Second Welfare Theorem
Applying the second welfare theorem: a Pareto-efficient allocation can be supported as an equilibrium after lump-sum transfers.
Laura and Mary both own various quantities of bread and butter. They agree to trade these goods and eventually end up with a combination where neither Laura nor Mary can further improve their situation through trade. Assume the goods are divisible, everyone's preferences are continuous, convex and strictly increasing in each good, and the final allocation is Pareto efficient: no reallocation of the goods could make someone better off without making someone else worse off. Without any redistribution of the initial holdings, is it guaranteed that this same final allocation is a competitive equilibrium at some set of prices?
Use it
from datasets import load_dataset
ds = load_dataset("narunraman/steer_me", "welfare_theorem_2")curl "https://steer-benchmark.cs.ubc.ca/api/sample?element_name=welfare_theorem_2&n=5&seed=42"
See the Reference for the parameters.