long as preferences are convex, then every Pareto efficient allocation can be supported as a competitive equilibrium.
He then states on 604,
The Second Welfare Theorem implies that the problems of distribution and efficiency can be separated...Prices play two roles in the market system system: an allocative role and a distributive role. The allocative role of prices is to indicate relative scarcity; the distributive role is to determine how much of different goods different agents can purchase. The Second Welfare Theorem says that these two roles can be separated: we can redistribute endowments of goods to determine how much wealth agents have, and then use prices to indicate relative scarcity.
How does the second remark follow from the first?